The Definition of Points
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From: Lester Zick on 27 Apr 2007 18:56 On Fri, 27 Apr 2007 22:02:46 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >On Fri, 27 Apr 2007 11:58:29 -0700, Lester Zick ><dontbother(a)nowhere.net> wrote: > >>On Fri, 27 Apr 2007 09:11:24 +0100, Ben newsam >><ben.newsam.remove.this(a)gmail.com> wrote: >> >>>On Thu, 26 Apr 2007 16:16:01 -0700, Lester Zick >>><dontbother(a)nowhere.net> wrote: >>> >>>>Who cares whether it solves the equation if the equation does not >>>>determine the truth of x or 4? >>> >>>It determines nothing, it *states* that two things are equal. In other >>>words, it states that the two things being equal is "true". >> >>Well see, Ben, therein lies the rub. How do you know it's true? I'll >>grant you that's what you assume it says. But your statement that it >>says that is not a mathematical statement. The mathematical part >>simply says they're equal and makes no claim to truth in general. > >I'll say it again: it states that the two things being equal is >"true". That's the beauty of logic, it does what it says on the can. And where's the demonstration that what you says it is is true? I'll grant you it's beautiful. I just don't see your demonstration of what it says on the can. >In the nineteenth century, their version of logic was as convoluted >and complex as you seem to want to make it, and they didn't get very >far with it either. Only because they had no demonstration for the truth of their logic. ~v~~
From: Lester Zick on 27 Apr 2007 19:05 On Fri, 27 Apr 2007 22:17:31 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >On Fri, 27 Apr 2007 12:23:39 -0700, Lester Zick ><dontbother(a)nowhere.net> wrote: > >>On Fri, 27 Apr 2007 09:25:19 +0100, Ben newsam >><ben.newsam.remove.this(a)gmail.com> wrote: >> >>>>>>Presuming we already understand TvN binary mathematical logic >>>>>>sufficiently, what's the purpose of assigning the aliases "true" and >>>>>>"false" to 1 and 0? Obviously it's to pretend real truth and falsehood >>>>>>share identical properties with mathematical binary 1 and 0 when in >>>>>>fact we know nothing of the kind until we can demonstrate they share >>>>>>identical properties. And the fact you call 1 and 0 by other names has >>>>>>no affect on the properties of 1 and 0 or on the properties associated >>>>>>with those other names. >>>>> >>>>>They are both mutually exclusive, and everything must be either one or >>>>>the other. If you think they are not synonymous, perhaps you could >>>>>point out how they are not? >>>> >>>>Or perhaps you could point out how they are synonymous? >>> >>>1 = true >>>true = 1 >>>0 = false >>>false = 0 >>> >>>To say that something is either true or false is true, 1 + 0 = 1 >>>To say that something is both true and false is false, 1 * 0 = 0 >>> >>>Perhaps you could now point out how they are not? >> >>Well as long as we're drafting arbitrary synonymies and claiming >>arbitrary arithmetic properties for "true" and "false without proof >>perhaps you could demonstrate exactly why the same properties don't >>apply to "figs" and "ideas". I mean as long as you're guessing you >>might just as well guess what properties everything has that causes >>true=1 and false=0 where no other set of things does so there won't be >>any further confusion about which things are mutually exhaustive and >>which things aren't. I mean as long as you're guessing. > >Well... if everything that is not a fig is an idea, and everything >that is not an idea is a fig, then you have the set of everything, >same as you do with "true" and "false". Sure. But you're not demonstrating why "true" and "false" are mutually exhaustive but "figs" and "ideas" aren't. All you're doing is assigning mutually exhaustive binary arithmetic 1 and 0 to one set but not to the other. > The negation of "true" is >"false", and (IIRC) set theory states that the union of any set with >its complement equals the domain (something like that anyway). Well so you say but so you don't prove. It's very nice you think "true" and "false" are mutually exhaustive but I'd prefer a little proof for a change. > Now, >the symbol you choose for "false" is conveniently zero, but the symbol >for "true" is to a certain extent arbitrary, so long as the >arithmentic works. I have seen programming labguages where "true" is >-1. This has certain advantages that I won't go into here. I could care less which symbols you choose to represent "true" and "false". The fact is that we already have perfectly adequate symbols in "true" and "false". And we don't need other "arithmetic" symbols unless we intend to do arithmetic with them. ~v~~
From: Bob Kolker on 27 Apr 2007 21:17 Ben newsam wrote: > > A reasonable point in a way, as long as whatever scheme you eventually > come up with provides useful results. Useful and Lester do not coexist. Bob Kolker
From: Bob Cain on 27 Apr 2007 22:20 Lester Zick wrote: > How can truth in mechanically reduced universal terms not be useful? That could be. Why don't you give it a try? Provide a demonstration of such a truth using the mechanics of the world ("not" is not mechanics.) Given a demonstration we might be able to assess its usefulness. Until then the meaning of "truth in mechanically reduced universal terms" has meaning only to you (if to you.) Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
From: Lester Zick on 28 Apr 2007 13:36
On Fri, 27 Apr 2007 21:17:55 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Ben newsam wrote: > >> >> A reasonable point in a way, as long as whatever scheme you eventually >> come up with provides useful results. > >Useful and Lester do not coexist. Just as Bob and true do not coexist. ~v~~ |