tag:blogger.com,1999:blog-26706564.post5391173282414971054..comments2024-03-25T07:51:47.758-04:00Comments on Thoughts On Economics: Positions On The Philosophy Of MathRobert Vienneauhttp://www.blogger.com/profile/14748118392842775431noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-26706564.post-53847704351808767052007-09-04T15:45:00.000-04:002007-09-04T15:45:00.000-04:00Thanks, Robert, for the kind comments. Velupillai...Thanks, Robert, for the kind comments. Velupillai's collection does, indeed, look interesting.<BR/><BR/>An afterthought: Wittgenstein's philosophy has repeatedly been described as ultrafinitist, cf. [1]<BR/><BR/>[1] http://en.wikipedia.org/wiki/UltrafinitismCharles Stewarthttps://www.blogger.com/profile/12296890587882140573noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-58914890441237193332007-08-31T03:13:00.000-04:002007-08-31T03:13:00.000-04:00Thanks for the comment, Charles. I realize you kno...Thanks for the comment, Charles. I realize you know much more about set theory, logic, and the philosophy of mathematics than I will ever know.<BR/><BR/>I've been surprised to find some writing about computability and economics. In addition to Mirowski, <A HREF="http://ideas.repec.org/p/trn/utwpde/0308.html" REL="nofollow">Kumaraswamy Velupillai</A> is intriguing. (I did not check that the download button in that link works.)<BR/><BR/>I realize that anybody interested in an academic discipline will have a reading list that grows, not shrinks. Given the excerpt available on-line, I might order that.Robert Vienneauhttps://www.blogger.com/profile/14748118392842775431noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-67343908759391205842007-08-30T06:31:00.000-04:002007-08-30T06:31:00.000-04:00It's good to see you post this, since you have hin...It's good to see you post this, since you have hinted that you see some non-superficial parallels between foundational issues in maths and economics.<BR/><BR/>Some quibbles, points and subjective reactions:<BR/>* On your "thinkers list": Russell also contributed type theory (along with Alonzo Church), which has been a fertile stream marrying with structuralism (esp. Lawverian algebra) and constructivism (through Bishop & Martin-Loef). Lakatos' school is sometimes called "quasi-empiricist", and I don't suppose that Mill really had all that much lasting influence. I don't think that either Poincare can Wittgenstein can really be directly associated with much other than anti-foundationalist criticism, although W certainly has had a big indirect influence through Dummett on intuitionism. I certainly wouldn't call Poincare an intuitionist.<BR/>* Hilbert's 10th problem, solvability of Diophantines, certainly wasn't settled by Goedel's theorem or its refinements, though some techniques Goedel originated were essential to Matiyasevich's counterexample.<BR/>* I should probably stop recommending unwanted reading, but you may find <A HREF="http://www.dcorfield.pwp.blueyonder.co.uk/Towards.htm" REL="nofollow">David Corfield's book, <I>Towards a Philosophy of Real Mathematics</I></A> very interesting and agreeable if you did read it, especially on Lakatos and the relationship between the philosophy and practice of mathematics.Anonymousnoreply@blogger.com