Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!philabs!cmcl2!yale!husc6!panda!genrad!decvax!ittatc!dcdwest!sdcsvax!ucbvax!brahms!zafrany From: zafrany@brahms.BERKELEY.EDU (Samy Zafrany) Newsgroups: talk.philosophy.misc Subject: Re: Emotion and Logic Message-ID: <15679@ucbvax.BERKELEY.EDU> Date: Mon, 15-Sep-86 18:30:26 EDT Article-I.D.: ucbvax.15679 Posted: Mon Sep 15 18:30:26 1986 Date-Received: Fri, 19-Sep-86 00:34:15 EDT References: <11700119@inmet> <11700370@inmet> <698@ihlpf.UUCP> <15628@ucbvax.BERKELEY.EDU> <485@ccd700.UUCP> Sender: usenet@ucbvax.BERKELEY.EDU Reply-To: zafrany@brahms.UUCP (Samy Zafrany) Organization: University of California, Berkeley Lines: 72 In article <485@ccd700.UUCP> jim@ccd700.UUCP (prototype account) writes: >In article <15628@ucbvax.BERKELEY.EDU>, m128abo@brahms.BERKELEY.EDU (Michael Ellis) writes: >> For instance, once I had a cat whose name was "Gunnar", because I >> WANTED his name to be "Gunnar". For another, I consider 2+2=4 >> because I prefer laws of arithmetic that yield "2+2=4", although >> in certain circumstances I have on occasion PREFERRED laws >> yielding "2+2=0". Note that the truth of such facts is based on >> little more than my DESIRE that they be true. > >In the case of your cat, this may be so, however, the laws of arithmetic >are standardized because a group of people (society) "desire" them to >be a certain way. This has nothing to do with personal emotions. In >order for the laws of arithmetic to be *meaningful*, they must mean the >same thing to everyone. I suppose that it is correct to base the truth >of a statement on emotions, but, if the statement is meaningless, the >truth is pretty irrelavent. Consider the term "chair". A chair is a >piece of furniture used for sitting. It is not called a chair because of >any "chairlike" qualities intrinsic to it. You may elect to call it >a splitzleboard. No one can tell you that it isn't, but, you may spend >a lot of time standing around. > >Jim Sitek > >"Know what I mean?" > Hans Reichenbach Still fur from refuting Michael's argument about the conventionalism of mathematics. Maybe Michael by himself cannot postulate any arithmetical laws that he wishes to, but as Wittgenstein does it many times in his "Philosophical Investigations" (remember how he starts his paragraphs "Imagine a tribe ... "), we can imagine a primitive society (if my memory doesn't deceive me, I think that some tribes somewhere were found to have the arithmetic I'm trying to describe) whose number system consists only of: 1, 2, 3, 4, 5, many. Somehow these people don't need more numbers in their lifes. Their arithmetic will consist of theorems like: 1+1=2, 2+2=4, 3+3=many, 4+5=many, many+3=many, many+many=many, and so on, which is a perfectly logically consistent theory. If we were lucky to live in a world with infinite objects in it, we would probably have another natural number incorporated to our arithmetic, i.e. the number used to count an infinite set of chairs (or splitzleboards), which we may call: INF. Our arithmetic will be like: 19+INF=INF, INF*INF=INF, "INF is the greatest natural number" (note that we don't have such natural number in our current arithmetic!), and so on. We may go on like that and imagine more strange cultures and tribes..., there is no logical reason why they all should look like ours. The point I'm trying to make is what I believe what Michael was trying to make. Even a perfect exact science like mathematics is not free from being shaped and influenced by common forms of life (using Wittgenstein's terminology), which apparently don't seem to have anything to do with it. A mathematical truth is one which is agreed by all the members of a society (or at least by those members who are still interested in math) as an elegant short way to summerize some common rules in the society's basic way of life. So, in our civilization, 2+2=4, since if you ow me 2 dollar from yesterday and 2 dollars from today, then you ow me 4 dollars. But imagine that in some other civilization from a different planet, if X loaned to Y 2 dollars (assuming they're using American dollars) yesterday and 2 dollars today, then in total, Y ows X only 3 dollars out of some strange ethical law of "Be too nice to your fellow volcan!" or some sort of reason like that. Ofcourse, we have to imagine that the same sort of thing happens in other aspects of their lifes. So probably their arithmetic will contain the equality:2+2=3. But I'm only trying to give the flavour of this, and a complete account needs more work. ucbvax!brahms!zafrany Samy Zafrany/UCB Math Dept/Berkeley CA 94720