My Ontology Is Bigger Than Your Ontology

Meinongianism and Skepticism

2009-12-14T12:18:00.000-08:00

Some people hold that there are a plurality of concrete possible worlds inhabited by concrete individuals who have experiences, abstract thoughts, and beliefs. One might hold this view and also believe that the actual world is ontologically special; all and only actual things exist. This is a kind of Meinongian Modal Realism.

Similarly, there are those who hold that there are a plurality of concrete times inhabited by individuals who have expereinces, abstract thoughts, and beliefs. One might hold this view and also believe that the present is ontologically special; all and only present things exist. This is Meinongian Presentism.

One problem for these views is that they seem to lead to skepticism. Consider Meinongian Modal Realism. On this view, there are lots and lots of people who have evidence much like ours that seems to indicate that they are actual. However, they are all mistaken. There is no significant difference between their evidence and our evidence. Moreover, there are so many more individuals who are mistaken than individuals who are not. So, it is highly likely that each one of us is mistaken when we believe that we are actual. So, we don't know that we are actual. A similar problem arises for Meinongian Presentism (I have also heard that Parson's briefly discusses a problem like this for Meinongianism in general).

I would like to sketch two solutions to this puzzle. I am attracted to both of these solutions and I am not sure which I like the best.

On the first solution, we must make some claims about evidence. Suppose that some experiential states are evidence (and let's, for simplicity, ignore non-experiential evidence). Should we believe that all experiential states are evidence? Perhaps not. Moreover, we might say that someone's having an experiential state is evidence for a belief only if he/she actually has that experiential state. On this view it is false that there are lots and lots of people who have evidence much like ours for the mistaken belief that they are actual. No non-actual people have any evidence whatsoever.

One strange consequence of this view is that we have to be careful how we state reductions of modal claims. Consider the claim that possibly, someone has sufficient evidence to believe that there is a dinosaur in front of him (and suppose that no one actually has sufficient evidence for that belief). On a standard modal realist view, we would say that this claim is grounded in the claim that there is an individual who is in a non-actual world and who (in that world) has sufficient evidence for believing that there is a dinosaur in front of him. But, we cannot say this if we accept the proposal above. This is because, on the proposal above, no non-actual experiential states are evidence. So, this non-actual person's experiential states are not evidence.

What we have to say, if we are going to accept the proposal above, is that the claim that possibly, someone has sufficient evidence to believe that there is a dinosaur in front of him is grounded in something else. We have to say that there are experiential states that are not evidential but that ground claims about possible evidence.

My second proposal is a bit more dogmatic (which makes me kind of like it). We might simply admit that there are lots of people who have evidential states much like ours and that those people are even justified in believing that they are actual. Unfortunately for them, they are mistaken. We, on the other hand, have evidential states that make us justified in believing that we are actual and, moreover, we are correct. So, assuming we are not in a Gettier situation with respect to the claim that we are actual, we know that we are actual.

This solution needs to be augmented a bit since the original argument for skepticism inferred from the high likelihood of mistake to a lack of knowledge. What we have to say is that even though there are lots of people out there like us and that makes it (in some sense) highly likely that we are mistaken, we still have knowledge.

Here is an analogy. Suppose we come to learn that a significant portion of the human population has been abducted and envatted by aliens. These envatted individuals have experiential states much like ours (or lets just assume that for the sake of this post), yet they are mistaken. In fact, we learn that most humans are envatted and only a small portion of the human population has true beliefs based on experiential evidence. Should this new knowledge make us suspend judgment about whether we are on earth, living non-envatted lives? I think now. We and our envatted brethren have all the same kind of evidence. We should believe that we are living non-envatted lives and so should they. It doesn't matter that we have some evidence for the claim that (in some sense) it is highly likely that we are envatted. We also have overwhelming evidence for the claim that (in some sense) it is highly unlikely that we are envatted. So do the poor envatted folks. I think we are justified in believing that we are not envatted and the envatted folks are also justified in believing that they are not envatted. We are lucky in that our justified beliefs are true and they are unlucky in that their justified beliefs are false. Hence, we have knowledge and they do not.

(Cross Posted at joshuaspencer.net)

Iterative Conception of Propositions

2009-12-09T13:49:00.000-08:00

(Cross Posted at joshuaspencer.net)

The iterative conception of propositions works like this. First, we start out with some propositions at the bottom level. None of these propositions contain as a constituent the property of being true. These propositions are combined in a Boolean kind of way to get conjunctions, disjunctions, conditionals etc. Then, for each proposition at the base level and for each proposition constructed in a Boolean kind of way, there is the proposition that that proposition is true. That is, for any P such that P is a proposition at the base level or P is a proposition formed by Boolean operations on propositions at the base level, there is the proposition that P is true. This is the second level of propositions. Now, we combine these propositions and the ones at the base level and the ones formed by Boolean operations in Boolean kind of way. We get even more propositions and we do the trick over again ad infinitum. There are no propositions other than the ones formed by this series of operations.

This iterative conception of propositions will look a lot like typed propositions but will not involve a hierarchy of truth predicates. Moreover, I believe this conception of propositions will avoid certain kinds of paradoxes. There will be no liar proposition. Moreover, for any proposition P, the proposition that P is true is not a conjunct of P. Hence, there will be no Russell proposition that has itself as a conjunct iff it does not. This iterative conception of propositions is rather attractive given that it avoids these paradoxes.

We might also add to our iterative conception of propositions a kind of anti-deflationist principle. That is, for any proposition P, the proposition that P is true is not identical to P. This anti-deflationist principle will be attractive to all those who believe that there really is a property of truth.

Here is a principle that seems to follow from the iterative conception of propositions combined with the anti-deflationist principle:

Particularized Principle of Sufficient Reason (PPSR):

For any true proposition, P, there is a particular sufficient reason, S, such that (i) S is identical to the proposition that P is true, (ii) S is true, (ii) necessarily: S only if P, (iii) S is not identical to P or to any contingent conjunct of P.

However, in An Essay on Free Will, Peter van Inwagen presented a strong argument against the principle of sufficient reason (which is implied by the particularized principle above). Hence, there is a strong argument against PPSR. Very briefly, I will set out the assumptions that underlie van Inwagen’s argument and present the argument against PPSR. My formulation will follow Hudson’s formulation of van Inwagen’s argument (“Brute Facts” AJP March 1997).

Here are the five assumptions that underlie the argument:

A1. There are contingently true propositions.

A2. Any conjunction of contingently true propositions is itself contingently true.

A3. Any true proposition is either contingently true or necessarily true.

A4. For any P and Q, if both Necessarily: P and Necessarily: P only if Q, then Necessarily: Q

A5. If there are contingently true propositions, then there is a conjunction of all contingently true ptopositions.

The argument against PPSR is rather straightforward.

1) P is a conjunction of all contingently true propositions (A1, A5)

2) Hence, P is contingently true (1, A2)

3) Hence, there is a sufficient reason for P, S, such that S is true and S is identical to the proposition that P is true. (2, PPSRi, PPSRii)

4) Hence S is either contingently true or necessarily true. (3, A3)

5) S is not necessarily true (proof below)

6) Hence S is contingently true. (4, 5)

7) But, S is not contingently true. (proof below)

The proof of 5 is as follows:

a) S is necessarily true (reductio assumption)

b) Hence, necessarily: S only if P (3, PPSRii)

c) Hence, necessarily: P (b, A4)

d) It is not the case that P is necessary (2)

e) Hence S is not necessarily true (from a-d)

The proof of 7 is as follows:

f) S is contingently true (reductio assumption)

g) Hence, S is a contingent conjunct of P (e, 1)

h) S is not a contingent conjunct of P (2, 3, PPSRiii)

i) Hence, S is not contingently true (from f-g)

Since PPSR followed from the iterative conception of propositions and the anti-deflationary principle, we can conclude that A1-A5, the iterative conception of propositions and the anti-deflationary principle are jointly inconsistent. I take it that A1-A4 are all very strong. So, that leaves us with a choice. We must decide on whether we are going to give up on the iterative conception of propositions, the anti-deflationary principle, or the assumption that if there are contingent truths then there is a conjunction of all such truths. Those who are attracted to the iterative conception of propositions because it sidesteps paradox must decide between being a deflationist about truth (that is accepting that for any proposition P, the proposition that P is identical to the proposition that P is true) or denying a conjunction of all contingent truths.

Let’s consider the second option. It seems that the second option is inconsistent with the iterative conception of propositions. After all, at any level of proposition construction, we are supposed to perform Boolean operations on all those propositions constructed up to that point. We should get a conjunction of all contingent propositions at the end of our (infinitely long) construction procedure. Remember that the construction procedures should not be thought of as an actual process. Rather, we should think of the iterative conception as a thesis that involves a base clause (about the existence of certain propositions) and a recursive clause (that tells us what propositions exist given the existence of those in our base clause). The recursive clause will have a quantifier over propositions. Hence, if we are to hold on to the iterative conception without accepting a conjunction of all contingently true propositions, we must say that the quantifier in the recursive clause is indefinitely extensible. If this is all correct, then the only way a person who believes in the iterative conception of propositions can avoid a conjunction of all contingently true propositions is by endorsing a rather radical thesis about quantification (namely that the quantifiers that range over propositions are indefinitely extensible).

Hence, it looks like the defender of the iterative conception of propositions is faced with a choice. Become a deflationist about truth. Say that for every proposition P, the proposition that P is true is identical to P. Or, alternatively, claim that quantifiers that range over propositions are indefinitely extensible. Neither option seems too attractive.

Truthmakers for Negative Existentials

2009-11-09T10:43:00.000-08:00

Some assumptions:

- Atomic singular sentences of the form a is F encode atomic Russellian propositions.
- Atomic sentences that contain non-referring names encode atomic gappy propositions.
- Atomic sentences that contain a name for a property that does not exist encode atomic gappy propositions.
- Atomic sentences that include 'exists' or cognates encode the first-order property of existence.
- Non-singular existence statements encode a second-order property of existence.
- All atomic gappy propositions are false. All of their negations are true.

That a proposition is true or false is not a fundamental fact. Truthmaker theorists want to capture this nonfundamentality by holding that for every true proposition there is some state of affairs that makes it true. (I'm ignoring the trope option here. I'm also joining truthmakerists in ignoring the issue of falsemakers. After all, that something is false is no more fundamental than that something is true. But falsemakers never seem to come up. Maybe the assumption is that we could do falsemakers in terms of truthmakers if we could just nail truthmakers. I'm not sure this assumption is true, but I'll bracket it here.) True negative existentials are a major bugaboo for truthmaker theorists. Two main constraints on truthmakers is that they must necessitate the relevant truth and the truths must be about them. Another is that they are supposed to not be "suspicious". (This is related to the power of truthmakers to "catch cheaters".)

It is widely held that the best shot for being a truthmaker for a singular or non-singular true negative existential is something like the entire world plus the fact that there's nothing more. Opponents of truthmaker complain that this sort of truthmaker does bad on all counts. I wonder if there is not a better one to be had. (I don't know the truthmaker literature very well though.)

Here's the idea: the gappy proposition < __, smokes > is false and it represents nothing at all as smoking. This is to say that it represents the gappy state of affairs [ __, smoking ] as obtaining. Paradoxes aside, suppose a liberal account of states of affairs, including gappy ones. To be true is to represent a state of affairs that is among the states of affairs that obtain. To be false is to fail to do that.

So < NEG, < __, exists > > is true because [ __, exists ] is not among the states of affairs that obtain.

< NEG, < hobbits, exist > > is true because nothing has the property of being a hobbit. That is to say, [ __, is a hobbit ] is not among the states of affairs that obtain, and neither is any state of affairs [ o, is a hobbit ] for any o that exists.

Following Kripke, suppose 'is a unicorn' does not express a property. Then 'Unicorns don't exist' encodes something like < NEG, < __, exist > > where the existence property is second-order. This is true for reasons parallel to the first-order case.

This view seems to beat others in terms of necessitation and aboutness, though perhaps gappy states of affairs are suspicious. I don't know.

Perhaps the fact that the gappy states of affairs are not among those that obtain is not itself a fundamental fact. Maybe it holds in virtue of the totality of things plus the fact that there is nothing more. Maybe that eases suspicion while maintaining aboutness. But it does not merely collapse into the usual account. If I say that Joshua's life is longer than JonBenet Ramsey's, I am talking about their lives. But that is consistent with their lives being nonfundamental. So I think this is okay.

Perhaps one could object to the intrinsic weirdness of gappy states of affairs. But if one accepts gappy propositions, one should not have this problem with gappy states of affairs. Russellian propositions are so very states-of-affairs-like that I can't think of a principled reason for accepting one and not the other. The link is even tighter if we accept the identity theory of truth (I don't): the true propositions just are the states of affairs that obtain. Then gappy propositionists get gappy states of affairs "for free".

What's not to like?

On the proposition that there are a plurality of worlds

2009-11-04T16:23:00.001-08:00

David Lewis thinks that there are many concrete possible worlds (at least one for each de dicto possibility) and propositions are sets of those worlds. I disagree. I will present two dilemmas against this view.

It seems clear that the following is true:

1. Possibly, there are talking donkeys.

On Lewis's view, this means that there is a world and there are talking donkeys in that world. But, this implies that:

2. There are (quantifiers wide open) talking donkeys.

This is a proposition. So, according to Lewis, it must be a set of possible worlds. But which set is it? As I see it, there are only two options. If propositions are sets of worlds, then either (2) is the set of worlds that contain (within their worldly boundaries) talking donkeys, or (2) is the set of all worlds.

Consider the first option: that (2) is the set of worlds that contain (within their worldly boundaries) talking donkeys. This option can't be right. After all, (2) is true. Moreover, for any proposition p, if p is true and propositions are sets of worlds, then the actual world is a member of p. The actual world, though, is not a member of the set of worlds that contain talking donkeys. So, if propositions are sets of worlds, then (2) is not the set of worlds that contain talking donkeys (within their worldly boundaries).

The only other plausible option is that (2) is the set of all worlds. This seems plausible since (given that the quantifiers in (2) are wide open) it is true at any world. But, then (2) is the same as the proposition that arithmetic is incomplete. But, that is absurd. So, (2) is not the set of all worlds.

Even if you deny the absurdity of identifying (2) with the proposition that arithmetic is incomplete, there are still problems for the second option. Consider the following proposition:

3. There are (quantifiers wide open) cats.

Since the quantifiers in (3) are wide open, just like those in (2), then it seems we have no reason to treat them differently. No reason to say, for example, that (2) is a set of worlds that contain cats whereas (3) is the set of all worlds. So, we should treat them the same. If (2) is the set of all worlds, (as the second option indicates), then it must be that (3) is the set of all worlds too. So, if (2) is the set of all worlds, then (2) is identical to (3). But, clearly those are different propositions. I believe (3) yet I think that (2) is false.

To recap, if propositions are sets of worlds, then (3) is either the set of all worlds that contain talking donkeys or the set of absolutely all worlds. But, it is not the set of all worlds that contain talking donkeys and it is not the set of absolutely all worlds. So, propositions are not sets of worlds.

That's the end of the first dilemma against the Lewisian view. Here, then, is the second dilemma. Consider Lewis's modal realist thesis itself:

PW: There are (quantifiers wide open) many concrete possible worlds.

If (PW) is true and propositions are sets of worlds, then either (PW) is the set of worlds that contain (within their worldly boundaries) many concrete possible worlds or it is the set of all worlds. If (PW) is a set of worlds that contain (within their worldly boundaries) many concrete possible worlds, then it is the empty set (since no world contains many concrete possible worlds). But, if it is the empty set, then it is false (since on the sets-of-worlds view of propositions, a proposition is true iff the actual world is a member of the set that is that proposition). So, if (PW) is true, (PW) is not the set of possible worlds that contain many concrete possible worlds.

Perhaps (PW) is the set of all worlds. But, if that is the case, then (PW) is identical to the proposition that 2+2=4. But, it if it is identical to the proposition that 2+2=4, then I believe (PW) (since I believe that 2+2=4). But, I don't believe (PW). So, (PW) is not a set of all worlds.

It follows that either (PW) is not true or propositions are not sets of worlds. If propositions are sets of worlds, then (PW) is false. But, since the view that propositions are sets of worlds is true only if (PW) is true (the view makes sense only if (PW) is true), it follows that propositions are not sets of worlds.

Priority Questions

2009-10-19T13:30:00.000-07:00

Let's suppose that there is a two place priority relation that obtains between individuals (we'll ignore the plural priority relation that I talked about in a previous post). So, our basic locution will be x is prior to y.

Now, there are clearly some questions that we can ask about priority. First, we might try to find a reduction of priority or (perhaps equivalently) an answer to the General Priority Question:

(GPQ) necessarily, x is prior to y iff ______?

One plausible answer to the above question, perhaps favored by certain kinds of pluralists, is the following.

(A1) necessarily, x is prior to y iff x is a proper part of y.

Another answer, perhaps favored by certain kinds of monists, is the following:

(A2) necessarily, x is prior to y iff y is a proper part of x.

These two views are very simple. But, there are, of course, those who think that the answer needs to be more complicated. For example, some might think that the particles that compose me are prior to me, but I am prior to any other things that are composed of any number of those particles (for example, I am prior to my hand). If you hold this kind of view, you need cannot accept the simple answers (A1) and (A2) above.

In addition to a General Priority Question, there is also the Special Priority Question:

(SPQ) Necessarily, x is prior to something iff ___________?

If we answer this question by saying that any conditions are necessary and sufficient for x to be prior to something, that is if we accept unrestricted priority, then we are committed to infinite ascent of priority. This is because the priority relation is anti-symmetric. So, if x is prior to something, then that something must be prior to some further distinct thing and so on. So, if we think that priority has a top level, then we must accept a restriction on priority.

We might also ask the Inverse Special Priority Question:

(ISPQ) Necessarily, something is prior to x iff ____________?

Again, if we answer this question by saying that any conditions are necessary and sufficient for something to be prior to x, that is if we accept unrestricted priors, then we are committed to infinite descent of priority. Again, this is because the priority relation is antisymmetric.

Finally, we might introduce the following definition for fundamentalilty:

(D1) x is fundamental =df x is prior to something and nothing is prior to x.

Now we can ask the fundamentality question:

(FQ) Necessarily, x is fundamental iff ___________?

It looks to me like the following is true. If we have answers to the (SPQ) and (ISPQ), then we will have an answer to the (FQ). Hence, if there is no answer to the (FQ), if we must accept brutal fundamentality, then we must say that one of (SPQ) or (ISPQ) has no answer as well. But, I wonder if the following is true: If there is no answer to one of (SPQ) or (ISPQ), then there is no answer to (FQ). I wonder whether saying that there is no answer to either (SPQ) or (ISPQ) commits one to brutal fundamentality. I have not thought this through yet, but I hope to have some ideas soon.

Gunk and Points

2009-10-05T15:23:00.000-07:00

Gunky space contains no spatial points. That is, Gunky space contains no regions that are unextended and have no further subregions. However, there are points. After all, when we say things like "given any two points, there is exactly one line that passes through them both" we speak truly and what we say is in some sense about space.

"Have no fear", says the gunky space theorist, "of course there are points, they just have different features than you expect". According to the gunky space theorist, a point is an infinite series of nested solid spheres. Tarski showed us that we can recover all of geometry within a gunky space by using these series of nested spheres in place of points.

But, now I have a question. What exactly are the points? Are they fusions of nested spheres? It seems that can't be right since the fusion of nested spheres that converges on the "point" at the end of my cats nose just is the fusion of the nested spheres that converges on the "point" at the end of the statue of liberty's torch. Moreover, this fusion just is all of space. Since we think that the "point" at the end of my cat's nose and the "point" at the end of the statue of liberty's torch are different "points", and (moreover) since we are not point monists (who believe there is one and only one point that is identical to all of space), we must reject the claim that points are fusions of series of convergent solid spheres.

Might we take the original view at face value and say that points are ordered sets of convergent solid spheres? I think not. First, we will run into a Benacerraf problem with respect to points. But, more intuitively, the "point" at the end of my cat's nose is located (in some sense) at the point of my cat's nose. No abstract entity like a set is so located. So, points are not ordered sets.

I think that the gunky space theorist has a reason to accept structure in composition of spatial regions. Perhaps, points are special kinds of fusions of convergent series of solid spheres. They are fusions that preserve a certain kind of structure, an ordered structure to the parts. One consequence of this view seems to be the following. There are uncountably many things that are co-located with the entirety of space, each one of which is a point and each one of which has a different structure than the others. This seems like quite a robust ontology of spatial regions.

MaxCon and Gunk

2009-10-01T19:09:00.000-07:00

Greg Fowler has recently shown that the Maximally Continuous View of Simples is consistent with the possibility of Gunk (AJP 2008). The idea is that an extended MaxCon simple might have lots of complex objects that occupy the proper subregions of a simple. In fact, as Fowler notes, if MaxCon is true and there is some gunk, then that gunk must be in subregions of some extended simple.

Here is a view that I'd like to consider:

(MaxCon+G): MaxCon is true and for every proper subregion of the region occupied by a simple, there is a complex material object that occupies that subregion.

I think this view is false. Here is how to show that it is false. Let S be an extended simple. There are point sized subregions of the region occupied by that simple. By MaxCon+G, there must be a complex object in that region, call that object 'C'. No, suppose that for any object x, there is an intrinsic duplicate of x that that exists in a world without any objects other than x's parts. So, there is an intrinsic duplicate of C, C*, that exists in a world that has no objects other than the parts of C. Moreover, C* must have parts. Here is why. The mereological structure of an object is an intrinsic feature of objects. C is complex. So, any intrinsic duplicate of C is complex as well. Hence C* is complex. But, the shape of an object is intrinsic as well. So, since C is point sized, C* is point sized as well. Since, there are no objects other than C* and C* is point sized, it must be that C* is maximally continuous. So, by MaxCon, C* is a simple. So, C* is a simple and it is complex. Contradiction! Hence MaxCon+G is false.

I think there are a lot of moves that can be made to save MaxCon+G. One might deny that the mereological structure of an object is intrinsic (MaxCon itself certainly seems to suggest otherwise). One might deny that shapes are intrinsic (there is a precedent in the literature). One might also deny that C* is maximally continuous. Perhaps its parts occupy super-regions of the region it occupies. That is a pretty weird view.

Quick Question

2009-09-29T09:45:00.000-07:00

Can anyone think of a non-intentional property that any two entities possibly instantiate, but no two entities necessarily co-instantiate?

I also want to assume that there are some necessarily existing entities, in particular I want to assume that there are propositions and that propositions necessarily exist.

UPDATE:

I'd like to revise my question. What I need is a propositional schema that is such that for any entity it is possibly true of that entity and there are no two entities that are such that necessarily the propositional schema is true of the first entity iff it is true of the second entity.

Same assumptions as before.

Indefinite Extensibility and Contractibility of Plurals and Ensamblism

2009-09-24T07:39:00.000-07:00

Let's introduce some definitions:

our primitive notion will be xx are amongst yy and we will assume that there are no empty plurals.

xx are ancestorally amongst yy =df either (i) xx are amongst yy or (ii) xx are amongst somethings that are ancestorally amongst yy.

xx are contractible =df for any yy amongst those xx, there is a zz such that zz are amongst yy.

xx are indefinitely contractible =df for any yy ancestorally amongst xx, there are some zz such that zz are ancestorally amongst yy.

xx are extensible =df there are some yy such that xx are among yy

xx are indefinitely extensible =df there are some yy such that xx are ancestorally amongst yy and for any zz such that xx are ancestorally amongst zz, there are some vv such that zz are ancestorally amongst vv.

Some restricted plurals are indefinitely contractible. For example, take a quantifier that is restricted to countably infinite pluralities of integers. If we restrict our attention to only plurals that satisfy the variables of that quantifier, then those plurals will be indefinitely contractible.

Some restricted plurals are indefinitely extensible. For example, take a quantifier that is restricted to finite pluralities of integers. If we restrict our attention to only plurals that satisfy the variables of that quantifier, then those plurals will be indefinitely extensible.

Two Questions: Will our fundamental theory talk about pluralities that are indefinitely extensible? Will our fundamental theory talk about pluralities that are indefinitely contractable?

A while ago I posted about Priority Ensamblism. Priority Ensamblism says that there are some things such that they are basic. Priority Ensamblism comes in two varieties. Distributive Priority Ensamblism and Non-distributive Priority Ensamblism. You can read about these views and an argument for the latter view in my previous post here. My thoughts right now is the following: If our fundamental theory contains plurals that are indefinitely contractible, then that is a reason to favor non-distributive priority ensamblism. However, if our fundamental theory contains plurals that are indefinitely extensible, then that is a reason to favor distributive priority ensamblism. I need to think this through a bit more and see what kind of premises might be lurking behind these rough thoughts.

The Impossibility of Higher Dimensions in Gunky Space

2009-09-19T13:14:00.000-07:00

Some people think that space is gunky. That is some people think that every region of space has proper subregions. There are two interesting questions that might be answered if space turns out to be gunky. First, are there higher spatial dimensions? Second, could there be higher spatial dimensions? I am going to suggest that the person who thinks that space is gunky should also think that there are no higher spatial dimensions. Moreover, the person who thinks that space is gunky should also think that there could be no higher spatial dimensions (or at least that there could be no higher gunky spatial dimensions).

Here is how the argument goes against higher spatial dimensions goes. If space is gunky, then there are no points, there are no edges and there are no surfaces. Moreover, (P1) if space is gunky and there are four spatial dimensions (or more) rather than three, then there are no volumes either. This is because volumes would be like the surfaces of hypervolumes and just as we should deny the existence of surfaces in a gunky space of at least three dimensions, so too we should deny the existence of volumes in a gunky space of at least four dimensions. But, (P2) there are volumes (for example, my tea cup encompasses a volume of space and you and I also encompass volumes of space). So, (C1) if space is gunky, then there are not four spatial dimensions (in fact there are no more than three spatial dimensions).

Here is how the argument against the possibility of higher spatial dimensions in gunky space goes. (P3) If there could be more than three gunky spatial dimensions, then there could be an exact duplicate of our spatial world within a four (or more) dimensional gunky space. Moreover, (p4) if there were an exact duplicate of our spatial world within a four (or more) dimensional gunky space, then there would be volumes in such a gunky space. But, (P5) necessarily, if there are four (or more) dimensions of gunky space, then there are no volumes in such a gunky space. So, (C2) there could not be a duplicate of our spatial world within a four (or more) dimensional gunky space. So, (C3) there could not be more than three gunky spatial dimensions.

Interestingly, similar reasoning should get us that there are not, nor could there be fewer gunky spatial dimensions than there in fact are. This is a rather radical and suprising result.

I am inclined to think the first argument is sound. I might worry about the second argument though. In particular, I might worry that (p3) is false. But, then if (P3) is false, then I worry that there are restrictions on plausible modal recombination principles. I also wonder if (P3) might be stronger than is needed. In any case, it seems to me that (P3) is the weakest part of the argument.

The Gaps in Gappy Propositions

2009-09-15T13:10:00.000-07:00

Some of you are familiar with The Gappy Proposition View (GPV). According to (GPV), the meaning of a name is the thing to which it refers and if a name such as 'Vulcan' has no referent, then when it is used in a sentence, such as 'Vulcan is a planet', that sentence expresses a gappy proposition. We might represent the proposition expressed by 'Vulcan is a planet' as follows {____, planethood}. On (GPV) we assign truth values to propositions as follows: A simple sentence of the form 'N is F' expresses a truth iff N has a referent and the referent of N has the property expressed by 'is F'. A simple sentence is false otherwise. Truth values for non-simple sentences are determined in the standard way.

(GPV) seems to have some ontological commitments. For example, (GPV) is committed to propositions. (GPV) along with the thesis that there are genuinely empty names is committed to gappy propositions. Finally, it seems that (GPV) along with the thesis that there are genuinely empty names is committed to gaps. Gaps, of course, are the unfilled positions in gappy propositions. But, now it seems that there is a problem for the gappy proposition view.

Consider the following sentence:

S1 'Vulcan exists.'

Assuming that 'Vulcan' is an empty name, then according to (GPV), (S1) expresses the following proposition:

P1 {_____, exists}

But, now let's introduce a new name. Let's introduce 'Gappy' as a name for the gap in proposition P1. Now consider the following sentence:

S2 'Gappy exists.'

Since the meaning of a name is the thing to which it refers (that is, since a name contributes its referent (if any) to the proposition it expresses) it should follow that S2 expresses the following proposition:

P2 {____, exists}

But, P1 is clearly identical to P2. There is a problem because S1 clearly does not express the same proposition as S2. For one thing, S1 expresses a falsehood whereas S2 expresses a truth. (In fact, given the truth conditions outlined above it seems that S2 cannot express a truth. This is a further problem for (GPV)).

The Gunk Question

2009-09-10T16:19:00.000-07:00

It may be that we have talked about this question here before. I don't remember for sure. But, I am wondering if anyone has asked the following question:

Necessarily, for any x, x is a hunk of gunk iff _______?

I take it that one popular view might be the following:

Necessarily, for any x, x is a hunk of gunk iff x occupies a region that contains no points.

This view has a number of problems. One problem is with the possibility of tile space. One might think that an object that occupies a single tile region is a simple. But, since tile regions contain no points, such an object would be counted as gunk on the view above. So, it seems that there is some reason to believe that the view above is false.

Perhaps a more pressing problem is the following. Many of us reject liberal views of decomposition according to which any subregion of a region occupied by an object contains a part of that object. But, if we are inclined to reject such a view, then we are probably also inclined to reject the view above.

So, I am wondering what kind of answer someone might give to the gunk question that fits well with a rejection of the liberal view of decomposition. And, I am also wondering what kind of answer someone might give if that person is inclined to accept that possibility of tile space.

Is Julius Ceasar Identical to the number 2?

2009-08-19T18:14:00.000-07:00

Suppose we got a bunch of arithmatical truths like 2+7=9 and 5+7=12 and so on. Those truths have referring expressions such as '1' and '2' and so on. Some people wonder what those expressions refer to. I guess I really don't know much about this, but I think there are a few things that people tend to accept about arithmatical truths. First, we have an incomplete axiomatization of arithmatic. Those axioms have certain structural properties that arithmatic must satisfy. But, other things satisfy those axioms as well. For example, under one interpretation of the axioms, the number 2 is identical to the set containing the set containing the null set. On another interpretation, the number 2 is identical to Julius Ceasar. Just like with other logical axioms, there is nothing in the structure that guarantees that the referring expressions refer to the some things rather than others. This is supposed to be problematic for arithmatic because it is hard to see what kind of causal relations would help to fix the referent of the referring expressions in arithmatic. So, how do we solve this problem?

Some people solve it by claiming that arithmatical expressions are quantified expressions that quantify over the things that satisfy the axioms of arithmatic. So, for example, 2+2=4 turns out to say something like for any interpretation of the referring expressions and function in '2+2=4' that satisfies the axioms of arithmatic, the function expressed by '+' on that interpretation applied to the referents of '2' and '2' on that interpretation yeilds the referent of '4' on that interpretation (or something like that). Views like this are structuralist views. I think structuralist view is mistaken. Simply put, '2+2=4' just doesn't have a quantificational structure. So, structuralist views are mistaken.

However, I wonder if structuralist views are on the right track. Suppose that we have some arithmatical axioms. We might simply supervaluate over those axioms. Thus, 2+2=4 turns out to be supertrue in virtue of the fact that on any admissiable interpretation of the terms, '2+2=4' expresses a truth. However, it does not express a quantificational truth. One happy consequence of this view is that the Julius Ceasar problem goes away. Although 2=Julius Ceasar on some interpretation, it does not on others. So, it is not supertrue that 2=Julius Ceasar. In fact for any thing whatsoever, it is not supertrue that 2= that thing. However, it is supertrue that 2=something. Supervaluationists allow for supertrue existential statements without true instances. Now, if we simply identify truth in arithmatic as supertruth, we have a solution to the Julius Ceasar problem and we can have all the supposed benefits of structuralism (epistemic access to arithmatical truths, no causal contact with any abstract entities, etc).

