Kripke's Puzzle

This handout clearly explains Kripke’s argument in his seminal paper ‘A Puzzle about Belief’. Kripke derives a puzzle from just two assumptions:

(D): If a normal English speaker, on reflection, sincerely assents to ‘p’ [supple correctly understands ‘p’], then he believes that p.  

(T): If a sentence of one language expresses a truth in that language, then any translation of it into any other language also expresses a truth (in that other language).

He also gives a version (the ‘Paderewski’ puzzle) that doesn’t even use (T). His point therefore is that it would be a mistake to criticize Millianism as follows:

Millianism implies SUB (=Names are substitutable salva veritate, even inside attitude reports), and SUB is wrong. Suppose we have ‘S believes that Tully isn’t famous’ and ‘S believes that Cicero is famous’. Then SUB lets us derive ‘S believes that Tully is famous,” so we incorrectly attribute contradictory beliefs to a normal person.

This is a mistake because that sort of result is obtainable without SUB, i.e. using just (D) and (T) we end up incorrectly attributing contradictory beliefs to normal people.

Objection: But if Millianism implies SUB and SUB results in paradox, then Millianism is wrong. Why does it matter if some other principles also result in the same paradox?

Reply: They aren’t just other principles – SUB just amounts to an intralinguistic application of (T), where e.g. we translate ‘S believes that Cicero is famous’ into ‘S believes that Tully is famous.’  Since (T) seems obviously true independent of Millianism, there’s no reason to blame the paradox on (SUB) and therefore on Millianism.