From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Sun Mar 4 17:38:31 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 l24McVgj017034 for ; Sun, 4 Mar 2007 17:38:31 -0500 (EST) Received: from front1.acsu.buffalo.edu (warmfront.acsu.buffalo.edu [128.205.6.88]) by ares.cse.buffalo.edu (8.13.6/8.13.6) with SMTP id l24McPLK046392 for ; Sun, 4 Mar 2007 17:38:25 -0500 (EST) Received: (qmail 3832 invoked from network); 4 Mar 2007 22:38:25 -0000 Received: from mailscan3.acsu.buffalo.edu (128.205.6.135) by front1.acsu.buffalo.edu with SMTP; 4 Mar 2007 22:38:25 -0000 Received: (qmail 26896 invoked from network); 4 Mar 2007 22:38:25 -0000 Received: from deliverance.acsu.buffalo.edu (128.205.7.57) by front3.acsu.buffalo.edu with SMTP; 4 Mar 2007 22:38:25 -0000 Received: (qmail 19879 invoked from network); 4 Mar 2007 22:38:11 -0000 Received: from listserv.buffalo.edu (128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 4 Mar 2007 22:38:11 -0000 Received: by LISTSERV.BUFFALO.EDU (LISTSERV-TCP/IP release 14.5) with spool id 3625069 for CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU; Sun, 4 Mar 2007 17:38:11 -0500 Delivered-To: cse584-sp07-list@listserv.buffalo.edu Received: (qmail 519 invoked from network); 4 Mar 2007 22:38:11 -0000 Received: from mailscan3.acsu.buffalo.edu (128.205.6.135) by listserv.buffalo.edu with SMTP; 4 Mar 2007 22:38:11 -0000 Received: (qmail 495 invoked from network); 4 Mar 2007 22:38:11 -0000 Received: from castor.cse.buffalo.edu (128.205.32.14) by smtp1.acsu.buffalo.edu with SMTP; 4 Mar 2007 22:38:11 -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 l24McBPI017026 for ; Sun, 4 Mar 2007 17:38:11 -0500 (EST) Received: (from rapaport@localhost) by castor.cse.Buffalo.EDU (8.13.6/8.12.9/Submit) id l24McBBR017025 for cse584-sp07-list@listserv.buffalo.edu; Sun, 4 Mar 2007 17:38:11 -0500 (EST) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Message-ID: <200703042238.l24McBBR017025@castor.cse.Buffalo.EDU> Date: Sun, 4 Mar 2007 17:38:11 -0500 Reply-To: "William J. Rapaport" Sender: "Philosophy of Computer Science, Spring 2007" From: "William J. Rapaport" Subject: IF-THEN vs. IF & ONLY IF (and definitions) 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=-2.5 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 0.88.6/2723/Sun Mar 4 15:50:33 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean Status: R Content-Length: 3649 ------------------------------------------------------------------------ Subject: IF-THEN vs. IF & ONLY IF (and definitions) ------------------------------------------------------------------------ A student writes: | I have been having this difficulty with the logical implication of a | statement in the form of a definition like, "an apple is a fruit." First, that's not a definition. If it were a definition, then "apple" would be synonymous with "fruit", which it isn't, because there are other fruits besides apples. What this gives you is class-membership or categorization information about apples. | Can that be expressed, "if an A, then a F?" I think that is obvious. | Something that is an Apple entails it being a fruit (fruithood?). Yes, though more accurately, it would be: If something is an apple, then it is a fruit. | However, it seems that a def requires a stronger connection like, "A iff | F." However this suggests that being a fruit implies being an apple. (A | iff T) translates to (A -> F) & (F -> A). That doesn't follow. You're right about definitions, and you're right that such a definition doesn't follow from the class-membership statement we began with. | In the context of the argument for position paper 2 the biconditional of | P1 not only seems true but is presented as one and so removes the | problem of translation. However P2 and P3 are definitions. P2 works. A | computer is any physical device that computes and any physical device | that computes is a computer. For P3: a human brain is a thing that can | do what a UTM can do. Sure! But: a thing that can do what a UTM can do | is a human brain? No! So definitions don't seem biconditional. Good observation! And welcome to the world of ambiguous English. In ordinary English, we often (carelessly) use "is" for both class-membership and for definitions (as well as other things), and a careful reader has to decide which reading is most appropriate in any given context. When it can't be figured out from the context, then a reader analyzing it needs to make an explicit assumption about how to interpret it, and proceed on the basis of that assumption. | I also wonder about getting to a point in the argument where I have | concluded that a human brain is thing that computes and a computer is | (any) thing that computes. This is easy to show as long as "physical | device" and "thing" can be interchanged. I think it would be fair to say that any "physical device" is a "thing" (as "thing" is used in Premise 1), but not necessarily the other way round: Some "things" are not physical, e.g., Turing machines abstractly conceived. | However, two things that imply | the same thing are not necessarily equivalent. "An apple is a fruit" and | "a banana is a fruit" does not mean that "an apple is a banana." Correct. | However, this may be related to my misunderstanding of how to handle | definitions where "one thing is another thing." The "any" in the part | about "a computer being any thing that computes" also seems to make a | difference. I'm not sure where that quote comes from. Premise 2 says, "A computer is any physical device that can compute." Here, I intended the following meaning: "computer" can be defined as "a physical device that can compute", or: Something is a computer =df it is a physical device that can compute. In any case, no matter how you interpret something that someone else says, if you explicitly present your interpretation, and then present your analysis in terms of that interpretation, you can't be faulted for *mis*interpreting (unless you make a logical error :-)