Like I said, I don't know much about philosophy of math. So, maybe this view has already been expressed. If it has, I would like to know. If it hasn't I'd like to know what others think of it.

Variation

2009-05-20T12:25:00.000-07:00

we are all familiar with problems of variation. There is the problem of temporal variation: How can something be bent and then be straight? The problem of spatial variation: How can something be striped purple and red? The problem of modal variation: How can something be contingently solid? Some people turn these problems of variation into arguments for their own preferred metaphysical views. But, we all know that there are lots of answers to these questions, some of them more amenable to certain metaphysical views than others and some of them more plausible than others. Here is a brief list of some of the solutions to the problem of variation:

Objects have temporal/spatial/modal parts and and it is in virtue of the fact that various parts exemplify various properties that those objects have temporal/spatial/modal variation.

Objects have temporal/spatial/modal counterparts and it is in virtue various counterparts exemplifying various properties that those objects have temporal/spatial/modal variation.

Properties are exemplified relative to times/spaces/worlds and it is in virtue of an object exemplifying various properties relative to various times/spaces/worlds that objects have temporal/spatial/modal variation.

Properties have temporal/spatial/modal parts and it is in virtue of exemplifying the various temporal/spatial/modal parts of properties that objects have temporal/spatial/modal variation (this is my simplified version of the trope solution defended by Ehring).

Properties are distributive across times/spaces/worlds and it is in virtue of exemplifying such distributive properties that objects have temporal/spatial/modal variation (Parsons' distributive properties solution).

This list is not exhaustive. But, I take these to be some of the top candidate solutions. Some of these solutions might be more plausible explanations of one kind of variation than of another kind of variation. For example, it seems that spatial parts is a rather plausible solution to the problem of spatial variation whereas modal parts is not a very plausible solution to the problem of modal variation. One thing that I like to do is compare the plausibility of the solutions in various arenas of variation. Another thing that I like to do is try to find new arenas of variation and see how plausible counterpart solutions might be in that arena. For example, I suggested in a post a while ago that there is a problem of divine variation for a God that satisfies Aquinas' doctrine of divine simplicity. I thought that something like distributive properties might be able to help out Aquinas.

Last night I thought of another arena of variation: Sortals. I am both a thinker and a karaoke singer. But, whereas I am a good thinker, I am a bad (very bad) karaoke singer. So, it seems that I am both good and bad. What can account for this variations.

Some people might think that this simply a variant of the problem of temporal variation. But, it is not. The problem can arise for sortals that I have, and will satisfy all my live. For example, I am and will always be a human animal and I am and will (probably) always be a sibling. But, wereas I think I am a good human animal (or at least a decent one) I have not always been a good sibling. In fact it is possible for someone to always be a bad sibling and a good human animal. So, the problem is not simply one of temporal variation. So, what can we say. Here is a list of some solutions to the problem of sortal variation and my initial judgments of those views:

View:
Objects have sortal parts and and it is in virtue of the fact that various parts exemplify various properties that those objects have sortal variation.

Reaction:
Not very plausible I think.

View:
Objects have sortal counterparts and it is in virtue various counterparts exemplifying various properties that those objects have sortal variation.

Reaction:
What??

View:
Properties are exemplified relative to sortals and it is in virtue of an object exemplifying various properties relative to various sortals that objects have sortal variation.

Reaction:
I think this is the standard view. It seems rather plausible to me. But, I wonder if some other view would have greater theoretical virtues. For example, we might be able to have a better account of the semantics of "qua" sentences of we adopt one of the alternative views.

View:
Properties have sortal parts and it is in virtue of exemplifying the various sortal parts of properties that objects have sortal variation.

Reaction:
interesting and not completely implausible. This might be worth thinking about more.

View:
Properties are distributive across sortals and it is in virtue of exemplifying such distributive properties that objects have sortal variation.

Reaction:
Again, this seems interesting. I think this might be worth thinking about more as well.

I have only just started thinking about this topic but right now I am thinking that these last two views might be worth thinking about more. My initial thoughts are about "qua" sentences and whether these latter two views might be able to handle the semantics of "qua" sentences better than other views. I am also interested in the following: If I am in a deep sea dive and see a strange thing and my guide tells me that it is a fishus strangicus, then once he tells me that it is a bright colored fishus strangicus, I will be able to identify other bright colored fishi strangici. However, if he tells me that it is a beautiful one, then I probably still won't be able to identify other beautiful fishi strangici. I wonder if one of these latter views can help out with this problem. Those are just some of my initial thoughts. I will think more about this in the future and see if I can come work out these theories and figure out some of their various theoretical virtues and vices (their theoretical variation).

CONGRATULATIONS

2009-03-24T09:15:00.000-07:00

To Joshua and Neal!

Two fantastic positions. Two great philosophers. Representin' WWU!!!

Spatial and Temporal Zeno Walls

2009-03-23T20:28:00.000-07:00

We might be familiar with the following puzzle. Suppose that there is a football field at the end of an inclined plan. On the field there are a bunch of walls, each facing the inclined plane. One wall is at the 50 yard line, another wall closer to the inclined plane, at the 25 yeard line. Still another wall is even closer to the invlined place at the 12.5 yard line and so one all the way to the end zone. The walls form a zeno series whose open end is at the end zone at the foot of the inclined plane. Now, suppose we roll a ball down the inclined plane. The laws of nature in this world include the law that an object in motion remains in motion. Moreover, there are no impuritied in the plane that will make the ball deviate from its course toward the zeno series of walls. Finally, there are no stray objects that will intervene in the balls trajectory. The ball will make it to the end zone and it will make it all the way to the zeno series of wells. However, there are also physical laws that prevent the ball from passing through any walls and discontinuously passing through space. So, the ball must stop before it passes through the end zone. But, what makes it stop? It can't be any one of the walls. After all, if any one of the walls made it stop, then it must have reached that wall. But, in order for it to reach that wall, it would have to pass through some previous wall. That, however, is not physically possible. Hawthorne has suggested that the fusion of the walls stops the balls. This commits Hawthorne to a liberal view of composition. I am inclined to say that the walls have irreducibly plural causal powers. In any case, some thing or things has to stop the ball from moving. Since there are no other objects in the vacinity, it must be that some walls or fusion of walls stops the ball from moving.

Here is a new puzzle though. Suppose that there is a man who is happily persisting through time. He is healthy and the laws of nature are inconsistent with his sudden and unexpected demise. However, at 12:20 tomorrow a solid object composed of a single substance and filling all of space comes into existence for a mere instant. At 12:10 tomorrow, a solid object composed of a single substance and filling all of space comes into existence for a mere instant. At 12:05 tomorrow, a solid object composed of a single substance and filling all of space comes into existence for a mere instant . . . and so on . . . There is a zeno series of walls in time whose open end is at 12:00 and no member of which exists before 12:00. The young healthy man will persist all the way to 12:00. However, the laws of nature prevent a young healthy man from passing though the solid objects or discontinuously persisting through an interval of time. So, the young man must stop persisting through time. In other words, the young man must cease to exist at 12:00, he must die. But, what stops him from persisting, what makes him cease to exist or die? Just as before, we might think that the fusion of the walls stops the man from persisting. But, that commits us to a liberal view of diachronic composition. In fact, that solution seems to commit us to the existence of something that has temporal parts. We might say that the walls have irreducibly plural causal powers. But, then something that doesn't yet exist seems to cause something else to go out of existence. These are strange consequences. Nevertheless, something must make the young man cease to exist.

This last puzzle is particularly troubling for a presentist. We can describe a world like the one above using only presentist friendly phrases. There is a man and at 12:20 tomorrow a solid object composed of a single substance that fills all of space will come into existence for an instant. At 12:10 tomorrow solid object composed of a single substance that fills all of space will come into existence for an instant . . . The laws of nature guarantee that the young man will make it to 12:00 in perfect health. However, the young man will not exist after 12:00. So, it must be that something will make him cease to exist. But, at no time will there be anything that makes him cease to exist. So, nothing will make him cease to exist. But, it cannot be that something will make him cease to exist and yet nothing will make him cease to exist. Perhaps we have a reason, then, to think that presentism is false.

Williamson on Judgment Skepticism

2009-03-17T14:39:00.001-07:00

In chapter 7, Williamson discusses a type of skepticism he calls judgment skepticism. As he explains it, judgment skepticism "does not target the distinctive features of perception, memory, testimony, or inference" but instead "targets our practices of applying concepts in judgment" (p. 220). Williamson's paradigm example of a judgment skeptic is the person who, with van Inwagen, denies that mountains exist. Since it is the view of these folks that our ordinary geographical judgments are systematically false when understood strictly and literally, they count as judgment skeptics. Williamson then goes on to argue that judgment skepticism is on a par in important ways with skepticism about the external world.

There is some interesting stuff in this chapter about philosophical methodology, but I'm not quite sure what to say about that. So instead I'll raise two issues with the way he construes judgment skeptics like those who deny the existence of inanimate macroscopic objects.

First, he seems to think that judgment skepticism is going to have drastic consequences for the natural sciences. He says:

Judgment skeptical arguments apply to standard perceptual judgments, on which the natural sciences systematically depend: microscopes, telescopes, and other scientific instruments enhance ordinary perception but do not replace it, for we need ordinary perecption to use the instruments. If the contents of those perceptual judgments concern ordinary macroscopic objects, they are vulnerable to judgment skepticism about common sense ontology. If so, the empirical evidence for scientific theories is threatened. To assume that the evidence can be reformulated without relevant loss in ontologically neutral terms, in the absence of any actual such reformulation, would be optimistic to the point of naivety.

Well, perhaps I'm just being naive here, but I feel much more optimistic for such a reformulation project. At least, I don't see any reason to think that it couldn't be successfully carried out. Exactly what drastic consequence would follow for natural science if we agreed with van Inwagen that, strictly speaking, there are no mountains, or even that there are no telescopes? I just don't see it.

Also, he talks about judgment skeptics as though they argue for their position in a way precisely analogous to the more familiar sort of skepticism, but that doesn't seem true to me. As he points out, the skeptic about the external world may well argue employing the following bit of reasoning: since everything would appear to us exactly as it currently appears to us even if we were just brains in a vat, we don't know that we're not. The parallel move in the case of the van Inwagen-style skeptic would be: since it would still appear to us that there were mountains even if there were no mountains, we don't know that there are mountains. Perhaps someone who argued for mountain-skepticism using this sort of reasoning would be open to Williamson's objections, but van Inwagen doesn't argue in this way, does he? I thought the argument was supposed to employ more general mereological considerations about, for example, the downsides of DAUP and Unrestricted Composition, among other things. So it's unclear to me that judgment skepticism really is the sort of view Williamson is painting it to be -- or perhaps eliminativist views like van Inwagen's shouldn't count as versions of judgment skepticism after all?

Lying about PowerPoint

2009-03-13T10:48:00.000-07:00

In chapter 6, Williamson says that sometimes when he is teaching his students about Gettier cases, he says certain things to them so that they are actually in a Gettier case themselves. But I'm wondering whether what he says to them actually succeeds in Gettierizing their beliefs. He says he starts off by telling them:

(1) The only time I've used PowerPoint in the past it was a complete disaster.

From this they naturally come to believe:

(2) Williamson has never successfully used PowerPoint.

(2) is in fact true, and they seem to be justified in believing it (given that they have no reason to distrust his testimony in (1)), but they don't know (2) because the belief it represents is based on a lie. In fact, Williamson has never even tried to use PowerPoint and thus he says that (1) is false. Since they base (2) on something false, it looks like they don't know (2) despite the fact that it is a justified true belief.

But is (1) false? I guess it depends on what's being said. If what he is saying is this:

There exists a time at which I used PowerPoint and my using PowerPoint at that time was a disaster,

then it is indeed false. But if what he is saying is this:

Every time I've used PowerPoint in the past it has been a disaster,

then it looks vacuously true given the peculiarity of the universal quantifier.

Of course, maybe what this shows is that Gettier situations can arise even if the belief in question isn't based on a false belief. And, in any case, Williamson could just as well start his classes by saying, "I have used PowerPoint once before and it was a failure". So I'm not questioning the possibility of Gettierizing students...I'm just wondering whether the case as he presented it does the trick, and what it might tell us about Gettier cases even if it does.

Anaphora and Conditionals

2009-03-10T11:37:00.000-07:00

Let me say, before I get started, that I am way out of my league when it comes to issues involving anaphora and conditionals. In spite of that fact, I will be expressing a bit of skepticism about Williamson's treatment of conditionals with anaphora.

Williamson takes the following sentence to express one of the primary propositions in a Gettier style argument against the justified true belief account of knowledge:

(5) If a thinker were Gettier related to a proposition, then he/she would have a justified true belief without knowledge.

Williamson wants to formalize this statement. Surprisingly, Williamson's formalization of (5) is the following (again, I hope everyone can figure out my crude notation system. If not, this is intended to be identical to what Williamson labels (3*) in the book):

(3*) ExEp GC(x, p) []--> AxAp (GC(x, p) --> (JTB(x, p) & ~K(x, p)))

I find this a surprising formalization of (5) because it seems to have a lot more quantifiers and conditionals that (5) does. Put another way, (3*) seems to say that if something were in a Gettier situation, then it would be the case that anything in a Gettier situation has justified true belief without knowledge. But, that doesn't seem to be what (5) says. So, it does not seem like (3*) is a correct formalization of (5).

Williamson happens to have a few argument for the claim that (5) is a correct formalization of (3*). To understand Williamson's argument, we need to first have another candidate formalization in front of us. Here it is:

(10) AxAp (GC(x, p) []--> (JTB(x, P & ~K(x, p))

We also need a couple of candidate formalizations of the following monkey sentence:

(13) if an animal escaped from the zoo, it would be a monkey.

Here are the candidate formalizations:

(14) Ax ((animal(x) & Escaped(x)) []--> Monkey(x)

(15) Ex (animal(x) & escaped(x)) []--> Ax ((Animal(x) & Escaped(x)) --> Monkey(x)

Williamson seems to have two arguments. The first argument says that if (10) is the correct formalization of (5), then (14) is the correct formalization of (13). But, (14) is not the correct formalization of (13). So, (10) is not the correct formalization of (5).

The second argument says that if (15) is the correct formalization of (13), then (3*) is the correct formalization of (5). Moreover, (15) is the correct formalization of (13). So, (3*) is the correct formalization of (5).

Williamson seems to think that the sentences are similar enough that their formalizations will have (roughly) the same logical structure. But, this isn't obviously true to me. For instance, it seems like it follows straightfowardly from (5) that if Neal were in a Gettier situation, then Neal would have justified true belief without knowledge. But, it does not seems to follow straightforwardly from (13) that if George had escaped from the zoo, then George would be a monkey. But, if the sentences have the same logical structure, then the inferences would be both be valid.

I have to admit I've been agonizing over these sentences for a while. In fact, I've been agonizing long enough that I think I should have more to say. Unfortunately, I do not. I am unhappy with both the proposed formalizations and I have not been able to think of any plausible alternatives.

Counterpossibles

2009-03-03T15:30:00.001-08:00

Sorry I'm late posting on chapter 5...I just finished reading it today. I found this chapter more interesting than the rest of the book so far, but then again I also felt like Williamson was here just doing straightforward modal epistemology instead of furthering the overall project of the philosophy of philosophy. In any case, I like the suggestions he makes connecting the epistemology of counterfactuals with the epistemology of modality.

I'm unconvinced, though, by his responses to the counterpossible objection. The objection is that Williamson is wrong to say that counterfactuals with impossible antecedents are vacuously true since some such counterfactuals are false. For example, suppose you ask me what is the sum of 5 and 7 and I say '11'. Further suppose that I mistakenly think I said '13' and I then go on to assert: "If 5 + 7 were 13 I would have got that sum right." This counterfactual has an impossible antecedent, but it seems straightforwardly false. Since I actually answered '11', I would still have gotten the sum wrong even if 5 + 7 were 13. This seems right to me.

One of Williamson's objections is that when we think through the example, it falls apart. He says: "For example, if 5 + 7 were 13 then 5 + 6 would be 12, and so (by another eleven steps) 0 would be 1, so if the number of right answers I gave were 0, the number of right answers I gave would be 1." But I don't understand what Williamson is saying here. Is he saying that the friend of counterpossibles in this case has to say that if 5 + 7 were 13, then I would have got the sum right, since it would follow from my giving 0 right answers that I did give 1 right answer after all? If this is what he's saying, I'm not sure why the friend of counterpossibles has to follow him in reasoning this way. It's much less clear to me, for example, that if 5 + 7 were 13 then 5 + 6 would be 12, than it is that if 5 + 7 were 13 then I would have got that sum right. Moreover, his objection here seems to rely on the fact that this is a mathematical example. But surely there are plenty of other intuitively false counterpossibles. Suppose, as Joshua does below, that it is impossible for two objects to be co-located. Then isn't the following both false and a counterpossible: "If Joshua's finger and my finger were co-located, then Joshua would be my son"?

Aliens and Ghosts

2009-03-03T14:26:00.000-08:00

There are no ghosts haunting our attics and there are no aliens flying in saucers at night. I will assume that we all agree to these claims. Nevertheless, we might wonder what evidence might make us change our minds. I have some strange intuitions that I think others might share. I'd like to present those intuitions and see if there is anything interesting we can learn from the fact that we have those intuitions.

Suppose we learn that there really are skinny gray creatures that fly around in saucers abducting humans and cows; We learn that many of those people who claim to have seen or experienced such events really did have such sights and experiences. However, we also learn that the little gray creatures are actually creatures who evolved on earth; they are creatures who have never left earth, but have lived in secret for thousands of years deep in the ocean. Some of these creatures have traveled far from their majestic cities and have begun observing life on dry land. they travel in their finely constructed saucer shaped aircraft and sometimes they take a human or cow on board for close observation. If we were to learn that all this is true, would we say that there really are aliens flying in saucers at night? It seems to me that we would not. Rather we would say that what we thought were aliens turned out to be something like highly evolved fish.

However, suppose that we learned that there really are human shaped apparitions that move through our houses at night, disturbing our pets and making various noises; we learn that many people who claim to have seen or experienced such events really did have such sights and experiences. However, we learn that the apparitions are actually semi-corporeal creatures who evolved on earth. They were never any spiritual part of any human being, but have lived in secret for thousands of years in various dark places. Some have moved into our attics and move around at night making a little noise and sometimes disturbing our pets. If we were to learn that all this is true, then would we say that there really are ghosts haunting our attics? It seems to me that we would. We would be surprised to learn that ghosts aren't really the spirits of deceased human beings but rather a new life form living amongst us.

So, why do I have different intuitions about the two cases? Why do I think that in the first case we do not learn that there are aliens flying in saucers, but in the second case we do learn that there are ghosts? Moreover, do others share my intuitions?

I have tried to think of a couple of explanations for my different counterfactual judgments. My first idea was that the concepts applied in the two cases might have been introduced in different ways. One might think that the concept of a ghost was introduced into the community by ostension whereas the concept of an alien was introduced by way of a generalization. Thus, particular judgments about ghosts might carry more weight than general judgments and visa versa for judgments about aliens. But, this doesn't seem right. after all, I have no idea how the concept was first introduced into the community.

Perhaps I was introduced to the concept of a ghost by ostension whereas the concept of an alien was introduced by way of a generalization. But, this doesn't seem right. I am willing to bet rather heavily that I was introduced to the concepts in rather similar ways (perhaps via Robert Stack and Unsolved Mysteries). I suppose if I am mistaken, then we can test this hypothesis by introducing the various concepts to children in different ways and then asking them to make counterfactual judgments various cases while employing those concepts.

My second idea was that I have the judgments that I do because I think the concept of an alien is satisfied whereas my concept of a ghost is not. My concept of an alien is probably satisfied by some lifeform on a distant planet. But, I don't think anything satisfies my concept of a ghost. If this fact could explain why I make different judgments, then we should expect people who do believe in ghosts (as in disembodies spirits) to make a different judgment than me about the counterfactual circumstances in the ghost case above. I have done an unscientific survey of one person (who believes in disembodied spirits) and found that this was not the case; my survey participant had the same judgments that I did.

So, I guess I am at a loss. I’d like to know if any of you have the same judgments that I do and I’d like to know if any of you has an explanation for those judgments.

Williamson's Modal Epistemology

2009-02-25T14:09:00.000-08:00

Williamson believes that our knowledge about what might have been and what must be derives from our knowledge about counterfactuals. His rough idea is as follows. There are interesting biconditionals schemas that relate metaphysical possibility and necessity to certain kinds of counterfactuals. We can formulate these biconditionals as follows (please excuse my crude notation system. I hope everyone will be able to figure out what these are supposed to say):

17. []A iff (~A[]--> (P&~P))
18. <>A iff ~(A []--> (P&~P))

Since these biconditional schemas are true, if we can come up with an account of how we come to know certain counterfactuals, then we might be able to extend that account to say how we come to know that certain claims are necessary and that certain claims are possible. This is Williamson's project.

Williamson has a lot to say about how we come to know ordinary counterfactuals. I'd like to grant to him that we come to know ordinary counterfactuals in the way he indicated. However, I think there are still problems with his account of how we come to know that a claim is necessary or that a claim is possible.

My first objection to Williamson's account involves noting that the counterfactual schemas above involve strange, non-ordinary counterfactuals. Although Williamson has given us an account of how we come to know ordinary counterfactuals, he has not said much about how we come to know these strange counterfactuals. I might be willing to grant that we can come to know some of these non-ordinary counterfactuals. For example, I can come to know that if there were a barber who shaved all and only those who don't shave themselves, then there would be a barber who both shaves himself and does not shave himself. I can come to know this simply by drawing out the logical consequences of the antecedent of that counterfactual. But, suppose it is impossible for two objects to be co-located. Now, I'd like to know how I might come to know that if two things were co-located, then pigs fly and it is not the case that pigs fly. The claim that two objects are co-located is not inconsistent. So, I cannot draw the contradiction as a logical consequence of the claim that two objects are co-located. But, presumably some metaphysicians know that it is impossible for two objects to be co-located (given our supposition). So, how do they come to know this fact? It doesn't seem to me that Williamson has said much about this.

My second objection to Williamson's account is that his account seems to require that we know (17) and (18) above. If we did not know (17) and (18) then we would not be justified in believing that possibly P is true even through we are justified in believing that it is not the case that if P were true then P and not P would be true.

My third objection is merely an extension of one of the objections that Williamson considers. Williamson responds to the objection that his acocunt requires that all counterfactuals with necessarily false antecedents are vacuously true. However, the objector claims, there are some counterfactuals with necessarily false antecendents that are true and others that are false. Williamson gives several good explanations of why we might be mistaken in thinking that these counterfactuals are sometimes true and sometimes false. I find his explanations very plausible. However, the theorist who thinks that some counterfactuals with necessarily false antecedents are true while others false has more to say than simply that he has an intuition regarding certain counterfactuals. Such a theorist can say both that he has an intuition and that he has a prior commitment to an ersatzist account of worlds that allows for impossible worlds which can be used in an account of counterfactuals that satisfies his intuition. So, it seems to me that Williamson needs to say more in response to such a theorist. Not only does Williamson need to explain away our intuitions about these counterfactuals, but he needs to say why it is better to explain away our intuitions rather than accept an account of counterfactuals that satisfies those intuitions.

An Argument against Presentism

2009-02-24T08:20:00.000-08:00

Presentism is the thesis that no non-present objects. I was just thinking about this simple argument against presentism and I was wondering what all of you might think of it.

1. The proposition that 2+2=4 is not ever anywhere.
2. for anything whatsoever, if that thing is ever present, then it is somewhere at sometime.
3. So, the proposition that 2+2=4 is not ever present.

(1) seems intuitive. It does not seems as though we would be able to find a proposition if we just looked hard enough. Even if we could check every spatial region at every time, we would not be able to find the proposition that 2+2=4. but, if that proposition did at some time exist at some region, then it seems like we would be able to find it if we just looked.

Premise (2) is true because of the manifold nature of space-time. Given that space is three dimensional, no object can be some distance from me along one dimension without also being some distance from me along the other two dimensions (perhaps that distance is a zero distance). This is because the regions of one dimension are just composed of the regions of another dimension. So too, since time is putatively just composed of blocks of space, anything that is ever present must also at some time be spatial. (3) seems to follow from (1) (though the validity of the inference might be in question, there is no question that the inverence is cogent)

4. If the proposition that 2+2=4 is not ever present, then it is not present.
5. So, the proposition that 2+2=4 is not present.

Premise (4) seems very plausible. If something is not ever present, then it simply is not present. If something is present, then it is present at some time (namely the present). (5) follows from (3) and (4).

6. If the proposition that 2+2=4 is not present, then presentism is false.
7. So, presentism is false.

(6) seems obviously true. If presentism is the thesis that everything is present, then if something is not present, then presentism is false. So, if the proposition that 2+2=4 is not present, then presentism is false. (7) follows validly from (5) and (6).

I see several responses that someone might make to this argument. Some of the responses would probably be more widely accepted than others. Someone might, for example, reject (6) on the grounds that propositions do not fall within the scope of the quantifier 'everything'. This view might be most acceptable to non-serious presentists. such presentists might already accept that Socrates stands in relations to me and even that 'Socrates' refers. However, they reject that Socrates refers to anything that falls within the scope of 'exists' or 'everything'. If we are willing to accept the non-serios presentists position, then it shouldn't be too difficult to accept that the proposition that 2+2=4 also stands in relations, that 'the proposition that 2+2=4' refers but that that referent fails to fall within the scope of 'exists' and 'everything'. Moreover, this view might actually be held by Graham Priest. I think this is my preferred response to the argument (though I do have worreis about how to analyze the definite description), but I think this response would not be widely accepted.

I think that some presentists would deny (1). They might say that I am confusing the relation of existing-at with the relation of being located-at. To exist at a region is merely to be in the domain of quanfification for a region. To be located at a region is to have some kind of presence at that region. For example, I am not located at my apartment right now. However, I am within the domain of quanfication for my apartment. Hence, I exist-at my apartment without being located there.

I think that this way of rejecting (1) is mistaken. I am not sure I completely understand 'exists-at' but insofar as I understand it, it seems obvious that it implies a presence of some kind. If I exist-at my apartment, then I better be in my apartment. My opponent might push further by saying that I am only introducing further confusions. I am confusing 'exists-in' and 'exists-at' or maybe I am confusing 'exists with respect to' with 'exists-at'. But, I think it is my opponent who is introducing confusions. In the argument above, I refrained from using any phrase like 'exists-at'. So, it is not enought to simply say that I am confusing 'exists-at' with some other relation. My opponenent needs to say something about how this relates to premise (1).

My guess is that someone who claims that I am confusing 'exists-at' with 'exists-in' or 'exists with respect to' has some kind of analysis of 'The F is not ever anywhere' in mind; she has an analysis that employs 'exists-at' or 'exists with respect to' or whatever. But, any analysis of 'The F is not ever anywhere' that implies that 'The proposition that 2+2=4 is not every anywhere' expresses a falsehood has a singnificant strike against it. Such an analysis better do a lot of good theoretical work to account for such a counterintuitive consequence. I don't know for sure, but my guess is that there are not such strong theoretical benefits to the proposed analyses.

So, if (1) and (6) are okay, then we are left with (2) and (4). I can't think of any theorist who denies (2) or (4) and I can't think of a plausible metaphysical view that implies the denial of (2) or (4). If any of you can, I'd like to hear about it. In any case, it seems to me that a view that denies (2) or (4) will have something interesting to say about the particular quantifiers 'ever', 'sometime' and 'somewhere'. I'd like to hear what such a view has to say.

Sketching the First Half

2009-02-17T13:33:00.000-08:00

Having just completed the (epic) fourth chapter, it seems to me that the general agenda Williamson had for the first half of the book is now over and the fifth chapter will take us onto something new. With this in mind, perhaps it will be helpful (I'll find it helpful, at any rate) to look back on what Williamson was up to in the first half, now that I have the wisdom of hindsight.

Here's the short version as I see it, though I'm certainly open to being corrected.

Some people seem to think that what distinguishes philosophy from other disciplines is that philosophy is in some distinctive sense merely linguistic or conceptual (chapter 1). Two questions: what could they mean by this, and is it true? Here's one thing they could mean: all philosophical theses are about language or thought. But this is false (chapter 2). Here's another thing they could mean: all philosophical theses are analytic and so less substantial than the theses of other disciplines. But this is false if we understand analyticity in terms of a metaphysical criterion like "truth in virtue of meaning" (chapter 3). It's also false if we understand analyticity in terms of an epistemological criterion like "assent entailed or constituted by understanding" (chapter 4). So without any idea about what else people might mean by saying that philosophy is primarily linguistic or conceptual, we can tentatively conclude that it's not.

Does this seem like a fair characterization of the first half of the book? If so, why the heck was the first half so long? :)

My main complaint about the argument up to this point is the same one I've shared before: that it doesn't seem like he clearly identifies his opponent. Surely someone could admit that not all philosophical theses are about language (or thought) and also admit that not all philosophical theses are analytic in any sense and yet also maintain that at best philosophy can help us learn about ourselves and not the world around us. Perhaps this character would have to deny the sort of claim that Joshua has pushed in some of the previous comment threads -- namely, that one perfectly good way to learn about the world is by learning about ourselves. But it seems to me that THIS is where the dispute is located...not in the sort of pedantic maneuvers involved in trying to come up with an adequate conception of analyticity.

Epistemic Analyticity

2009-02-17T12:50:00.000-08:00

I'm sorry this post is a bit late. This chapter was rather long and I only just finished reading it. It also turns out that, due to the length of the chapter, a significant amount of time has passed since I read the beginning sections. I mention this because I think that Williamson addressed the idea that I am going to bring up in this post. But, since he addressed it toward the beginning of the chapter and since he said a lot in this chapter, I don't remember exactly what he said in response to the idea I'm going to present.

In the last chapter, Williamson considered metaphysical accounts of analyticity. However, such accounts suffered from a gap problem; there always seemed to be a gap between the analytic status of a sentence and our putatively easy knowledge of the proposition expressed by that sentence. That is, it seemed that there was no way to support the idea that if a sentence is metaphysically analytic, then it expresses a proposition that is epistemically accessible independant of various experiences. In this chapter, Williamson considers epistemic accounts of analyticity. The hope is that epistemic accounts will not suffer from such a gap problem.

Williamson approaches the subject in a rather circuitous way. He first introduces understanding/assent links and then suggests that such links can be used to support the claim that analytic sentences express propositions that are (in some sense) easily known. I am not exactly sure why he didn't just get straight to the heart of the issue. Although he considered unserstanding/knowledge links and understanding/justification links, he did not make them the central issue of his discussion. In this post, I'd like to consider approaching the idea of epistemic analyticity more directly.

Let's start with the intuitive idea that any possible native English speaker who understands a sentence like "Every vixen is a vixen" should have some positive epistemic status toward the proposition expressed by that sentence unless s/he has strong evidence against that proposition. Alternatively, some one might say that any possible native English speaker who understands the sentence in question will be justified in believing the proposition expressed by that sentence as long as s/he has no defeaters. Or, perhaps someone might say that any possible native English speaker who understands the sentence will be prima facie justified in believing the proposition expressed by that sentence. I am not exactly sure how to spell out this intuitive idea and I am not sure if the three things I wrote above are even (in any sense) equivalent. but, I think the idea, vague though it is, is clear enough to think about. So, let's just take the following principle and run with it under the assumption that prima facie justification can be overwhelmed by countervailing evidence:

(EA) For any English sentence S, S is epistemically analytic (if and) only if any possible native english speaker who understands S is prima facie justified in believing S.

The idea here seems to be that analytic sentences are such that understanding them is constitutive of some kind of evidence for the proposition expressed by that sentence. Of course, one can have evidence against the proposition expressed by an analytic sentence. So, for example, the theorists from Williamson' example have evidence against the proposition expressed by "every vixen is a vixen" because they believe or have evidence for some alternative theory that suggests that the claim that every vixen is a vixen is not true. Thus, Peter is not justified in believing that every vixen is a vixen becuase he has reason to believe that such a claim entails that vixens exist. This does not show, though, that he is not prima facie justified in believing that every vixen is a vixen. He might very well be prima facie justified yet have evidence that makes him ultimately not justified in believing that proposition. Similar things can be said for Stephan who denies "every vixen is a vixen" because he thinks that certain sentences with vague expressions are indeterminate in truth value.

