From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Wed Mar 21 19:51:28 2007 Received: from ares.cse.buffalo.edu (ares.cse.Buffalo.EDU [128.205.32.79]) by castor.cse.Buffalo.EDU (8.13.6/8.12.10) with ESMTP id l2LNpRKj000661 for ; Wed, 21 Mar 2007 19:51:27 -0400 (EDT) Received: from front1.acsu.buffalo.edu (upfront.acsu.buffalo.edu [128.205.4.140]) by ares.cse.buffalo.edu (8.13.6/8.13.6) with SMTP id l2LNpPnf074320 for ; Wed, 21 Mar 2007 19:51:25 -0400 (EDT) Received: (qmail 13627 invoked from network); 21 Mar 2007 23:51:25 -0000 Received: from mailscan8.acsu.buffalo.edu (128.205.7.55) by front1.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:51:25 -0000 Received: (qmail 12514 invoked from network); 21 Mar 2007 23:51:25 -0000 Received: from deliverance.acsu.buffalo.edu (128.205.7.57) by front2.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:51:25 -0000 Received: (qmail 17005 invoked from network); 21 Mar 2007 23:51:07 -0000 Received: from listserv.buffalo.edu (128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:51:07 -0000 Received: by LISTSERV.BUFFALO.EDU (LISTSERV-TCP/IP release 14.5) with spool id 4005336 for CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU; Wed, 21 Mar 2007 19:51:07 -0400 Delivered-To: cse584-sp07-list@listserv.buffalo.edu Received: (qmail 9692 invoked from network); 21 Mar 2007 23:51:07 -0000 Received: from mailscan6.acsu.buffalo.edu (128.205.7.95) by listserv.buffalo.edu with SMTP; 21 Mar 2007 23:51:07 -0000 Received: (qmail 13540 invoked from network); 21 Mar 2007 23:51:05 -0000 Received: from castor.cse.buffalo.edu (128.205.32.14) by smtp1.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:51:05 -0000 Received: from castor.cse.Buffalo.EDU (rapaport@localhost [127.0.0.1]) by castor.cse.Buffalo.EDU (8.13.6/8.12.10) with ESMTP id l2LNp5mN000653 for ; Wed, 21 Mar 2007 19:51:05 -0400 (EDT) Received: (from rapaport@localhost) by castor.cse.Buffalo.EDU (8.13.6/8.12.9/Submit) id l2LNp567000652 for cse584-sp07-list@listserv.buffalo.edu; Wed, 21 Mar 2007 19:51:05 -0400 (EDT) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Message-ID: <200703212351.l2LNp567000652@castor.cse.Buffalo.EDU> Date: Wed, 21 Mar 2007 19:51:05 -0400 Reply-To: "William J. Rapaport" Sender: "Philosophy of Computer Science, Spring 2007" From: "William J. Rapaport" Subject: FORMAL SYNTACTIC SYSTEMS To: CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU Precedence: list List-Help: , List-Unsubscribe: List-Subscribe: List-Owner: List-Archive: X-UB-Relay: (castor.cse.buffalo.edu) X-DCC-Buffalo.EDU-Metrics: castor.cse.Buffalo.EDU 1336; Body=0 Fuz1=0 Fuz2=0 X-Spam-Status: No, score=-1.2 required=5.0 tests=AWL,BAYES_00, RCVD_IN_BL_SPAMCOP_NET,SUBJ_ALL_CAPS autolearn=no version=3.1.7 X-Spam-Checker-Version: SpamAssassin 3.1.7 (2006-10-05) on ares.cse.buffalo.edu X-Virus-Scanned: ClamAV 0.88.6/2893/Wed Mar 21 15:48:02 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean Status: R Content-Length: 1157 ------------------------------------------------------------------------ Subject: FORMAL SYNTACTIC SYSTEMS ------------------------------------------------------------------------ We've discussed formal syntactic systems (and don't forget to take a look at the webpage for it: http://www.cse.buffalo.edu/~rapaport/584/S07/formalsystems.html Bertrand Russell, a famous 20th-century philosopher and logician, described mathematics in a way that fits perfectly with our concept of a formal syntactic system: "Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing... It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true... If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." (From his _Mysticism and Logic_ (1917), ch. 4.) From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Wed Mar 21 19:54:16 2007 Received: from ares.cse.buffalo.edu (ares.cse.Buffalo.EDU [128.205.32.79]) by castor.cse.Buffalo.EDU (8.13.6/8.12.10) with ESMTP id l2LNsGo9000740 for ; Wed, 21 Mar 2007 19:54:16 -0400 (EDT) Received: from front3.acsu.buffalo.edu (coldfront.acsu.buffalo.edu [128.205.6.89]) by ares.cse.buffalo.edu (8.13.6/8.13.6) with SMTP id l2LNsC4R074524 for ; Wed, 21 Mar 2007 19:54:12 -0400 (EDT) Received: (qmail 25357 invoked from network); 21 Mar 2007 23:54:12 -0000 Received: from mailscan5.acsu.buffalo.edu (128.205.6.137) by front3.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:54:12 -0000 Received: (qmail 3798 invoked from network); 21 Mar 2007 23:54:11 -0000 Received: from deliverance.acsu.buffalo.edu (128.205.7.57) by front1.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:54:11 -0000 Received: (qmail 20374 invoked from network); 21 Mar 2007 23:54:07 -0000 Received: from listserv.buffalo.edu (128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:54:07 -0000 Received: by LISTSERV.BUFFALO.EDU (LISTSERV-TCP/IP release 14.5) with spool id 4005374 for CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU; Wed, 21 Mar 2007 19:54:07 -0400 Delivered-To: cse584-sp07-list@listserv.buffalo.edu Received: (qmail 10114 invoked from network); 21 Mar 2007 23:54:07 -0000 Received: from mailscan4.acsu.buffalo.edu (128.205.6.136) by listserv.buffalo.edu with SMTP; 21 Mar 2007 23:54:07 -0000 Received: (qmail 5501 invoked from network); 21 Mar 2007 23:54:06 -0000 Received: from castor.cse.buffalo.edu (128.205.32.14) by smtp4.acsu.buffalo.edu with SMTP; 21 Mar 2007 23:54:06 -0000 Received: from castor.cse.Buffalo.EDU (rapaport@localhost [127.0.0.1]) by castor.cse.Buffalo.EDU (8.13.6/8.12.10) with ESMTP id l2LNs6TF000734 for ; Wed, 21 Mar 2007 19:54:06 -0400 (EDT) Received: (from rapaport@localhost) by castor.cse.Buffalo.EDU (8.13.6/8.12.9/Submit) id l2LNs6Uv000733 for cse584-sp07-list@listserv.buffalo.edu; Wed, 21 Mar 2007 19:54:06 -0400 (EDT) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Message-ID: <200703212354.l2LNs6Uv000733@castor.cse.Buffalo.EDU> Date: Wed, 21 Mar 2007 19:54:06 -0400 Reply-To: "William J. Rapaport" Sender: "Philosophy of Computer Science, Spring 2007" From: "William J. Rapaport" Subject: Peter Suber, "Logical Systems" To: CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU Precedence: list List-Help: , List-Unsubscribe: List-Subscribe: List-Owner: List-Archive: X-UB-Relay: (castor.cse.buffalo.edu) X-DCC-Buffalo.EDU-Metrics: castor.cse.Buffalo.EDU 1336; Body=0 Fuz1=0 Fuz2=0 X-Spam-Status: No, score=-2.5 required=5.0 tests=AWL,BAYES_00 autolearn=unavailable version=3.1.7 X-Spam-Checker-Version: SpamAssassin 3.1.7 (2006-10-05) on ares.cse.buffalo.edu X-Virus-Scanned: ClamAV 0.88.6/2895/Wed Mar 21 19:46:31 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean Status: R Content-Length: 364 ------------------------------------------------------------------------ Subject: Peter Suber, "Logical Systems" ------------------------------------------------------------------------ Here's a website that some of you might find useful and/or interesting: Peter Suber's "Logical Systems" course website http://www.earlham.edu/~peters/courses/logsys/lshome.htm