Motto:

"There are none so blind as those who will not see." --

Google+ Badge

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?

Saturday, December 01, 2007

Quote of the Day: Russell on Leibniz on the Problem of Evil

This post over at Brain Hammer reminded me of the following quote from Russell:


Leibniz’s solution of the problem of evil, like most of his other popular doctrines, is logically possible, but not very convincing. A Manichaean might retort that this is the worst of all possible worlds, in which the good things that exist serve only to heighten the evils. The world, he might say, was created by a wicked demiurge, who allowed free will, which is good, in order to make sure of sin, which is bad, and of which the evil outweighs the good of free will. The demiurge, he might continue, created some virtuous men, in order that they might be punished by the wicked; for the punishment of the virtuous is so great an evil that it makes the world worse than if no good men existed. I am not advocating this opinion, which I consider fantastic; I am only saying that it is no more fantastic than Leibniz’s theory. People wish to think the universe good, and will be lenient to bad arguments proving that it is so, while bad arguments proving that it is bad are closely scanned. In fact, of course, the world is partly good and partly bad, and no “problem of evil” arises unless this obvious fact is denied.

--Bertrand Russell, A History of Western Philosophy, Simon & Schuster (1972), p. 590



Personally, I think the problem of evil may well be soluble, but I seriously doubt that Leibniz's "Best of all Possible Worlds" solution makes the cut.