Williamson does consider a couple of objections to something like (AE). If I remember correctly, he considers a case involving a man who decides to believe phlogiston theory simply because he likes the word or has good memories involving the word or something like that. Williamson claims that such a theorist is not even prima facie justified in phlogiston theory. I am a bit confused by this example though. Are we supposed to be taking certain tenets of phlogiston theory as analytic? why can't we, for example, simply say that our theorist is not at all justified in believing the central tenets of phlogiston theory and, moreover, those tenets are not analytic? I honestly don't remember what Williamson says in response to these questions. So, if someone can help me out, I would appreciate it.

However, I think there is a decent response to this criticism even if we accept that certain central tenets of phlogiston theory are analytic. We should make a distinction between being justified in believing and justifiably believing a proposition. Someone can be justified in believing a proposition, yet fail to justifiably believe that proposition. The theorist who believes phlogiston theory might be in such a position. Perhaps his mere understanding of certain sentences of phlogiston theory provides him with prima facie justification for the propositions expressed by those sentences. Moreover, absent any evidence against those propositions, he might even be justified in believing them. However, if he believes those propositions because of his fond memories, then he is not basing his belief appropriately. That is, he is not justifiably believing the propositions even though he is justified in believing them.

I kind of like (AE). I'm sure there will be problems with it. But, as far as I can see, Williamson has not introduced any such problems. One might worry that if there is such a link between understanding and prima facie justification, there needs to be an explanation of that link. In other words, we need a theory of why those sentences like "every vixen is a vixen" are such that mere understanding of them implies prima facie justification in the propositions they express. I am not sure how to respond to a demand for an explanation of such a link. However, I am inclined to say that nothing more needs to be said. Understanding such sentences is enough to provide prima facie justification for the propositions they express. Perhaps understanding them even constitutes prima facie justification. But, I am not sure about the plausibility of defense.

Pragmatics

2009-02-11T11:45:00.000-08:00

We often say just a little and convey quite a bit. When there is a small kitchen fire, I might say "There is a fire extinguisher under the cupboard" and pragmatically convey that the nearest working fire extinguisher is under C (some particularly salient nearby cupboard). There is a question, though, that I want to ask about pragmatics. When we utter a sentence and pragmatically convey some bit of information, is it the sentence that we utter that triggers the pragmatic conveyance or the content of the sentence that triggers the pragmatic conveyance?

One initially plausible answer is that it is the content of the sentence that triggers the pragmatic conveyance. After all, if I say "there is a fire extinguisher under the cupboard" to someone who does not speak any English, then no information will be pragmatically conveyed to that person. but, if the sentence (and not the content) triggers the pragmatic conveyance, then it seems that information would be pragmatically conveyed to such a person.

Here is another reason to favor the view that pragmatic conveyance is triggered by the content of a sentence rather than a sentence itself. If someone says a a native Spanish speaker "hay un extintor de incendios en el marco del armario" then he will convey to that Spanish speaker the same thing that I convey when I say "There is a fire extinguisher under the cupboard". The best explanation of this is that the content of my sentence and the content of the Spanish sentence is the same and that content conveys that the nearest working fire extinguisher is under C (some particularly salient nearby cupboard).

Unfortunately, there are some troubling cases. First, there is a problem of particular conversational implicatures. Suppose that we have two people, one of whom is a believer is in a pagan religion that believes that Bolti is a vile god that throws thunderbolts from heaven on those whose corps fail. The other is a pagan who believes that Mani is a kind god who throws mana from heaven on those whose crops fail. Assuming that there are no such gods as Bolti and Mani and assuming a certain kind of Millianism, the content of "Mani is listening" is the same as the content of "Bolti is listening". Hence, if pragmatic conveyance is triggered by the contents of sentences rather than the sentences themselves, then someone who utters "Bolti is listening" will convey the same information as someone who utters "Mani is listening". But, this is just not correct. If our first pagan says to one of his friends "Bolti is listening" after the friend confesses that his crops might fail, it seems he has pragmatically conveyed that thunder bolts might fall on his friend. On the other hand, if the second pagan says "Mani is listening" to a friend who has just confessed that that his crops might fail, then it seems he has not pragmatically conveyed that thunder bolts might fall on his friend, but rather that mana might fall on his friend. Thus, it seems that it is not the content of those sentences that triggers the pragmatic conveyance.

Here is another example. Suppose I introduce the word "flugi" to mean the same thing as whatever adjective would be most offensive to Mr. Wake. I then say "Mr. Wake is a flugi" to Mr. Wake. I presume he will not be offended. But, that seems to indicate that whatever is offensive about a use of a particular word, it is not part of the content of that word, but rather part of whatever is pragmatically conveyed. But, now we have another reason for thinking that pragmatic conveyance is triggered by the words or sentences and not the contents of words or sentence. This is becuase if I say to Mr. Wake "You are a flugi", then (as I said before) he will not be offended. But if I say to Mr. Wake "you are an A" where 'A' is whatever word is the one that is most offensive to Mr. Wake, then I will offend him. Since "You are a flugi" and "you are an A" have the same content (in thier respective contexts), then it looks like the pragmatic conveyance is not triggered by the content.

I am not exactly sure what to take away from this discussion. I am inclined to say that pragmatics is much more complicated than one might expect. Pragmatic conveyances aren't just triggered by contents and they are not just triggered by sentences or words either. Rather pragmatic conveyances are triggered by words or sentences in combination with their meanings. On this view, it is not simply the word (taken as a sound of inscription) that triggers a pragmatic conveyance and it is not just the meaning of the word either. Rather, it is something like the word combined with the meaning.

The opposition?

2009-02-09T06:14:00.000-08:00

Despite having gotten off to a good start, so far I'm not nearly as impressed with this book as I thought I would be. Part of the problem, I think, is that it's unclear to me exactly who Williamson means to be addressing. In my post on the last chapter, I complained that he was setting up a straw man because those in favor of the conceptual turn must have something more interesting in mind than merely the claim that all philosophical theses are *about* language/thought in Williamson's various senses of 'about'. When I started chapter 3, then, I was excited because it seemed like Williamson was going to address this very point. But I still think he must be misunderstanding or misrepresenting his opposition, whoever they are.

His main point in this chapter is to argue that thinking about analyticity as "true in virtue of meaning" doesn't entail that analytic truths are insubstantial. I take it that in the next chapter he'll argue that thinking about analyticity in terms of some epistemological formulation also doesn't entail that analytic truths are insubstantial, and hence we get a fuller defense of the claim that philosophy is more than merely conceptual. But I'm a bit skeptical of this strategy, in part because I would think we should *begin* with the presupposition that analytic truths are less substantial and then go on to investigate both what this means and also whether all philosophical truths count as analytic. Doesn't it just seem obvious that the truth expressed by "Vixens are female foxes" is somehow less substantial than that expressed by "There are black swans"? Maybe this means I'm just coming at it from a different perspective, but I wouldn't have thought that the burden was on those who made these claims of insubstantiality. Or, at least, the burden on them is not to show THAT these truths are insubstantial but instead to say in what their insubstantiality consists. That seems like an interesting project, but I don't really see Williamson engaging concretely with those who would wish to embark on it.

P.S. Sorry I don't really have anything terribly penetrating to say about the book so far...I'm still trying to get my head around the general project, and I haven't been very impressed so far with the clarity of his writing.

Modal-Analytic Truths

2009-02-08T20:34:00.000-08:00

I think I agree with much of what Williamson says in this chapter. It seems clear, for example, that no metaphysical conception of analyticity will vindicate the idea that analytic truths are insubstantial. There are, however, a couple of small points that Williamson makes that I disagree with.

Williamson claims that this sentence:

S1: It is raining iff it is actually raining.

expresses a modal-analytic truth. I disagree.

A modal-analytic sentence is a sentence the meaning of which is sufficient for truth. A meaning is sufficent for truth "just in case necessarily, in any context any sentence with that meaning is true." In what follows, I will assume that the meanings of sentences are propositions. Hence, it will be ligitimate to say that a proposition is sufficient for truth. With this definition in mind, we can easily show that S1 is not a modal-analytic truth.

To see that S1 does not express a modal-analytic truth, first consider the following sentence:

S2: It is raining iff it is raining in actuality.

If we take 'actuality' as an indexical that picks out the world of whatever context it is expressed in, then this sentence, just like S1, will express a true proposition in any context. Whatever proposition it expresses will be contingent. And, most importantly, whatever proposition it expresses will fail to be sufficient for truth. To see that this latter claim is true, let 'Alpha' name whatever world happens to be the actual world. Now, it is clear that the proposition expressed by S2 in a context that has alpha as its world will be the same as the proposition expressed by the following sentence:

S3: It is raining iff it is raining in Alpha.

Let's call the proposition expressed by S2 and S3 in such a context, say our context, 'P'. Since 'Alpha' is a name, rather than an indexical, then in any context, S3 will express P. Consider a context C that is such that alpha is not the world of C. Suppose that in the world of C it is not raining whereas in the alpha it is raining. Then, the proposition expressed by S3 in C will be false. That is, P will be false in C. But, that means that the sentence S3 will be false in C. So, possibly, in some context, a sentence that has P as its meaning is false. So, P is not sufficeint for truth. But, P was the meaning of S2 in our context. So, the meaning of S2 (in our context) is not suffient for truth. So, S2 is not modal-analytic

I say that the same kind of argument will show that the meaning of S1 is not sufficient for truth. That is, S1 is not modal-analytic. All we need is a non-indexical adverb that happens to have the same meaning as 'actually' in our context. Let's introduce the adverb 'alpha-ly' to be just such an adverb. Now, we can run an argument perfectly parallel to the one introduced above. The conclusion of that argument is that the meaning of S1 is not sufficient for truth and hence S1 is not modal analytic.

I think a general lesson can be learned from this exercise. Namely that sentence is modal-analytic only if its meaning is necessary. If the meaning of a sentence is contingent, then we can always come up with a way of expressing that meaning using non-indexical terms. Whatever sentence we come up with will express the contingent proposition in a context where that proposition is false. Hence, the proposition will not be suffient for truth. Hence, any sentence that expresses that proposition will fail to be modal-analytic. So, contrary to what Williamson says, the notion of modal-analyticity does not violate the Kripke contstraint on analytic truths. That is, if analytic truths are modal-analytic, then analytic truths are necessary, just as Kripke claims.

Rights and Permissions

2009-02-05T13:59:00.000-08:00

I have some ethical issues that I want to discuss. I know that it is not normal for me to discuss such issues, but I hope everyone will forgive me for this unusual diversion. I have been teaching ethics classes for a little while now and I've noticed that my students tend to use the word 'right' when philosophers would typically use the word 'permitted'. For example, my students might object to a view by saying 'no one has a right to do that' whereas a philosopher would put the objection by saying that 'no one is permitted to do that'. Similarly, my students often say 'we have a right to do A' in a situation where a philosopher might typically say 'we are permitted to do A'.

Many years ago, I took a class on moral rights theory and my students comments have made me start to think about the nature of moral rights again. In my rights class, we talked about two reductive theories of rights. The first reductive rights theory can be stated as follows:

(RR1) Necessarily: for any S and any action A, S has a moral right to do A iff S is morally permitted to do A and no one is morally permitted to stop S from doing A.

(Let's ignore complications that might arise with the generality of these claims and take all permissions, obligations and (hence) rights to be presumptive or prima facie.)

If (RR1) is correct, then it is logically consistent to say that someone is permitted to do A and yet doesn't have a right to do it. That is, to be a bit more precise, the conjunction of (RR1) with the thesis that someone is permitted to do some action yet does not have a right to do that action is logically consistent. So, from a logical point of view, it seems that we are saying something more when we say that a person has a right to do something than when we say that he is permitted to do so. but, my students don't seem to talk this way. They seem to take having a right to do something as equivalent to being permitted to do it.

I think that my students might be on to something. Although the position that someone is permitted to do something even though they don't have a right to do so is logically consistent, I am not sure that it is metaphysically possible. I can't seem to think of a situation where some one is morally permitted to do something yet some second person is morally permitted to stop that first person from doing that thing. That is, the following permission principle seems true to me:

(PP) Necessarily, for any S and any A, if S is morally permitted to do A, then no one is morally permitted to stop S from doing A.

Here is my quick defense of that thesis: Suppose that possibly, there is a person, S1, who is permitted to do A and yet there is a second person S2 who is morally permitted to stop S1 from doing A. If S2 is morally permitted to stop S1 from doing A, then there must be some negative moral feature of S1's action that warrents its being stopped. But, if there is some negative moral feature about S1's action that warrants its being stopped, then S1 is not really morally permitted to perform that action (contrary to our supposition). So, it seems to follow that necessarily, for any S and any A, if S is morally permitted to do A, then no one is morally permitted to stop S from doing A. That is, (PP) is true.

If (PP) is true, then although my students might be saying something with greater logical content when they say that someone has a right to do something as apposed to saying that he merely has a permission to do so, their claims might still be acceptable. After all, it is not really possible to have a permission without also having a right.

Of course, all this depends on my rather rough argument for (PP) and the controversial thesis (RR1). Some people, for example hold an alternative view about rights. They often say that a right implies more than just an obligation of non-interference. Some say that rights imply a kind of obligation of protection. It is hard to express this idea in a reductive principle, but the rough idea is something like the following:

(RR2) Necessarily: for any S and any A, S has a moral right to do A iff S is morally permitted to do A and everyone is morally obligated to ensure that no one interferes with S's doing A.

(RR1) is often called a negative rights theory whereas (RR2) is called a positive rights theory. Now, I have not thought about whether similar considerations would indicate a kind of metaphysical equivalence between having a right and having a permission given (RR2). So, someone might tentatively object to my claim that my students are on to something by endorsing (RR2). But, I think I might be inclined to turn such an objection on its head. That is, if (RR2) really does indicate that having a right is different from having a permission, then since my students are so inclined to take these two things as equivalent, we have some reason to favor (RR1) over (RR2). Of course, it is only a small reason and it might be defeated by other considerations in favor or (RR2). But, right now, I am inclined to reject this tentative objection.

So, that is my digression into moral philosophy for the day. I would be interested to hear what others think of my argument for (PP). I am also interested in thinking about whether a similar argument can show that the following permission/obligation principle is true:

(POP) Necessarily, for any S and any A, if S is morally permitted to do A, then everyone else is morally obligated to ensure that no one interferes with S's doing A.

If (POP) does happen to be true, then having a right and having a permission would be the same even if (RR2) is true. Unfortunately, this principle sounds less plausible to me, but I honestly haven't thought much about it.

Philosophical Questions

2009-01-25T14:08:00.000-08:00

I think that Williamson's arguments for the conclusion that philosophical questions are not always about (either implicitly or explicitly) language are (for the most part) sound. It seems clear to me that the original question:

Was mars always either dry or not dry?

is not question about language or concepts. However, I do think that this is a question that is best answered by thinking about our language or concepts. In fact, here are three theses, each of which seems rather plausible to me, about the nature of philosophical questions:

T1: Philosophical questions are questions that can be answered only by analyzing our concepts or language (if they can be answered at all).

T2: Philosophical questions are questions that can be best answered by analyzing our concepts or language (if they can be answered at all).

T3: Philosophical questions are questions that are appropriately answered by analyzing our concepts or language (if they can be answered at all).

Williamson doesn't really address any of these theses. Although, some of the things he says may suggest that some of these theses are true or that some of them are false. However, each of these theses seems plausible to me and might be a way of holding onto the view that (in some sense) philosophy is primarily conceptual. Perhaps a defense of one of these theses is put philosophy right back into the concepual turn.

That being said, although I find these theses plausible, I do have worries about them. One worry is that some philosophical questions can seem to be answered by methods that are just as easily done from the armchair as philosophical analysis, but which are not methods of philosophical analysis. For example, Lewis attempts to answer the philosophical question "Are there any possible worlds?" by weighing the pros and cons of the various answers to that question against one another. It seems that if the philosophical question "Are there possible worlds?" can be answered by Lewis' method, then T1 is be false. Moreover, if there is no better way to answer that question than by Lewis' method, then T2 is false. Finally, if it is perfectly appropriate to answer that question by Lewis' method, then T3 is false.

As I see it, one can try to show how a Lewisian kind of argument can be turned into a argument involving conceptual analysis or one can give up on theses T1-T3. I do not know what the best response to this kind of worry is. In any case, it seems that these theses might be appropriate ways of characterizing the thesis that philosophy is concpetual. Moreover, even though the lewis example provides a decent case against theses T1-T3, it is not clear to me that these theses are false.

Being About or Being Stuck Within?

2009-01-24T20:06:00.000-08:00

I was not a big fan of chapter 2. In part, this was because I felt like the detour through the details of various theories of vagueness was a distraction. For his overall purposes, Williamson certainly could have left the details of three-valued logic and fuzzy logic and all that to one side. But also, I'm not sure he really addressed the worries of those who think that the only things we study in philosophy are the structures of thought and/or language.

I think he did a good job of showing that some philosophical questions are not either explicitly or implicitly about language and thought, in any natural sense of the word 'about'. But I suspect that people who think all philosophy is in some sense conceptual philosophy don't need to construe their thesis using the word 'about'. Rather, couldn't they say that although there are some questions that aren't even implicitly about language and/or thought, nevertheless the only things we learn from asking and answering those questions are things about language and/or thought? In other words, even if we grant that some philosophical questions aren't even implicitly about language and/or thought, can't we still coherently worry about always being "stuck within" the realm of language and/or thought? I have some friends here at Riverside who seem to take this sort of line, at least.

So, I felt a little bit like Williamson wasn't taking the opposition as seriously as he ought to have been.

Progressives

2009-01-21T09:07:00.000-08:00

Suppose I am baking a loaf of bread. Does this entail that there will, at some time, be a loaf that I baked. I think so. But, I have recently learned that this is a rather unpopular position. I'd like to consider the case for my position and how it fares compared to the standard position.

The standard position implies the fact that I am baking a loaf of bread does not entail that there will, at some time be a loaf of bread that I baked. This is upheld by our intuitions in the following case. Suppose that I am engaged in what seems like bread making activities. I make a dough and let it rise and stick it in the oven. However, soon after putting the dough in the oven, my kitchen explodes. The police come by to take a report on the incident. It seems like I can truly say to the police that I was baking a loaf of bread when the kitchen exploded. In fact that seems like a natural thing to say. However, this supports the standard position: the fact that I am baking a loaf of bread does not entail that there will, at some time, be a loaf that I baked.

I think the case for the standard position is rather strong. But, I don't think it is definitive. Let's give a second case and see if there is any intuition (even a slight one) against the standard position.

Suppose that while I'm giving my statement to the police I say that I was baking a loaf of bread when the kitchen exploded. But, suppose that one of the police officers asks to see the loaf of bread I was baking. I respond by saying that there is no loaf, that my dough was destroyed in the disaster. He responds by saying "I guess you weren't baking a loaf of bread then". What the officer says is annoying. What he says isn't even a funny joke. But, what he says doesn't strike me as obviously false. In fact, it seems that his joke relies on taking our language literally. If this intuition is right, then the standard view is false. That I am baking a loaf of bread does entail that there will, at some time, be a loaf that I baked.

That second case is not obvious. But, I do have a slight intuition in favor of saying that the officer spoke truly. That gives me a small reason to believe that the standard view is false. But, perhaps it isn't enough of a reason to defeat the very plausible case that was made in favor of the standard view.

But, here is a third case. Suppose I am engaged in what seems like bread making activities. I make a dough and let it rise and stick it in the oven. However, soon after putting the dough in the oven, some crazy quantum even occurs that rearranges the material in the oven to form cookies. The police come by to take a report on this very strange incident. I say that I was baking a loaf of bread but that when I opened the oven I discovered cookies instead of a loaf of bread. Now the officer says "I guess you weren't baking a loaf of bread then." Now I have an even stronger intuition to say that the police officer spoke truly.

Now, if we add to these intuitions that the semantics for "Joshua is baking a loaf of bread" will be much simpler if standard view is false, then I think we have a decent case against the standard view. On the non-standard view I am considering, "S is baking a loaf of bread" expresses a truth in English iff S is baking and S's baking activity will result in a loaf of bread. In fact, I am inclined to make success a necessary condition of any progressive verb phrase.

On the other hand, one who endorses the standard view will have to say something like the following: 'S is baking a loaf of bread' expresses a truth in English iff S engaged in an activity that tends toward a loaf of bread being produced. It is very unclear what "tends toward" means here. Moreover, if we try to make a general semantics for progressives, the standard view seems to get into more trouble. It seems very that an activities tending toward a loaf of bread being produced is different from, for example, an activities tending toward a leaf being produced. But, presumably, the semantics for 'X is growing leaves' on the standard position will be something like x is engaged in an activity that tends toward leaves being produced. Finally, the standard view will have to accept that some progressives have success conditions. For example, the fact that S is conquering Poland definately entails that S succeeds in his conquest. So, the standard view will have an even sloppier semantics because the standard view will have to distinguish between those progressives that have success conditions and those that do not.

So, the fact that my non-standard view supports the intuitions in cases 2 and 3 and the fact that my non-standard view allows for a clear and simple semantics whereas the standard view does not, seems to provide a pretty decent case in support of that non-standard view.

Putnam's Paradox

2009-01-20T07:28:00.000-08:00

I was thinking about Putnam's paradox the other day. I thought of a parallel between Putnam's paradox and a problem in the vagueness literature that seems interesting. I'd like to talk about this parallell in this post, but let me warn everyone that there are two things that I don't know much about that play an important role in this post: First, I don't know much about Putnam's paradox and second, I don't know much about vagueness. So, I might be completely confused and not really understand the issues.

First, let me present Putnam's paradox and a kind of naive response. then, I'll present an objection to that response. finally, I'll introduce a vagueness problem and a naive response along with an objection to that response. I hope to give a kind of response to both objections that might seem unsatisfactory.

So, here is my attempt to remember Putnam's paradox. I might be misremembering the problem and I am very sorry if I am. Let's take a theory to be a set of sentences in a first order language. Now, these three things seem true, but cannot all be true: (1) The meaning of the terms in a theory is determined by our use of those terms. But, (2) for any consistent theory, there is an interpretation of that theory which is both consistent with our use of the terms in the theory and that makes the theory true of the actual world. And, of course, (3) not every theory is true of the actual world.

I believe that the standard reply is to reject (1) and say that something besides our use determines reference (perhaps some entities are reference magnets). However, here is a different, naive response that appeals to a hiarchy of theories. Let's take theory T and take a second theory T* that is a theory about the referents of the words in T. Perhaps T* says something about causal connections betweem various objects and terms or perhaps it says something about spatiotemporal eligability. Who knows. It doesn't really matter. What does matter is that there is a theory that says that some interpretation of T that is the intended interpretation and explains why that is the intended interpretation. This is the niave response. Hee is what I like about it. It does not metaphysically privilage any particular properties in the world. Unfortunately, I am not exactly sure which of (1)-(3) this view rejects.

Putnam has an objection to this kind of response. He points out that T* is just more theory. For any theory about T, there will be an interpretation of that theory which is both consistent with our use of the terms in the theory and that makes the theory true of the actual world. the paradox just arises again at another level. Of course, we can go up another level, but the paradox will rear its ugly head up there as well. There is no way to escape the problem.

So, that is the paradox, the naive response and the objection to that response. Now, I'd like to consider a problem concerning vagueness.

Some people like linguistic theories of vagueness. They say that vagueness is rooted in our failure to determine by our word use one particular meaning over some other meanings. What a niave linguistic theorist would like to say is that there are a bunch of vague terms T1, T2, ..., Tn and that T1 is vague because out use of it indicates that it might mean P or Q or R and T2 is vague because out use of it indicates that it might mean . . . and so on.

Unfortunatley, one can object to the niave view by pointing out that the niave linguistic theorists theory is expressed in a vague language as well. Moreover, although we might be able to give an account of the vagueness in that second langauge, we will only do so by introducing more vagueness. Just as with Putnam's paradox, there is no escape.

What I'd like to say in response to the objection to the niave linguistic view of vagueness is that there is just vagueness all the way up. sure we have a theory T that is vague and a theory about T that is also vague and a thoery about that that is also vague. But, that is just the nature of vagueness. T is vague, our theory about T is vague, our theory about our theory about T is vague and so on.

I'd like to say something similar about Putnam's paradox. Lets say a theory that is subject to radical interpretation is Putnamable. Now, a theory T is putnamable. And there is a theory about T that indicates why one interpretation is favored over another. But that theory is Putnamable as well. Moreover, there is a theory about the theory about T and this third theory is Putnamable and so on.

McDowell's Argument

2009-01-18T17:55:00.000-08:00

Williamson criticises Mcdowell's argument for the conclusion that the things one can mean or think just are the things that are (or might be) the case. I don't quite understand how this thesis is supposed to fit into the broader picture that Williamson is criticising (perhaps someone help me understand that), but it seems to me that Williamson's criticisms are mistaken. Here is Mcdowell's argument:

1. When we think truly, what we think is what is the case.
2. The world is everything that is the case.
3. So, when we think truly, what we think is the world.

I think that this argument is rather confusing. But, Williamson seems to suggest that (1) is false. Many things about this argument confuse me, but the truth of (1) is not one of them (at least on the charitable readings of (1)). Williamson's objections to (1) have to do with the claim that (A) the content of our thoughts are fine grained whereas (B) the things that are the case are not. So, for example, Williamson says that what we think when we think that Hesperus is hot is different from what we think when we think that Phosphorus is hot. But, what is true when Phosphorus is hot is the same thing that is true when Hesperus is hot. So, that which is the case is different from what is thought.

It seems to me that there are two options here. Either some broadly Fregean-like thesis is true or it is not. That is, either the thought that Hesperus is hot is the same as the thought that Phosphorus is hot or it is not. If it is, then it seems that there are two different things that are true. Namely that Hesperus is hot and that Phosphorus is hot. That is, there are two different things that are the case: that Hesperus is hot and that Phosphorus is hot. This commits us to the claim that what is the case is not merely an object's having a property. Rather what is the case is a complex entity made up out of fregean senses. In other words, the very same fregean proposition that is believed is also the thing that is the case. This indicates that (B) is mistaken.

On the other hand, if the broadly Fregean thesis is false, then the thought that Hesperus is hot is the same as the thought that Phosphorus is hot. But, this indicates that (A) is mistaken.

Williamson admits that there are various ways to take McDowell's claims, some of which will make the argument go through and others of which will not. However, Williamson also claims that the weaker readings will not bear the weight of the arguments McDowell puts on them. Of course, I don't know exactly what McDowell hopes to accomplish and how it fits into the broader picture that Williamon is criticising. So, for all I know, Williamson is right. But, I wish I understood this section of the chapter better enough to know whether he is right and to know why he is right.

I also have a couple of questions/complaints about Williamson's objection involving elusive objects. Williamson says that McDowell's argument relies on the thesis that everything is thinkable. He then suggests that we have no reason to think that there are no elusive objects (objects which are not individually thinkable). Suppose Williamson is right that we have no reason to think that there are no elusive objects. If that is true, does it really hurt McDowell. Can't McDowell make his point (whatever it may be) with the thesis that everything is either individually or collectively thinkable. If McDowell's argument requires only this weaker thesis, then Williamson's criticism is no good.

Finally, I am skeptical of the claim that we have no reason to believe that there are no elusive objects that are not also enigmas (objects which cannot be thought of either individually or collectively). Here is an argument that relies on several conroversial claims, but which I think may be sound. Suppose that arbitrary naming really does result in a particular object being named and that we can think of an object when we have a name for it. Now, if some objects can be thought of collectively, then we can name any one of them by saying "let 'Fred' name an arbitrarily chosen object from amongst those that we can think of collectively". Once we have the name 'Fred' we can think about whichever object was named. But, since any one of the objects could have been named, any one of the objects can be thought of individually. So, any objects that can be collectively thought of can also be individually thought of. So, any elusive objects must also be enigmas.

Philosophy vs. Science

2009-01-18T15:13:00.000-08:00

Okay so I guess I'll get things started here on the Williamson book. First, let me say to Joshua: nice pick. The first chapter has sufficiently whetted my philosophical appetite. Second, let me say that I haven't ever thought very hard about issues of philosophical methodology, so you should certainly take all of my posts here in a spirit of open inquiry. With that, I'll give a bit of autobiography that was inspired by chapter one.

When I teach intro to philosophy, I usually start with a thought-experiment. (Typically, I have them imagine that Harry and Hermione switch brains in an attempt to foil Lord Voldemort's plan to kill Harry. I then ask them to imagine that they are Voldemort's closest advisor and they have to tell him which brain-body pair to kill, given that he wants to kill (and only kill) Harry.) I then usually give a spiel about thought-experiments in general and their value for philosophy. My explanation of their value is an analogy usually along the following lines.

If you want to know how a microwave succeeds in heating up whatever you put in it, you would come up with an hypothesis and then put it to the test. Hypothesis: It works by agitating water molecules. Test: Put oil in the microwave and see whether it gets hot. Depending on the results, your hypothesis is either confirmed or disconfirmed by the data. Something similar happens in philosophy. If you want to know why humans are more morally valuable than ants, you would come up with an hypothesis and then put it to the test. Hypothesis: They are more morally valuable because they have human DNA. Test: Imagine that we encountered a race of non-human aliens that were otherwise exactly like us. Would they be less morally valuable just because they didn't share our DNA? Again, the hypothesis is confirmed or disconfirmed by the data.

Drawing this parallel seems to steer the students away from thinking of philosophy merely as the analysis of our concepts and toward thinking of it as a way of finding out things about the world itself. At the same time, however, the data of thought-experiments seem to be some sort mental stuff -- intuitions, considered judgments, or something like that. Moreover, I sometimes describe the point of the Harry Potter thought-experiment in terms of the pressure that it puts on our ordinary concept of personhood. So am I really still stuck inside the conceptual turn that Williamson argues we have moved beyond?

In light of the above autobiography, I'd be curious to hear how you all describe the goal of philosophy to your intro students, or whether you even think it is useful to do so. And, more generally, how far off is my above description, even if it is pedagogically useful?

A Default Argument for Atheism

2009-01-04T20:40:00.000-08:00

Michael Tooley (2008) argues that atheism is the default position. His argument is simple and can be strengthened. I will state his argument briefly and then strengthen it. I will then discuss a few responses that one might make to the strengthend argument, and, following this, offer a few reasons to doubt that these responses are successful. My conclusion will be a rather strong one: we should be atheists.

Tooley's Argument

Premise One: The prior probability that God exists is 1/3.
Premise Two: If (P1), then atheism is the default position.
Conclusion: Atheism is the default position.

An Argument for (P1)

Premise One*: The prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
Premise Two*: If (P1*), then the prior probability that God exists is 1/3.
SubConclusion: The prior probability that God exists is 1/3.

An Argument for (P1*)

Premise One**: A being that is jointly omnipotent and omniscient will be either (a) morally bad, or (b) indifferent, or (c) morally good.
Premise Two**: The prior probabilitity that a being that is jointly omnipotent and omniscient will be morally good = the prior probability that he will be morally indifferent = the prior probability that he will be morally bad.
Premise Three**: If (P1**) and (P2**) are true, then the prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
SubConclusion: The prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.

An Argument for (P2)

Premise One***: If the prior probability that God exists is 1/3, then we should believe it is 1/3 likely that God exists before considering any other evidence.
Premise Two***: If we should believe it is 1/3 likely that God exists before considering any other evidence, then were we forced to believe that (a) God exists, or (b) God does not exist, we should believe that God does not exist.
Premise Three***: If were we forced to believe that (a) God exists, or (b) God does not exist, we should believe that God does not exist, then atheism is the default position.
SubConclusion: If the prior probability that God exists is 1/3, then atheism is the default position.

That's the argument. Note, too, that it is assumed throughout the argument that God exists iff God is jointly omnipotent, omniscient and morally good. Now, I don't think that believing it is 1/3 likely that P makes it reasonable to believe that not-P. But Tooley can concede this point and simply stipulate that by 'default position' he means simply that, were we forced to gamble as to whether God exists, prior to obtaining further evidence, we should gamble that God does not exist.

