From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Thu Jan 25 08:53:15 2007 for ; Thu, 25 Jan 2007 08:53:15 -0500 (EST) for ; Thu, 25 Jan 2007 08:53:10 -0500 (EST) 08:52:59 -0500 Delivered-To: cse584-sp07-list@listserv.buffalo.edu for ; Thu, 25 Jan 2007 08:52:56 -0500 (EST) cse584-sp07-list@listserv.buffalo.edu; Thu, 25 Jan 2007 08:52:56 -0500 (EST) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Date: Thu, 25 Jan 2007 08:52:56 -0500 Reply-To: "William J. Rapaport" From: "William J. Rapaport" Subject: SHAPIRO AND PROCEEDURES To: CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU List-Help: , List-Unsubscribe: List-Subscribe: List-Owner: List-Archive: X-UB-Relay: (castor.cse.buffalo.edu) X-Spam-Status: No, score=-2.0 required=5.0 tests=AWL,BAYES_00,SUBJ_ALL_CAPS X-Spam-Checker-Version: SpamAssassin 3.1.7 (2006-10-05) on ares.cse.buffalo.edu X-Virus-Scanned: ClamAV 0.88.6/2488/Thu Jan 25 04:57:17 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean A student writes: | Shapiro states than any procedure can be constructed using the | Bohm-Jacopini criteria of sequence, selection, and looping. Yes; for more on this, take a peek at my website "What is computation?": http://www.cse.buffalo.edu/~rapaport/computation.html which we'll discuss later this semester. | He also | states that if animals are mechanistic then a computer can do what an | animal can do (i.e. a further implication of the Church-Turing thesis). That depends on what "mechanistic" means. If it means "computational", then this is correct. But if it means something like "mechanical" (think of gears, levers, and pulleys), then maybe not. | It seem to follow from these two claims that [I] if animals are mechanistic | then anything animals do can be replicated using procedures constructed | with the Bohm-Jacopini criteria. On the computational interpretation of "mechanistic", this seems to be correct. | Would it then follow that [II] if animals | did things which could not be replicated using the Bohm-Jacopini | criteria, then animals were not mechanistic in Church-Turing sense? Yes, but for an uninteresting logical reason. Let: M = animals are computationally mechanistic R = anything animals do can be replicated using procedures constructed with the BJ criteria Then the claim labeled "I" above is: if M, then R Claim II is just: if not-R, then not-M which is logically equivalent to I by a truth-table analysis.