I am trying to learn a bit about the philosophy of language and I am puzzled by Kripke’s modal argument against Frege’s description theory of names. I’m guessing, and guessing is what I mean since I have never been any good at “real” philosophy, that Kripke is arguing that identifying a name with a description requires necessity and sufficiency, just as formal logic demands for equivalence.
Consider, for example, the sentence “Aristotle is the best student of Plato.”
From the point of view of possible worlds, it is clear the the description “the best student of Plato” is contingent in the sense that, as we traverse our modal space picking out “the best student of Plato”, we will not necessarily pick out Aristotle in all possible worlds. Thus, the description fails the necessity requirement of (modal) logical equivalence. Fair enough.
What I am puzzled by is why this is relevant with respect to Frege's theory. Frege is not talking about possible worlds. In our world, which is the one world of Frege, Aristotle is the best student of Plato and therefore this description correctly and uniquely identifies Aristotle - i.e., Frege is not using "is" in the sense of logical equivalence as Kripke appears to be, rather as a sufficient condition for identifying Aristotle.
The text I am reading, Colin McGinn’s The Philosophy of Language - The Classics Explained, highlights many objections to Kripke’s modal argument though this is not one of them.
Q: What is the relevance of possible worlds in arguing against Frege’s description theory of names? Frege's theory is not modal, so why is Kripke modal argument against it relevant.
To be clear, McGinn begins his account of Kripke's theory by outlining what he calls Kripke's Modal Argument and Epistemic Argument against Frege's description theory of names. This is done as a direct argument against Frege. My problem with this is that Kripke is using a different logic than Frege, so it is not so much a direct argument against Frege as an alternative theory to Frege's theory.