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Full Idea
When we follow long mathematical proofs we lose our a priori warrants for their beginnings.
Gist of Idea
In long mathematical proofs we can't remember the original a priori basis
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2)
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.45
A Reaction
Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2.
9343 | To achieve pure knowledge, we must get rid of the body and contemplate things with the soul [Plato] |
3617 | I aim to find the principles and causes of everything, using the seeds within my mind [Descartes] |
5571 | Reason contains within itself certain underived concepts and principles [Kant] |
12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
9342 | Understanding needs a priori commitment [Horwich] |
9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
17714 | Aristotelians dislike the idea of a priori judgements from pure reason [Mares] |