Thursday, August 23, 2012

Mereology Map

Recently, my colleague David Faraci posted a "flowchart" for metaethics on PeaSoup, and he impressed on me how much useful feedback he received. Not long ago, I composed something analogous for mereology, and was hoping to get feedback as well. (I realize my "road map" is incomplete, e.g., it does not address growing block theories, though I am hoping to revise it in the near future.)

The document is at: http://www.unc.edu/~tparent/Identitymap.pdf

1. I don't think you've understood supervaluationism. All supervaluationists *accept* claims like:

There is some n such that n is small and n+1 is not small

2. Useful flowchart!
I guess it would be even more useful if you added a bibliography

3. Thanks Fredrik! Good suggestion about the bibliography...I'll work on that.

Thanks also to Anonymous for your comment. I'm not sure I understand your point however. I would agree that, _on a given precisification_, there will be an n such that n hairs qualifies as "bald" and n+1 hairs qualifies as "non-bald." But part of the supervaluationist's point is that there are multiple precisifications. Accordingly, the truth-value of "S is bald" isn't determined by any one precisification. Rather, it is determined by all the precisifications: "S is bald" is true iff: S satisfies 'bald' on *every* precisification of the 'bald' predicate. Alternatively, "S is bald" is false iff: S fails to satisfy 'bald' on *every* precisification of the 'bald' predicate. (And if S satisfies 'bald' on some but not all precisifications , then the sentence counts as neither true nor false.) Thus, whether "S is bald" is not a matter of there being a unique n such that n hairs is bald and n+1 hairs is non-bald. Rather, the statement is "super" evaluated with respect to the evaluations of "S is bald" on each precisification (where n differs on each precisification).

But do let me know if I'm misunderstanding something here. Thanks again for your comments.

4. I take it that Anonymous's point is that "At t, there is a specific number n such that changing n clay particles would result in a numerically different statue, but changing n-1 particles would not" is true on every precisification. Thus, that sentence is supertrue and (since supervaluationism identifies truth with supertruth) is hence true according to supervaluationism.

(Note that something similar is true of "bald". On every precisification of "bald", "There is a number n such that someone with n hairs on his head is bad but someone with n+1 hairs on his head is non-bald" is true. So that sentence is supertrue and hence true according to supervaluationism.

This is why one major objection to supervaluationism is that it implies that there are true existential generalizations without true instances.)

5. I don't think Q5 is right about presentism. Typical presentists do agree that things that exist now also exist at other times. But they think that existing at other times is like existing at other worlds, in the sense that existing at other times or at other worlds doesn't entail existing simpliciter. I don't know which temporal paradoxes you were thinking of, but this is sufficient to avoid problems with temporary intrinsics.

At Q6's No, you can also have a stageless worm theory on which ordinary objects are four-dimensional but there are no slices, and exdurantism on which ordinary objects are three-dimensional but count as persisting because they have continuants at other times (analogous to Lewis's counterpart theory).

6. Thanks Greg, nicely spotted! Would this alternative phrasing work?
-At t, is there a numeral _n_ such that [changing _n_ clay particles would result in a different statue] is true? (where square-brackets are being used as corner-quotes)

Thanks also, Professor Pruss, for mentioning exdurantism. Good suggestion. With the stageless worm theory, I assume the worm is "stageless" because the whole worm is seen as metaphysically prior to its parts? (I mean, one could mark out stages of the worm, but I assume the point is that those stages would not be fundamental. Yes?) Also, do you have a good suggestion for a reference on stageless worm theory? Thanks again.

7. I am a nihilist about composition, so I think of the stageless worm as an extended simple.

But one could also have the view that there are stages, but they're not fundamental.