This is an interesting argument and what seems to me even more interesting is that it can be significantly strengthened. We can partition degrees of moral goodness more finely than Tooley does. That is, assuming that (a) moral goodness comes in infinitely many quantities and (b) God exists only if he has exactly the highest possible quantity of goodness, and (c) there is a highest possible quantity of goodness, we get the conclusion that the prior probability that God exists is either zero or infinitesimal. If the prior probability is zero, no evidence can raise the probability that God exists. If it is infinitesimal, then it would take, well, a whole lot of evidence to raise the probability that God exists. We have no such evidence (even fine-tuning wouldn't get us this) and so we should be atheists.

The Strengthened Argument

Premise One: The prior probability that God exists is 0 or infinitesimal.
Premise Two: If (P1), then atheism is the default position.
Conclusion: Atheism is the default position.

An Argument for (P1)

Premise One*: The prior probability that a being that is jointly omnipotent and omniscient is also morally good to the highest possible degree is 0 or infinitesimal.
Premise Two*: If (P1*), then the prior probability that God exists is 0 or infinitesimal.
SubConclusion: The prior probability that God exists is 0 or infinitesimal.

I won't repeat the rest of the defense. The defense is relevantly the same. But here is another way to make the point in the form of an argument from analogy.

Suppose a solid were to pop into existence moving at a constant velocity. Let's say the solid is the referent of 'Fred' iff the solid has a mass of exactly 6 units, a volume of exactly 6 units, and a velocity of exactly 6 units. Suppose now that, in fact, a solid pops into existence in front of you and you can see it and watch it moving. What is the prior probability that that solid is Fred? The idea is that the prior probability is either 0 or infinitesimal. In order to be Fred the solid must have a precise combination of three properties, each of which comes in infinitely many quantities. Since any combination is, prior to evidence, just as likely as another, the probability that the solid is Fred = 1/infinity (which means it is either 0 or infinitesimal depending upon which math is correct). Thus, we should think that it is very likely indeed that the solid we are looking at is not Fred. What's more, it would take a whole lot of evidence to make it reasonable to believe the solid is Fred. The same goes for God.

Response One:

Surely we could get evidence that I exist (just look at me) and we could know that I have some exact quantity of a variety of properties that come in infinite quantities. So, can't the same be true of God?

No. God is defined as a being with the highest quantity of omniscience, omnipotence, and moral goodness. Unlike God, I am not defined as such a being. We could get evidence that I exist without getting evidence that, for some particular weight, I have that weight. This is not so for God. If we get evidence that God exists, then we must get evidence that a being with the highest quantity of those three properties exists.

Response Two:

We could still get evidence, even if this argument is sound, that there is a being that is jointly omniscient and omnipotent is also very morally good, for some range of quantities of goodness.

Yes. I am assuming that God, if He exists, has the highest of such a range. A being that has less than the highest degree of goodness, I am assuming, is unfit to be the referent of 'God'.

Response Three:

But it seems possible to get evidence that the solid is Fred. Couldn't God tell you this? And couldn't you imagine a possible instrument that could, having measured the solid, make it reasonable to believe the solid is Fred. And so, shouldn't we say the same for God?

First, supposing this is right, what premise is false? Second, perhaps we should simply say that 'no' we could not get such evidence and that's just a strange, but correct consequence of dealing with properties that admit of infinitely many quanitities. Infinitity is strange, but notice, even the theists trafficks in infinity talk and so she should be the last person to doubt the intelligibility of its application.

So, what do you think readers?

Motion and Temporal Density

2008-12-18T12:22:00.000-08:00

Today I was introduced to an interesting problem. The following five theses are jointly inconsistent:

1. Some object changes from being at rest to being in motion.
2. Any object which changes from being at rest to being in motion has a first instant during which it is in motion.
3. Any object which changes from being at rest to being in motion has a last instant during which it is at rest.
4. No object is both at rest and in motion during the same instant.
5. For any object and any instant, that object is either in motion during that instant or at rest during that instant.
6. Time is dense (for any instants t1 and t3 where t3 is later than t1, there is an instant t2 that is earlier than t3 and later than t1)

Let's prove that these six statements are inconsistent. (1) says that there is an object which changes from being at rest to being in motion. Call that object 'O'. According to (2) and (3), there is a last instant during which O is at rest and a first instant during which O is in motion. Call the last instant during which O is at rest 'Tr' and call the first instant during which O is in motion 'Tm'. So, Tr is the last moment during which O is at rest and Tm is the first moment during which O is in motion. Moreover, according to (4), Tr is not identical to Tm. So, according to (6), there is an instant, Tx, later than Tr but earlier than Tm. By (5), The object is either at rest or in motion during Tx. If it is at rest and Tx is later than Tr, then Tr is not the last instant during which it is at rest. But, since Tr is the last moment during which O is at rest, it follows that O is not at rest during Tx. So, O is in motion during Tx. But, if O is in motion during Tx and tx is earlier than Tm, then Tm is not the first moment during which it is in motion. But, Tm is the first moment during which O is in motion. So, O is not in motion during Tx. We have arrived at a contradiction.

All of these claims seem plausible. I should admit that there is an a strong claim implied by (5). That claim is that for any object and any time that object exists during that time. Although this is very strong, we can weaken (5) so that it only implicitly implies that an object does not go out of existence between its last moment of rest and its first moment of motion. But that claim seems plausible enough. It would be very strange, for example, if an object briefly went out of existence every time it changed from being at rest to being in motion. so, I am going to keep (5) the way it is in order to avoid making the argument too complicated.

My guess is that the weakest claims are (2) and (3). The friend of dense time should give up on one of these. But, it seems that to give up on one rather than the other would be arbitrary. at first I thought that there are probably possible worlds where (2) is true and (3) false and there are other possible worlds where (3) is true and (2) is false. But, now I am not sure about this solution. Now, I am beginning to think this is a problem of indeterminacy.

It seems to me that some version of the At-At theory of motion is true. There are various problems with simple formulations of the At-At theory of motion, but we can ignore those problems for the purposes of this discussion. So, let's consider the following Simple At-At view:

(AT-AT) An object O is in motion during an extended interval T iff O is located at one region during one instant of T and O is located at a different region during a different instant of T.

Now instantaneous motion is a derivative notion that can be spelled out in one of two ways:

(IM1) An object O is in instantaneous motion during an instant t iff there is an extended interval T such that t is an instant in T and O is in motion during T and for any extended sub-interval of T, O is in motion during that sub-interval as well.

(IM2) An object O is in instantaneous motion during an instant t iff there is an extended open interval T such that t is an instant in T and O is in motion during T and for any extended sub-interval of T, O is in motion during that sub-interval as well.

One difference between these (IM1) and (IM2) is that according to (IM1) any object that changes from being at rest to being in motion has a first instant of being in motion whereas according to (IM2) any such object has a last instant of being at rest. Let me show each of these consequences in turn.

First, let's focus on (IM1) and consider an object that changes from being at rest to being in motion. Suppose for reductio that that object has no first moment of motion. It follows that it has a last instant during which it is at rest. Call that instant 't'. If the object has a last moment during which it is at rest, then there will be an open interval during which it is in motion. Moreover, that open interval during which the object is in motion will have t as a boundary point. Call that open interval 'T'. The union of T and t is an interval of time. Moreover, the object in question is in motion during the union of T and t. Moreover, during any extended sub-interval of the union of T and t, it is in motion. So, by (IM1) the object is in instantaneous motion during t. But, if it is in motion during t, then it is not at rest during t. but, we already said that it is at rest during t. So, we have arrived at a contradiction. It follows that if (IM1) is true, then any object which changes from being at rest to being in motion will have a first instant of motion.

Now, let's focus on (IM2). I said that (IM2) implies that any object that changes from being at rest to being in motion will have a last insant of being at rest. To show that this is true, let's suppose that (IM2) is true and suppose that there is an object, O, that changes from being at rest to being in motion. Now consider an arbitrary instant t during which O is in instantaneous motion. I will show that there is a time before t during which O is in motion as well. Since O is in instantaneous motion during t, it follows by (IM2) that both (A) there is an extended open interval T such that t is an instant in T and O is in motion during T and (B) for any extended sub-interval of T, O is in motion during that sub-interval as well. Since, by (A), there is an open interval that includes t during which O is in motion, it follows that there is an open sub-interval of that open interval which is before t. but, by (B), O is in motion during that open sub-interval that is before t. So, O is in motion before t. So, t is not the first instant during which O is in motion. But, since t was an arbitrarily chosen instant, it follows that there cannot be a first instant during which O is in motion. So, there must be a last moment during which O is at rest. Since O was arbitrarily chosen as well, we can conclude that any object that changes from being at rest to being in motion will have a last insant of being at rest. So, (IM2) implies that any object that changes from being at rest to being in motion will have a last insant of being at rest.

Now, my current belief is that use of 'is in instantaneous motion' is indeterminate between (IM1) and (IM2). So, currently, I think that either (2) or (3) from our original puzzle is false and necessarily so. But, it is indeterminate which is false.

Quick Side Note:

You might think that any legitimate precisification of our language has to obey the following constraint: any sentence of the form 'if O is in motion during T then for any time in T, O is in motion during that time as well'. Moreover, you might think that if this is right, then we have some reason to prefer (IM1) over (IM2).

Although this sounds plausible at first, It seems to me that in addition to the following traditional At-At view:

(AT-AT) An object O is in motion during an extended interval T iff O is located at one region during one instant of T and O is located at a different region during a different instant of T.

there is an alternative, open interval At-At view:

(Open At-At) An object O is in motion during an extended interval T iff T is an open interval and O is located at one region during one instant of T and O is located at a different region during a different instant of T.

It seems to me that our use of 'is in motion' is probably indeterminate between (At-At) and (open At-At). But, that also supports the claim that it is indeterminate which of (2) or (3) is false. So, the suggestion above just seems to push the solution back a level.

Agency Question

2008-12-15T16:04:00.000-08:00

Some composite things are agents and some are not. For example, I am an agent but a rock is not (unless it is rock*). One might wonder what features distinguish the agents from the non-agents. Although this is an interesting question, I will not be pursuing that question in this post. Instead I want to consider what might be called derivative agency. Consider the Supreme Court. That entity has some kind of agency; it makes decisions and is morally blameworthy for some of those decisions. It has what we might call derivative agency. However, consider the fusion of me and all the furniture in my office. That thing does not make decisions and is not morally blameworthy for anything. It does not have derivative agency. But, what exactly is the difference between the Supreme Court and the fusion of me and all the furniture in my room?

Here is one thought: Perhaps it is because the Supreme Court completely decomposes into agents that it has derivative agency. The fusion of me and all the furniture in my office, however, does not completely decompose into agents. So, that is why it does not have agency.

Although perhaps appealing, I don't think this initial thought is right. For we can consider the thing that happens to be composed of me and some alien millions of light-years away. It does not seem to me that that latter thing has derivative agency and yet it (just like the Supreme Court) completely decomposes into agents.

Here is a second idea. Perhaps the Supreme Court essentially decomposes into agents whereas the thing that happens to be composed of me and that distant alien does not. If agents, derivative or otherwise, are essentially agents and derivative agents completely decompose into agents, then we can say that the Supreme Court is a derivative agent whereas the thing that happens to be composed of me and the alien is not. We can say that this is the case because the Supreme Court could not have failed to be composed of agents whereas the thing composed of me and the alien could have failed to be composed of agents (it might have had me and the alien and an extra particle as a part).

SCQ and the Brutality of Parthood

2008-12-02T10:29:00.000-08:00

The Special Composition Question is often formulated as follows:

The Special Composition Question (SCQ): What necessary and jointly sufficient conditions must any xs satisfy in order for it to be the case that there is an object composed of xs?

And answers to the Special Composition Question often take the following form:

The Special Composition Schema (SCS): Necessarily, for any non-overlapping xxs, there is a y such that y is composed of xs iff ____________________.

Often, however, those who are concerned with SCQ take SCQ to be a question about what it is in virtue of which some things compose something. The formulations of SCQ and SCS given above do not make this clear.

I will not attempt to formulate more satisfactory versions of SCQ and SCS. Rather, I want to investigate whether we should expect there to be an answer to SCQ on the assumption that it is a question about what it is in virtue of which some things compose something.

Consider the simples that compose me. Call these simples 'ggs'. ggs compose something. We may now ask: In virtue of what is it the case that there is an x such that ggs compose x?

It seems to me that there is an obvious answer to this question: There is an x such that ggs compose x in virtue of the fact that ggs compose me. (Compare with this case. In virtue of what is it the case that there is someone to whom I am married? Answer: There is someone to whom I am married in virtue of the fact that I am married to Mary.)

If, then, SCQ is a question about what it is in virtue of which some things compose something else, it appears that the answer to SCQ will look something like this:

ggs compose something in virtue of the fact that ggs compose Greg, ees compose something in virtue of the fact that ees compose the Eiffel Tower, etc.

There is a further question that can be asked, however. Suppose that ggs compose something in virtue of the fact that ggs compose me. In virtue of what do ggs compose me? This is an interesting question as well.

Now to say that ggs compose me is to say that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs. So, we can reformulate our question as follows: In virtue of what is it the case that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs?

But then consider the following thesis:

The Brutality of Parthood (BT): Necessarily, for any x and y, if x is a part of y, then there is nothing in virtue of which x is a part of y.

BT is relatively plausible. But it seems to me that if BT is true, then the correct answer to the question "In virtue of what is it the case that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs?" is "Nothing".

Against Legal Dialetheism

2008-11-03T11:31:00.000-08:00

Priest presents the following case for Dialetheism in his book In Contradiction: Suppose that there is a country that has a legislative body that passes a law saying that all land owners are legally permitted to vote and another law that says that no women are legally permitted to vote. We might also suppose that at the time these laws were passed the legislature also passed a law barring women from owning land, but that this last law was eventually repealed. Now, given that there is now no ban on women owning property, we might suppose that a woman, Bridget, buys a piece of land. But, it seems to follow from the first two laws that Bridget is legally permitted to vote and it is not the case that Bridget is legally permitted to vote. so, if this scenereo is a possible scenario, then it looks like it is possible for a contradiction to be true. This seems unacceptable though.

Let's try to make the argument more precise. It seems that all of the following propositions might jointly be true.

1. A legislature governing state S passes a law that says that all land owners are legally permitted to vote in S.
2. If (1), then all land owners are legally permitted to vote in S
3. A Legislature governing state S passes a law that says that no women are legally permitted to vote in S.
4. If (3), then no women are legally permitted to vote in S.
5. Bridget is a women who owns some land.
6. So, Bridget is legally permitted to vote in S and it is not the case that Bridget is legally permitted to vote in S.

It seems that statements (1)-(5) are jointly possibly true. So, it seems that statement (6) is possibly true as well. However, (6) is not possibly true. The puzzle for anyone who objects to (6) is to give an informative explanation of why (1)-(5) are not jointly possibly true.

I take it that all the action is in premises (2) and (4). But, these premises seem to simply embody the fact that legislatures have the power to make certain things true. they can make certain truths about what is legally permitted and what is not. It is important to note that (2) and (4) are not justified by some general principle that says legislatures can make anything true. That would be silly, legislatures obviously can't make it true that my hand is green. Moreover, they are not justified by some general principle that says legislatures can make any claim involving legal permissibility true. If this latter view were true, then legislatures could make contradictory legal statements true. Rather (2) and (4) are justified by the intuitive claim that a legislature can make these particular claims true. These claims are consistent with one another and it seems plausible that a legislature might make both of them true along with a third law that says no woman is legally permitted to own land. Once that third law is repealed, it might very well be the case that Bridget purchases some land and (5) becomes true.

I want to give a plausible view according to which either (2) or (4) is false. The plausible view is as follows. Either the legislature governing state S cannot make it so that no women are legally permitted to vote in S or they cannot make it so that all land owners are legally permitted to vote in S. Rather, they can definitely make the following true:

(a) According to laws L of S, all land owners are legally permitted to vote.

and

(b) According to laws L of S, no women are legally permitted to vote.

No contradiction follows from the combination of (a) and (b) along with the fact that Bridget is a woman who owns land. Rather, it simply follows that according to the laws of S, Bridget is legally permitted to vote and according to the laws of S, it is not the case that Bridget is legally permitted to vote.

On this view, we think that (2) and (4) are true because the legislature of S can make (a) and (b) true. Moreover, we often say that land owners are legally permitted to vote or that no women are legally permitted to vote, when we intend to convey the truths expressed by (a) and (b).

As for the literal truth or falsity of (2) and (4), I guess I am not sure what to say. However, I think that most people would be happy to say that the sentences used to express (2) and (4) are context sensitive and that they they really express (in this context) conditionals with (a) and (b) in their consequents. I am against the context sensitivity claim and think there is something literally expressed by (2) and (4) that is different from what the contextualist thinks might be expressed by (2) and (4) in the appropriate context. But, I don't know enough about what is expressed to know which of (2) or (4) is false.

Another version of divine simplicity

2008-10-31T11:08:00.000-07:00

as I promised in the comments on rock*'s last post, here are some of my
notes on divine simplicity.  If I remember correctly Aquinas seemed to
hold something like the following views:

1.  God has no proper parts
2.  God has exactly one divine attribute
3.  Amongst God's attributes are his omniscience, omnipotence and
omnibenevolence.  
4.  God is identical to his one divine attribute.  

From (2)-(4) it follows that

5.  God = God's omniscience = God's omnipotence = God's omnnibenevolence.  

Now, you might think that there is a complex God property that is
built up out of omniscience, omnipotence and omnibenevolence.
God's omniscience, omnipotence and omnibenevolence would then
just be identical to this complex God property.  However, this seems
to be ruled out by (1) and (4) above.  This is because if the God
property were built out of omni-p, omni-s and omni-b, then it would
have parts.  But that claim, along with (4) entails that God has parts. 
But, (1) says he does not.  

Here is a solution.  In my paper "A tale of two simples" I talk about a
distributional properties explanation of the following seeming
possibility:

(*) Possibly, there is an extended, heterogeneous atomic object that
occupies a region with no proper subregions.  

trypically a person who believes in extended heterogeneous simples
will connect property exemplification to regions in some way.  So, for
example, if the person believes that possibly there is a striped red and
purple atomic object, then he will say that that object has red-at-R and
Purple-at-R*.  But, this will not help to explain (*) since the atomic object
in (*) occupies a region with no proper sub-regions.  

According to the distributional properties approach, there are fully
determinate distributional properties that guarantee the seeming
heterogeniety of such a simple.  These are properties like polka-
dottedness but they are not built up out of "smaller" color properties.
Rather the smaller properties are built out of disjunctions of these
distributional properties.  

One thing that I noticed is that God seems to be heterogeneous in some
sense: he seems to be both omniscient and omnipotent.  But, God, is an
atomic object as well and there is nothing we can index his omniscience
and omnipotence to.  This situation looks rather similar to the situation
of a heterogeneous simple that occupies an atomic region of space.  So,
here is a view about divine simplicity:  

There is one God property that is like a distributional property.
Exemplifying that God property guarantees the seeming distribution
of omnipotence and omniscience.  But, there really aren't these "Smaller"
properties (except insofar as they are built up out of the disjunctions of
the fully determinate God property).  On this view God's Omniscience and
Omnipotence are just identical to this distributional property.  Moreover,
we could connect this view to a bundle theory of individuals and get that
this single God Property just is God himself.

A Non-Stupid Version of the Doctrine of Divine Simplicity (or Something Like It, at Least)

2008-10-23T11:33:00.000-07:00

Jonathan Schaffer has recently argued that the traditional debate concerning monism was a debate concerning whether the first of the following theses is true rather than a debate over whether the second is true:

Priority Monism (PM): The world is fundamental (i.e., is a substance in the traditional sense--it does no depend on anything else for its existence), while every proper part of the world depends on the world for its existence.

Existence Monism (EM): The world has no proper parts.*

Now I think that (PM) and (EM) are both false (or at least have serious doubts about their truth), largely because I am inclined to think that "the world" is a non-denoting definite description; that is, I am inclined to say that there is no such thing as the world. Schaffer's paper is still quite interesting, however. Furthermore, my most recent reading of it made me think about whether there are any connections between Schaffer's discussion and the doctrine of divine simplicity.

The doctrine of divine simplicity is usually formulated as follows:

The Doctrine of Divine Simplicity (DDS): God has no proper parts and each of God's properties is identical to God.

(DDS) is, I think, a pretty bad view (and not just because the view that there is such a thing as God is a pretty bad view). Assuming that God exists, it does not seem implausible that God has proper parts. (One heterodox interpretation of the doctrine of the Trinity is that God has the three persons of the Trinity as proper parts, which contradicts (DDS).) Worse, if (DDS) is true, then:
-God is a property,
-God instantiates himself, and
-I instantiate God. (After all, both God has the property of being self-identical. So, if (DDS) is true, then God is identical to the property of being self-identical. But I instantiate the property of being self-identical. Therefore, if (DDS) is true, then I instantiate God.)

Now what Schaffer's paper got me wondering about is this. Consider the following thesis:

The Doctrine of Divine Simplicity* (DDS*): Every proper part of God and every property of God depends on God for its existence.

While (DDS) is the analogue of (EM), (DDS*) is the analogue of (PM). So if the traditional debate concerning monism was a debate concerning the truth of (PM) rather than the truth of (EM), then perhaps the traditional debate over the divine simplicity was a debate concerning the truth of (DDS*) rather than the truth of (DDS). Furthermore, even if the traditional debate over divine simplicity was not a debate about the truth of (DDS*) but was rather a debate about the truth of (DDS), (DDS*) is a more plausible thesis than (DDS). For one thing, suffers from none of the problems for (DDS) noted above. For another, it is strongly suggested by other, not terribly implausible, traditional views.

Take the claim that every proper part of God depends on God for its existence. As Schaffer argues, Aristotle--and presumably Aquinas as well--held that each of a living thing's proper parts is dependent upon that living thing for its existence. Thus, given the claim that God is alive, which I take to be a traditional view, it follows that every proper part of God depends on God for its existence.

Next, take the claim that every property of God depends on God for its existence. According to one traditional view, properties depend upon the schmubstances that instantiate them for their existence. (A schmubstance is a substance in Aristotle's second sense; that is, it is something that has properties (or stands in relations) but is not itself a property (or a relation).) Thus, according to this view, the property of being green depends upon the green schmubstances for its existence; this is a dependence relation that obtains between a property and a plurality. Now take any property P of God. According to this view, P depends for its existence on the schmubstances that instantiate it, bbs, and God is one of bbs. Now this doesn't quite get us to the view that P depends on God for its existence. Rather, it gets us to the view that P depends on bbs for its existence, and although God is one of bbs, another schmubstance may also be one of bbs. However, another traditional view is the view that every other schmubstance depends upon God for its existence. And the following is a plausible principle: for any x, y, and zzs, if x depends on zzs for its existence and each thing that is one of zzs is either identical to y or depends on y for its existence, then x depends on y for its existence. It follows from this principle, the claim that properties depend on the schmubstances that instantiate them for their existence, and the claim that every other schmubstance depends on God for its existence that P depends upon God for its existence. But P was an arbitrarily chosen property of God. So it follows from that principle and those two traditional (and not terribly implausible) views that every property of God depends upon God for its existence.

Putting the conclusions of the last two paragraphs together, both the claim that every proper part of God depends on God for its existence and the claim that every property of God depends on God for its existence follow from traditional, and not terribly implausible, views (plus a very plausible principle concerning pluralities and dependence). But these two claims together entail (DDS*). So (DDS*) follows from traditional, and not terribly implausible, views.

*See "Monism", available on Schaffer's website, for his argument. My formulation of existence monism differs from the formulation Schaffer gives. Schaffer's formulates existence monism as follows: For all x, x is identical to the world. My formulation is superior to Schaffer's because, at least as I interpret him, Schaffer does not take the world to be the mereological fusion of absolutely everything. Rather, he takes it to be the mereological fusion of absolutely every concrete entity. Given this, the debate concerning existence monism is, it seems to me, a debate over whether the fusion of absolutely every concrete entity has any proper parts, and thus evidence in favor of the existence of abstract entities is irrelevant to the debate. However, given Schaffer's formulation, evidence in favor of the existence of abstract entities is relevant to the debate. An alternative formulation of (EM), given that the world is the mereological fusion of absolutely every concrete entity, is: For all concrete entities x, x is identical to the world.

Necessity and Natural Species Kinds

2008-10-14T11:37:00.000-07:00

There are some natural species kinds. for example, Tiger is a natural species kind and Kangaroo is a natural species kind. We tend to make certain claims about these species. For example, we say that Tigers are striped. Whatever the literal content of this claim, it seems we are trying to convey that the species tiger has a certain property related to being striped. For simplicity, let's restate this conveyed truth as one that is explicitly about the species tiger. We can introduce a new predicate, 'striped*' to be whatever property the species has in virtue of which it is acceptable to say that tigers are striped. Now we can explicitly say that the species tiger is striped*. One thing to point out is that it is sometimes acceptable (though perhaps not true) to say that Tigers are striped even though some tiger is not striped. Similarly, it may be true that the species tiger is striped* even though some tigers are not striped (no '*' intended). Now, I am wondering whether it is necessary that the species tiger is striped*.

Here is an argument against that position. Tigers have a certain genetic makeup. Tigers have genes G. We can introduce the new predicate 'has genes G*' to express the property that the species has in virtue of which it is acceptable to say that Tigers have genes G. So, the species tiger has genes G*. But, tigers don't all have the same genetic makeup. There is always genetic variation within a species. Indeed, although the species tiger has genes G*, it seems like there may well be a tiger that lacks genes G* in virtue of having a very slightly different genetic makeup. If more tigers had been like that particular tiger, then it would not have been true that the species tiger has genes G*. The species tiger is susceptible to small variations in genetic makeup*. Moreover, this will be true across some set of possibilities. But, small changes add up to big ones and given that what is possibly possible is itself possible, it follows that the species tiger might have had a genetic* makeup significantly different than G*. In fact, that genetic makeup* might ground the truth that the species tiger is not striped*. Hence, it might be acceptable to say that Tigers are striped, but tigers might not have been striped.

Some of you might recognize that this is related to the Salmon's argument against S5. Of course, there are various responses to that argument and those responses would probably carry over to this argument as well. But I wanted to point out one thing that might follow if we accept the argument I have just presented. It seems that we can have small genetic variations that add up to drastically differences. If that is right and we accept the kind of argument that I just presented above, then it might follow that the species tiger could have been just like the way that the species kangaroo actual is. Moreover, If the species tiger could have been like the way the species kangaroo actually is, then a particular tiger could have been just like a kangaroo. But, if it could have been just like a kangaroo, then it could also have been a kangaroo. Hence, tigers are not essentially tigers. I know this argument goes pretty quickly, but it seems rather interesting to me.

Knowledge as the Norm of Assertion

2008-09-22T20:35:00.000-07:00

I have recently been talking to one of my colleagues about norms of assertion. during the course of our conversation, there was some amount of miscommunication between us. My friend wanted to defend that the following is a rule of language:

R1. Assert only what you know.

I expressed skepticism about that rule and suggested that perhaps the following rule was both true and the strongest epistemic rule governing assertion:

R2. Assert only what you justifiably believe.

My friend pointed out that if one were to try to follow R1 he would do all the same things as he would if he were to try to follow R2 (and vice versa). He suggested that we think of our situation like an internal dialogue. Think about a situation in which you are about to assert something and imagine asking yourself if you know the thing you are about to assert. Record whether you said "yes" or "no" in answer to that question. Now ask yourself whether you justifiably believe that same thing. Your answer should be the same as before. So, it looks like you will get the same results regardless of whether you try to follow R1 or R2.

At this point one might think that following R1 amounts to the same thing as following R2. However, I am inclined to think is incorrect. Although you will do the same actions regardless of which rule you try to follow, you will be criticizable in some situation if R1 expresses an accurate rule of assertion but not criticizable if R2 is the strongest rule governing assertion. Let me explain. If you are in fake bark country and assert that the object in front of you is a barn, then you will be criticizable under R1 but not under R2. After all, you asserted something you didn't know but you did not assert something you were not justified in believing.

This, at least, is what I thought a couple of days ago. But, perhaps I don't know what it means to follow a rule. It seems that we can distinguish an internalist interpretation of following a rule and an externalist interpretation. To make these two interpretation clear consider the following scenereo:

Late last night we were all kidnapped and hooked up to the matrix. Now, although we think we are living our lives as usual, we are in fact trapped in a computer generated world. While we were in this world, Greg ordered me to bring him a pen. I picked up what seemed to me to be a pen and seemingly brought it to him. Of course, in reality I did whatever it is that envatted people do when they seemingly pick up a pen and hand it over to another person. Now the question is this: Did I follow Greg's command. In an externalist sense of following commands I did not. After all, Greg is speaking English to me and asked for a pen not a vat-pen and (at most) I brought him the latter and not the former. However, in an internal sense I did follow the command. From the inside I thought, "Greg wants a pen" and then I was appeared to pen-wise and thought "oh there is a pen"and proceeded to do something that I thought was picking up and handing over a pen. So, it seems clear that I internally followed the command but externally did not.

What goes for commands goes for rules as well. We might internally follow a rule while not externally following it. Now, given this background information, we might accept that we should follow the rule R1. However, we might still disagree with whether we should follow it in an internal sense or an external sense. If we decide that we should follow it in an external sense, then we will come up with a very different principle about assertion than we would if we had decided that we should follow it in an internal sense.

If we decide we should externally follow R1, then we might affirm this principle:

P1. One is permitted to assert P only if one knows P.

If however, we decide that we should follow it in an internal sense, then we'll get something more like the following:

P2. One is permitted to assert P only if one is justified in believing P.

As I see it, there are several different positions one might have. One might think that we should follow R1 in an external sense and hence believe that P1 is true. On the other hand, one might think that we should follow R1 in the internal sense and hence believe that P2 is true. On the third hand, we might think that we should follow R2 in the external sense and hence believe P2. Finally, one might think we should follow R2 in the internal sense and believe . . . Oh myhead is spinning! Well, I hope you get the picture.

It is clear though that if we start thinking about norms of assertion by thinking about rules we should follow, then we should do two things: (1) figure out which rule we should follow and (2) figure out what we mean by "follow". Once we have done these two things, then we'll be able to formulate a principle about assertions.

A New Solution to the Problem of Easy Knowledge

2008-09-18T11:45:00.000-07:00

I originally wrote this as a response to Chris's comments on my post "Easy Knowledge and Millianism". Something Chris said suggested this as a plausible solution to the puzzle. I thought it might be good to post this independently and see what everyone thinks. However, this post relies on some background information that can be found in my previous post and in the comments to that post.

This new solution is inspired by the Hawthorne/Stanley view that something is known only if it can be "used as a premise in practical reasoning". I am beginning to be attracted to something like this Hawthorne/Stanley position. I will try to spell out a bit of the view below.

Let's let JTB be a three place relation that bears between an individual, a proposition and a way or guise. We can say that someone, S, has a justified true (non-gettierized) belief that P just in case S stands in the JTB relation to a proposition under some guise or other. Further we can say that S knows that P just in case S stands in the JTB relation to P under some guise or other and that belief can be used under that guise as "a premise in practical reasoning". I know this last bit is a little bit vague. But I hope you'll still be able to follow me.

Now, we have gotten rid of the problem of easy knowledge. Ned the navigator does not justifiably believe the truth that that the oldest tree in Washington is at L under a guise that can be used in practical reasoning. (Although he does justifiably believe that truth). So, he does not know that the oldest tree in Washington is at L.

Moreover, we can still connect up knowledge-wh to knowledge-that by saying things like "S knows where x is just in case S knows an answer to the question 'where is x?'". Since we got rid of the problem of easy knowledge, we don't have a problem of easy knowledge-wh.

This solution matches our intuition that you can't have easy knowledge. It also matches with our intuitions about when a person knows-wh. It might also fit better with our ordinary use of the word 'knows'. Moreover, it does not invoke the weird acquaintance relation.

