From a recent post at Siris:
"Logic makes us reject certain arguments, but it cannot make us believe any argument." Lebesgue
- the editors of Lakatos, Proofs & Refs (p. 53n4) claim that modern logic shows this is false if taken literally; we can determine, precisely, that some arguments are valid, & therefore logic can make us believe the argument even if not the conclusion.
- But what we can characterize precisely is validity for a domain; and thus we are back at Lebesgue, for one can say that we still have the question of whether the domain is rightly chosen. The editors have slipped, either they have forgotten Lakatos for the moment or think logic works differently from mathematics.
-I see by their further note on Lakato's historical note (56n) that this is their considered opinion. Disappointingly unimaginative and uncritical; what is worse, they think they can have this for free: infallible arguments without infallible principles. This is simply absurd; it is pulling certainty out of a hat.
Incidentally, if anyone was wondering about the short piece on Lakatos in the recent Quine collection, here's a summary: "This is a book about Euler's formula. It is a lot of fun and I enjoyed it." About the only point of substance was: Quine liked that mathematics looked like it was being revised like happens in the other sciences. Apart from that, it's pretty much "This is fun, you should read the book if you like things that are fun." Which is a reasonable way to do a book review.