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.