Kripke’s Gödel and Schmidt case: why would my word still pick out Gödel?
Every year when we reach the incompleteness theorems one student asks the same thing: what if somebody else actually did it? This year I went looking and found that Kripke used exactly that scenario.
The setup, as I understand it: suppose the only thing I know about Gödel is that he proved the incompleteness of arithmetic. Now imagine (contrary to fact) that a man called Schmidt proved it, died, and Gödel took the credit. If my name "Gödel" just means "the man who proved incompleteness", then whenever I say "Gödel" I am really talking about Schmidt. Kripke says that is wrong: I would still be talking about Gödel, and saying something false about him.
My intuition agrees with Kripke, but I cannot say why. If all I have in my head is the description, what else could be connecting my word to the man? And where do Frege and Russell come into it? The books I found assume you already know who held which view.
Could someone lay out the positions in order, and say what the example is actually supposed to prove? Mathematicians like to know which assumption a counterexample is aimed at.