The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 21 Dec 2007 12:59 On Thu, 20 Dec 2007 14:37:39 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >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". > >David R Tribble wrote: >> 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". > >Lester Zick wrote: >> 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. > >So, just to be clear, you're saying that mathematical theorems >are not based on logical implication? No. Just to be clear I'm saying mathematical theorems are inferences drawn from various axiomatic assumptions of truth through logical implications no one really quite seems to understand in exhaustively true terms. Otherwise we would be dealing with the "science of math" instead of the "art of math". ~v~~
From: Lester Zick on 21 Dec 2007 13:54 On Thu, 20 Dec 2007 14:34:12 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >Lester Zick wrote: >> Exactly. 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. > >David R Tribble wrote; >> You've stated that you define "point" as the intersection >> of two lines. Okay, now demonstrate this is true. > >Lester Zick wrote: >> A very reasonable question but that's not quite the way it works. >> >> The way it works is you get to ask a question. You asked what my >> definition of a point is, which I answered. >> >> Then I get to ask a question, what your definition of a point is, >> which you haven't answered. So you don't get to ask further questions >> until you answer my question. > >Heh. Slippery, you are. I know. I'm so slippery I define terms which you won't. >You claim that mathematical axioms are not >demonstrations of truth. Are you suggesting they are? > You have an axiom (or perhaps >it's only a definition) for "point". I conclude, using your >own argument, that your axiom is not a demonstration of >truth. It's a definition because that's what you asked for whereas when I ask the same of you all I get is a blank stare. Definitions are not demonstrations; otherwise, we wouldn't need two words (I mean assuming I can use the word "two" without your "set theoretic" permission). > I assume that you are forced to agree by your >own logic. Agree with what? >Your hesistance to demonstrate your axiom as true >only bolsters my conclusion. What it bolsters is apparently your own reluctance to specify any "set theorectic" definition of your own which could explain putative constituency of points in lines. I don't claim constituency of points in lines. You do. It's up to you to provide some definition for points which explains this rather bizarre property of "set theoretic" points as distinct from the intersection of lines. >> Now I'm very happy to discuss the basis of demonstrations of truth; >> however. you've already dismissed the only basis of demonstration >> possible when you declared that I haven't proven anything by saying >> "not" is true of everything because "not not" is self contradictory or >> "differences" are true of everything because anything "different from >> differences" is self contradictory. > >"Not" is a unary logical operator. So, by definition, "not" >cannot stand by itself as a well-formed logical statement. By what definition? You're just determined to discuss my definitions without providing much less discussing any of your own aren't you? Since I claim "not" is true of everything, are you claiming "unary logical operator" has some universal truth of its own which would preclude my own demonstration of the universal truth of "not"? >Similarly, "not not" is simply two operators, the second of >which has no operand, so it too is an ill-formed logical >statement. Which you can't possibly know and certainly can't demonstrate is true because you have no concept of truth or any demonstration of truth. So I can say with certainty that you cannot demonstrate "A not B" is not true nor can you demonstrate "not not" is necessarily an ill formed logical statement. All you appear to have are a bunch of philosophical principles regarding what you consider but can't demonstrate is true. >Even if "not" or "not not" made any sense as logical >constructs, they would not "demonstrate truth" any more >than does the statement "0 is a natural". Which means what exactly, that self contradiction as represented by "not not" is not false? Or alternatives to self contradiction denoted by "not" are not of necessity true? >This has also been explained to you many times. Incorrectly every time. All you seem to have are so many philosophical presumptions you consider truer, without any demonstrations of truth, than my demonstrations of truth which you consider false because they aren't your philosophical presumptions. Not much of an explanation. >> So you really need to make up your mind how the conversation is to >> proceed. > >Your attempt to make me weary of the whole thing might >just succeed. Well I think we all understood at the outset that demonstrations of truth would weary you more than your grab bag of philosophical presumptions and correlates which which can be assumed true without having to demonstrate their truth. Goes with the territory I expect. >> Based on attributions to Hilbert I don't believe you actually >> have any credible definition for points which accounts for their >> supposed constituency of lines. However being perfectly reasonable >> individual, I am willing to wait and see. > >Perhaps I have only incredible points to work with. Credibility not being your long suit. >My working definition of point is a geometric object >isomorphic with a real number. But you already knew >that. What I already didn't know was the putative point line constituency you claimed for geometric objects such as real number isomorphisms which don't strike me as geometric objects off the top of my head but I'm sure do you off the top of your head. Are these "real number iso- morphisms" conjoined at the hip to form lines or what? ~v~~
From: Lester Zick on 21 Dec 2007 14:09 On Thu, 20 Dec 2007 14:45:07 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >David R Tribble wrote: >> An axiom is an assumed truth. Period. >> There are no "demonstrations" of whether it's true or not, >> because they are not needed. > >Lester Zick wrote: >> 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. > >I'm curious here. I've got an axiom: > A1. 0 is a natural. > >Is it true, or is it false? False. > How do I demonstrate this? You don't. Your axiom is false. And if you don't believe me I'll tell you again. >Or how about this axiom: > A2. A point is the intersection of two lines. > >How do I demonstrate that this axiom is true? You don't. > Or maybe it's a >false axiom, so how would I demonstrate that? You don't. The definition is true. If you don't believe me I'll tell you again. Now why don't you tell us again how "geometric object real number isomorphisms" define points and how ennui is your objective in life. ~v~~
From: Lester Zick on 22 Dec 2007 05:35 On Thu, 20 Dec 2007 14:34:12 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >My working definition of point is a geometric object >isomorphic with a real number. Even ignoring the problematic phrase "working definition" the problem here is that you can't demonstrate that "real number isomorphisms" are necessarily linear or that any "real number isomorphism" is a point. ~v~~
From: Lester Zick on 22 Dec 2007 06:35
On Thu, 20 Dec 2007 14:34:12 -0800 (PST), David R Tribble <david(a)tribble.com> wrote: >> Now I'm very happy to discuss the basis of demonstrations of truth; >> however. you've already dismissed the only basis of demonstration >> possible when you declared that I haven't proven anything by saying >> "not" is true of everything because "not not" is self contradictory or >> "differences" are true of everything because anything "different from >> differences" is self contradictory. > >"Not" is a unary logical operator. So, by definition, "not" >cannot stand by itself as a well-formed logical statement. Your form of argument is defective. I say X is true since alternatives to X are false. You say X is false because X isn't Y and you assume Y to be true. You're interested in Y only because assumptions of truth can be false. ~v~~ |