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Full Idea
Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought.
Gist of Idea
Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted)
Source
report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics
Book Ref
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.154
A Reaction
I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault.
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |