Non Deductive Mathematics
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Seminar Notes
Just a quick little note on some issues raised at Alex Paseau’s talk on Hilbert’s program and consistency. Alex’s overall aim was to show that the attach from Godel’s second incompleteness theorem could be refuted by a slightly modified Hilbertian program (whether this is actually a program that one would wish to adopt seems questionable however, due to the limited epistemological value of the real/ideal mathematical divide).
On the way to doing this, he argued that inductive methods are used quite often when mathematicians form a belief (e.g. Goldbach’s conjecture, etc.). Furthermore, if one is worried about the uncertainty that is introduced via the acceptance of inductive methods in mathematics, one needs to give an account of how this is different to the uncertainty that arises as a result of human error in proofs and uncertainty regarding the fundamental axioms one is deducting from.
[[crimson Oh, good. That’s what I was hoping he’d say. Sorry I missed it. Jason ]]
How does it fit?
Once I get to dealing with the aspect of the indispensability argument that involves an association with IBE and hence non-deductive reasoning it would be good to have this as something to incorporate into the debate.
Contact Details Dr Alex Paseau Wadham College, Oxford alexander.paseau@philosophy.ox.ac.uk
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