Monday, March 14, 2011

Indiscernibility of Identicals

One of the assumptions in the substitution problem was the indiscernibility of identicals:

Fa and a=b implies Fb

Is this always true? A slightly different way of expressing the law is that if Fa, and if 'a' denotes exactly what 'b' denotes then Fb. But in this form the law is clearly not valid. Suppose there is a shortage of red paint, and that only Ferraris are red. Then it follows that if Ferraris are fast, then red cars are fast, and conversely. But it does not follow that if John thinks Ferraris are fast, then he thinks that red cars are fast – perhaps he is imagining a red reliant Robin that he once saw. I.e. F = ‘John thinks that every – is fast’ and a = ‘Ferrari’ and b = ‘red car’. Then Fa and the fact that ‘a’ denotes everything that ‘b’ denotes does not entail Fb.

You will object that indiscernibility of identicals applies only when a and b are proper names. Proper names are referring terms, not common terms like ‘Ferrari’ or ‘red car’. I reply: what is a referring term? If it is defined as something to which indiscernibility of identicals necessarily applies, then the ‘Shakespeare’ arguments in the previous posts suggest that indiscernibility of identicals does not apply to ordinary proper names at all.


Leo said...

Thanks for the post.

All of the criticisms I have seen of the Indiscernibility of Identicals make use of intentionality. Do you, or anyone else, know of any non-intentional objections to the thesis?

Edward Ockham said...

Thank you for the comment. Shouldn't that be 'intensionality' with an 's'? Intensionality is simply 'meaning' or 'intension' as opposed to 'extension'. An intensional context is one where IofI fails to apply. See SEP.

I don't know of any other objections to the thesis.

Leo said...

No, I did mean intentionality: the aboutness of mental states. Every counterexample to the IofI I have seen goes something along the lines of "If IofI were true, then necessarily (x=y)—>(Fx—>Fy). But if F be 'is thought of by A' or 'believed to be fast by A' or the like, then it is possible that ~(Fx—>Fy). Therefore, etc."

"F" is always related to a mental state's aboutness of x and y. That this never varies gives rise to some suspicion on my part concerning these objections. Surely, if the IofI is wrong, there ought to be other kinds of objections raised, no?

Edward Ockham said...

Well, not all such contexts involve mental states. E.g. ‘it is necessary that’, ‘it is possible that’. Again, see SEP.

I agree that most examples do.