Quick Question

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

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

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

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

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.