From owner-cse584-sp07-list@LISTSERV.BUFFALO.EDU Wed Jan 24 16:43:24 2007 for ; Wed, 24 Jan 2007 16:43:24 -0500 (EST) for ; Wed, 24 Jan 2007 16:43:19 -0500 (EST) 16:43:05 -0500 Delivered-To: cse584-sp07-list@listserv.buffalo.edu for ; Wed, 24 Jan 2007 16:43:04 -0500 (EST) cse584-sp07-list@listserv.buffalo.edu; Wed, 24 Jan 2007 16:43:04 -0500 (EST) X-UB-Relay: (castor.cse.buffalo.edu) X-PM-EL-Spam-Prob: : 7% Date: Wed, 24 Jan 2007 16:43:04 -0500 Reply-To: "William J. Rapaport" From: "William J. Rapaport" Subject: ON SYMBOLS AND COMPUTATION 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=-2.1 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 0.88.6/2487/Wed Jan 24 10:53:17 2007 on ares.cse.buffalo.edu X-Virus-Status: Clean ------------------------------------------------------------------------ Subject: ON SYMBOLS AND COMPUTATION ------------------------------------------------------------------------ A student writes: | Newell and Simon's use of the word "symbol" reminds me very much of | Wittgenstein's view of language in the Tractatus. For those of you who may not be familiar with this, Wittgenstein was one of the leading philosophers of the 20th century, a German student of Bertrand Russell. He was very charismatic, but only wrote two major books (his other writings are largely based on his students' lecture notes, so, just in case I become as famous as Wittgenstein, you might want to hold on to your notes from this course :-). The first book was the Tractatus Logico-Philosophicus, which consisted of numbered propositions outlining his view of how language relates to the world. Among other things, it introduced truth tables, and ended with a famous saying: "Whereof one cannot speak, thereof one must be silent", the point of which was that language only allows you talk about certain things. In his second book, Philosophical Investigations, he repudiated almost everything he had said in the Tractatus. For more information, go to: http://plato.stanford.edu/entries/wittgenstein/ | That is, symbols are | composed of other symbols and there are rules for determining (i.e. a | grammar) how symbols can be put together. This reminds me of W's notion of | atomic propositions and how they can be logically put together. Do you | think there is a connection between the two? Absolutely! This is one of the origins of the notion of a formal symbol system; we'll look at this again later on. | If so, can Newell and Simon be said to hold a correspondence theory of truth? They probably do, but I'm not sure how that follows from the connection that you point out. | W of course | went on to reject a lot of what he had written in the Tractatus. Do his | objections to the Tractatus apply to Newell and Simon's symbols? I'm not overly familiar with the "later Wittgenstein"'s Philosophical Investigations, so I'm not sure, but, in any case, I doubt there's a simple answer. This sounds like a term-paper topic :-) | Also, how does the notion of symbols fit in with Phil of Language | concepts of sense and reference? A bit more background for the non-philosophers/non-linguists who might be reading this. Gottlob Frege was a turn of the 19th century German mathematician and philosopher who pretty much single-handedly invented modern symbolic logic. He also wrote a very influential series of philosophy papers, including one called (in the original German) "Ueber Sinn und Bedeutung", variously translated as "On Sense and Reference" or "On Sense and Denotation". Put overly simply, his claim was that there were really two different kinds of meanings of a linguistic expression: Its reference (or "referent", or denotation) was a thing in the world; so, for example, the reference of "horse" would be a horse. But some words lack references; e.g., "unicorn" has no real-world reference. Yet it is meaningful. How? By having a "sense": A sense is the way in which an expression picks out its reference. So, perhaps, the sense of "unicorn" might be something like "white, horselike, single-horned animal". For more information, go to: http://www.blackwellpublishing.com/content/BPL_Images/Content_store/Sample_chapter/9780631222231/001.pdf for a copy of his paper, and to: http://plato.stanford.edu/entries/frege/ for more on Frege's philosophy in general. | I think there is a connection between | Phil of Language and CS, but I'm unsure how to articulate it. The best | I can do is something like this: "The limits of language limit what we | can know. Therefore, the limits of a computer language limit what we | can compute." Am I barking up the wrong tree here? Do you have any | thoughts? There's probably something to your argument. When we discuss hypercomputation later, you'll see that some people argue that there are some "computable" problems that are not computable in Turing's sense. That seems consistent with your slogan.