A hasty nominalist argument
Here's a quick and dirty argument against the view that properties are things.
You can easily make parallel arguments against numbers, propositions, and any other domain where you think there are parallel logical truths. (E.g., "If there are eight planets then the number of planets is eight." "If snow is white then the proposition that snow is white is true.") The proposition case is very similar to an argument David Lewis makes in chapter 3 of Plurality—though he worries about necessary truth, rather than logical truth.
I don't find the argument especially convincing, but I think it's interesting anyway. And I think that's all I'll say about it just now.
- "If Fido is a dog then Fido has the property of being a dog" is a logical truth. (Premise)
- Logical truths are permutation invariant: that is, they remain true when individuals are arbitrarily exchanged. (Premise)
- Suppose "the property of being a dog" refers to an individual D, and "the property of being a cat" refers to an individual C. (For reductio)
- Consider a model M in which C and D are exchanged. "If Fido is a dog then Fido has the property of being a dog" is true in M if and only if Fido has C—that is, if and only if Fido is a cat. So the Fido sentence is false in M.
- But this contradicts (1) and (2). So (3) is false.
You can easily make parallel arguments against numbers, propositions, and any other domain where you think there are parallel logical truths. (E.g., "If there are eight planets then the number of planets is eight." "If snow is white then the proposition that snow is white is true.") The proposition case is very similar to an argument David Lewis makes in chapter 3 of Plurality—though he worries about necessary truth, rather than logical truth.
I don't find the argument especially convincing, but I think it's interesting anyway. And I think that's all I'll say about it just now.
Posted by Jeff on Saturday, January 26, 2008
2 Comments:
Hi Jeff,
Curious: where, exactly, does Lewis give an analogous argument in Plurality?
Also, logical truths are not always permutation invariant in your sense: consider the logical truth "a=a", which clearly does not remain true under arbitrary individual exchange. Maybe I am missing something.
Finally, shouldn't the argument's target simply deny (1)? If by "logical truth" you mean "truth of logic", then I certainly would. Though I might find (1) acceptable if by "logical truth" you mean metaphysically necessary truth. But then (2) would seem false: for example, consider "if a exists, then a is a child of b". (Pick some other necessary a posteriori truth if you do not like this one.)
(Personal aside: I might be in New York-New Brunswick for the following year! Any idea who will be around, or any clues about the schedule of courses at Rutgers-NYU in the Fall?)
The argument I was thinking of as analogous is the part of the argument against "magical ersatzism" at pp 179ff. He complains that the necessary connection between "a donkey talks" and "the proposition that a donkey talks is true" is mysterious. This stems from some kind of combinatorial intuition, which is analogous to the permutation invariance principle—maybe. I'm not sure how far the analogy can be pressed.
I'm especially unsure because I think my argument is confused, and I don't see an easy way to straighten it out. The notion of permutation invariance I appeal to isn't the standard one, and I'm not really sure how to state it clearly. I might try again later.
As for the personal aside: that's great! Send me an email (jeff dot russell at nyu dot edu) and I'll send you the draft of the NYU course schedule.
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