Topics Philosophers

Question First of all, I'd like to express my personal thanks for having this resource online. I'm having difficulty understanding the distinction between metaphysical possibility and logical possibility. It is said that Kripke's example, "Water is H2O" is an example of a metaphysically necessary truth, but not a logically necessary one. However, to me it seems that the extension of the terms "water" and "H2O" is the same, so the meaning of the statement is of the form A is A. (Isn't it with the meaning of a statement that logic is concerned, and not whichever semantically equivalent terms are used?) Isn't the statement that A is A logically necessary? A world where A is not A seems to be a violation of the law of identity. I guess it's likely that I am wrong. What are my mistakes? Thanks again.

Accepted:
June 17, 2016

Comments

Interesting question! First,

Interesting question! First, I should note that some philosophers object to the claim that the ordinary term "water" refers to the chemical kind H2O. See here and here. Just for simplicity, my answer will ignore their objections.

Second, a point about form. Using italics for propositions, I think we should replace the proposition Water is H2O with the universally quantified proposition Whatever is water is H2O, because, as I see it, the first proposition is false in all those possible worlds in which water doesn't exist, whereas the second proposition is (vacuously) true even in such worlds. Likewise, as I see it, the proposition Pegasus is Pegasus is contingently false (there being, as a matter of contingent fact, no such thing as Pegasus), whereas Whatever is Pegasus is Pegasus is necessarily true. So, on this view, the law of identity has the form "Whatever is A is A."

I'd say that the important difference between Whatever is water is H2O and Whatever is A is A isn't a modal difference: both propositions are true in exactly the same worlds, namely, all worlds. Instead, the difference is that one can't understand the sentence "Whatever is A is A" without believing the sentence to be true, whereas one can understand the sentence "Whatever is water is H2O" without believing the sentence to be true. Believing the first sentence is an implication of understanding it; not so for the second sentence. One can know the meaning of the terms "water" and "H2O" without knowing that those terms refer to the same thing, and one can't know a priori that they do refer to the same thing. For this reason, I think Kripke is right that the proposition expressed by the sentence "Whatever is water is H2O" (namely, the proposition Whatever is water is H2O) is both necessarily true and knowable only a posteriori.