One thing that is slightly counter-intuitive is that even though Ned introduced the name 'L' by saying "let 'L' name the location of the oldest tree in Washington" and even though he can easily reason his way to the conclusion that the location of the oldest tree in Washington is at L, he does not know this. He has a justified true (non-gettier) belief because he JTBs that proposition under some guise or other. But, he doesn't know that proposition because he can't use that justified true belief as a premise in practical reasoning.

I kind of like this view. Does anyone see anything immediately wrong with it or does anyone have a suggested amendment?

Easy Knowledge and Millianism

2008-09-07T14:16:00.000-07:00

Millianism is the thesis that the meaning of a proper name is the object to which it refers. Some people who believe Millianism also endorse certain principles connecting the possession of a proper name to the ability of a thinker to think things about the named object and principles that allow the introduction of a proper name into language by way of a definite description. These philosophers seem to face a problem of easy knowledge. In this post I will present this puzzle of easy knowledge. I will note some of the replies that a Millian can give to such a puzzle, including the deflationist reply which says that we do have such easy knowledge but it is not as bad as one might expect. Finally, I will press the deflationist position with a worry and suggest the best response that a deflationist might give. Before I begin, I should note that this puzzle has been extensively discussed amongst the members of our little tribe for several years. so, many of the things I say here may have come up in conversations between us in the past. I have just recently become interested in this puzzle again because I recently heard a talk on this subject.

So, let's begin by presenting the puzzle. Let's assume that Millianism is true and introduce two new theses that will help generate the puzzle. The first thesis is that a person can introduce a proper name for an individual into a language simply in virtue of using a definite description that refers to that individual. For example, I can introduce a proper name for Benjamin Franklin into English by saying something like this: "Let 'Fred' be a proper name for the guy who invented bifocals". Similarly, I can introduce a proper name for the guy who invented the wheel by saying "let 'Gorg' be a proper name for the guy who invented the wheel". This trick can be used for anything that can be (properly) named and which can be picked out by a definite description.

The second thesis is that someone can have de re beliefs and other attitudes about an individual simply in virtue of possessing a name for that individual. So, for example, after introducing the name 'Gorg' for the inventor of the wheel, I can wonder whether Gorg was tall. I can believe of Gorg that he was a clever man. And I can (with the appropriate evidence) know that Gorg lived a long time ago.

With these theses in mind, we can now present the puzzle of easy knowledge. Suppose I introduce the name 'Gorg' by saying "let 'Gorg' be a proper name for the guy who invented the wheel". Now I think to myself that if anybody invented the wheel, then the guy I named 'Gorg' invented the wheel. I also think that if I named anyone 'Gorg', then Gorg is the guy I named. finally, I conclude that if anybody invented the wheel, then Gorg invented the wheel. At each step, I seem to be justified in my belief. Moreover, my beliefs are true. One migh think that these are justified, true beliefs that don't amount to knowledge. but, the situation certainly doesn't look like classical Gettier situations. So, we may reasonably conclude that I know that if anybody invented the wheel, then Gorg did. but, such knowledge seems too easy. How can I know anything about Gorg when I have never met him. Moreover, it seems that this trick can generalize in a way that indicates that I have a lot more knowledge than one might initially expect. This is the problem of easy knowledge.

There are several solutions to this puzzle. One might think that my beliefs about Gorg are unjustified or that even though they are not justified, they do now amount to knowledge. I think this is an interesting response which I am not going to explore in this post (though I may explore it in a later post). I think the best option here is to suggest that I fail to meet a safety condition on knowledge. Although I believe that if anyone invented the wheel, then Gorg did, in the nearby worlds where I form such a belief, it is not justified. I suspect this strategy will have many problems, but (as I indicated) I will not be exploring those problems here.

One might say that proper names cannot be so easily introduced. some Millians think there are two kinds of names out there: proper names and descriptive names. A name that is introduced by way of a description is a discriptive name. Moreover, although the meaning of proper names are the things they refer to, the meanings of such descriptive names are the descriptions that were used in their introduction. On this view, the content of the sentence "if anyone invented the wheel, then Gorg did" is actually "if anyone invented the wheel, then the guy who invented the wheel did". But, this is trivial knowledge that most people can have simply be reflection.

Finally, some people might think that although we can introduce a proper name with a description, we cannot have thoughts about the thing so named. This view breaks the connection between possessing a proper name and being able to have a thought about the thing named. (I believe this is Salmon's view).

These are some of the ways out of our puzzle of easy knowledge. But there are a few people out there who think the best option is simply to accept that we have such easy knowledge. (Some of us might even be attracted to such a view). Part of the job for these people is to explain why it isn't so bad to have such easy knowledge. But, their job is made even more difficult by the following fact. It seems that we are not able to act on knowledge such easy knowledge and yet knowledge that is acquired in the traditional way can typically be acted upon.

To make this problem more acute, let's focus on an example. Suppose that Ned the navigator is a man who is extremely good at getting to places given the appropriate information. In fact, he boasts that he can take anyone to any coordinate on Earth. However, Ned is also a philosopher and he introduces a name for the coordinates of the oldest tree in Washington state by saying "Let 'L' be a proper name for the coordinates of the oldest tree in Washington state". then, through a simple series of justified inferences he comes to know that if there is a location of the oldest tree in Washington state, then it is at L. Fred the navigator, on the other hand, has the same navigational abilities as Ned, but looks up the location of the oldest tree in Washington state in an encylopedia. Fred knows that if there is a location of the oldest tree in Washington state, then it is 48 degrees north by 124 degrees west. Now, since 'L' is a proper name for the location of the oldest tree in Washington state and since that location is 48 degrees north by 124 degrees west, it turns out that Ned and Fred know the exact same thing. Yet, if I were to ask to takes to the location of the oldest tree in Washington state, Ned wouldn't be able to take me there whereas Fred would. This seems like a difference that needs to be explained.

I take it that there are a couple of explanations available to the Millian who accepts easy knowledge. First, He can say that although we can have easy knowledge it is not usefull because there is some difference between the easy knowledge and regular knowledge. such a Millian would be required to explain what that difference is.

On the other hand, a Millian might simply say that we are looking for explanations in the wrong direction. He might simply say that the difference between easy knowledge and regulary knowledge lies in the fact that we have abilities to act on regular knowledge that we lack with mere easy knowledge. That is to say that knowledge is easy in virtue of the fact that we cannot act on it.

Finally, a Millian might simply reject explanations at this point and say that although there is a correlation between having abilities and having knowledge that is acquired in the traditional way, such a correlation need not be explained.

I think the first option is the way to go. I will quickly argue against each of the other two options and then explain how one might flesh out the first option in more detail. the Final option is not good because such a correlation will be a strong, perhaps necessary connection. It is hard to imagine, for example, a world in which most people's knowledge comes by way of naming and yet they are still able to act on that knowledge. It is hard to imagine, for example, a world in which Ned does exactly what he does in our actual world to come to know the location of the oldest tree in Washington and yet takes us right to the tree when we ask. Even if he did so, we would simply say that he was lucky in his guess.

The second option seems weird. It seems like easy knowledge is easy knowledge in virtue of the way it is acquired rather than in virtue of any correlation between our lack of abilities. Moreover, it seems intuitively plausible to say that there is a difference between Fred and Ned's knowledge that accounts for their differences in ability. This all leads me to believe that the first option is the one that a Millian who accepts easy knowledge should take.

Here is what such a Millian can say: Although Fred and Ned know the same things, Fred has an ability the Ned lacks because his knowledge is had under an appropriate guise or way of believing. Ned knows the location of the oldest tree in a particular way. He knows navigational facts in one way and the fact about the location of the oldest tree in another. So, he is not able to connect up those bits of knowledge and act appropriately. On the other hand, Fred's navigational knowledge and knowledge about the location of the oldest tree are had in the same way. So, he is able to connect up those bits of knowledge and act appropriately. So, it seems to me that the deflationist solution to the problem of easy knowledge is best when combined with an endorsement of Ways Millianism.

Something akin to Monism

2008-08-01T20:20:00.000-07:00

Jonathan Schaffer has recently posted a paper called "The Internal Relatedness of All Things" in which he argues for Priority Monism. He presents a couple arguments in his paper, each one in two stages. His arguments, as Schaffer admits rely on rather heavy Mereological principles. I believe there are arguments, analogous to the ones Schaffer presents, for a thesis akin to Priority Monism. Before I introduce the thesis akin to Priority Monism and the arguments for that thesis, I suggest that everyone read Schaffer's paper first (or at least the first 10 pages of it).

Schaffer's argument is presented in two stages. In the first stage, he argues for the conclusion that all things are internally related in ways that make them interdependent. In the second stage, he argues that this internal relatedness implies Priority Monism (the thesis that there is one Basic concrete thing and it is the Universe). Schaffer focuses on the second stage first and that is the stage that will concern me in this post.

I will not be arguing for Priority Monism, though. I am going to be arguing for something akin to Priority Monism. To spell out this view, I will first introduce a priority relation which is slightly different than Schaffer's. Schaffer says that some things are prior to others. For example, I am prior to the proposition that I exist. I will introduce a plurals version of this relation. A two place relation that takes pluralities and individuals rather than just individuals as relata. Just as I am prior (in Schaffer's sense) to the proposition that I exist, so too the philosophers in New York are prior (in the new sense) to the singular existential propositions about those philosophers. We might think that this relation is distributive. That is, the philosophers in New York are prior to the singular existential propositions about them in virtue of the fact that each philosopher in New York is prior to the singular existential proposition about him or her. But, I will argue that this is false. I am going to argue for Non-Distributive Priority Ensemblism. This is the thesis that there are some things that are jointly and non-distributively basic and they encompass all of reality (if anyone asks I'll spell this out in more detail in the comments).

Schaffer gives two arguments for Priority Monism in the second stage of his project. I will give an analogue to the first of these arguments for Non-Distributive Priority Ensemblism. Moreover, my argument will rely on less controversial principles than Schaffer's. I will also point out how an analogue to the second of Schaffer's arguments would also be less controversial than Schaffer's own argument.

Here are Schaffer's mereological presuppositions: First, there is some concrete thing such that every concrete thing is a part of it. Second, any concrete thing that has a concrete proper part has another concrete proper part disjoint form the first (Concrete Weak Supplementation). I believe that the first of these presuppositions is highly suspect and I am also slightly suspicious of the second.

In my argument I will use two fairly uncontentious presuppositions about plurals. First, some concrete things are such that anythings whatsoever are either amongst the first things or are such that each of their parts overlaps with some things amongst the first things. That presupposition is a bit of a mouthful (and might need to be qualified a bit more), but it is true. Consider all the concrete atoms in the universe. Everything is either one of those atoms or is such that all of its parts overlaps with those atoms. My second presupposition is that if some concrete things are properly amongst some other concrete things (each of which is discrete from one another), then there are some third concrete things that are distinct from the first things and also property amongst the second. This is just a plurals analogue of Weak Supplementation. Unlike the mereological principle Weak Supplementation, this plural principle is not suspect at all.

Now, let 'xxMyy' mean the xx are modally independent of the yy. Let 'Bxx' mean that the xx are jointly basic (let it remain neutral as to weather they are non-distributively basic). Let, xxDyy mean that the xx are pairwise disjoint form the yy. Now, my analogues of Schaffer's Assumptions are as follows:

AS1: No pairwise disjoint things are modally independent: (xx)(yy) (if xxDyy, then ~xxMyy)
AS2: There are some basic things: (Exx) Bxx
AS3: Any things that are jointly basic will be modally independent of any things they are pairwise disjoint from: (x)(y) ((Bxx & xxDyy) then xxMyy)

AS1 is argued for in the first stage of the project. Unfortunately, I am not going to recreate the first stage in this post. So, although it seems suspect, I am not going to say anything more in this post about it. AS2 seems true. As Schaffer points out, AS3 just embodies an intuition that certain things (namely disjoint and basic things) are modally recombinable. I believe AS3 has as much plausibility as Schaffer's third assumption.

Now here is the argument: Arbitrarily choose somethings that are pairwise disjoint from one another and jointly encompass all of concrete reality. Call those things 'uu'. Now assume that some things properly amongst those things are basic. Using 'xxAyy' to represent that the xx are properly amongst the yy, we can formulate this reductio assumption as follows:

1. (Exx) (Bxx & xxPAuu)

Now we existentially instantiate and call those basic things the aa:

2. Baa & aaPAuu

Now from (2) and Weak Supplementation of Plurals we get:

3. (Ex) aaDxx

existentially instantiate:

4. aaDbb

From (2) and (4) and AS3, we get:

5. aaMbb

But (4) and AS1 imply that:

6. ~aaMbb

Since we have arrived at a contradiction, we may conclude that our assumption is false:

7. ~(Ex) (Bxx & xxPAuu)

But, since AS2 says that some things are basic, we may conclude that:

8. Buu

Moreover, these things are non-distributively basic since, in accordance with (7), no things amongst them are basic. Hence, Non-Distributive Priority Ensemblism is true. One cool thing about this argument is that we learn that the plural property of being basic is a non-distributive plural property. Moreover, we learned this without the heavy mereological assumption that there is some concrete thing such that every concrete thing is a part of it.

Schaffer has a second argument that relies on even stronger mereological principles. Namely, it relies on complementation: the thesis that for any thing, there is another thing disjoint from the first and the two together compose the universe. So, for example, there is something that is all of the universe except my left pinkie toe. That is a weird thing. But, there is a plural analogue of this second argument and, moreover, complementation with respect to pluralities is not a controversial thesis. So, again, we'll be able to argue for Non-Distributive Priority Ensemblism without the heavy tools that Schaffer uses. (I still need to work this one out though)

Now, I think that the argument is cool as it stands. But, someone like Schaffer might want to argue for priority monism. Well, we can do so if we introduce the following principle:

(Basic Plurals to Basic thing) If some things are pairwise disjoint and non-distributively basic then they jointly compose something that is basic.

I don't know if this principle is true, but it sounds like something someone would believe. Moreover, it sounds like something defensible. But, with this principle we can get from my conclusion to Schaffer's conclusion. That is, we can get from Non-Distributive Priority Ensemblism to Priority Monism.

My immaterial Twin

2008-08-01T14:23:00.000-07:00

Some people believe that the shapes of material objects are extrinsic. Kris McDaniel, for example has argued for this conclusion with an argument that involves a kind of Humean principle that bars necessary connections between the intrinsic features of distinct contingent entities. It is difficult to formulate such a Humean principle well and I have worries about McDaniel's formulation. But, let me set those worries aside for now and briefly restate his argument.

According to McDaniel, and most of us, material objects and the regions they occupy are distinct entities that stand in an occupation relation to one another. It turns out that the shape of a material object must match up with the shape of the region it occupies. But, if the shapes of both material objects and regions are intrinsic, then that means that there is a necessary connection between the intrinsic features of these distinct (contingent). This connection is barred by the Humean principle alluded to above. So, either the shapes of material objects or the shapes of the regions they occupy are extrinsic. McDaniel, and others, take it that the shapes of regions are intrinsic. In the near future I will question this premise (but not now). granting this premise we must conclude that the shapes of material objects are extrinsic.

That is, roughly, how the Humean argument for the extrinsic account of the shapes of material objects goes. Although, I don't think this argument is sound, let me assume for the moment that it is and present an interesting argument involving the extrinsic account of shapes.

Many people accept a Lewisian account of intrinsicality according to which intrinsic properties of particular objects are properties taht never differ between the duplicates of those objects. This is yet another principle that needs to be more carefully formulated. I have not come across a satisfactory formulation in the literature. But, for the sake of this argument, let me try to come up with one. Let's try this one:

(LAI) Nec, for any x and any F (x is F intrinsically iff (for any y that is a duplicate of x, y is F as well).

For simplicity I'll just take the quantifiers in this formulation to be possibilist and I'll pretend that counterpart theory is true (the principle can be ammended to avoid these commitments, but it only obscures the issue I want to get at).

As I said above, this kind of Lewisian account is accepted by many philosophers including McDaniel (though I'm not sure he'd accopt my formulation). But, (LAI) in combination with the extrinsic account of shapes leads to a rather surprising conclusion. It seems that if shape properties are extrinsic properties of material objects, then the property of being shaped is also an extrinsic property of material objects as well. Moreover, I am a material object and I have a shape. But, it follows from (LAI) and the claim that my shape is extrinsic that I have a duplicate that is not shaped at all. But, if something has no shape whatsoever, then it is not spatially located and hence immaterial. So, I have a duplicate that is immaterial. But, any duplicate of mine presumably has consciousness. So, there is a (perhaps merely possible) conscious duplicate of me that is immaterial.

That seems to me like a rather radical conclusion. I'd like to see if I can get an even more radical conclusion. I thought I might be able to argue for dualism. But, I'm not sure how to proceed from here.

Sider on Intrinsicality

2008-06-16T11:56:00.001-07:00

A few years ago, Sider argued against Lewis's second account of intrinsicality and in favor of Lewis's first account. In this post, I will do the following. First, I will present Lewis's two accounts of intrinsicality (I will assume the doctrine of world bound individuals in my presentation, but that is simply to make things simpler). Second, I will present Sider's objection to Lewis's second account. Third, I will suggest an amendment to Lewis's second account. And finally, I will present my own objections to Lewis's first account.

Lewis First Account of intrinsicality says that a property is intrinsic just in case it never differs between duplicates (where two things are duplicates just in case there is a one-one correspondence between their parts that preserves perfectly natural properties). Intuitively, if something looks just like me and has all the same perfectly natural properties that I have, then that thing has all the intrinsic properties that I have.

Lewis's second account starts with the notion of a lonely object. A lonely object is one that exists alone in a possible world. A property is independent of loneliness just in case (i) it is had by a lonely object, (ii) it is lacked by a lonely object, (iii) it is had by a non-lonely object, and (iv) it is lacked by a non-lonely object. Finally, Lewis's Second Account says that a property is intrinsic just in case it is both independent of loneliness and non-disjunctive.

Sider seems to favor Lewis first account over his second. Sider argues that there are counterexamples to the second account which are not also counterexamples to the first account. His counterexamples rely on the notion of maximality. A property F is maximal just in case (roughly) large parts of an F thing are not themselves Fs. Some refinements need to be made to this notion, but let's ignore those for now. According to Sider, being a rock is a maximal property because large parts of rocks are not themselves rocks. Similarly, being a house is a maximal property because large parts of houses are not themselves houses. Sider also claims that maximal properties are not intrinsic. This is because whether or not something has a maximal property will depend on whether it is a large part of something that has that maximal property. For example, something is not a house if it is a large part of a house; all of a house except one of its windows is not a house because that thing is a large part of a house. Since the exemplification of these maximal features by an object depends on what is going on outside the borders of that object, they are not intrinsic.

Now Sider's argument is as follows:
1. If Lewis's second account is true, then being a rock is intrinsic.
2. But, being a rock is not intrinsic.
3. So, Lewis's second account is not true.

The justification for (2) is in the paragraph above. The justification for (1) is as follows. Being a rock is not a disjunctive property. Moreover, being a rock is had by a lonely object and lacked by a lonely object (there are lonely rocks and lonely non-rocks). And also, being a rock is had by a non-lonely object and lacked by a non-lonely object (simple empirical investigation will verify this). So, according to Lewis's second account, being a rock is intrinsic. So, (1) is true.

Sider notes that a similar problem does not arise for the first account of intrinsicality. There could be a duplicate of a rock that is embedded in a larger rock. That duplicate is not a rock. So, bieng a rock is not shared by these two duplicates and hence is not intrinsic (according to the first account).

I like Sider's argument. I guess I think it is sound. However, I think a simple amendment to the second account will save it from this sort of objection. I wish I could say that a property F is intrinsic just in case it is (i) independent of loneliness, (ii) non-disjunctive and (iii) non-maximal. But, this is not quite right. Sider points out that it is not maximality that is troublesome but rather border sensitivity. Sider says that a property is border-sensitive iff "whether it is instantiated by an object depends on what is going on, intrinsically, outside that object at its border." All border sensitive properties are non-intrinsic and some are not maximal. This led me to think that the following account might be true: a property F is intrinsic just in case it is (i) independent of loneliness, (ii) non-disjunctive and (iii) non-border-sensitive. But, unfortunately, because of the occurrence of 'intrinsic' in the definition of 'border-sensitive' this account is circular. So, let's introduce a new notion. Let's say that a property is outwardly-sensitive just in case whether it is instantiated by an object depends on what is going on outside that object (at its border) (I'm not sure if this last little parenthetical bit is needed). If a property is outwardly-sensitive, then it is border-sensitive. Now we can say the following:

Lewis's Amended Second Account: a property F is intrinsic just in case it is (i) independent of loneliness, (ii) non-disjunctive and (iii) not outwardly-sensitive.

I kind of like this account. Question: are there any immediate problems with this account?

Now, I'd like to suggest that there are counter-examples to Lewis's first account which are not also counterexamples to Lewis's Amended Second Account. First, if Lewis's First Account is true, then being identical to Joshua is not an intrinsic property. This is because some duplicates of me are not identical to me. But, it is an intrinsic property. So, Lewis's First Account if false. Second, if Lewis First Account if true, then co-existing with the number 2 is an intrinsic property. This is because the number 2 is a necessary existent and no two duplicates fail to co-exist with it. But, co-existing with the number 2 is not intrinsic (at least it is not intrinsic to me). So, Lewis's First Account is false.

I like these two arguments, though, I do not think they are knock-down. David, for example, has suggested a problem for the first argument. I am not sure what I think of the problem that he suggests. But, it is interesting to note that the Amended Second Account is not so obviously subject to these counterexamples. First, as long as you do not endorse certain kinds of essentialism, we can maintain that being identical to Joshua is independent of loneliness. It is also clear that co-existing with the number 2 is not independent of loneliness.

There is a worry that I have, though. It seems that co-existing with the number 2 is an extrinsic property of me and an intrinsic property of the number 2 (thanks to Rock* for pointing out this worry). I am not sure how to amend the account further to get this result. I can make the following amendment. First, call W2 a subtraction of a world W1 iff W2 is either possible or impossible and it is just like the W1 except that something that exists in the W1 does not exist in W2. Now we can say that a lonely object* is one that exists alone in a possible world or alone in a subtraction of a possible world. We might be able to give a disjunctive account of intrinsicality where we use the notion of loneliness for contingent things and the notion of loneliness* for non-contingent things. I am not sure how this will work out. I'd prefer to come up with an account of F is intrinsic to x and wed the notion of intrinsicality to objects. I'm sorry this post has gotten a little messy toward the end, but I am still thinking through these things. If anyone has any ideas, please let me know what you think.

The meanings of definite descriptions

2008-06-06T08:11:00.000-07:00

Nathan Salmon has recently written a paper on that very confusing passage from Russell's 'On Denoting'. Salmon's paper appears in a special issue of Mind. I have not read his paper but I have talked to Rock* about it. In this post, I am going to present an argument that is inspired by my discussions with Rock* about Salmon's paper. I do not claim that that my formulation of the argument below is a decent formulation of the argument presented in Salmon's paper (I am not even sure if it is a formulation of Salmon's argument at all). But, I think it is interesting anyway.

Let's consider the definite description "The center of mass of Earth". The unit meaning of "The center of mass of Earth" is the meaning of that whole phrase which built out of the meanings of words in that phrase, if there is such a meaning. I am inclined to think that there is a unit meaning of "The center of mass of Earth". But, the argument that I present below is supposed to show that there is not such a unit meaning.

Let's also introduce a principle of naive compositionality. I am never sure about how to formulate compositionality principles. Roughly, we want to say that the meaning of a sentence is determined by the meanings of the words that make up that sentence and their order. Here is an attempt to make something like that principle more precise.

Naive Compositionality Principle: If S1 and S2 are made up of some phrases that can be put in a one-one correspondence that preserves their individual meanings and their order in the sentence, then S1 and S2 express the same proposition.

Here is an example of how this principle should work. Consider the following two sentences:

S1. All bachelors are unmarried.

S1. All unmarried adult males are unmarried.

Sentence (S1) can be broken up into the following parts:

P1.1 All Bachelors
P1.2 are unmarried

Whereas sentence (S2) can be broken up into the following parts:

P2.1 All unmarried adult males
P2.2 are unmarried

Clearly, there is a one-one correspondence that preserves word order. We just associate P1.1 with P2.1 and P1.2 with P2.2. Moreover, P1.2 and P2.2 definitely have the same meaning. So, if P1.1 and P2.1 have the same meaning, then according to our principle (S1) and (S2) express the same proposition. A plausible case can be made for the claim that P1.1 and P2.1 have the same meaning. But, I won't get into that right now. I just wanted to give an example which helps to show how the Naive Compositionality Principle works.

Now, here is how the argument goes. First, let's introduce "Fred" as a name for the unit meaning of 'The center of mass of Earth". Now, consider the following sentences:

S3. The center of mass of Earth is a point.

S4. Fred is a point.

Clearly (S3) expresses a truth. However, it seems that (S4) does not. (S4) is about the thing named by "Fred", a meaning, and meanings are not points. So, (S4) expresses a falsehood. But, according to Naive Compositionality and Millianism and under the assumption that "The center of mass of Earth" has a unit meaning, (S3) and (S4) express the same proposition. This is puzzling. We can formulate an argument as follows:

1. If "the center of mass of Earth" has a unit meaning, then (S3) and (S4) express the same proposition.
2. (S3) expresses a truth whereas (S4) does not.
3. If (2), then (S3) and (S4) do not express the same proposition.
4. So, "The center of mass of Earth" does not have a unit meaning.

(1) is justified by appealing to Millianism and the Naive Compositionality Principle. (2) seems pretty plausible. The fact that (S3) expresses a truth is an empirical discovery and I argued for the claim that (S4) expresses a falsehood above. Finally, (3) is justified by Leibniz's Law. So, our argument is valid and has strong support. Moreover, the argument can be generalized in a particular way to show that no definite description has a unit meanings. (Moreover, as Rock* pointed out to me, the same thing can be done with other quantificational sentences such as "All cats are furry" and "some dogs are happy".)

I disagree with the conclusion of the argument and I think the best premise to deny is (1). I think that Naive Compositionality is false. It seems to me that the fact that the subject of (S3) is grammatically a definite description whereas the subject of (S4) is not makes it so that (S3) and (S4) express different propositions. However, these propositions are made up of the same meanings in the same order. We have to replace Naive Compositionality with a principle that allows for grammatically different sentences with the same meanings in the same order to express different propositions.

I know this post is not exceedingly clear, But I hope it is clear enough to convey the puzzle and my solution. I'd like to know what others think of this puzzle.

Eternal Life

2008-06-01T09:11:00.000-07:00

Suppose that a nearly omnipotent being comes to you and offers you eternal life. "This is how it works", he says. "You'll live out your life and grow old just as you normally would. But, at a ripe old age, your body will regenerate to the healthy state it is currently in and you'll be able to continue living and growing old from that point onward. This will happen an infinite number of times. Moreover, I guarantee that you will never suffer or be bored. You'll seem to live an infinite number of exciting and interesting lives, each one psychologically connected to the previous one."

This seems like a good deal to me. Moreover, I have asked a few other people about this case and they also seem to agree that this is a good deal. However, here is a slight twist to the case.

Suppose that the nearly omnipotent being suddenly says "oh darn, I just remembered that I can't offer you that deal. However, I can offer you something else. Here's the new deal. Instead of an infinite number of sequential regenerations, I'll make you an infinitely multiply located individual. There will be a series of life-like events hosted by you at your various locations. Each life-like event will persist for another 50 or so years. Moreover, each life like event will have a successor in the following sense. The mental states that are involved at the end of any one life-like event will be psychologically connected to the mental states of its successor. Just as before, you'll never suffer or be bored. You'll seem to live an infinite number of exciting and interesting lives, each one psychologically connected to the previous one.""

My intuitions, and the intuitions of those I surveyed, seem to indicate that this is not such a good deal. Some even think that it is not a deal worth taking. That is, you are no better off if you take the deal than if you don't. But, let's add another twist to the case.

Suppose another nearly omnipotent being comes to you and says "I can't believe that other yahoo just offered you that second deal. That deal is not very good and I can offer you a better one. He is right that the first deal is off the table. The reason is that the universe is going to end just a few minutes after you reach that ripe old age of 90. So, we can't give you a sequence of regenerations and guarantee your safety. However, I can offer you something just as good. Just like in the first deal, you'll regenerate to your current healthy state when you reach a certain age. However, you'll also be warped back in time to the moment when you first take the deal. You'll then live another 50 years or so, regenerate again and time warp again. This will happen an infinite number of times. So, you'll have eternal life (in some sense), much like in the first case. I also guarantee that you will never suffer or be bored. You'll seem to live an infinite number of exciting and interesting lives, each one psychologically connected to the previous one.""

Again, the intuitions of those I surveyed seem to indicate that this deal is better than the second. In fact, it seems to be just about as good as the first. But, it is not exactly clear why. The third deal will have results that are significantly similar to the second deal. Why is it that the third deal is better than the second and the second is worst than the first even though the third has results that are remarkably similar to the second?

Here is a suggested answer: (1) Somehow the causal connections between the various life-like events and preserved in the first and third deal but not the second. This is why the first and third are good deals and the second is not. Notice that this response might require a kind of robust realism about causation. I am not sure if this is a good answer and I am not sure why these preserved causal connections are so great. Why is it that the second case seems significantly lamer than the first or third?

If anyone has an idea about why the first and third deal are better than the second, I'd like to hear them. And if anyone thinks that the suggested answer above is on the right track, I'd like to know why the causal connections are so important that they make the second deal significantly worse the the first and third.

Bare Conditionals

2008-05-22T18:29:00.000-07:00

It seems to me that the relationship between (1) and (2) might be analogous to the relationship between (3) and (4). Does this sound right to anyone?

1. Whenever I go to the store, I get milk.

2. I go to the store, I get milk.

3. All Cats are furry.

4. Cats are furry.

Of course, I don't know much about any of these kinds of sentences. But, if there is an analogous relationship, then we might be able to learn more about sentences like (2) by thinking about sentences like (4).

I guess I am slightly worried that (2) has no truth value. Since all the other sentences definitely have truth values, that would be a significant difference between the relationship between (1) and (2) and (3) and (4). But, my worry is not very strong since I do think that (2) has a truth value.

My own naive idea is that (3) and (4) are necessarily co-extensive in truth value. That makes me think that (1) and (2) are as well. But, like I said, I don't know much about this stuff.

Countercurrents

2008-05-20T12:29:00.000-07:00

I have been thinking about certain temporal sentences like the following:

1. When I go to the store, I will get milk.

and

2. When I went to the store, I got milk.

I do not know anything about the literature on this topic (if there is any). So, what I am about to say might have been said by someone else or definitively disproven. If anyone has any information about the literature on this topic, I would be happy to hear it.

Here is an initial idea that seemed plausible to me:

3. Necessarily ((when I go to the store, I will get milk is true) iff (the
nearest future time during which I am going to the store is a time at which I get milk))

Unfortunately, there are several counterexamples to this suggestion. Here is one. Suppose I utter sentence (1) and then set out to get milk. One time during which I am going to the store is a time that ends the moment I step through the grocery store doors. But, that is not a time during which I get milk. However, if I get milk shortly after stepping through the door, then it seems spoke truly when I uttered (1).

Here are two modifications. The first is my lame suggestion and the second is Andrews more interesting suggestion:

4. Necessarily ((when I go to the store, I will get milk is true) iff (the
nearest future event during which I am go to the store is an event during which I get milk))

This might be subject to the same sorts of objections as (3). It all depends on what you think about events. Here is a variant of Andrew's suggestion:

5. Necessarily ((when I go to the store, I will get milk is true) iff (the
nearest future continuous time every subinterval of which is a time during which I am going to the store and no continuous superinterval of which includes more times during which I am going to the store is a time during which I get milk))

There are similar accounts of the (2) involving past times which I will not spell out here. What do you guys think of this suggestion? Are there any obvious counterexamples? I have had at least one person tell me that these accounts are too narrow because (1) is true if I get milk at any time in the future while I am going to the store. Does anyone else share that intuition about (1)?

UPDATE: Please note that I have revised (5) in my comments below and ignore the formulation in the post.

