From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Sun Mar 4 20:35:29 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 l251ZT4Z019894 for ; Sun, 4 Mar 2007 20:35:29 -0500 (EST) Received: from front3.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 l251ZPkv062581 for ; Sun, 4 Mar 2007 20:35:25 -0500 (EST) Received: (qmail 13481 invoked from network); 5 Mar 2007 01:35:25 -0000 Received: from mailscan6.acsu.buffalo.edu (128.205.7.95) by front3.acsu.buffalo.edu with SMTP; 5 Mar 2007 01:35:25 -0000 Received: (qmail 25103 invoked from network); 5 Mar 2007 01:35:25 -0000 Received: from deliverance.acsu.buffalo.edu (128.205.7.57) by front1.acsu.buffalo.edu with SMTP; 5 Mar 2007 01:35:25 -0000 Received: (qmail 29621 invoked from network); 5 Mar 2007 01:35:11 -0000 Received: from listserv.buffalo.edu (128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 5 Mar 2007 01:35:11 -0000 Received: by LISTSERV.BUFFALO.EDU (LISTSERV-TCP/IP release 14.5) with spool id 3627903 for CSE584-SP07-LIST@LISTSERV.BUFFALO.EDU; Sun, 4 Mar 2007 20:35:11 -0500 Delivered-To: cse584-sp07-list@listserv.buffalo.edu Received: (qmail 26924 invoked from network); 5 Mar 2007 01:35:11 -0000 Received: from mailscan7.acsu.buffalo.edu (128.205.6.158) by listserv.buffalo.edu with SMTP; 5 Mar 2007 01:35:11 -0000 Received: (qmail 27643 invoked from network); 5 Mar 2007 01:35:10 -0000 Received: from castor.cse.buffalo.edu (128.205.32.14) by smtp3.acsu.buffalo.edu with SMTP; 5 Mar 2007 01:35:10 -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 l251ZA7K019886 for ; Sun, 4 Mar 2007 20:35:10 -0500 (EST) Received: (from rapaport@localhost) by castor.cse.Buffalo.EDU (8.13.6/8.12.9/Submit) id l251ZA9L019885 for cse584-sp07-list@listserv.buffalo.edu; Sun, 4 Mar 2007 20:35:10 -0500 (EST) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Message-ID: <200703050135.l251ZA9L019885@castor.cse.Buffalo.EDU> Date: Sun, 4 Mar 2007 20:35:10 -0500 Reply-To: "William J. Rapaport" Sender: "Philosophy of Computer Science, Spring 2007" From: "William J. Rapaport" Subject: MISSING PREMISES IN PP2? 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 1335; 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 0.88.6/2723/Sun Mar 4 15:50:33 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean Status: R Content-Length: 5048 ------------------------------------------------------------------------ Subject: MISSING PREMISES IN PP2? ------------------------------------------------------------------------ A student writes: | In paper one the missing premise was a necessary part of the argument. | It was a needed statement, ... Correct. | ... a definition, ... Nope: It was "computers are not natural phenomena", which is a (negative) class-membership statement, not a definition. | ... which could not be derived from | any of the other premises. | The arg. was clearly invalid without it. Correct. | In this paper's argument, there are some missing premises. However, both | of them can be derived from the given premises. I originally ignored | them, but I'm wondering if they are actually missing premises now and | not just missing steps. | Example: | P1. A thing can compute iff it can do what a UTM can do. | P1a. This entails that if a thing can do what a UTM can do, then it can | compute. Correct. Note that this is not a missing premise, for 2 reasons. First, it is actually 1/2 of P1. P1 says both that, if a thing can compute then it can do what a UTM can do, and that, if a thing can do what a UTM can do, then it can compute. P1a is just this second half of P1. Second, missing premises, technically, are necessary parts of an argument that are independent and cannot be derived from the other premises. Although "missing" in the sense that it's not explicitly stated, it's not a "missing premise" in the technical sense. | P2. A computer is any physical device that computes. | P3. The human brain is physical device that can do what a UTM can. | ?.. | Here is where there this technically a missing premise. To be explicit | we should say that from P1a and P3 we can say that a human brain is a | physical device that computes (MP1). Then the conclusion P4, that a | human brain is a computer, follows from MP1 and P2. | There is a missing step, but it is not a stand alone premise like in | paper one. It can be derived from the given premises. Right; so although it is not explicitly stated, it's not a "missing premise" in the technical sense. Perhaps we can call these non-explicit premises "derived premises". They're derived, like the conclusion is derived, but they're not the final conclusion; they serve as intermediate premises. | Does not stating it then make the argument invalid? No. Invalidity has to do only with whether it's possible for the premises to be true yet for the conclusion to be false. Because the missing steps in the above argument logically follow from the premises, the validity of the argument is independent of them; they were "implicit" in the premises. In the now infamous PP1, the argument as it stood without the missing premise was invalid, because there was no necesssary connection between the premises and the conclusion, thus making it possible for the premises to be true yet for the conclusion to be false. With its missing premise explicitly stated, a link between the (three) premises and the conclusion was forged, making it impossible for all (three) premises to be true yet for the conclusion to be false. Maybe it's worth seeing this more formally. Here's (a simplified version of) the argument of PP1: 1. Science studies natural phenomena. 2. Computer science studies computers. So, 3. computer science is not a science. Note that 1 and 2 have nothing to do with each other. 1 doesn't talk about computer science or computers, and 2 doesn't talk about science or natural phenomena. 3 talks about computer science and science, but not about computers or natural phenomena, so it's perfectly possible for 1 and 2 to be true and 3 to be false. Compare it to these arguments: 1a. Rodents eat fish. 1b. Cats eat fish. 2a. Mice eat cheese. 2b. Mice eat cheese. So, 3a. Mice are not rodents. So, 3b. Mice are not cats. All 3 of these arguments have exactly the same form. Argument "a" shows pretty clearly, I think, that it's possible for the premises to be true but the conclusion false. (Argument "b" shows that it's possible for the premises and conclusion to be true. The argument of PP1 shows that it's hard to tell whether it's more like "a" or like "b".) The general form is: 1c. Anything that is an A is a B (any rodent is a fish eater, any cat is a fish eater, any science is a natural-phenomenon studier) 2c. Anything that is a C is a D (any mice is a cheese eater, any (branch of?) computer science is a computer studier) So, 3c. Anything that is a C is not an A. Think of this in terms of set theory: 1d. A is a subset of B 2d. C is a subset of D Does it necessarily follow that C is not a subset of A? No; it might if D is a subset of B. (Draw a Venn diagram if you're not convinced!) Suppose, however, we add the following missing premise: MPd. D is not a subset of B. Now it does necessarily follow that C is not a subset of A; again, draw a Venn diagram if you don't see why! Now