From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Sat Jan 27 08:22:45 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 l0RDMjB8001406 for ; Sat, 27 Jan 2007 08:22:45 -0500 (EST) Received: from front2.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 l0RDMf7h077224 for ; Sat, 27 Jan 2007 08:22:41 -0500 (EST) Received: (qmail 1362 invoked from network); 27 Jan 2007 13:22:41 -0000 Received: from mailscan1.acsu.buffalo.edu (128.205.6.133) by front2.acsu.buffalo.edu with SMTP; 27 Jan 2007 13:22:41 -0000 Received: (qmail 25026 invoked from network); 27 Jan 2007 13:22:41 -0000 Received: from deliverance.acsu.buffalo.edu (128.205.7.57) by front3.acsu.buffalo.edu with SMTP; 27 Jan 2007 13:22:41 -0000 Received: (qmail 28634 invoked from network); 27 Jan 2007 13:22:27 -0000 Received: from listserv.buffalo.edu (128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 27 Jan 2007 13:22:27 -0000 Received: by LISTSERV.BUFFALO.EDU (LISTSERV-TCP/IP release 14.5) with spool id 2926903 for CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU; Sat, 27 Jan 2007 08:22:27 -0500 Delivered-To: cse584-sp07-list@listserv.buffalo.edu Received: (qmail 16482 invoked from network); 27 Jan 2007 13:22:27 -0000 Received: from mailscan3.acsu.buffalo.edu (128.205.6.135) by listserv.buffalo.edu with SMTP; 27 Jan 2007 13:22:27 -0000 Received: (qmail 4659 invoked from network); 27 Jan 2007 13:22:26 -0000 Received: from castor.cse.buffalo.edu (128.205.32.14) by smtp1.acsu.buffalo.edu with SMTP; 27 Jan 2007 13:22:26 -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 l0RDMQrV001395 for ; Sat, 27 Jan 2007 08:22:26 -0500 (EST) Received: (from rapaport@localhost) by castor.cse.Buffalo.EDU (8.13.6/8.12.9/Submit) id l0RDMQiX001394 for cse584-sp07-list@listserv.buffalo.edu; Sat, 27 Jan 2007 08:22:26 -0500 (EST) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Message-ID: <200701271322.l0RDMQiX001394@castor.cse.Buffalo.EDU> Date: Sat, 27 Jan 2007 08:22:26 -0500 Reply-To: "William J. Rapaport" Sender: "Philosophy of Computer Science, Spring 2007" From: "William J. Rapaport" Subject: LOGIC QUESTIONS 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 1029; Body=0 Fuz1=0 Fuz2=0 X-Spam-Status: No, score=-2.0 required=5.0 tests=AWL,BAYES_00,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 0.88.6/2493/Fri Jan 26 07:00:46 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean Status: R Content-Length: 1750 A student writes: | I have some questions concerning Martinich's remarks on logic. | | First: | | On page 25 of the text Martinich claims the following argument is valid: | | | Ima Hogg was a great Philanthropist. | ____________________________________ | Either Aristotle is or is not a great Philosopher. | | | I understand that the conclusion is supposed to be a tautalogy, and thus | contains "no information". The argument is valid, then, on grounds that | it always possible to deduce a tautology. That is, it is always | possible to deduce a propostion of the form "(A is B) or (A is not B)" | (e.g. "It is raining or it is not raining"). | I am, however, uncomfortable with calling this argument valid. Can you | ease my discomfort? An argument is valid iff it is impossible for all the premises to be (simultaneously) true while (i.e., and) the conclusion is false. Since, in this case, because the conclusion is a tautololgy, it is impossible for the conclusion to be false (whether or not the premises are all true). Therefore, it is impossible for all the premises to be true *and* the conclusion false. Therefore, it's (trivially) valid. But it's not sound: The premise is false. So it's not a very good argument (and it's certainly not "cogent"). | Second: | | On page 50 Martinich states: | | "... from any proposition, an infinite number of propositions follows." | | Does he mean you can deduce any number of tautoligies (like the question | above)? | Or does he mean you can always deduce the proposition disjoined with another | proposition? | e.g. | A is X | _______ | (A is X) or (B is Y) or etc... I suspect that he means both. You can also always deduce the proposition *conjoined* with itself :-)