At 04:25 PM 9/21/2014, Frederik wrote: [snip]
But Howard, this is a different position than the one you presented in the earlier quote just some lines before. There, each foundation of math was legitimized by specific tasks - now they are deemed mere empty epistemological conventions.
HP: I did not say that epistemologies are empty. I meant only the arguments for a "winner" epistemology are empty. All these epistemological models in our brains have proven historically to be full of meaning, or at least useful for creative thinking. As I try to get across, they are complementary. What I have not found productive are the ones like the >2000 years of argument over realism vs. nominalism. Few working scientists argue this way any more. Some logicians and philosophers still do.
FS: It may well be the case, as you suggest, that there is no simple solution to be found in any of the foundation headlines stemming from the crisis around 1900. But that might just as well be a sign this field is still open for further investigation and progress.
HP: <http://en.wikipedia.org/wiki/Foundations_of_mathematics>These arguments were more than headlines. What would you call progress? Elimination of one epistemology?
FS: I still think this discussion address deep issues which are not solved by archiving the whole field as one of indifferent conventions.
HP: I agree (except indifference is not the same as complementary). This discussion is great! My last complaint of "unproductive arguments" was too strong. Of course I agree we should openly consider the values of all epistemologies. But I do not see the value of trying to eliminate all of them except Peirce's, whatever it is.
Howard
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