Meinongianism and Skepticism

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

(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

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

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

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

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

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.