What is the relevance of Kripke’s modal argument against Frege’s description theory of names?

Question

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.

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EDIT

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.

Answer 1

If your question is "why is Kripke allowed to appeal to our modal intuitions about the way the world could have been in?", then I think the answer is because he's putting forward a theory of how we actually use names, and that his theory of names is closer to how we actually use names than the descriptivist theory. Since it's a theory about language and its use by us, he's allowed to appeal to intuitions about what we would say if we were in different circumstances or the world were different in some way. And this is just what he means by a "possible world".

We would still use the name "Aristotle" to refer to the same man Aristotle we do in this actual world, even if he hadn't done those things we typically associate with him. If someone else had become the best student of Plato, we wouldn't then say "okay, now that person is now Aristotle".

You could insist that this is how you mean a name, as an abbreviated description. But for any given name you'd be saying some things that are strange to speakers of your language. Like in the example of Aristotle, you would have to say whatever is the greatest student of Plato, that's what "Aristotle" refers to.

Answer 2

According to the description theory, the meaning of names is given by a list of descriptions. For example, the name "Aristotle" just means "the best student of Plato & the teacher of Alexander the Great & ...", and the name "Aristotle" picks out Aristotle because that is the person that satisfies all these descriptions.

To this Kripke objects that Aristotle could have failed to satisfy some of these descriptions while still remaining Aristotle. That is, the name "Aristotle" picks out Aristotle even in possible worlds where he isn't the best student of Plato, or where he doesn't even become a philosopher, etc.

Instead, Kripke argues that names are rigid designators. That is, they refer to the same object in all possible worlds in which that object exists. According to the description theory, on the other hand, names are not rigid designators.

The SEP entry on names explains both the description theory and Kripke's argument against it in more detail.