Ideas from 'On the Concept of Number' by David Hilbert [1900], by Theme Structure

[found in 'From Kant to Hilbert: sourcebook Vol. 2' (ed/tr Ewald,William) [OUP 1996,0-19-850536-1]].

green numbers give full details    |     back to texts     |     unexpand this idea


6. Mathematics / C. Sources of Mathematics / 7. Formalism
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency
                        Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence.
                        From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist'
                        A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!).