'would'

2008-05-18T11:38:00.000-07:00

The results of my test, collected from personal interviews and the last post, seem to suggest that the following is a correct way to report Fred's assertion:

"Fred, you said that when you went to the store, you would get milk."

This is exactly as I expected. But, now I am a bit puzzled. Why is it that the verb 'to be' is in the 'would' form in this sentence? Is there a connection between the use of 'would' in this sentence and the use of 'would' in typical counterfactuals? Is this a natural development and do other languages exhibit the same seemingly dual use of the word 'would'? If anyone knows anything that will help illuminate these issues, please feel free to post.

Test

2008-05-15T17:15:00.000-07:00

Please read the passage and answer the question. Please have many other people do so as well. I'd like to see what many people have to say in response to this question. Thank you.

Fred is a very absentminded. He needs to be reminded of lots of things. But, when you remind him, you need to be very direct. One morning you and Fred find that there is no milk in the fridge. Fred says “When I go to the store, I’ll get milk”. Later that afternoon, Fred remembers to go to the store but forgets to buy milk. Remembering that Fred is very absentminded you decide to patiently remind him of what he said. What do you say to Fred? In the blank space below, please write down exactly what you say to Fred when you remind him of what he said.

You: _________________________.

Time Travel, Life, and Death

2007-10-10T07:35:00.000-07:00

In this post, I'd like to describe a rather typical time travel case in order to elicit views concerning whether a certain claim is true in the case. Having presented the case and asked the question, I will explain some of the reasons for my interest in whether that claim is true.

Time Travelling Tim: Tim Travell was born at t1 in a rural area in Connecticut. He lived a normal (non-time travelling) life until t20, when he came into possession of a time machine. Using this time machine, Tim travelled forward in time to t500. However, soon becoming bored of the futuristic lifestyle, at t502, Tim travelled back in time to t21 and lived out the rest of his life without ever again time travelling. He died at t90.

Assuming that no (non-time travelling) funny business (for instance, resurrection) happened in this case, the claim concerning which I'd like to elicit views is:
(T) At t501, Tim is dead.
So, what do you guys think? Is (T) true or false?

Now let me explain some of the reasons why I am interested in whether (T) is true or false. First, if (T) is true, then being alive and being dead are not (contrary to common opinion) contraries. For it is clearly true that at t501, Tim is alive. So, if (T) is true, then there is a time at which something is both alive and dead.

Second (but relatedly), if (T) is true, then certain analyses of being dead are false. For instance, consider the following proposed analysis:
Proposed Analysis of Being Dead (PABD): Necessarily, for all x, x is dead (at t) iff (i) x was alive (at some time earlier than t) and (ii) x is not alive (at t).
If (T) is true, then (PABD) is false. For if (PABD) is true, then (T) is not true (since Tim is alive at t501 and hence, according to (PABD), isn't dead then).

Anyway, what do you guys think?

Possible Worlds and "Cases"

2007-10-04T07:18:00.000-07:00

Some philosophers would like to (reductively*) analyze possibility and necessity in terms of possible worlds. As I understand their position, it is something like this:

Analysis of Possibility and Necessity (APN): There is a property P ("the property of being a possible world") and a relation R ("the relation of being true at") such that (i) being possible = being an x such that there is a y such that Py and Rxy and (ii) being necessary = being an x such that for all y, if Py, then Rxy.**

One argument some have offered in favor of (APN) is that treating possibility and necessity as existential and universal quantification over worlds, respectively, allows us to explain the validity of various inferences containing 'necessarily' and 'possibly'.*** The idea, I take it, is that sentences of the form:
(N) Necessarily, S.
are in fact ascriptions of the property of being necessary to the proposition that S:****
(N') That S is necessary.
which, given (APN), is equivalent to:
(N'') That S is such that for all possible worlds w, it is true at w.
Similarly for sentences of the form:
(P) Possibly, S.

Now it is interesting to note that to explain certain inferences containing 'necessarily' and 'possibly', proponents of (APN) are going to have to attribute hidden structure to sentences of English. For instance, consider the following inference:
(1) Necessarily, S.
(2) Therefore, S.
Given what has been said before, proponents of (APN) will claim that (1) is equivalent to:
(1') That S is such that for all possible worlds w, it is true at w.
But then whence the inference from (1) to (2)? Presumably, the proponent of (APN) will have to say that (2) is equivalent to something like this:
(2) Therefore, that S is true at a ("the actual world").

Now I want to draw an analogy between the argument for (APN) that I have been discussing and an argument for a different thesis. Call the (relevant) relation that obtains between the propositions that P and that Q iff if P, then Q being conditioned on. Now consider the following thesis:

Analysis of Being Conditioned On (ABC): There is a property P ("the property of being a case") and a relation R ("the relation of being true in") such that being conditioned on = being an x and a y such that for all z such that Pz and Rxz, Ryz.

The idea behind (ABC) is that a (material) conditional is true if and only if (the proposition expressed by) its consequent is true in all cases in which (the proposition expressed by) its consequent is true. Just as 'is a possible world' and 'is true at' are technical terms used to express whichever property and relation appear in the correct analysis of being necessary and being possible, so too 'is a case' and 'is true in' are technical terms used to express whichever property and relation appear in the correct analysis of being conditioned on.

Notice that just as (APN) allowed us to "explain" the validity of inferences containing 'necessarily' and 'possibly', so too (ABC) allows us to "explain" the validity of inferences containing the material conditional. For instance, hypothetical syllogism:
(1) If P, then Q.
(2) If Q, then R.
(3) Therefore, if P, then R.
HS can be explained by the proponent of (ABC) by treating (1), (2), and (3) as, respectively:
(1) For all cases x such that that P is true in x, that Q is true in x.
(2) For all cases x such that that Q is true in x, that R is true in x.
(3) Therefore, for all cases x such that that P is true in x, that R is true in x.

Also notice that a proponent of (ABC) will also need to attribute hidden structure in sentences of English to explain the validity of certain inferences, such as modus ponens:
(1) If P, then Q.
(2) P
(3) Therefore, Q.
In particular, they will need to postulate that (2) and (3) contain a case constant referring to the "real case".

It seems, then that the argument from the explanation of the validity of inferences for (APN) has an analogue: an argument from the explanation of the validity of inferences for (ABC). However, I take it that many of those who find the first argument plausible will not find the second argument plausible. But why? The cases seem relevantly similar. Via translation, we can explain the validity of inferences involving 'possibly' and 'necessarily' using possible worlds, and we can do the same for the validity of inferences involving the material conditional using cases. In addition, both views seem to involve positing hidden structure to English sentences. So what gives?

[One potential answer is that restricted quantification of the sort used in the statement of (ABC) is usually explained in terms of unresticted quantification and the material conditional. Hence, some may take (ABC) to be circular. However, restricted quantification needn't be construed in this way. Inference rules for restricted quantification can be introduced. So can a semantics. Thus, we are not forced to explain restricted quantification partly in terms of unrestricted quantification.]

* I include 'reductively' here because some philosophers make a distinction between reductive and non-reductive analyses. However, I must admit that I don't know what a non-reductive analysis is supposed to be.

** We could introduce an accessibility relation into the analysis as well without affecting the point I am trying to make.

*** I take it that only a "reductive" analysis would explain the validity of these inferences.

I got the idea for this post from teaching "baby logic" to undergraduates. They seem to grasp why certain inferences using the material conditional are valid/invalid best when those conditionals are translated into talk of cases and Venn diagrams are used.

Vagueness and 'part'

2007-10-04T06:54:00.000-07:00

Let's restrict our attention to possible worlds where the meanings of words in the English language the same as they actually are. Given, this assumption, it is generally accepted that:

(V) Necessarily, if the English phrase 'is a part of' is vague, then so is the English phrase 'is identical to'.

It turns out that this is not a logical truth. There are models on which 'is a part of' is vague yet 'is identical to' is not. Moreover, some of these models obey Classical Extensional Mereology. But, there are some decent metaphysical reasons to believe that the claim is true. But, this is very troublesome since most philosophers want to link the content of 'is identical to' to the content of 'exists'. This all seems to lead to vague existence, which very few people want to accept.

The lesson is supposed to be that any vague phrases of the form 'a is part of b' are vague in virtue of the vagueness of the singular terms not in virtue of the vagueness of the word 'part'. I would like to challenge this lesson.

Consider the computer on by desk and call it 'Computer'. Now find an arbitrary atom near the surface of the computer that is such that 'that atom is a part of the computer' is vague when the complex demonstrative 'that atom' refers to the arbitrary atom. Now name the atom 'Fred'. Here is the vague phrase that I want to consider:

'Fred is a part of Computer'.

According to the lesson above, this phrase is vague in virtue of the vagueness of 'Fred' or the vagueness of 'Computer' but it is definitely not vague in virtue of the vagueness of 'part' (lest we fall prey to the vague identity and existence).

Now for the challenge. If 'Computer' is vague, then it is vague in virtue of the fact that there are multiple candidate referents of 'Computer'. Similarly, if 'Fred' is vague, then it is vague in virtue of the fact that there are multiple candidate referents of 'Fred'. Let's make the terms more precise. Let 'Computer*' name an arbitrary candidate referent of 'Computer' and let 'Fred*' name an arbitrary candidate referent of 'Fred'. Now, given that the names 'Computer*' and 'Fred*' are precise and that 'part' is precise as well, it is clear that the following sentence is not vague:

'Fred* is a part of Computer*'

This sentence is either definitely true or it is definitely false. Each case is relevantly just like the other. So, let's just suppose that it is definitely true. Now consider a continuous series of worlds each one just like the actual world except that the referent of 'Fred*' has been moved some small distance, n, away from it's actual position. There is a corresponding series of counterfactuals of the form:

(CS1) if Fred* had been n units from its actual position, then the English sentence 'Fred* is a part of Computer*' would be vague.

It seems that one of the counterfactuals in this series expresses a truth. But, since the names 'Fred*' and 'Computer*' are actually precise and since we restricting our attention to worlds where the meanings of English are held fixed, it is clear that:

(CS2) If Fred* had been n units from its actual position, then it would not be a fact that 'Fred*' is vague and it would not be a fact that 'Computer*' is vague.

But given the plausible necessary truth:

(N) Necessarily, if the English phrase 'Fred* is a part of Computer*' is vague, then either 'Fred*' is vague or 'Computer*' is vague or 'is a part of' is vague.

It follows from (CS1), (CS2), (N) and the obvious claim that it is possible that Fred* is n units from its actual position that:

(PV) Possibly, the English phrase 'is a part of' would be vague.

Of course, since we have been restricting our attention to worlds where the meanings of English are the same as they actually are, it follows that

(AV) it is actually the case that the English phrase 'is a part of' is vague.

But, this is contrary to the lesson that we were supposed to learn. (AV) in combination with (V) gets us the unwanted consequence that 'is identical to' is vague and ultimately gets us vagueness of existence.

Right now, I think that the best response is to reject that any instance of (CS1) is true. One might claim that some instance of (CS1) seems true because the following is true:

(VCS2) the sentence 'if Fred* had been n units from its actual position, then Fred* would be a part of Computer*' is vague.

We, the defender of the lesson might say, just think that (CS1) is true because (VCS1) is true. Moreover, the vagueness of the sentence talked about in (VCS1) is vague in virtue of the vagueness of subjunctive conditionals.

I am not happy with this response. But, I am having a hard time thinking of an alternative.

The Concept of Logical Consequence

2007-09-29T10:11:00.000-07:00

So this is just an advertisement with a bit of philosophy in it.

How would you explain necessity to the uninitiated? Here's (roughly) a way I've done it in the past: in terms of nested necessities of increasing strength. Small circle encompasses the technological possibilities. Bigger: Nomological possibilities. Bigger: Metaphysical possibilities. Bigger: Logical possibilities. Then necessity is specified in the usual way: blah necessity is truth in all blah possibilities.

Now for a question: Which do you care the most about philosophically? The merely technologically possible is boring and laws of nature are only a little more interesting than that. Metaphysical possibility is the thing. But what about logical possibiliy? I think in one respect it's lame. So a non-lame respect is trying to figure out the limits of the logically possible. That has to do with correct accounts of logical consequence. But here's the lame way: To say that P is logically possible is merely to say P has a model in which it's true. But what's that mean? Well it means (roughly) that there is a way of interpreting the non-logical constants that is consistent. Big whoop. This seems like it amounts to saying 'Oak is a type of metal' is logically possibly true simply because there's a language in which that sentence is true. (Since interpretations are in the business of hooking up the formulas to the domain(s) in different ways.) Not very illuminating.

Russell said that logic was just as concerned with the world as zoology, but with its most general features. I think that's basically correct but does not seem borne out by what counts as logical possibilities. It's really the metaphysical possibilities that do that. That's because metaphysical possibilites "hold fixed" meanings and vary worlds as opposed to holding fixed formulas and varying ways of hooking that formula to the world(s). (In fact we caution that the latter approach is an elementary mistake in thinking about metaphysical possibility.) But that's what logical possibility does.

Just recently I discovered John Etchemendy's 1999 book, The Concept of Logical Consequence. The book argues (basically) that logical possibility should be pursued in the manner in which we pursue metaphysical possibility and in fact the Tarskian tradition amounts to a mistake. This strikes me as a very deep and important issue. I suspect that y'all might sympathize so I thought I'd pass along the recommendation.

Knowing How to Know

2007-09-12T12:15:00.000-07:00

Massively Unreflective Ralph has no attitudes whatsoever about any of his attitudes. This massive unreflectiveness is no obstacle to Ralph’s having some propositional knowledge. After all, one need not have attitudes about attitudes in order to know. So let’s suppose that Ralph is a knower. Then it is intuitive to count Ralph as someone who knows how to know things. After all, he succeeds in knowing some things. But on Stanley and Williamson’s account of knowledge how, if Ralph knows how to know that A, then he knows that B is a way to know that A under a “practical mode of presentation”. As this conflicts with the supposition that Ralph is massively unreflective, it follows that any situation so conceived is impossible or Stanley and Williamson’s account is incorrect.

I have things to say about some possible replies I've thought of but I was wondering what others think.

Simples and "Occupation"

2007-07-27T07:45:00.000-07:00

Two of the main competing views of simples are occupation accounts. These two competing views are the Pointy View (PV) and MaxCon. Each of these views was originally formulated by Ned Markosian in his paper "Simples". Kris McDanial has argued, however, that occupation accounts are false on the grounds that there can be fusions of co-located individuals. This, in combination with the fact that non-occupation accounts of simples are false, suggests a brutal view of simples. I am inclined to think that McDaniel's arguments are sound. My inclination is as strong as my inclination toward accepting co-location. But, if it should turn out that co-location is impossible, then I think that these occupation accounts of simples are the strongest views thus far discussed. However, I think that there is a serious worry for PV and MaxCon that has not yet been addressed. In this post, I wish to spell out this worry and suggest alternative occupation accounts of simples.

I will take the pointy view as my main example. But, notice that everything I say about the pointy view can be said (with very slight modification) about MaxCon. Thus, the problem that I pose is a problem for both views. According to the pointy view,

Necessarily: for any x: x is a simple (at t) iff x is a pointy object (at t).

x is a pointy object (at t) =df the region occupied by x (at t) contains exactly one point.

This seems clear enough. However, there are some terms that we have been using that has not been fully defined. These terms are are related to the verb 'to occupy'. Markosian borrows from van Inwagen the following definition (I have added subscripts for help in later disambiguations):

O occupies1 R (at t) =df R is the set containing all and only those points that lie within O (at t).

Here are some comments that I would like to make at this point. First, this definition puts the burden of understanding this view of simples squarely on the primitive 'lie within'. I think I have an intuitive grasp of this primitive. However, there is some room for confusion. For example, one might believe that for one thing to lie within another it must be a part of the other. But, this is not the correct sense of 'lie within' for van Inwagen's definition. Another way that one object might lie within another is when the first is completely surrounded by the second. For example, a ring might lie within a box. But, again, this is not the correct sense of 'lie within'. For the record, even though I think I understand how van Inwagen is trying to use 'lie within' I am inclined to think that it is a deviant use of the phrase. If it is not a deviant use of the phrase, then it is certainly a restricted use and the restriction should be made explcit by ruling out the kinds of examples I suggested above.

The more important worry that I wish to address is the following. This definition seems to suggest that the relation picked out by 'occupies1' is functional. That is, every material object occupies1 exactly one region. This suggests that the definition of ' O occupies1 R' is equivalent to Parson's definition of 'O is exactly located at R' (correct me if I am mistaken here). This fact makes it clear why Markosian uses the definite article in his formulation of PV. But, there is a problem with this assumption.

Here is a case. Suppose that there is a single point sized object that persits for an hour. After an hour of its life has passed by, it appears as if another point sized particle appears along side the first. Then it seems like these two particles persist together until the first particle dissappears. One seemingly metaphysically possible event that fits this discription is a case of time travel. It could be that a single particle persists for a while until it materializes alongside itself. This materialization is the result of the particle time traveling from the future. It seems appropriate to say that his particle is a mereological simple. After all, it doesn't seem like an object can gain parts simply by time traveling in the way that this particle did. But, under PV, this particle is not a simple (during the time when it sits alongside itself). This is because the particles occupies a region that contains two points during those times. This suggests that the pointy view is false. (this example should also show that MaxCon is false since a region containing exactly two points cannot be continuous).

It is not enough to modify the pointy view by getting rid of the definite article. This is because 'occupies1' picks out a relation that is functional. So, eleminating the definite article will not solve the problem. We must also reinterpret the word 'occupies'. McDaniel (and independantly our very own Rock*) has suggested that there is a primitive occupation relation. This occupation relation is not functional. Let's use 'occupies2' to pick out this new relation and use 'might' in some kind of epistemic sense. When an object occupies2 a region it might also occupy2 another region. Moreover, when it occupies2 two regions, it need not occupy2 the union of those two regions. Finally, when we say that one thing occupies2 a region it might be that that thing or parts of that thing occupy2 subregions of that region and it might not. This is not entirely clear, but I think that we get the idea.

Now, we can simply reinterpret PV with 'occupies2'. But, this will not solve the problem. The definite article has to go. Here is one variant of the pointy view which turns out to be inadequate.

PV*: Necessarily: for any x: x is a simple (at t) iff a region occupied2 by x (at t) contains exactly one point.

Here is why this account is inadequate. Suppose we accept DAUP and the Liberal View of Recepticles. Suppose also that there is an object that occupies a pointy region and also occupies an extended region. Then, by the combination of DAUP and the Liberal View of Recepticles, this object has parts. It will have parts that occupy each of the subregions of the extended region it occupies. However, according to PV* it is a simple since one of the regions it occupies contains exactly one point.

Here, I think, is the best reformulation of the pointy view:

PV**: Necessarily: for any x: x is a simple (at t) iff x occupies2 (at t) a region and every region occupied2 by x (at t) contains exactly one point.

There is a similar reformulation of MaxCon that avoids the time travel counterexample given above. However, I worry about cases of time travel where a MaxCon simple comes into contact with itself. But, I have not thought through that example yet.

Propositions and Sets

2007-07-06T12:30:00.000-07:00

Are propositions sets? I don't think so, but I'm worried about how good the arguments are against the view.

There are several reasons in the literature for thinking that propositions are not reducible to set-like entities. Here is one from Plantinga:

1. Some propositions have truth values and no sets have truth values.
2. If (1), then some propositions are not sets. (by Leibniz's Law)
3. If some propositions are not sets, then not all propositions are sets.
4. If not all propositions are sets, then propositions are not reducible to sets.
5. So if (1), then propositions are not reducible to sets. (2-4)
6. So propositions are not reducible to sets. (1,5)

Plantinga contends that (1) is obvious. Those who endorse the view that propositions are sets will of course think it is not obvious. Let's concede the point to Divers unless someone can come up with another way to support (1).

Another objection, from Jeff King's SEP entry on structured propositions, is as follows:

7. If some sets are propositions, then some sets have truth values (modal properties, etc) and others do not.
8. If some sets have truth values and others do not, then there is an explanation of why this is the case.
9. So if some sets are propositions, then there is an explanation of why some sets have truth values and others do not. (7,8)
10. There is no explanation of why some sets have truth values and others do not.
11. So it's not the case that some sets are propositions. (7,10)

I think someone like Lewis can resist (10) with some plausibility. Here's a view that Lewis and some of his opponents, like Salmon and Soames, both seem to hold:

Propositions are pieces of information semantically encoded by well-formed declarative sentences. They are truth-apt objects of cognitive attitudes (like belief, etc).

This characterization serves to specify the role of propositions. Something is a proposition iff it's the best candidate for that role. If that turns out to be shoes or fish or whatever, then propositions may be identified with shoes, fish, whatever. Now Lewis holds that certain sets occupy this role. (For what it's worth, Salmon and Soames give their theories of propositions in set-theoretic terms but are not explicit about whether the set-theoretic entities are supposed to be propositions or if they merely represent them.) If he's right about that, then it seems he has a not implausible explanation of why (e.g.) some sets are true and others have no truth value. There's more that can be said about this objection, but I'll leave it at that for now.

King's second objection is a version of the Benacerraf problem. (Link requires JSTOR access.) It requires a bit of set-up. Consider sentence *:

* Brendan loves Adam

Suppose we held that propositions were ordered n-tuples. Consider the following ordered triples:

(i) bLa
(ii) aLb
(iii) Lab
(iv) Lba
(v) abL
(vi) baL

Furthermore, there are many ways to construct ordered n-tuples. For each way, there is a non-equivalent set that corresponds to each of (i)-(vi). Let's suppose there are only seven ways. Then there are 42 sets: each of (i)-(vi) constructed in each of the seven ways. Here's the objection:

12. If propositions are sets, then there is a unique most eligible candidate among the sets for being the proposition expressed by * in English.
13. There are (at least) 42 sets that are equally eligible candidates for being the proposition expressed by * in English.
14. If there are (at least) 42 sets that are equally eligible candidates for being the proposition expressed by * in English, then there is no unique most eligible candidate among the sets for being the proposition expressed by * in English.
15. So there is no unique most eligible candidate among the sets for being the proposition expressed by * in English. (13,14)
16. So it's not the case that propositions are sets. (12,15)

Here's a reason for denying (1): given a multiplicity of equally eligible candidates, a proponent of the "propositions are sets" view could hold that it's indeterminate which of the 42 sets is the proposition that Brendan loves Adam. One could add that picking any of the 42 to represent the information that Brendan loves Adam is harmless as long as one makes the appropriately uniform choices for representing other propositions. One could also hold that it's appropriate to talk about the proposition that Brendan loves Adam iff according to any legitimate way of eliminating the indeterminacy, there is only one candidate for the proposition. (The view is underdescribed, but hopefully the idea is clear.)

Some thoughts:

A. The sharpenings would have to be done with care. Suppose one pursued the same tack for numbers. There may be admissible sharpenings for propositions according to which S is a proposition and admissible sharpenings for numbers according to which S is a number; 0, for instance. Then 0 would have a truth value and it would be possible to believe 0. That's no good. But it seems like it could be prevented by adding the relevant constraints on admissible sharpenings.

B. I worry on the indeterminacy proposal that it would be true that, were we to have decided on a different sharpening, then the proposition expressed by 'Brendan loves Adam' would have been the proposition expressed by 'Adam loves Brendan' (while all the facts about the English sentences 'Brendan loves Adam' and 'Adam loves Brendan' remain fixed). The counterfactual strikes me as false. There are probably ways around this too: there are similar views about vagueness according to which there are several admissible sharpenings for 'red' and 'orange' and some things that are red under one sharpening are orange on another, but under no sharpening are some things both red and orange. But note a lack of parallel: all of the set-theoretic candidates for being the proposition that Brendan loves Adam are the set-theoretic candidates for the proposition that Adam loves Brendan. In spite of the disanalogy, I confess that the objection does not strike me as especially serious.

C. It would be self-refuting for me to believe that there are no beliefs. On one usage of 'belief', the word refers to the objects of belief. On this understanding, 'I believe there are no beliefs' expresses a proposition that entails that I bear a relation to the proposition that there are no propositions. Contrast this with my (pretend) belief that there are no sets. This does not seem similarly self-refuting. But it would be on the "propositions are sets" view. This is the basis for a Leibniz's Law objection, but I think it's better than Plantinga's because it does not rest on the contention that it's just obvious that sets don't have truth-values. A proponent of "propositions are sets" will cry "hyperintensionality" here, but I don't buy it. The two beliefs really strike me as different in the way described.

D. There are cardinality problems for the view that propositions are sets. There are several ways to state these. Here's one. The proposition that absolutely everything is self-identical is (logically) true. But there is no ordered pair with absolutely everything as one member and the property of being self-identical as the other. That is because there is no set that has as a proper subset absolutely everything. That is because if sets are things, there are too many things for all of them to be a subset (even an improper subset) of a set. (Given any set, the set of all of its subsets has a strictly greater cardinality. So any candidate for being a set that has absolutely everything as a subset is such that there's a "bigger" set: the set of all of its subsets.) Furthermore, if there were a proposition that absolutely everything is self-identical, and it was a set, then it would be a proper subset of itself (since it, too, is one of absolutely everything). This violates standard axioms of set theory ("well-foundedness"). Upshot: if the "propositions are sets" view is true, then there is no proposition that absolutely everything is self-identical. So if propositions are sets, then some logical truth is not true.

I take the last sort of problem to be the most serious. But note it will not do to rest with the claim that propositions are not sets. A positive theory is needed. And part of the burden of the proponent of the positive theory is to show that propositions don't run into cardinality problems anyway. More work is called for.

Any other thoughts on general reasons for/against the view that propositions are sets?

A Puzzle About Justice

2007-06-24T12:54:00.000-07:00

In this post I am going to introduce a puzzle about justice. This is a puzzle that I've been thinking about for a couple of weeks now and I think the version that I present here is the best that I have developed so far. Before I get started, though, I want to discuss some of the concepts that will be involved in this puzzle.

First, let me consider justice. There is a legal notion of justice. According to this notion, which actions are just and which are unjust depends on the laws. But, clearly, this is not the notion that I will be concerned with. There is another notion of justice. A moral notion. In some sense we can evaluate actions that are in accordance with laws as being just or unjust. In fact some laws are either flat out unjust or unjust in their implementation. For example, it is legally permissible to punish someone for possessing small quantities of marijuana. But it is arguably unjust to do so. If it truly is unjust to do so, then the law is in some sense unjust. It is this moral notion of justice that I want to focus on in this post.

This moral notion of injustice seems to have an egalitarian element and a retributive element. Justice, somehow involves treating people equally. This is the egalitarian element. It is this element of justice that is being invoked when we criticise certain laws as being unjust. For example, certain anti-drug laws are criticized as being unjust in virtue of the fact that they call for stricter punishment of the possession of drugs that are more widespread among minority or lower class groups than among other groups. Moreover, the way in which some laws are enforced seems to treat minority and lower class groups more harshly than other groups. This, too, seems to be an unjust.

But, the moral notion of justice also seems to have a retributive element to it. Many people think that is it just to harm someone who has inflicted gross harm upon others. It is this moral notion of justice that is sometimes used to justify state execution. People seem to believe that a person who has committed heinous may, for the sake of justice, be punished.

This last element of justice has been questioned in recent times. Sometimes, people claim that we should punish wrong doers in an effort to rehabilitate. Notice, though, that this is not enough to undermine the retributivist element of justice as a justification for punishment. We might accept that a person may be punished in virtue of the fact that it is just to inflict some kind of punishment on those who have committed heinous acts but the kind of punishment we should inflict is that which will best rehabilitate the criminal. The new position, the one that seems to have gained some kind of ascendancy, should claim that the following is false: A person who has committed a heinous act may, for the sake of justice, be punished. Some people claim that this is false on the grounds that justice does not have the retributive element mentioned above. But another position is that justice does have the retributivist notion, but sometimes the just act is not the morally right act.

For the record, I am inclined to think that the second option is the better of the two. This is because I am inclined to think that if the meanings of our words are determined by our use at all, then our use of the word 'justice' corresponds to something that has a retributivist element.
For the rest of this post I will assume that our moral notion of justice does have some kind of retributivist element to it. This, though, is something that might be questioned later.

The second things that I want to talk about is the notion of a morally heinous action. It is sometimes argued that some groups can commit morally heinous acts without the individuals in the group doing so. Consider, for example the meat eaters of the United States. One view holds that these people are collectively committing a morally heinous act by supporting the factory farming industry. But, some argue that individual meat eaters do not commit any heinous act by purchasing small packages of meat at the supermarket. according to those who hold this position, a person who purchases a small package of meat does not have the kind of causal influence to affect the farming industry. So, the individual has not committed a heinous act by doing so. (note that it is consistent with this claim to say that a person who purchases meat has committed a bad or morally wrong act).

So, lets consider the following moral non-distributivity thesis:

(MND)
Possibly, some people commit a morally heinous act but no individual amongst those people commits a morally heinous act.

This is the first principle in the puzzle that I want to consider. The first quantifier is a plural quantifier whereas the second is not. So, this principle says, roughly, that some people might collectively do something morally heinous whereas no individual amonst them has done so. The next two principle are principles of justice. The first is the just punishment principle:

(JPP)
Necessarily, it is just to severely punish those people who commit morally heinous acts.

Again this principle invokes plural predication. Since some pluralities are pluralities of one person, it follows from this principle that it is just to punish a person who has committed a heinous act. But, this principle also says that if some people collectively commit a heinouse act, then it is just to punish them. This principle should be justified on the grounds that justice has a retributivist element to it.

Now, let's call the kind of punishement that it is just to serve to those who commit heinous acts 'severe punishments'. I take no stand on which punishments are severe punishments. But, clearly if JPP is true, then there are some severe punishments. Let's use the verb 'to severely punish' for the act of inflicting a severe punishment on someone. The next principle to be considered is the unjust punishment principle:

(UPP)
Necessarily, it is unjust to severely punish anyone who has not committed a heinous act.

Finally, the last principle I want to consider is a principle according to which severe punishment is distrbutive. We'll call it the 'distributivity of severe punishment principle':

(DSPP)
Necessarily, if some people are severely punished, then someone amongst them is also severely punished.

This seems like a plausible principle. It is hard to imagine how we could punish a group of individuals without also punishing some individual in that group. Moreover, it seems hard to imagine who we could inflict a severe punishment on a group without also inflicting a severe punishment on some individual in that group.

But, these four principles generate a puzzle For suppose that some people have committed a heinous act but no indivual amongst them has committed a heinous act (as MND says is possible). Then, by (JPP) it is just to severely punish those people. But, by (DSPP) it follows that if those people are severely punished, then someone amongst them must also be severely punished. But, since no individual has done anything morally heinous, it follows that if the group is severely punished, then it follows by (UPP) that someone is unjustly severely punished.
This is, of course, inconsistent. But it is certainly weird. It seems to show that the following weird consequence is true:

(WC)
it is possible to justly punish some people yet thereby unjustly punish some individual as well.

If (WC) seems false to you, then one of the above principles is must be false. In other words, the original four principles, (MND), (JPP), (UPP) and (DSPP) along with (~WC) are inconsistent. That is the puzzle about justice. I have some ideas about which principles are weaker than others and which are probably false. But, I'll remain silent about those opinions for the moment.

Does Lewis Reject K?

2007-05-25T15:33:00.000-07:00

Lewis's concrete modal realism endorses the view that (speaking unrestrictedly) there exists a plurality of possible worlds. By a principle of plenitude, we have that every way something could be is a way that something is (speaking unrestrictedly). Given that a way this world could be is such that it has blue swans, Lewis's view logically entails that (speaking unrestrictedly) there are blue swans. (We might have to pack a lot into the statement of Lewis's view in order to get logical entailment, but I think we can do that in a way Lewis would accept.)

So let's call the relevant theses of Lewisian Modal Realism 'LMR', for short. Given the foregoing point, LMR faces a dilemma. Call the claim that blue swans exist 'BS'. One the basis of the foregoing, we have:

1. LMR --> BS (where '-->' is the arrow of logical entailment)

But by necessitation (N), we have:

2. [](LMR --> BS)

But by K, (3) follows from (2):

3. []LMR --> []BS

But Lewis does not take LMR to be merely contingently true; he aims to give a metaphyiscal account of all of reality (as opposed to what's "merely" actually the case or "merely" what is possible with respect to what is actually the case). So Lewis should accept (4):

4. []LMR

But now it follows from the foregoing that (5) is the case:

5. []BS

But (5) seems to be manifestly false. So either (4), K, or N have to go, or we need to explain how to live with (5).

