more from David Hilbert

Single Idea 10115

[catalogued under 6. Mathematics / C. Sources of Mathematics / 7. Formalism]

Full Idea

Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1).

Gist of Idea

Hilbert substituted a syntactic for a semantic account of consistency


report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.153

A Reaction

Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application.