Monday, October 19, 2009

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.

4 Comments:

Blogger Alex said...

Hi Joshua,

Two nit-picky comments, then something slightly more substantive.

First, another (more worrisome) problem with (A1) and (A2) is that they foreclose the possibility of priority relations between sets and their members, holes and their hosts, creatures of fiction and their authors, and so forth. Presumably, these entities do not enter into mereological relations.

Second, your observations about (SPQ) and (ISPQ) only apply if the priority relation is not only anti-symmetric but transitive, as well.

Third, and finally, I'm highly skeptical of inferences you suggest in the final paragraph. For it's controversial whether fundamentality is definable in terms of grounding: at all, and in the particular way you suggest.

Suppose one instead analyzes priority in terms of fundamentality, rather than vice versa (e.g., as Bricker seems to suggest in "The General and the Particular", and as I do in my own work). Then both (SPQ) and (ISPQ) can have an answer even though (FQ) does not.

11:18 AM  
Blogger Joshua said...

Alex,

Thanks for the comments. I just read the Bricker paper. In the paper, he suggests that:

Necessarily, x depends on y if y is fundamental and x is not fundamental and x supervenes on y.

He was explicit that this is supposed to be a sufficient condition for dependence and not a necessary condition. I take it that he doesn't want it to be a necessary condition because he thinks that some things depend on others yet neither is fundamental. For example, perhaps my hand depends on my finger, but neither is fundamental. So, this leaves us with the big question: What are the necessary conditions on dependence?

I also worry that if there are any necessarily existing fundamental entities, then anything will depend on those entities. For example, if the pure sets are necessarily existing and fundamental, then I will depend on the null set. But, that doesn't seem right to me. Presumably dependence is more fine grained than that.

11:57 AM  
Blogger Alex said...

Hi Joshua,

Thanks for the response! I agree: Bricker's account fails for various reasons, including for those reasons you mention. But it wasn't my intention in the previous post to defend Bricker.

I mentioned (though did not endorse) Bricker's account only to make the point that for all that's been said, fundamentality might be analyzed in terms of grounding, rather than vice versa. The claim that fundamentality might be analyzed in terms of grounding is, of course, not refuted by showing that Bricker's particular account does not succeed. A general argument against this type of analysis would have to be provided. But so far, none has been offered.

Now, *if* one can analyze grounding in terms of fundamentality, then having no answer to (FQ) doesn't entail having no answer to either (SPQ) or (ISPQ). That's all I intended to point out. (I think such an analysis *is* successful, but that's a long story!)

8:23 PM  
Blogger Lewis Powell said...

I think you want asymmetry rather than anti-symmetry.

A relation is anti-symmetric just in case, if x bears it to y, and y bears it to x, then x = y. (example: Parthood in classical mereology)

A relation is asymmetric just in case if x bears it to y, y does not bear it to x. (example: Proper parthood in classical mereology)

While asymmetry is a species of anti-symmetry (since any asymmetric relation will vacuously satisfy the condition on anti-symmetry), merely assuming the anti-symmetry of priority would not be sufficient to establish the regress. You'd also need the assumption that the relation is transitive (as Alex noted), _and_ that it is irreflexive. Obviously those are both plausible assumptions about priority -- it is quite intuitive that: 1) if x is prior to y and y is prior to z, then x is prior to z and 2) nothing is prior to itself -- it is just that the conjunction of anti-symmetry and irreflexivity amounts to asymmetry.

7:35 AM  

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