(This form of the dilemma is from Parsons; Parsons is responding to a proposed solution to this problem from Divers. The presentation of the problem in Divers occurs in his book Possible Worlds but I understand it has an earlier source. I think Parsons' and Divers' proposed solutions are no good and I won't discuss them further in this post.)

I think the responses by a proponent of LMR may differ depending on whether that proponent accepts QML or counterpart theory (CT). Here is what I take to be the best reply for a proponent of QML and LMR:

(5) is true. Since nothing in the semantics of '[]' interacts with the unrestricted quantifier in BS, and since identity is necessary, (5) is a nearly trivial consequence of BS, and BS is entailed by LMR. But we should take care to note that (5) does not commit us to the following:

Domain Existence Principle (DEP): For all individuals x, features F, and domains d, if 'x is F' under the intended interpretation is true at d, then x is a member of/part of/among d.

Consider the spatial case: It's plausible that a proposition that is true at any place is true at every place. (I'm assuming that sentences under intended interpretations are sentences associated with propositions.) So 'Joshua has a head' expresses something that is true at my living room, but, unfortunately, Joshua and his head are not located within (are not members of/are not parts of/are not among the plurality of things in) my living room. So DEP is false.

A more controversial instance of DEP is MEP:

Modal Existence Principle (MEP): For all individuals x, features F, and worlds w, if 'x is F' under the intended interpretation is true at w, then x is a member of/part of/among w.

I think the proponent of LMR should reject (MEP) as well. Lewis does as much in "Postscript to CT and QML": he says that something can be in a world by being either a part of that world, by having a part that is part of that world, or by "belonging to the least restricted domain that is normally--modal metaphysics being deemed abnormal--appropriate in evaluating the truth in that world of quantifications." (Postscript pp. 40 in Phil Papers I.)

So properly understood, (5) amounts to the claim that blue swans are a part of the totality of what is. And that is no shocker, given LMR.

What I take to be the second best response for proponents of LMR and QML basically endorses the first response but adds something about semantic context-sensitivity of quantifier expressions. Since I believe this view is false, I do not believe it is part of the best response. But it also certainly would be part of the story for Lewis, were he to convert to QML and retain LMR.

But what should Lewis say? Lewis was no fan of QML. But we can begin by noting that Lewis recognized that 'Everything actual necessarily exists' comes out true even if something actual lacks a counterpart in another world. Since nothing is special about actuality in obtaining the result, we can obtain a parallel result for w: blue swans are a part of w. So given this, and that Lewis rejects (MEP), one response for Lewis would be just to accept the replies I suggested on behalf of the proponent of QML.

But I don't think Lewis's more mature view would accept that everything actual exists necessarily. In Plurality, Lewis says:

"According to what I said, . . . Humphrey satisfies 'necessarily x exists' and fails to satisfy 'possibly x does not exist' iff he has no counterpart at any world W who does not exist at W. but what can it mean to say that the counterpart is 'at W' if not that, at W, the counterpart exists? So it seems that Humphrey does satisfy 'necessarily x exists' and doesn't satisfy 'possibly x does not exist'. That is wrong. For all his virtues, still it really will not do to elevate Humphrey to the ranks of the Necessary Beings."

"What I want to say, of course, is that Humphrey exists necessarily iff at every world he has some counterpart, which he doesn't; he has the possibility of not existing iff at some world he lacks a counterpart, which he does. It's all very well to say this; but the problem is to square it with my general account of the satisfaction of modal formulas."

". . . Shall we dump the method of counterparts? --That wouldn't help, because we can recreate the problem in a far more neutral framework. . ."

"What is the correct counterpart-theoretic interpretation of the modal formulas of the standard language of quantified modal logic? -- Who cares? We can make them mean whatever we like. We are their master. We needn't be faithful to the meanings we learned at mother's knee--because we didn't. If this language of boxes and diamonds proves to be a clumsy instrument for talking about matters of essence and potentiality, let it go hang. Use the resources of modal realism directly to say what it would mean for Humphrey to be essentially human, or to exist contingently." (pp. 10-13)

So let's take Lewis's advice and use the resources of modal realism directly: 'Necessarily blue swans exist' is false because at some worlds, nothing that is a part of those worlds is a member of the set of blue swans. (Things are complicated somewhat by not just considering an individual, but I don't think this affects any point I want to make substantially.)

But transworld individuals, like the fusion of all possible worlds (reality itself) is in any world by the account of being in a world given in "Postscript" and quoted above. So 'LMR is necessarily true' is true in CT. But this corresponds to the acceptance of the CT translation for (4) above, along with the denial of the CT translation for (5). So given (1), Lewis must reject N or K. I'm thinking if one has to go, it's K.

Lewis might not sweat this much. His dim view of QMP was registered in the above quote, and elsewhere in "Postscript" (pp. 45 in Phil Papers I) he says "if counterpart theory calls for the rejection of some popular modal principles, that needn't worry us." And K is (ahem!) popular. So maybe this is a question of how we proponents of QML should understand Lewis on this issue rather than the basis of some sort of crippling objection to him.

On the other hand, saying things in English that correspond to instances of K sound like ways to say something true in English. We can again follow Lewis and use the resources of LMR directly to say what they mean, but I don't see how we could say something that is compatible with (1), the CT translation of (4), and the CT translation of (5). So I guess I do think there's a problem for him here.

The only other clear option that I see is to cop out and say that when writing Plurality, in particular in the quoted section, his quantifiers were restricted so he said something true when he said that it just wouldn't do to elevate Humphrey to the status of the Necessary Beings. This, I think, would amount to adopting a version of the second strategy for proponents of LMR and QML.

(There are some other options, those disappointments Lewis mentions for a "friend of boxes and diamonds" on pp. 12 of Plurality. I am assuming he does not want any of those disappointments for himself and believes he can avoid them.)

The Vagueness of 'Very'

2007-05-02T06:50:00.000-07:00

Since nothing's been posted around here recently, I thought I'd post something in an attempt to stimulate conversation. The topic of the post is the vagueness, or lack thereof, of 'very'. Joshua, Andrew, and I discussed this on the way to Syracuse last week, so I'd especially like to get the opinions of others. But Joshua and Andrew are also encouraged to register their thoughts, of course.

It is clear that many predicates of the form 'very F' are vague. For instance, there seem to be borderline cases of being very tall, very nice, and so forth. What is at issue is whether the vagueness of expressions of this form is due at all to the vagueness of 'very' or whether in all such cases the vagueness is due to the adjective 'F' to which 'very' attaches. Or, in other words, the question is whether 'very' is vague at all.

One way to show that 'very' is vague is to discover an adjective 'F' such that 'F' is not vague but 'very F' is vague. Since the vagueness of 'very F' could not then be due to the vagueness of 'F', it must be due to the vagueness of 'very'. But are there any such adjectives?

On the way to Syracuse, Joshua, Andrew, and I puzzled over this for a bit. We each came up with different candidates for an adjective meeting the above condition, but many of the proposed candidates were either plainly vague or not clearly nonvague. However, one of us then suggested 'late'. This seemed like a plausible candidate. It seemed to us that 'late' is not vague but 'very late' is vague.

I would like to know what the rest of you think about this case. I would also like to know whether any of you can come up with a spatial adjective 'F' that seems not to be vague but is such that 'very F' is vague. (One might expect that if there is a temporal adjective, like 'late', that has this feature, then there is a spatial adjective that has it as well.) In addition, I would like to note that some (for instance, Peter Unger) have thought that adjectives like 'flat' are not vague, claiming that a necessary condition on something's being flat is that nothing could be flatter than it. But presumably 'very flat' is vague. Is 'flat' another plausible example that can be used to show that 'very' is vague? (I'm inclined to think not, since I think that Unger was mistaken. But I'm wondering what the rest of you think.)

Pro-Attitude Theology

2007-04-16T12:53:00.000-07:00

In this post I'd like to discuss an issue I've discussed in more detail on my personal blog, The GLFer. Those who would like more details are encouraged to look at what I have written there.

First, the background. Western philosophical theology has been dominated by a certain approach to theology often called "perfect being theology". The central concept of perfect being theology is that of a great-making property, where a property is said to be great-making iff all other things being equal, something is greater if it has that property than if it lacks that property. (Great-making properties can be conceived of via analogy to intrinsically good-making features.) Given this concept, proponents of perfect being theology claims that something is divine iff it has every great-making property to the highest degree. And, of course, they claim that there is something that is divine. The central question, then, of perfect being theology is whether there is something that has every great-making property to the highest degree.

I would like to propose an alternative to perfect being theology. The alternative is what I call "pro-attitude theology". There are two versions of pro-attitude theology that I would like to discuss, a simpler one (addressed in my post on The GLFer entitled "Pro-Attitude Theology Redux") and a more complex one (addressed in "Perfect Being Theology and Pro-Attitude Theology). The central concept of both versions of pro-attitude theology, however, is the same. It is the concept of a pro-attitude worthy property, where a property is a pro-attitude worthy property iff there is some pro-attitude such that all other things being equal, something that has that property deserves to have that pro-attitude borne to it.

According to the first version of pro-attitude theology, something is divine iff there are some pro-attitude worthy properties such that it has those properties and because it has those properties it deserves having every pro-attitude borne to it to the highest degree. According to the second, on the other hand, something is divine iff it has every pro-attitude worthy property and for every pro-attitude worthy property P that it has and every pro-attitude A, if all other things being equal, something that has P deserves having A borne towards it, then it has P to such a degree that it deserves having A borne towards it to the highest degree. I take it that it is obvious how to construct the central questions of both versions of pro-attitude theology.

There is one interesting difference between the first version of pro-attitude theology and the second. The difference is that, on the first version, there may be different "ways of being divine". For one thing might be divine in virtue of having certain pro-attitude worthy properties while something else is divine in virtue of having other pro-attitude worthy properties. On the other hand, on the second version of pro-attitude theology, there aren't different ways of being divine. This is because each divine being has every pro-attitude worthy property according to the second version and has that property to whatever degree is necessary to make it the case that it deserves to have the corresponding pro-attitude borne to it to the highest degree.

Let me close with some remarks about my motivation for introducing pro-attitude theology as an alternative to perfect being theology. I do not do so because I find it plausible that there is a being that is divine in the pro-attitude theology sense although there is no being that is divine in the perfect being theology sense. I find it likely that there is no being that is divine in either sense. However, I think that it is worthwhile investigating this alternative to perfect being theology because I think that just as it is an interesting question whether there is a divine being in the perfect being theology sense, it is an interesting question whether there is a divine being in the pro-attitude theology sense. And whereas philosophical theologians in the Western tradition have addressed the first question, they have not addressed the second. In addition, it is an interesting question whether an affirmative answer to either the central question of perfect being theology or the central question of pro-attitude theology has any religious significance. Finally, one interesting question of perfect being theology is what properties a being must have in order to be divine; or, in other words, what properties are great-making and what does having these properties to the highest degree entail? Similarly, I think, it is an interesting question what properties a being must have in order to be divine in the (second version of) pro-attitude theology sense; in other words, what properties are pro-attitude worthy properties and to what degree does something have to have each of those properties in order to deserve to have the corresponding pro-attitude borne to it to the highest degree?

What does it take to believe a proposition?

2007-04-04T11:06:00.000-07:00

Just yesterday I read about a recent Newsweek poll according to which almost half of Americans deny the theory of evolution and over a third of college graduates believe that the Biblical creation story is true. These finding are, of course, rather disturbing for many reasons that I do not plan on going into here. But they got me thinking about a different issue: If someone were to ask me to state what the theory of evolution is, I don't think that I would be able to. I know the following: There is a theory, the theory of evolution, such that most scientists believe it be true because, they say, it is the best explanation of a number of facts of various sorts (biological, geological, etc.). Presumably I can, on the basis of the evidence I have, come to know (or at least reasonably believe) that the theory of evolution is true and that the theory of evolution is the best explanation of a number of facts of various sorts. However, given that I am unable to state what the theory of evolution says, it seems that I am unable to know or reasonably believe the theory of evolution itself since it seems that I am unable to believe that theory at all.

Let me make a few clarificatory remarks. I accept latitudinarianism about de re belief. In other words, I think it is very easy to have beliefs about particular things. If there is a shortest spy and I introduce the name 'Shorty' by saying "Let 'Shorty' refer to the shortest spy", then I can believe things about the shortest spy; that is, I can believe things about the guy out there who is the shortest spy. For instance, I can believe that he is the shortest spy, that he is less than 6' tall, and so forth. In other words, on my view de re belief is really easy. (I should note that I also think that so-called de rebus belief is really easy as well. If there are some spies that are shorter than 6' tall and I introduce the plurally referring name 'Shorties' by saying "Let 'Shorties' refer to the spies that are shorter than 6' tall", then I can believe things about the spies who are shorter than 6' tall. For instance, I can believe that they are the spies that are shorter than 6' tall, that each of them is shorter than 6' tall, and so forth.)

I take it that many non-latitudinarians would deny that I can have any beliefs about the theory of evolution at all because I am not well enough "acquainted" with that theory to have such beliefs. I deny this since I think that I do have beliefs about the theory of evolution; for instance, I believe that it is true. So, the issue I'm raising here is not an issue concerning whether I can have beliefs about the theory of evolution. I think that I can have such beliefs. Rather, the issue is whether I can believe the theory of evolution, given my ignorance concerning how to state it.

It will, perhaps, be helpful when considering this question to take scientific theories to be conjunctive propositions. (Or, perhaps, sets (or pluralities) of propositions. If they are sets (or pluralities) of propositions rather than propositions, then I take it that someone believes a scientific theory just in case he believes each of its members (or just in case he believes each proposition that is one of the scientific theory) and a scientific theory is true just in case each of its members are true (or just in case each proposition that is one of the scientific theory is true).) I take it that it is only if we take scientific theories, such as the theory of evolution, to be propositions that it makes sense to talk, as we usually do, about believing a scientific theory (modulo my remarks about sets or pluralities of propositions). So let us assume, for the sake of argument, that scientific theories are conjunctive propositions.

(I should note that the view that scientific theories are conjunctive propositions (or sets or pluralities of propositions) is a controversial one. As far as I am able to discern from the philosophy of science I've learned, many philosophers of science reject this view. Some hold rather that scientific theories are a set methods for explaining phenomena. I do not have space to do this view justice. However, it seems to me that this view has a difficult time making sense of the way we speak about scientific theories; in particular, it has difficulty making sense of the fact that we often talk about believing scientific theories and we often talk about scientific theories as being true or false.)

Back to the main line of argument. I claim that although I can have beliefs about the theory of evolution, which I take to be some particular conjunctive proposition, I cannot believe the theory of evolution given my inability to state that theory. Is this so?

Here is a sort of argument for my view. Suppose that there is a language of thought. Call it "Mentalese". Someone believes a proposition just in case he or she has a Mentalese sentence that expresses that proposition in his or her belief box. A Mentalese sentence expresses a proposition only if its syntactic structure corresponds to the structure of that proposition, its syntactic constituents express the constituents of that proposition, and its syntactic constituents are arranged in the right way. (I add the last clause because, presumably, the Mentalese sentence that expresses the proposition that John loves Mary and the Mentalese sentence that expresses the proposition that Mary loves John have the same syntactic structure and their syntactic constituents each express the constituents of both propositions.) Now it seems to me that the fact that I am unable to state the theory of evolution provides good evidence to think that I have no Mentalese sentence in my belief box expressing the theory of evolution that satisfies these conditions and thus provides good reason to think that I have no Mentalese sentence in my belief box that expresses the theory of evolution.

Notice that this is not to say that I have nothing in my belief box that expresses the theory of evolution. I think I do. In particular, I think that I have a Mentalese singular term that expresses the theory of evolution and that, in virtue of this, I am able to believe things of the theory of evolution. However, this is not sufficient to allow me to believe the theory of evolution, I say, because surely there will be syntactic rules specifying which Mentalese expressions are sentences (well-formed formulas, if you like) according to which a Mentalese singular term is not a Mentalese sentence. And, as I have claimed, one can only believe a proposition if one has a Mentalese sentence in one's belief box that expresses that proposition.

Anyway, what do the rest of you think? What does it take to believe a proposition? Do I believe the theory of evolution or simply believe that it is true?

The Mere Addition Paradox

2007-03-28T11:52:00.000-07:00

In this post, I formulate the Mere Addition Paradox, a paradox in so-called "population ethics". I would like to know what others think of the paradox.

Consider the following three possible populations:
Population A: A population of 10,000 people each of whose level of well-being is +100,000
Population A+: A population of 20,000 people, 10,000 of whom have a level of well-being of
+100,000 and the other 10,000 of whom have a level of well-being of +90,000
Population B: A population of 20,000 people each of whose level of well-being is +95,000
(I should explain what I mean by "well-being" here. The well-being of an individual is simply how well things go for that individual. The well-being of one individual is greater than the well-being of another individual just in case things go better for the first individual than they do for the second individual.)

There are then two versions of the Mere Addition Paradox:

Mere Addition Paradox (Version 1)
1. The existence of Population A+ is better than the existence of Population A.
2. The existence of Population B is better than the existence of Population A+.
3. If (1) and (2), then the existence of Population B is better than the existence of Population A.
4. Therefore, the existence of Population B is better than the existence of Population A.

Mere Addition Paradox (Version 2)
1*. The existence of Population A+ is just as good as the existence of Population A.
2. The existence of Population B is better than the existence of Population A+.
3*. If (1) and (2), then the existence of Population B is better than the existence of Population A.
4. Therefore, the existence of Population B is better than the existence of Population A.

Premise (3) is justified by appeal to the transitivity of being better than: For all x, y, and z, if x is better than y and y is better than z, then x is better than z. Premise (3*) is justified by appeal to the slightly different principle that for all x, y, and z, if x is just as good as y and z is better than y, then z is better than x. On the assumption that both of these principles are true, the two versions of the Mere Addition Paradox show that whether we accept premise (1) or premise (1*), so long as we accept premise (2) we get the conclusion that the existence of Population B is better than the existence of Population A.

I have already stated why one might accept premises (3) and (3*). Why might one accept premises (1), (1*), and (2)?

Let's begin with (2). The reasoning for two goes as follows: The existence of Population B is better than the existence of Population A+ because the average level of well-being does not differ between the two populations and Population B is more equitable than Population A+. Assuming that equality is a good-making feature of a population, then, the existence of Population B is better than the existence of Population A+.

What about premises (1) and (1*)? Few have attempted to argue for one of these over the other, preferring to argue instead for disjunction. But arguing for their disjunction is good enough, since which of the disjuncts is true doesn't matter for the success of the argument. If (1) and (2) are true, then (given (3)), the conclusion follows and if (1*) and (2) are true, then (given (3*)), the conclusion follows. So, why believe the disjunction of premises (1) and (1*)? Well, it seems that merely adding some people with high well-being to a population each of whose members has even higher well-being can't make the existence of the resultant population worse than the existence of the original. After all, presumably the existence of people with high well-being is a good thing and so cannot detract from an already good thing. Thus, either the existence of Population A+ is better than the existence of Population A or the existence of Population A+ is just as good as the existence of Population A.

Let me end by saying why the Mere Addition Paradox is supposed to be paradoxical. Consider Population B+, a population of 40,000, 20,000 of whom have a level of well-being +95,000 and 20,000 of whom have a level of well-being of +85,000. By reasoning similar to the reasoning in favor of the disjunction of premises (1) and (1*), the existence of Population B+ is either better than or just as good as the existence of Population B. But then, by reasoning similar to the reasoning in favor of premise (2), the existence of Population C (a population of 40,000 people each of whose level of well-being is +90,000) is better than the existence of Population B+. So, by reasoning similar to the reasoning in favor of premises (3) and (3*), the existence of Population C is better than the existence of Population B and hence, since the existence of Population is better than the existence of Population A, the existence of Population C is better than the existence of Population A. By repeated applications of the same sort of argument, then, we reach the conclusion (sometimes called "The Repugnant Conclusion") that the existence of a large population each of whose members has the same very low positive level of well-being is better than the existence of Population A.

So, what do you all think of this paradox? What should one say to the arguments? Should one accept that the existence of a very large population each of whose members has a very low positive level of well-being (described by some as having a life barely worth living) is better than the existence of a smaller population each of whose members has a very high level of well-being? If not, what should one say against the reasoning in favor of that conclusion?

[I should note before closing that the premises and conclusion of the arguments should probably include ceteris paribus clauses. That is, we are wondering about whether the existence of Population B is better than the existence of Population A assuming that the only relevant difference between the two populations is how many people they contain and the level of well-being each person has. I should also note that if you want to find out more about the Mere Addition Paradox and potential solutions to it, you should look at the SEP's entry entitled "The Repugnant Conclusion": http://plato.stanford.edu/entries/repugnant-conclusion/]

Is looking the same as transitive?

2007-03-27T05:45:00.000-07:00

Is the following thesis true?:

Transitivity of Looking the Same As: For all w, x, y, and z, if x looks the same as y to w and y looks the same as z to w, then x looks the same as z to w.

Many philosophers have denied this thesis. However, the following argument appears to be a compelling argument in its favor:
1. Let w, x, y, and z be arbitary individuals and suppose that x looks the same as y to w and y looks the same as z to w.
2. For all x, y, and z, x looks the same as y to z iff the way x looks to z is the same as the way y looks to z.
3. For all x, y, and z, the way x looks to z is the same as the way y looks to z iff the way x looks to z=the way y looks to z.
4. The way x looks to w=the way y looks to w and the way y looks to w=the way z looks to w. [From (1),( 2), and (3)]
5. For all x, y, and z, if x=y and y=z, then x=z.
6. The way x looks to w=the way z looks to w. [From (4) and (5)]
7. x looks the same as z to w. [From (2), (3), and (6)]
8. For all w, x, y, and z, if x looks the same as y to w and y looks the same as z to w, then x looks the same as z to w. [(1)-(7), conditional proof]

What, if anything, should one say to this argument in favor of the Transitivity of Looking the Same As? Should we accept its conclusion? Deny one of its premises? If deny one of its premises, which one?

[Delia Graff Fara seems to present such an argument in her "Phenomenal Continua and the Sorites", available at http://www.princeton.edu/~graff/papers/mindcontinua.pdf]

God and Ethics

2007-03-08T12:41:00.000-08:00

Some theists seem to think that there is an important connection between God and ethics, although those who are not philosophically trained often have a difficult time articulating what they take the connection to be.

One suggestion is that these theists accept some form of divine command theory (DCT) according to which the property of being right just is the property of having been commanded by God. However, this form of DCT is problematic. There are, for instance, Euthyphro-type worries. And, in addition, there is the worry that the property of being right and the property of being commanded by God are not necessarily extensionally equivalent, and so not identical. Whether or not one is persuaded by these objections, it is interesting to explore other options concerning what the connection between God and ethics might be.

Another suggestion is that whereas theists can be motivated to do what is right, atheists cannot. Unfortunately, this suggestion fails empirically. There clearly are atheists who are motivated to do what is right, and thus can be motivated to do what is right.

This leads me to my suggestion concerning what such theists should say: Whereas theists are rational in being motivated to do what is right, atheists are not rational in being motivated to do what is right. (This suggestion presupposes that it makes sense to say that someone is rationally motivated to do something. Those who do not agree needn't read any further.) Let's flesh out the suggestion. Suppose that we believe that people are sometimes rational in being motivated to do something. We might adopt an analogue of foundationalism for rational motivation according to which some of our motivations, our basic motivations, are simply rational regardless of their relation to other motivations but that other motivations are rational because they are supported by our basic motivations. If we adopt this view, which we might call "motivational foundationalism", a theist might say the following: There is a basic motivation to avoid suffering, but there is not a basic motivation to do what is right. Theists may be rational in being motivated to do what is right because they are rationally motivated to avoid suffering and they believe (rationally?) that if they do what is right they will avoid suffering (as they will avoid Hell). However, atheists cannot be rational in being motivated to do what is right because there are no basic motivations and beliefs that they have that jointly make it rational for them to be motivated to do what is right. So, whereas theists are rational in being motivated to do what is right, atheists are not.

It seems to me that this is an interesting suggestion concerning what a theist might mean when he or she claims that there is an important connection between God and ethics. It does not suffer from the same worries that DCT and the claim that atheists cannot be motivated to do what is right suffer from. On the other hand, it is not very well-developed. To develop it a theist would have to give accounts of rational motivation and of basic motivation that supports his or her claim that an atheist cannot be rationally motivated to do what is right. Regardless, I take it that this would be an interesting undertaking for a theist who was convinced that there is an important connection between God and ethics. Not only that, but any motivational foundationalist, whether a theist or an atheist, should be interested in giving a theory of basic motivation. And if that motivational foundationalist is an atheist, then he or she should be interested in explaining how an atheist can be rationally motivated to do what is right.

Arguments and Evidence

2007-03-08T12:10:00.000-08:00

The following principle seems plausible:

Arguments and Evidence (AE): Necessarily, for all x and y, if x is a valid argument and y has evidence for each of x's premises, then y has evidence for x's conclusion.

After all, we are concerned with valid arguments because we are concerned with evaluating evidence for and against different claims. Using valid arguments helps us to determine whether we have evidence for their conclusions, and the reason for this seems to be that valid arguments are evidence-preserving: If we have evidence for the premises of a valid argument, then we have evidence for its conclusion.

However, (AE) also seems to have implausible consequences. For instance, suppose that, at time t1, Alan's total evidence supports each of the premises of a modus ponens argument:
1. P
2. If P, then Q.
3. Therefore, Q.
Then, at t2, Alan gains some additional evidence without losing any of his previous evidence and that the evidence he has gained makes it the case that, at t2, his total evidence, while still supporting that if P, then Q, supports the negation of P. In addition, the evidence Alan gains at t2 does not support the negation of Q. Surely such a case is possible. But if (AE) is true, then it follows that, at t2, Alan has evidence in favor of Q, since he still has evidence in favor of P and if P, then Q, since he has not lost any of the evidence he previously had. Making certain other plausible assumptions, it also follows that Alan has just as much evidence in favor of Q at t2 as he had at t1. And this seems implausible. Are we then to reject (AE)?

One suggestion would be that we should reject (AE) and replace it with:

Arguments and Total Evidence (ATE): Necessarily, for all x and y, if x is a valid argument and y's total evidence supports each of x's premises, then y has evidence for x's conclusion.

However, (ATE) cannot do all of the explanatory work that (AE) did. For instance, consider the following argument:
1. The fact that the physical constants allow for the existence of life is more probable given theism than given atheism.
2. If (1), then theism is true.
3. Therefore, theism is true.
I take it that I have some evidence in favor of each of the premises of this argument and that because of this, I have some reason to believe its conclusion. However, I also believe that my total evidence supports the negation of premise (2). So, (ATE) does not help to explain why I have evidence in favor of the conclusion of this argument, whereas (AE) does. Thus, (ATE) cannot do all of the explanatory work (AE) did.

Let me end with some questions: Is (AE) false, as I have suggested? Are the reasons I have given to think that (AE) is false convincing? If (AE) is false, can we replace it with a principle that does not have its implausible consequences and yet still explains my situation with respect to the fine-tuning argument mentioned above and other such situations? More generally, what is the relationship between valid arguments and evidence?

Sextus Empiricus', I mean Hume's, Problem

2007-03-02T13:14:00.000-08:00

Okay so I apologize for the epistemology, but here comes some. Recall Hume's problem of induction: Either principles of induction are justified inductively or deductively. Principles of induction (like x% of observed As are Bs so x% of unobserved As are Bs) are not necessary truths, so they are not justified deductively. But justifying them inductively is viciously circular; so they are not so justified.

One can extend this argument as follows: If inductive principles are not justified, then nothing is justified inductively. But deduction is justified either inductively or deductively. And it's not justified deductively since that would be circular. So deduction is not justified.

Rich considers the former, but not the latter, argument in his book. His take on it is that inductive principles like the above are not justified inductively or deductively. But there are necessary a priori truths like 'knowing that x% of observed As are Bs gives one a reason to believe that x% of unobserved As are Bs' that justify inductive inferences. One can then block the extended argument by denying that nothing is justified inductively.

I am attracted to the claim that there are a priori truths that justify inductive inferences. What worries me is that it is not very plausible to suppose that deduction is justified inductively. So it seems that, ultimately, pressure must be put on the 'that's circular' part of the argument. But circular reasoning is bad, right?

It strikes me that there are a couple of options here: distinguish good and bad circularity and say why the justification of deduction involves the former, hold that any justified deductive principle stands in an infinitely long chain of reasons, or hold that there are justified basic beliefs that justify deductive principles (maybe those principles themselves are such beliefs). But these are exactly the options at play in the familiar infinite regress argument concerning the structure of justified beliefs--the only difference is that the familiar arguments focus on empirical beliefs.

I think foundationalism is just as plausible in the a priori case as in any other. But I won't plump for that here. I am more interested in whether the following are correct:

(A) Coherentism is an attempt to distinguish good and bad circularity for empirical beliefs. But coherentism seems especially implausible when brought to bear on a priori beliefs about principles of induction and deduction. This is because conditions on coherence typically include things like a requirement that the relevant propositions "jointly probabilify" each other and that they are logically consistent.

More interestingly:

(B) At bottom, Hume's problem of induction does not raise any problem not solved by a sufficiently adequate response to the infinite regress problem. It's really just a special case of that problem--not a fundamentally different one, as has been traditionally supposed.

Word?

Suppose you're not Joshua.

2007-02-19T13:21:00.000-08:00

Okay so here's a question that I've only thought a little about, but it seems important and underexplored in the philosophy of perception (not my AOS, so it might not in fact be underexplored). First, suppose you are not Joshua. Provided this supposition obtains, you believe that there are illusions. Cases of visual illusions abound. And illusions differ from hallucinations. What I wonder is to what extent there are cases of illusion for non-visual sensory modalities. I take it that examples of hallucinations are fairly easy to come by in many cases, but illusions seem to be much more rare. So are there compelling examples of haptic, kinesthetic, auditory, gustatory, or olfactory illusions?

Mass Terms

2007-02-14T07:22:00.000-08:00

Suppose that there is a single gold atom lying on a table, T. In such a situation, is the following sentence true?:

(G) Some gold is on T.

I'm curious about this because, in many ways, mass terms seem to behave a lot like plurals. Suppose, for instance, I have some gold and this gold is subsequently scattered. Then the gold I had still exists, although it has been broken up into different portions of gold. Similarly, if I have some coins, those coins still exist even if they become scattered.

A natural proposal, then, is to take (G) to be true in just the same circumstances as:

(A) Some gold atoms are on T.

But if (G) is true in just the same circumstances as (A), then (G) should be true in the circumstances described above, in which there is only one gold atom on T.

I suppose that this train of thought leads to the idea that the mass term "gold" means the same thing as "gold atoms", or something along those lines, along with some sort of explanation of why "is" is appropriate in (G) but "are" is appropriate in (A). And perhaps such an idea could be extended to other mass terms as well.

So, what do you guys think about (G) and (A) and what do you think about mass terms?

(Real) Time Travellers Should Believe in Presentism

2007-02-13T12:40:00.000-08:00

Okay so this is really inchoate, but I figured that's sorta what this is for. As far as I know, most philosophers are comfortable with the metaphysical possibility of Lewisian time travel. Lewisian time travel is just time travel as Lewis characterized it; roughly, a discrepancy between personal time and (external) time. I think this notion is perfectly coherent, but it does not capture another idea that seems probably worthy of the name 'time travel'. It's this. Often, as a kid, I wished I could go back and redo something I did in a different way. This usually happened when I got in trouble for doing something stupid and I deeply desired that I could undo my mistake. (I have wished similar things as an adult, but it occurred much more frequently when I was a kid.) It seems like something that I wanted to do might be naturally described as going back in time and doing things differently. Now forget whether I could do things differently without causing contradictions to be true for now. Note that the sort of time travel I wanted to do was not Lewisian time travel. I did not want my older self to go back and aid my younger self. I wanted to relive the experience (and change its outcome). In semi-Lewisian terms, I wanted to make some earlier personal time present again. It would have been cool, but not at all what I wanted, for a later "stage" of me in personal time to be simultaneous with a younger "stage" of me. (4d talk makes this easier to describe, but I use scare quotes to distance myself from the view--I don't think that one needs to accept stages, etc in order to make sense of all this.)

