cher@ihlpf.UUCP (Mike Cherepov) (09/11/86)
> There are PLENTY of things that are true because I want them to be true. > > The only sensible way I know to judge something so complex as an > ideology is to look at its advocates and what they are doing and > then decide whether I like the resulting personalities and their > actions. Gee, can't assert anything anymore without being blasted from all directions for every real or imaginary falla.., mistake, that is. How about internal consistency as your criterion?? Nazism is weak on it, for example. I try to choose the position with most self-contradiction. Why do I do that, you ask? - I confess, because I like consistency. It seems like a fundamental fondness, though. No ideology I know of declared itself inconsistent. And 2+2=4 is a part of pretty consistent net of axioms and theorems. Ah, have to get back to work. Actually I wonder if the search for consistency is an emotion.... I seems like trying not to be non self-contradictory is a logical thing ?-) Mike Cherepov
zafrany@brahms.BERKELEY.EDU (Samy Zafrany) (09/16/86)
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
ladkin@kestrel.ARPA (Peter Ladkin) (09/16/86)
In article <485@ccd700.UUCP>, jim@ccd700.UUCP (prototype account) writes: > In order for the laws of arithmetic to be *meaningful*, > they must mean the same thing to everyone. Are you familiar with the arguments of Quine that there is no such attribute as *meaning the same thing* ? However, he doesn't argue that everything is meaningless. So his arguments entail the falsity of your statement. For your statement to be true, one of his arguments must be incorrect. Which one? Peter Ladkin ladkin@kestrel.arpa
dmcanzi@watdcsu.UUCP (David Canzi) (09/16/86)
In article <15628@ucbvax.BERKELEY.EDU> m128abo@brahms.UUCP (Michael Ellis) writes: >>... whether you really would like something to be true is irrelevant. >>... [Mike Cherepov] > > There are PLENTY of things that are true because I want them to be true. > > For instance, once I had a cat whose name was "Gunnar", because I > WANTED his name to be "Gunnar". This is a misunderstanding based on an ambiguity in the English language. (There is a belief that the English language is the most precise language on Earth. This belief, which I have heard expressed by educated people with straight faces, is probably so widely believed among English-speaking people because of the apparently infinite human capacity for self-flattery, combined with the curious belief that one in possession of a better *anything* is a better person than one less fortunate. I call this the "mine-is-bigger-than-yours" syndrome. I don't know any other languages, but I figure that if our language is the most precise language on Earth, then all the non-English speaking world is in *big* trouble...) If, from knowing X we can conclude that Y is so, we sometimes say "Y because X". On the other hand, when one event, X, is the cause of another event, Y, we might say "Y because X". Even though the two statements look the same, they don't mean the same thing. Let's distinguish these two different meanings by expressing the first one as "Y because[1] X" and the second as "Y because[2] X". Let X = "I wish Y to be so". Mike Cherepov's statement I take as meaning that "Y because[1] I wish Y to be so" is not so. You have attempted to show a counterexample, but all you have really shown is a case where "Y because[2] I wish Y to be so". This doesn't work as a counterexample, because "because" doesn't have the same meaning in both statements. Thus, your attempt to prove that wishful thinking is a valid method of inference turns out to be invalid. > 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. The question of whether 2+2=4 because you wish it to be so is, um, beyond the scope of this article... -- David Canzi "If there is no God, who pops up the next Kleenex?"
ark@alice.UucP (Andrew Koenig) (09/17/86)
> 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. Maybe yes, maybe no. The trouble is that once you introduce INF, you give up some other useful properties of natural numbers, such as cancellation (x+z=y+z implies x=y).
zafrany@brahms.BERKELEY.EDU (Samy Zafrany) (09/18/86)
In article <12467@kestrel.ARPA> ladkin@kestrel.ARPA (Peter Ladkin) writes: >In article <485@ccd700.UUCP>, jim@ccd700.UUCP (prototype account) writes: > >> In order for the laws of arithmetic to be *meaningful*, >> they must mean the same thing to everyone. > >Are you familiar with the arguments of Quine that there is no >such attribute as *meaning the same thing* ? >However, he doesn't argue that everything is meaningless. > >So his arguments entail the falsity of your statement. >For your statement to be true, one of his arguments >must be incorrect. Which one? And are you familiar with the arguments of Wittgenstein that there is such an attribute as *meaning the same thing* ? Which only philosophers (like Quine) don't seem to use correctly like the rest of us and therefore fall into their routine traps (like Quine did). So Wittgenstein's arguments entail the falsity of your statement. For your statement to be true, one of his arguments must be incorrect. Which one? ucbvax!brahms!zafrany Samy Zafrany/UCB Math Dept/Berkeley CA 94720 "No matter how subtle the wizard, a knife between the shoulder blades will seriously cramp his style."
zafrany@brahms.BERKELEY.EDU (Samy Zafrany) (09/18/86)
In article <6068@alice.uUCp> ark@alice.UucP (Andrew Koenig) writes: >> 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. > >Maybe yes, maybe no. The trouble is that once you introduce INF, >you give up some other useful properties of natural numbers, >such as cancellation (x+z=y+z implies x=y). Well, no one said that all arithmetics have to have similar properties, what we view as a useful property on Earth might seem like a strange one on Ork and vice versa. Again concepts like "useful", "coherent", "nice" and so forth (even concepts like "exact" and "universal") are culture-dependent, deeply has to do with elementary common forms of life and so on.... . ucbvax!brahms!zafrany Samy Zafrany/UCB Math Dept/Berkeley CA 94720 Imagine a place in which the less money you have the better life you have. In this place 0 will be the greatest number.