tag:blogger.com,1999:blog-4987609114415205593.post639507408659374388..comments2022-12-08T08:31:08.950+00:00Comments on M-Phi: Deductive proofs: transferability and the 'built-in opponent'Jeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4987609114415205593.post-20349928173069172092014-01-17T20:26:50.237+00:002014-01-17T20:26:50.237+00:00There are proofs based on testimony. For example, ...There are proofs based on testimony. For example, a mathematician may not attempted to oppose the proposed argument for the classification of finite simple groups. Based on testimony, he may still use this classification in his own argument for another result. If conscientious, then he may write "if the classification of finite simple group holds, then my result holds." <br /><br />This use of testimony happens quite prevalently at extents not as extreme as the above. For example, someone who studies Riemann surfaces may use the topological classification by genus without prior attempt to oppose the topological classification. This happens as a mathematician who studied Riemann surfaces is versed in "analysis" or "algebra" but may not have the ability to intensely find counter examples to the classification by genus, which is in another branch of mathematics, namely "topology".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-64305781622539920172012-06-21T19:57:14.383+01:002012-06-21T19:57:14.383+01:00Hi Kenny, thanks! Yes, there were lots of interest...Hi Kenny, thanks! Yes, there were lots of interesting points in your paper that I had to leave out of the post, which was already too long. I did like a lot your brief discussion on philosophical methodology at the end, for example, but I just couldn't fit it in. Actually, one thing I'd really like to hear your thoughts on is the brief suggestion at the end of my post, whether Bayesianism is a suitable framework for the epistemology of mathematics. It always struck me that Bayesianism is a very individualistic framework, but maybe I'm oversimplifying things here.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-30817503609347502932012-06-21T17:10:30.383+01:002012-06-21T17:10:30.383+01:00Thanks for the discussion of the paper! I just wa...Thanks for the discussion of the paper! I just want to point out that I accept that all mathematicians do in fact come to know lots of mathematics merely on the basis of testimony. The role of transferability is in making sure that this is not essential for any specific result that is accepted into the body of mathematics.<br /><br />I think I make some minor points near the end of the paper trying to apply this idea to philosophy, to explain what appears to be going wrong in experimental philosophy - they are treating intuitions as evidence for a claim, rather than just as giving premises that the reader happens to accept. I suspect that in philosophy you get more preservation of the adversarial idea, but the same goal of transferability applies.Kennyhttps://www.blogger.com/profile/09588770173317316837noreply@blogger.com