So: Whatever kind of time travel this is, it's not Lewisian time travel. Call it 'Real time travel', for lack of a better name.

My problem is this. I believe Real Time Travel is a coherent notion. But I cannot for the life of me make sense of it without invoking A-properties. It seems that A-properties are needed to even make sense of Real Time Travel.

Furthermore, if I can engage in Real Time Travel and change what happened, then it seems to me some version of presentism must be true. Here I am assuming the following:

a. Travel in 2d time is not sufficient for time travel.
b. Branching universe is not sufficient for time travel.
c. It is not the case that in every possible case in which Real Time Travel occurs, the time traveller is just mistaken about what happened "the first time around" (so as to avoid contradiction between H's happening at t "the first time around" and H's not happening at t "the second time around".

So I guess I think that someone who is on board with (a-c) and thinks Real Time Travel is possible should be a presentist. But I am not a presentist and I am inclined toward (a-c) and the possibility of Real Time Travel. Help!

Saul Kripke: The Movie

2007-02-13T12:32:00.000-08:00

Just in case one of you didn't hear about it.

A related Point about mereology

2007-02-13T07:44:00.000-08:00

This is related to my last post. So, I suggest reading that post before reading this one.

I was wondering if a similar Salmon like view might lead us toward the view that certain conversational activities on the parts of classical mereologists result in certain activity dependent entities and an activity dependent part/whole-like relation that satisfy classical extensional mereology.

The idea would be that there is a relation expressed by ' is a part of' in the mouths of classical mereologists. This is not the relation expressed by ordinary english speakers (well probably not). Rather it is an activity dependent relation similar to the property 'is a unicorn' or 'is deposited in' (as used with respest to chacking accounts. Moreover, there are certain activity dependent entities that stand in this relation to other entities (some of them are activity dependent and others are not). Thus, the classical mereologists expresses a truth, in some strange language, when he says "there is something that both Chris and the Eiffel tower are a part of".

Such a view would have the following strange problems. Just by engaging in some activities, the classical mereologists will make it such that the number of entities in the universe is 2^n-1. But, it doesn't seem like anyone could have that kind of power. Also, certain mereologists can make it such that there are no omniscient beings or other kinds of entities (because of Rosen-like worries). But, how could any mereologists have that kind of power.

Finally, I worry that this entire enterprise of using activity dependant beings to solve various philosophical problems is going to lead down a slippery slope to a stupid kind of view according to which all sorts of seemingly metaphysically robust entities are just mind dependant. Are we, going to slide into a stupid Lockean view about properties for example? That would seem like a bad consequence.

The average philosopher disbelieves this thesis

2007-02-13T07:42:00.000-08:00

I take it most of us agree that some form of compositionality is true and that many of us have an aversion to paraphrase strategies. Nonetheless, even amongst those philosophers who share our commitments and aversions there are few, if any, who would accept that we should take phrases of the form ‘the average F is G’ at face value. Most of them will say either than it is literally false and conveys the some truth or other about philosophers or that it simply means the same thing as a truth that has a radically different grammatical structure. I wish to present a strategy for taking phrases of the form ‘the average F is G’ at face value.

Nathan Salmon, and others, have defended the view that certain activities give rise to certain kinds of mentally and socially dependant entities. For example, worship-like activities in ancient Greece gave rise to a particular kind of entity. These philosophers also think that some such entity is the referent of ‘Zeus’ in our mouths. I think that Salmon says, a bit more controversially, that some such entity is the referent of ‘Zeus’ in the mouths of the ancient Greeks.

The view sometimes seems a bit less crazy if we note that these entities are much like bank accounts. Few people would believe that bank accounts are physical objects. Rather, bank accounts seem to be entities the existence of which is dependant upon certain human activity.

I would like to suggest that the same strategy might be adopted to provide satisfiers to phrases of the form ‘the average F is G’. On this view, there would be an entity that arises from certain human activities and it is this entity that makes it true that the average philosopher has read Russell. This entity is the average philosopher. It is not itself a philosopher. But, the activities that give rise to its existence require that, for example, if the average philosopher has read Russell, then a randomly chosen philosopher will have read Russell. That is, there are interesting relations that obtain between the average philosopher and real philosophers.

Here is a problem for the view. Suppose that the average philosopher has 1.6 children. If the view suggested above is true, then it seems to follow that something has 1.6 children. It also seems to follow that there is an average philosopher. But, surely there is no thing that has 1.6 children and there is not average philosopher.

I am not sure how best to respond to this problem. I guess my first inclination is to adopt a kind of Meinongianism. I would reject that there is an average philosopher. This would require rejecting the seemingly plausible thesis that any instance of the following schema expresses a truth:

(S1) ‘Necessarily, if the F is G, then there is exactly one F and it is G.’

One idea might be to make a distinction, as Priest does, between the ‘there is’ quantifier and the ‘some’ quantifier. We might replace the schema above with the folloing:

(S2) ‘Necessarily, if the F is G, then some F is G and only one F is G.’

But, this doesn’t seem to get at the heart of the matter either. Although such a distinction allows us to avoid the inferences noted above, it doesn’t allow us to avoid the following inference: The average philosopher has read Russell. So, some average philosopher has read Russell. Moreover, (S2) just doesn’t sound quite right (even when we use some standard instances of the definite description).

I guess I would suggest rejecting any unrestricted schema like (S1) and (S2). But, I am not sure how plausible this is. So, I guess my questions to the crowd are the following: are there any more unhappy consequences of this view? Do the happy consequences outweigh the unhappy ones? And, relatedly, is it better to just say sentences of the form ‘the average F is G’ are just plain false but convey a truth?

Are the Following Sorts of Situation Possible?

2007-02-08T06:46:00.000-08:00

So, I talked about this with Joshua and Andrew a bit yesterday on th way to Syracuse, but I thought it might be interesting to post about it here and get reactions from all of you.

Is it possible for there to be someone such that he should perform each of actions A1-An, but shouldn't perform all of those actions? That is, is it possible for there to be an agent S and actions A1-An such that all of the following are true?:
(1) S should perform A1.
:
(n) S should perform An.
(n*) S should not perform A1, ..., and An.

Alternatively, is it possible for there to be someone such that he should perform all of actions A1-An, but shouldn't perform each of these actions? That is, is it possible for there to be an agent S and actions A1-An such that the following is true:
(n**) S should perform A1, ..., and An.
but one of the following is false?:
(1) S should perform A1.
:
(n) S should perform An.

Let me make these questions a bit more pressing by mentioning a slight variant on a principle employed by Peter Singer in "Famine, Affluence, and Morality":
(PS) If it is in one's power to perform an action A and if one is able, in performing A, to prevent something bad from happening without thereby sacrificing anything of comparable moral significance, then one should perform A.
Now it seems possible that there be two actions, A1 and A2, such that (i) it is in one's power to perform A1, (ii) it is in one's power to perform A2, (iii) it is in one's power to perform both A1 and A2, (iv) one is able, in performing A1, to prevent something bad from happening without thereby sacrificing anything of comparable moral significance, (v) one is able, in performing A2, to prevent something bad from happening without thereby sacrificing anything of comparable moral significance, and (vi) one is not able, in performing both A1 and A2, to prevent something bad from happening without thereby sacrificing anything of comparable moral significance. It seems that, if (PS) is true, then one should perform A1 and one should perform A2. However, it is plausible (although (PS) doesn't have this consequence) that, in such a situation, that one should not perform both A1 and A2. So, assuming the truth of (PS) and assuming the plausible judgment just mentioned, this is a case of the first sort mentioned above.

Anyway, what do you guys think?

A Simple Argument for a Fact/True Proposition Dichotomy

2007-02-02T11:40:00.000-08:00

The proposition that Andrew is male, it seems, is true in virtue of the fact that Andrew is male. (This seems like a perfectly good sentence of English, and I would expect that an ordinary English speaker would, if queried, agree to its truth.) However, this claim, call it 'C', spells trouble for the following thesis that I have been inclined towards:

Facts are True Propositions (FTP): For all S, if S is true, then the fact that S is the true proposition that S.

To illustrate a bit, if (FTP) is true, then the fact that snow is white is simply the proposition that snow is white, since that proposition is true and the fact simply is the corresponding true proposition.

Anyway, why does C spell trouble for (FTP)? Well, consider the following argument:

1. The proposition that Andrew is male is true in virtue of the fact that Andrew is male.
2. If the proposition that Andrew is male is true in virtue of the fact that Andrew is male, then: if (FTP) is true, then the proposition that Andrew is male is true in virtue of the proposition that Andrew is male.
3. Therefore, if (FTP) is true, then the proposition that Andrew is male is true in virtue of the proposition that Andrew is male.
4. The proposition that Andrew is male is not true in virtue of the proposition that Andrew is male.
5. Therefore, (FTP) is not true.

All of the premises of this argument seem true to me. I suppose that the best move for the proponent of (FTP) to make would be to deny either (1) or (4). But (1) definitely has ordinary language on its side and, insofar as I understand it, (4) seems true to me. So, facts are not true propositions.

(By the way, I don't mean to suggest a whole-hearted endorsement of this argument. As I said, all of its premises seem true to me. However, I also have some inclination to reject its conclusion. So, I'm not entirely sure what to say about the argument. I guess it pushes me towards somewhat towards accepting its conclusion. I also don't mean to claim that this is a novel or original argument. Honestly, I don't know the literature on facts very well, so I don't know if it is or not. However, given that it is such a simple argument, I suspect that someone's given it before.)

Paraphrasing! (Huh, yeah) What is it good for?

2007-01-25T10:42:00.000-08:00

Metaphysicians and other philosophers are often uncomfortable with the supposed ontological commitments of many seemingly true ordinary sentences of English. One approach to blunting these commitments is to offer paraphrases of them. I am interested in the details of the approach. In particular, I would like to know whether someone who offers a paraphrase of an ordinary English sentence should take that sentence to be true.

Consider the following English sentence:
(F) There are fictional characters.
Many metaphysicians are uncomfortable with (F)'s apparent commitment to fictional characters. Since the paraphrase approach is intended to help one avoid such commitments, many metaphysicians are likely to offer a paraphrase of (F). Should such philosophers take (F) to be true? If so, then the following claim is true:
(T-F) "There are fictional characters" is true.
However, the following instance of the Tarski bi-conditional also seems to be true:
(I-TB) "There are fictional characters" is true iff there are fictional characters.
However, (F), which is just the claim that one would've thought someone employing the paraphrase strategy would like to avoid, follows from (T-F) and (I-TB). That is, the following argument is valid:
1. "There are fictional characters" is true.
2. "There are fictional characters" is true iff there are fictional characters.
3. Therefore, there are fictional characters.
So, anyone who believes (1) and (2) should also believe that there are fictional characters. Since someone who is concerned with the apparent ontological commitments of (F) would like to reject the claim that there are fictional characters (after all, they are concerned about the apparent ontological commitments of (F) for the very reason that they believe that there are no fictional characters), they need to reject either (1) or (2). But (2) seems pretty obviously true. So, they should reject (1). That is, they should reject the truth of the very sentence that they are offering a paraphrase of. And it seems like such a result can be generalized: Whenever someone hopes to avoid ontological commitment by paraphrasing an ordinary English sentence S, that person should reject the truth of S.

Partless Hotdogs

2007-01-24T18:11:00.000-08:00

So none of the following views of persistence is committed to any particular view of time: endurantism, perdurantism, and exdurantism. But is there a coherent version of Partless Hotdog view that is presentist?

Green is the Color

2007-01-23T11:45:00.000-08:00

A while ago I read this post on Weatherson's blog. When I first saw Weatherson's powerpoint slides I thought "wow, that's kind of wierd." But, recently, I looked over more "color illusions" here and here. When I saw the spiral green and blue on the first of the sites linked to in the last sentence, I though "No way is that an illusion". I decided that any theory of color that entails that the green and blue spiral is an illusion must be a false view about color. I then came up with a rough thesis that would not have that unwanted consequence. Unfortunately, I discovered that Daniel Nolan presented roughly the same thesis in his comments on Weatherson's original post. In spite of that fact, I am going to talk about the thesis a bit any way and consider the best objection that I have come up with to that thesis.

The thesis is that, roughly, the color of an object sometimes depends on the things going on around the object. It might be put as a supervenience thesis. For example, perhaps the color of an object supervenes on the topological and geometric properties of that object and of the things nearby that object.

Thus, although the geometric and topological features that result of one of the spirals in the picture that has inspired me are roughly the same as the features in the other spiral, it seems that those featrues are slightly different in the surrounding objects. This is what makes one of the spirals green and the other one blue. Since the colors depend on the surrounding objects, we cannot demonstrate that they are the same color by covering up the surrounding area (as is often done). When we cover up things around the object, we change the color of the object.

Here is an objection, inspire by a conversation with Andrew a few days ago. Suppose we have one of our spiral pictures. We also have a wall situated several feet away from the spiral picture. The wall has holes in it so that an oserver on the other side of the wall can see the spirals but cannot see the stuff surrounding the spirals. Such an observer, the objection goes, would see the colors as the same. But an observer on the other side of the wall, that is, an observer who can see both the spirals and their surroundings, would see them as two different colors. One might think that we should say that the spirals are the same color (to the first observer) but different colors (to the second observer). But no two spirals can both be the same color and different colors at the same time. So, the view in question is incorrect.

Here are the responses that I am considering:

1. The first observer is just mistaken. Since the wall is partially blocking his view, he doesn't have the relavent information for determining the true colors of the sprials.
2. The first observer will in fact see the sprials as two different colors (this can be confirmed by expirment). This might be the case if the cause of the different colors observed is some kind of interference between the light waves bouncing off the spirals and the light waves bouncing off the surroundings. The interference will have already taken place before the light waves from the spirals travel through the holes in the wall. So, the first observer will in fact see the colors as different. This response will, of course, be subject to empirical confirmation or refutation.
3. Both observers are correct. One object (such as the spiral) can in fact be two different colors at the same time.

I like the first response best and the last response least. So, that is what I have been thinking about. What do you guys think?

vague fictional predicates

2006-12-18T12:26:00.000-08:00

I have been thinking about the possibility of vague fictional predicates. I have no thesis yet, but I have some ideas that I thought I could post.

Let's assume that a predicate is vague iff it is unclear whether it applies in some cases. This might be slightly non-standard. It is far more common to say that a sentence is vague iff it is unclear whether or not it is true. But, I think we commonly trace the vagueness of a sentence to the vagueness of the predicate and I think that we believe something like the principle stated above.

Now, suppose that we have a fiction, F1, in which two predicates are introduced. The first predicate is a kind of quantity, 'quaps'. Objects of certain kinds, according to the fiction, can have various numbers of quaps. The other predicate is 'quapful'. According to F1, when an object has lots and lots of quaps, it is quapful. However, when it only has a few quaps it is not quapful. It seems that the situation just descibed is one in which the predicate 'quapful' is vague, according to the fiction. However, is it really vague?

Here is a reason to think that the answer to that last question is 'no'. It is not unclear whether anything is quapful because it is clear that nothing is quapful. That is, it is clear in the sense relavent here. There is some sense in which it is unclear whether anything is quapful. But this is the unclarity that results from fictional discourse and that leads to the vexing metaphysical questions about fiction that we all know and love. But this is not the kind of unclarity that is relavant to vagueness. it is not unclear of any object that it is quapful because it is clear that every object is not quapful. So, 'quapful' is not vague.

You might think that we should revise our analysis of vague predicates to say that a predicate is vague iff either it is unclear whether it applies to something or according to some story, it is unclear whether it applies to something. But this will result in the unwanted consequence that necessarily, every predicate is vague. But surely it is possible that some predicate is non-vague. Consider a ladigodian language in which everything is a name for itself and every property is a predicate that picks itself out. This language is perfectly precise. But, on the above view, it cannot be.

So, what should we say about the vagueness of 'quapul'? I am not exactly sure. It looks like, perhaps a good thing to say is that 'quapful' is not vague, but rather 'according to fiction F1' is vague. But this seems strange. Why is the vagueness rooted in that expression? Moreover, there is some reason to believe that the that expression can be non-vague. Perhaps the best account of truth in fiction has the following consequence. It is possible to tell a fiction, perhaps F1, in such a way that makes it that for every name n either 'according to fiction F1, n is quapful' is determinately true, or determinately false. Moreover, if it is determinately false because the fiction is simply silent about whether the predicate applies or not. But in this situation, all else being equal, 'according to fiction F1' is non-vague even though we still have an intuition that there is vagueness somewhere.

I guess I am thinking that the best solution is the following. 'quapful' is not vague. Moreover, 'according to fiction F1' is not vague (at least given the right kind of circumstances). However, the following is a truth: according to fiction F1, 'quapful' is vague. It is this truth that makes us mistakenly feel that there is a genuinely vague predicate.

Vagueness and Supervaluationism

2006-12-11T06:49:00.001-08:00

One of the standard objections to supervaluationist views concerning vagueness is that if they are true, then there are true existential generalizations that lack true instances and true disjunctions none of whose disjuncts are true. However, I wonder if this is an essential feature of supervaluationist views. In particular, mightn't a supervaluationist say the following:

a. An atomic sentence S is true iff it is true under all precisifications, and
b. A non-atomic sentence S is true iff there are some true atomic sentences that entail it?

Anyway, I know this isn't worked out very well or anything, but it does seem to me that making this move allows the supervaluationist to avoid one of the major objections to his view. What do the rest of you think? And do you know if a move like this has been made by any supervaluationists in the literature?

Relational Space

2006-11-16T14:31:00.000-08:00

Leibniz has an argument against absolute space that employs the Principle of Sufficient Reason. Of course, PSR is false. So, the argument is no good. However, some philosophers have come to accept a new principle, the Principle of Necessary Reason. This principle may be formulated as follows (though it is not so formulated by its defenders):

For every contingently true proposition, P, there is true proposition N which is neither identical to P nor a part of P such that if N were not to obtain, then P would not obtain.

I believe that we can make a new argument against absolute space based on this principle. Let u be the universe and let O be a property that something has when it has all the geometric features that the universe in fact has. Finally, let R be the property that the universe in fact has in virtue of being oriented in space the way that it in fact is and let L be a the property that the universe would have if it were oriented in a mirror reverse way. Now consider the following proposition:

(Ou and Ru) or ~(Ou and Lu)

If space is absolute, then this is a contingently true proposition. But if that is a contingently true proposition, then by PNR, there must be a proposition, N such that if N were not to obtain, then it would not be the case that (Ou and Ru) or ~(Ou and Lu). That is, if N were not to obtain, then it would be the case that ~(Ou and Ru) and (Ou and Lu). But there is no such proposition. So, space is not absolute.

I take it that the weakest part of this argument is the principle PNR.

The Number of Zits on My Face

2006-10-28T07:15:00.000-07:00

Hi all.

I'm currently reading a paper by Thomas Hofweber called "Innocent Statements and Their Metaphysically Loaded Counterparts". (It is available on his website for anyone that is interested.) In his paper, Hofweber is concerned with the transition between sentences like (A) "I have four zits on my face" and (B) "The number of zits on my face is four". (Hofweber uses different examples.) Hofweber claims that (A) and (B) seem truth-conditionally equivalent and that we can infer either from the other in natural language, but (B) apparently entails the existence of numbers whereas (A) does not. His paper is an attempt to determine what is going on here.

Anyway, in Section 3.1 of his paper, Hofweber draws attention to a puzzle for those who think that "The number of zits on my face" in (B) functions as a singular definite description. He notes that, in general, a sentence containing a singular definite description "the F" entails the corresponding sentence containing the indefinite description "a F". However, Hofweber says, attempting to apply this general rule to (B) yields:
(C) A number of zits on my face is four.
And (C) seems very awkward.

So, my question to you guys is: Any idea what is going on here? It certainly looks to me like "The number of zits on my face" functions as a singular definite description in (B). So why does (C) sound so strange if a sentence containing a singular definite description entails the corresponding sentence containing the indefinite description?

An Argument for Actualism

2006-10-25T08:48:00.000-07:00

I came across an argument from van Inwagen for actualism recently. I was wondering what y'all thought about it. The idea is that to be red, in the most inclusive sense, is to be actually red. To fail to be red actually is to be red in no sense at all. Similarly, to exist in the most inclusive sense is to exist actually. To fail to exist actually is to exist in no sense at all. There is no relevant difference between redness and existence. So actualism.

The claim about redness seems right, but the corresponding claim about existence should offend possibilists. So the challenge is to note the relevant difference, if any, between redness and existence. There are clearly some moves to make here, but I was wondering what sort of move, if any, y'all found most attractive.

Kant's Cleavage II

2006-10-04T09:47:00.000-07:00

I just came across Putnam's account of analyticity. Here it is.

S is analytic iff S is deducible from the sentences in a finite list at the top of which someone who bears the ancestral of the graduate-student relation to Carnap has printed the words 'Meaning Postulate'.

This should settle the matter once and for all.

Kripke Semantics and Strange Truths

2006-10-02T20:42:00.000-07:00

On a standard Tarskian account of FOPL a model is taken to be an ordered pair where D is a non-empty domain of individuals. Given the non-empty constraint, there is no model on which some sentence (x)Fx expresses a vacuous truth. It is true in M iff every member of D in M (and there has to be at least one) satisfies the open formula Fx.

Now consider a Kripkean account of MFOPL. On this account a model includes a a set of world W, a domain D and a function Q from members of w to subsets of D. There is no constaint that says the subset must be non-empty. So, there are models with worlds that have an empty domain of quantification. This is wierd.

Why? Because on such a model the sentence <>(x)Fx will express a truth. Moreover, given a plausible extension of the semantics to allow for second order quantification (MSOPL) we will have the following turn out true in models that have empty world: <>(x)(F)Fx. This is very strange. Moreover, the situation becomes more strange when we realize that in the empty world it must also be true that (x)(F)~Fx. Why? Because the denial of (x)(F)~Fx is existentially commiting. But the empty world is empty. So, there are models on which the following is true <>[(x)(F)Fx & (x)(F)~Fx]. But that entails that <>[(x)(F) Fx & ~Fx]. But that can't be true. So what the hell is going on? Should there be a constraint on Q; should it be a function from worlds to non-empty subsets of D? Moreover, if that is the case, then do we have reasons from the semantics of modal discourse for the conclusion that necessarily, something exists?

Another false View

2006-09-30T12:25:00.000-07:00

I talked about a view in my last post that is certainly false. Here is another view that I have been thinking about, which is also certainly false. Let's suppose, as per the true, that counterpart theory is false and that individuals are in multiple possible worlds. This seems to cause problems for Lewis' account of truth in fiction because his account best fits with counterpart theory and descriptivisim about names.

Here is a view though. Suppose that 'Alyosha' is in fact empty. But there are worlds in which people speak something very much like english except that when they utter the sentences of The Brothers Karamozov they express truths and the symbol 'Alyosha' is a name that refers. However, there are lots of such worlds. There are worlds where 'Alyosha' is used as a name for one guy and worlds where it is used as a name for some other guy. Given transworld identity, it looks like we cannot appeal to some of these worlds when giving an account of truth in fiction without being arbitrary. We might appeal to them all and supervaluate in some sense. But another thing that we can do is pretend that any the individual, x, such that the symbol 'Alyosha' is used as a name for x in one world and any individual, y, such that the symbol 'Alyosha' is used as a name for y in another world are identical.

I know this theory is not worked out. But, I am wondering about necessary connections that might be noted between things that people commonly take to be true in a fiction and what various accounts say would be true in a fiction.

Names in Fiction

2006-09-30T11:58:00.000-07:00

Let's assume that 'Alyosha' is an empty name that appears in "The Brothers Karamozov". One might think that if 'Alyosha' is in fact empty, then it is necessarily empty. Here are two reasons to think so.

First, one might be convinced by Williamson style arguments for the conclusion that necessarily everything necessarily exists. If that is the case, then if 'Alyosha' possibly refers and if names are regid designators, then 'Alyosha' in fact refers. But of course names are rigid designators (in some sense). So, if 'Alyosha' possibly refers, then 'Alyosha' in fact refers. Equivalently, if 'Alyosha' does not in fact refer, then 'Alyosha' does not possibly refer. Equivelanly, if 'Alyosha' is in fact empty, then it is necessarily empty.

I want to set aside Williamson style arguments and assume that some things contingently exist. I hope everyone can play along with this.

A second reason to believe in fact empty names are necessarily empty is the following: if 'Alyosha' is in fact empty but it is possible that 'Alyosha' is not empty, then the actual world 'Alyosha' is a different name than the 'Alyosha' of the other possible world. This is a widespread belief in semantics. But I want to consider an alternative view.

Consider the following case. One that I do not buy, but I know some of you will like it. Suppose that sperm S and egg E are not in fact united. If that is the case, then given the necessity of origens and the denial of Williamsonian conclusions, the thing that would have resulted from their uniting does not in fact exist. However, we might introduce a name, 'Fred', by saying "I hereby name whatever would have resulted from the union of S with E 'Fred'" Here it looks like Fred is in fact empty yet it possibly refers.

If we accepted this case, then we would have to deny that for any symbol type N, if N is in fact an empty name but it is possible that N is not an empty name, then the N as used in the actual world is a different name than the N of the other possible world. Thus we have undermined our second reason for believing that 'Alyosha' is necessarily empty.

However, here is a response that someone might have if he wants defend the view that 'Alyosha' is necessarily empty. He might admit that there are strange situations like that involving the name 'Fred' where we have a name that is in fact empty yet possibly non-empty. However, he might say that the situation with 'Alyosha' is not the same. We did not introduce the name 'Alyosha' with a description that happened to pick out a particular merely possible object. Moreover, we can only get names like 'Fred' by invoking such a description. So, if 'Alyosha' is in fact empty, then it is necessarily empty.

This much, some of you might recongnize, is roughly the content of the exchange that David and I had last Wednesday. But now I want to add something for the side of the wierdos. Suppose we said that when an emtpy name is introduced and there is no discription that uniquely picks out a possible referent, then the name is super vague or multiply ambiguous. I am thinking that we might endorse a kind of meaning pluralism according to which sentences involving the name 'Alyosha' express multiple propositions. One proposition for every merely possible individual who satisfies the conditions laid out in the story. In this case, we might say that 'Alyosha' is in fact many empty names and there are many stories expressed by 'The Brothers Karamozov'. Moreover, we could then adopt something like Lewis' strategy for truth in fiction without endorsing counterpart theory.

Okay, I know that this is a false view. But I thought that I would put it out there anyway.

Gunk in Discrete Space

2006-09-27T10:25:00.000-07:00

So suppose that space is discrete at w. Does this rule out the possibility that there is gunk in w? It would surely be weird to suppose there were--for then it seems there would be objects that exactly occupy a region though no proper parts of those objects exactly occupy any region. Though this is weird, it does not seem contradictory or incoherent. So is gunk compatible with discrete space?

A Modest Proposal

2006-09-23T09:24:00.000-07:00

I wish to confess attraction to a version of Feldman's analysis of knowledge in Epistemology. According to the analysis,

S knows p iff:
(i) S believes p,
(ii) p is true,
(iii) S is adequately justified in believing p, and
(iv) S's justification for p does not essentially depend on any falsehood.

I say it is a version of Feldman's analysis, because (iv) is explained as follows:

(J) S's justification for p does not essentially depend on any falsehood iff the body of evidence that supports p for S is such that it's not the case that deleting any false proposition from that body of evidence results in S's not being justified in believing p. (It is "of the essense" of S's justification for p that it depends on falsehood if the right-hand side of (J) obtains.)

Feldman does not accept (J). I believe he thinks that in order for the account to be plausible, it requires not only (J) but some sort of "no defeater" clause. I deny that there are knowledge defeaters, however. So I am interested in the viability of an account of knowledge that includes only (i-iv), where (iv) is analyzed in terms of (J).

This account yields some perhaps surprising verdicts.

In Gettier cases, the target proposition is not known since deleting a falsehood from the knower's body of evidence destroys justification.

In a Feldman-Gettier case, where all propositions explicitly reasoned through are true, there is still a falsehood in S's grounds such that its deletion from S's evidence result in a lack of justification. So in Feldman-Gettier Nogot/Havit, S infers directly from S's evidence regarding Nogot that someone in S's office who has Ford papers, drives a Ford, etc., and from this S infers that someone in the office owns a Ford. But here, the original belief is arguably "Gettiered"; deletion of all falsehoods from S's evidence base for the proposition that someone in the office has Ford papers, etc., results in loss of justification for that proposition.

Russell's stopped clock case is treated differently. S knows what time it is if it is time t, the clock says it is t, it seems to S as if this is so, and S has some sort of belief/evidence for the general reliability of clocks. That there is some accident involved is irrelevant; accident is involved in any case of knowledge. (Duncan Pritchard has a mountain of paper on epistemic luck. I think this issue would be worth checking out but I am not familiar with the details of Pritchard's proposals.)

Perhaps more interestingly, the view can be employed to explain how testimony can be a generative source of knowledge, rather than serving merely to transmit it. For some reason or other, A may not know p, but A may testify that p to B, and B may come to know p on the basis of A's testimony.

Perhaps even more interestingly, this suggests a problem for epistemicism about vagueness. Suppose a philosophical neophyte, suddenly made interested in the problem of vagueness by Andy's tupperware dish full of rubble and a bit of classical logic, travels the world consulting vagueness experts on the sharp cutoff for heapness. Each expert, after carefully reflecting on the question, tells the neophyte that the cutoff is 4; any number of grains less than that a heap does not make. It's plausible to suppose that the experts do not know their own answers (insert whatever motivation you like for their asserting it here). But suppose they're right. Now the neophyte has a justified true belief where his evidence is the wealth of expert testimony. And by the analysis, the neophyte knows the cutoff for heapness. The problem for epistemicism is clear; epistemicists hold that the cutoffs are unknowable in cases of vagueness. (I'm blurring use-mention stuff here, but the problem is hopefully clear enough.)

I think this view of knowledge comports well with the standard view and is not liable to any significant problems that I am aware of. So would someone please make me aware of some significant problems?

Kant's Cleavage

2006-09-14T18:02:00.000-07:00

(Lots of fools apparently assess the cascade of craptasticity in "Two Dogmas" and conclude that there is no analytic-synthetic distinction.

That conclusion is unwarranted. But there are lots of features that analytic sentences were traditionally supposed to have and I doubt, for reasons independent of Quine, that they have any of them. So while I think there are analytic sentences, of course, I wonder if there is any philosophical usefulness to the distinction if analytic sentences don't in fact have the features they were traditionally supposed to have. That's my question for you guys.

So here are some of the features:
1. Analytic sentences are necessarily true.
False. With respect to an appropriate context, a usage of 'that student is a student' is intuitively analytic, though it is fobviously contingent (and a posteriori).

2. Analytic sentences encode propositions that are knowable a priori.
False. See (1).

3. Analytic sentences are true in virtue of meaning.
Wtf. 'That table is brown' is true because its meaning, the proposition that that table is brown, is true--that table is brown. Similarly, 'all bachelors are unmarried males' is true because its meaning, the proposition that all bachelors are unmarried males, is true--all bachelors are that way. There is no coherent distinction I know of between truth in virtue of meaning on the one hand and truth in virtue of meaning plus the way the world is on the other. So wtf.

4. Analytic sentences are such that understanding the terms in them and the way they're put together is sufficient for being in a position to know that they're true.
False. Given the panoply of perverse philosophical views on the market, it's not hard to counterexample this. Perverse logicians understand logical truths but are not in a position to know them given the perversity of their views. And so on.

What's left? Again, I don't deny that there's a distinction between analytic and synthetic sentences, but the sorts of metaphysical and epistemological claims made about them seem like crapezoids. Is there some other reason to be interested in this notion?