tag:blogger.com,1999:blog-4058766287077382431.post2063590756016186084..comments2024-03-23T04:01:39.348-04:00Comments on Understanding Society: Pragmatic inquiryDan Littlehttp://www.blogger.com/profile/15953897221283103880noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4058766287077382431.post-89401780961753537172009-06-21T11:23:33.978-04:002009-06-21T11:23:33.978-04:00I was about to protest the misspelling of Peirce&#...I was about to protest the misspelling of Peirce's name., but I see that it's Amazon error, not yours. It matters to me because he deserves respect as the first major American logician and a seminal influence on modern mathematics and the philosophy of science, and because he was unjustly neglected during his lifetime.<br /><br />Not only did he anticipate Heisenberg's Uncertainty Principle, and set out a finite axiomatization of arithmetic before Peano did, and the basis axiomatic set theory before Zermelo did, but also his notation and terminology were readable and suggestive, giving future logicians a better language to work in than the clunky terms of the Germans. (Perhaps I reveal my bias – my teachers were students of Alfred Tarski, who admired Peirce's work.)<br /><br />For what it's worth, Schleffer's Four Pragmatists: A Critical Introduction to Peirce, James, Mead and Dewey (spelled correctly) is up on Google Books in a fairly readable format.brosnanoreply@blogger.comtag:blogger.com,1999:blog-4058766287077382431.post-61485601987269731372009-06-20T13:40:52.954-04:002009-06-20T13:40:52.954-04:00"Proof of the Gödel incompleteness theorem di..."Proof of the Gödel incompleteness theorem didn't have direct practical consequences for computing, so far as I know"<br /><br />Gödel proved that in any finitely axiomatised logical theory of arithmetic there must be sentences that are true but not provable, by presenting a method of constructing them. <br /><br />His method involved a highly ingenious way of coding sentences, and indeed whole proofs, themselves as products of powers of prime numbers in such a way that "I am an unprovable sentence" is expressed as a property of a number.<br /><br />The bold yet delicate use of self-reference here was at least an inspiration for Turing and later for compiler design.brosnanoreply@blogger.comtag:blogger.com,1999:blog-4058766287077382431.post-50596940314717433102009-05-31T05:09:41.700-04:002009-05-31T05:09:41.700-04:00I adore this!I adore this!Agnesehttp://socuptodates.wordpress.comnoreply@blogger.com