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Showing posts with label Leibniz's Law. Show all posts
Showing posts with label Leibniz's Law. Show all posts

Sunday, December 30, 2007

On an Attempted Refutation of Leibniz's Law

At Inconsistent Thoughts, Colin Caret has a post which links to a post of Brian Rabern's over at armchair investigations which challenges Leibniz's Law. In case you're not familiar with it, Leibniz's Law states that if x is identical to y then x and y have all their properties in common. Brian's argument is intriguing, but as he suggests there is a premise in the argument which can plausibly be denied. I'm not sure if this is what he had in mind, but I posted my own diagnosis of what goes wrong with the argument in a comment on Colin's post, which I will reproduce here:

Hi Colin,

I think that attempted refutation you linked to is confusing (at least, it confuses me) because it expresses the property G (i.e., "if x had quotes around its last word, then x would have been true") counterfactually and then asks us to evaluate the truth of the statements A and B respectively in those counterfactual circumstances, without specifying clearly whether the letters refer to the sentences as they actually are or as they are in the counterfactual circumstances we are considering. The cruicial part of the proof is the following:

"A is not such that if it had quotes around its last word it would have been true (since if A had quotes around its last word its last word would have been “obscene” not ‘obscene’). Hence, ~G(B). But B is such that if it had quotes around its last word it would have been true (since if B had quotes around its last word it would have rightly said of A that its last word is ‘obscene’)."

I agree with the conclusion that A does not exemplify G. For if A had had quotes around its last word, it would have looked like this: 'The last word of A is 'obscene'.' and in those circumstances its last word is indeed ''obscene'' and not 'obscene'. But note that this is because when we evaluate the truth of A in those circumstances, we are taking A to refer to itself as it is in those counterfactual circumstances, not how it actually is. For as A actually is its last word *is* 'obscene', and if we evaluated A in the counterfactual scenario as referring to itself as it actually is (i.e., as 'The last word of A is obscene') then it would have been true, since it would have referred to itself as it is in our possible world and not the possible world in which its truth is evaluated. However, I think that B also does not exemplify G. For B, to recall, says 'The last word of A is obscene.' Now if B exemplifies G, it would have been true if it had quotes around its last word, in which case it would have looked like this: 'The last word of A is 'obscene'.' But if it had said that it would not have been true, for in those counterfactual circumstances A would, as above, have looked like this: 'The last word of A is 'obscene'.', and so in those circumstances A's last word would have been ''obscene'' and not 'obscene'.

Does this solution make sense to you, or am I still confused?


So what do you think? Is my diagnosis correct? Or is there some other way the argument goes wrong?