Category Archives: Autonomy of Math Knowledge

Hilbert’s consistency proof in the Foundations of Mathematics is model-theoretic. But of course the later Hilbert seeks consistency proofs that don’t depend on model-construction: what then are the resources can be brought to bear in syntactic proof-theory? Well, §3.4 on … Continue reading →

Back, after a longer-than-intended break, to Curtis Franks’s The Autonomy of Mathematical Knowledge. (You can read previous instalments of my comments here. And to keep things ticking over more regularly, I’ll blog about smaller chunks. Can you stand the suspense?) … Continue reading →

Hilbert writes Just as the physicist investigates his apparatus … the mathematician has to secure his theorems by a critique of this proofs, and for this he needs proof theory. (p. 61) Indeed: if you are physicist getting surprising results … Continue reading →

To return for a moment the question we left hanging: what is the shape of Hilbert’s “naturalism” according to Franks? Well, Franks in §2.3 thinks that Hilbert’s position can be contrasted with a “Wittgensteinian” naturalism that forecloses global questions of … Continue reading →

Hilbert in the 1920s seems pretty confident that classical analysis is in good order. “Mathematicians have pursued to the uttermost the modes of inference that rest on the concept of sets of numbers, and not even the shadow of an … Continue reading →

As I said, I’m planning to blog, chapter by chapter, about Curtis Franks’s new book on Hilbert, The Autonomy of Mathematical Knowledge (all page references are to this book). Any comments on my comments will of course be welcome! Let’s … Continue reading →

On Saturday, from the new books stand the CUP bookshop, I picked up a copy of Curtis Franks’s The Autonomy of Mathematical Knowledge: Hilbert’s Program Revisited. Two quick grumbles. First, the book is short: just a hundred and ninety very … Continue reading →