The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 19 Dec 2007 12:15 On Tue, 18 Dec 2007 15:45:42 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >Lester Zick wrote: >> And a chain is no stronger than its weakest link and no truer >> than is weakest assumptions of truth which in the context of modern >> mathematics don't constitute demonstrations of truth at all. > >Virgil wrote: >> Zick seems too stupid to realize that proving "A implies B" does not >> ever require that anyone prove "A". >> >> All mathematical proofs are of this form, "A implies B", where A is a >> set of axioms, and are quite independent on the truth of the axioms >> which form the "A". > >I'm currently reading "The Art of Mathematics" by Jerry King, >wherein the author makes this plainly clear. "If A then B" is >the fundamental basis of all theorems. His example was >"IF we can say that 1+1=2, THEN we can say that 2+2=4". We can say lots of things. Doesn't make them true. However since the author couldn't quite see his way clear to titling his art book "The Science of Mathematics" I think we can reasonably infer he doesn't have a clue either. ~v~~
From: Lester Zick on 19 Dec 2007 13:11 On Tue, 18 Dec 2007 15:37:54 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >David R Tribble wrote: >> Exactly. In the realm of mathematics, we call those assumed >> contexts "axioms". > >Lester Zick wrote: >> Which is exactly my point. You don't call those assumed contexts >> "true" because you have no demonstrations of truth for them. But then >> you turn right around and act as if I'd never said the word. > >You still don't understand what a mathematical axiom is >supposed to be, do you? I always have. Modern mathematikers have just spent the last several years in denial. >An axiom is an assumed truth. Period. What? Bite your tongue! You just used the T-word and "true" is a four letter word. I've just spent the last several years pointing out exactly this in my various threads on scientific epistemology. That makes mathematics' naive reliance on assumptions of truth empiricism in formal terms and formalized guesswork in less rigorous terms. >There are no "demonstrations" of whether it's true or not, >because they are not needed. Well that's certainly very reassuring. The only reason there are no demonstrations of truth is not because they aren't needed but because mathematicians don't know how to proceed. If mathematicians need demonstrations of truth for theorems I can't imagine they wouldn't be thrilled to be able to do the same for axiomatic assumptions of truth. > An axiom is true, because an axiom is a truth. A very touching confession of faith. Why not just say "an axiom is true because it's true because it's true . . ." You seem to function at the level of grade school epistemology where things are true because you want them to be. It's called faith based mathematics. >We use axioms to establish abstract logical frameworks, >and from these axioms (our "theory"), we deduce theorems >based on those axioms. If we've done a good job of >creating the axioms, we'll find that our axiomatic system >is free of contradictions, so we say it's consistent. >Otherwise, we derive contradictory statements from the >axioms and we say it's an inconsistent system. Sure. So what? It's not a minor achievement just not the subject under discussion, which is demonstrations of truth for axioms not theorems. >Theorems and logical statements only make sense within >the context of some axiomatic system we've established >and agreed on. They more than likely will be utterly >meaningless in the context of other axiom systems. Except you just keep reiterating such things without any ability or seemingly any desire to demonstrate the truth of what you say. >Theorems and statements are based entirely on implication, >"if A then B". When A is an axiom, it's assumed true. When >A is a proven theorem, it's proven true within our system at >hand. If our theorem "if A then B" is well-formed, then the >truth of B follows from A. > >And of course, the axioms themselves have no meaning >outside the interpretation we embue them with, if any >at all. Yes, yes. This is all just a just a recapitulation of conventional wisdom on the subject of mathematical philosophy. >> My observation was directed at your naive contention that "you can't >> demonstrate anything without some established context . . .". Anybody >> can do assumptions. We don't need mathematics for that, although it >> might be argued that we do need mathematics to establish consistency >> among axiomatic assumptions of truth. > >Yes, that's part of what mathematics is. > > >> However even this qualification >> is suspect when modern mathematikers insist their definitions can't be >> false even when they're self contradictory. > >Definitions can't be true or false, nor self-contradictory. This is demonstrably incorrect because a definition like "squircles are square circles" is certainly self contradictory in Euclidean terms if we are to attach any kind of rigorous meaning to these terms. >The definition "a yert is an apple that is a pear" is not >contradictory, it's just that all the objects that meet >the definition of "yert" comprise an empty set. And a self contradictory definition produces an empty set of necessity for a very specific reason: that the definition is self contradictory and not just because that empty set happens to be empty at the moment. >Axioms can be inconsistent with each other within an >axiomatic system, which leads to contradictory theorems >within that system. Any number of which I've pointed out over the years. Such as the definition of points as constituents of lines and the possibility of any single real number line. Doesn't seem to have made much of an impression so far but I suppose one can always hope. >How many times have these things been explained to you? Until you get it right, correct, and true. The problem is modern mathematics has gotten it wrong when it comes to the definition of points as constituents of lines, any single real number line, and the generation of naturals via the Peano axioms. Yet they continue to insist they've gotten it right and to justify that faith simply claim definitions and axiomatic assumptions of truth can't be true or false. ~v~~
From: Bob Cain on 19 Dec 2007 17:05 Randy Poe wrote: > I'm curious. Don't most people use pseudonyms and sock > puppets so they can at least pretend to talk in a different > voice? > > Why go through all the trouble of creating the sock-puppet > account, then reveal yourself within the first three words? > > - Randy To get around the kill file entries that most people have allocated to him. Remember that the sole purpose of all of his obfuscation is to generate a high response count. He must be in some kind of club that competes at that level. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
From: Lester Zick on 19 Dec 2007 20:01 On Wed, 19 Dec 2007 14:05:48 -0800, Bob Cain <arcane(a)arcanemethods.com> wrote: >Randy Poe wrote: > >> I'm curious. Don't most people use pseudonyms and sock >> puppets so they can at least pretend to talk in a different >> voice? >> >> Why go through all the trouble of creating the sock-puppet >> account, then reveal yourself within the first three words? >> >> - Randy > >To get around the kill file entries that most people have allocated to him. >Remember that the sole purpose of all of his obfuscation is to generate a high >response count. He must be in some kind of club that competes at that level. > > >Bob >-- > >"Things should be described as simply as possible, but no simpler." > > A. Einstein Well you may be simple, Bob. But apparently you're not quite as stupid as Randy. ~v~~
From: Lester Zick on 21 Dec 2007 12:54
On Thu, 20 Dec 2007 14:14:33 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >Lester Zick wrote: >> Of course it disagrees with and is unorthodox in the context of the >> current standard mathematical paradigm because I'm arguing against the >> current standard mathematical paradigm and you're simply arguing >> against my argument by saying my argument isn't the current standard >> mathematical paradigm, which I never suggested and wouldn't claim it >> was. What I'm exclusively interested in is whether my argument is true >> and all you seem able to suggest is it's not the current contemporary >> standard mathematical paradigm. > >David R Tribble wrote: >> Okay, now we might be getting somewhere. You're talking >> about your own system of arithmetic/geometry. >> But it's awfully confusing of you to use terms like "real number >> line" and "circular arc" when you mean something entirely >> different than the commonly accepted meanings. You see >> how someone could conclude that you're trying to say >> something about standard arithmetic and geometry when you >> say things like that, don't you? >> >> What, then, do you mean by "real number line" and "circular arc" >> within this system of yours? And how do your meanings apply >> to the concepts of the same name that Archimedes used in >> his geometric proofs? > >Lester Zick wrote: >> You know, I thought we'd had similar conversations before and it turns >> out I was right. Back in July you insisted that the phrase "cardinal >> numbers" was originally defined by Cantor when, of course, that was >> nonsense because cardinal and ordinal numbers were in use long before >> Cantor. Even Brian Chandler had occasion to take note of your mistake. > >To be fair, the set theoretic meanings of "ordinal" and >"cardinal" were formalized by Cantor. He simply used the >same words that people had been using for some time. > >But what does this have to do with anything I wrote? People have been using "circles" "points" "real numbers" etc. etc. etc. for some time and you have no exclusive, pre emptive right to those terms or interpretations just because you have "set theoretic" uses for them. What makes "set theoretic" uses mathematically exhaustive? You seem to think that putting the phrase "the set of all . . ." somehow makes a definition mathematical. And when you define a circle as "the set of all points equidistant from any point in a plane" you haven't defined anything until you've defined "points" as constituents of lines, which Hilbert certainly wouldn't do and you've proven curiously reluctant to attempt. As things stand "set theoretic" definitions for mathematical concepts are just private definitions having no more necessary and exhaustive validity and right to the mathematical use of a term than anyone else. So you can't claim your "set theoretic" understanding of terms as any basis for rejecting other peoples mathematical use of the same terms. ~v~~ |