The Definition of Points
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From: Wolf on 16 Mar 2007 12:06 Benj wrote: [...] > My huge gripe is the way so many people have attempted to replace > physics with mathematics. That's Lester's problem. He thinks vectors are Really Out There - not just handy ways of talking about forces or velocities. He thinks dimensions are Really Out There - not just handy ways of locating objects like roads and furniture. But he rejects lines made of points because he knows points have zero size - and how can you construct something out nothing? He rejects SR because it doesn't agree with his experience of time and space, so it must be wrong. But he believes that Science is Math, and Math is Truth (unlike whatever it is that "mathematikers" practice, which he says is mere guesswork.) So he has to interpret the SR math so that it agrees with his notions of what's Really Out There and with his experience. In order to do this, he invents his own notations and his own interpretations of mathematics. He's the most curious blend of idealist, materialist, and empiricist I've ever seen. He's quite amusing - until he starts pissing on people who try to help him make sense of his nonsense. [...snip the rest, with which I generally agree, except your slur on theoretical physicists. It's their work which has produced those very useful models that you use in your work. It's also corrected the ad-hoc models constructed by engineers, which have repeatedly led to more or less lethal disasters, and which the engineers couldn't explain until they decided to argue fine points of mathematics in their attempts to analyse the data.] HTH
From: SucMucPaProlij on 16 Mar 2007 11:18 "Lester Zick" <dontbother(a)nowhere.net> wrote in message news:1ukbv2hq1fo7ucv8971u9qo37b48bj6a5h(a)4ax.com... > > The Definition of Points > ~v~~ > > In the swansong of modern math lines are composed of points. But then > we must ask how points are defined? However I seem to recollect > intersections of lines determine points. But if so then we are left to > consider the rather peculiar proposition that lines are composed of > the intersection of lines. Now I don't claim the foregoing definitions > are circular. Only that the ratio of definitional logic to conclusions > is a transcendental somewhere in the neighborhood of 3.14159 . . . > > ~v~~ Can you prove that non-circular definition of existence exists?
From: Lester Zick on 16 Mar 2007 13:39 On 15 Mar 2007 21:15:18 -0700, "Eric Gisse" <jowr.pi(a)gmail.com> wrote: >On Mar 15, 4:01 pm, Bob Kolker <nowh...(a)nowhere.com> wrote: >> Eric Gisse wrote: >> > On Mar 15, 2:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> > [...] >> >> > What is your background in mathematics, Lester? >> >> You have asked: "what is the empty set". > >The empty set was my only source of amusement in my proofs class. Proofs of what pray tell? Certainly not the truth of your assumptions. Bob has similar difficulties. He knows quite a lot whereof he cannot demonstrate the truth but prefers to assume it instead. ~v~~
From: ken.quirici on 16 Mar 2007 13:48 On Mar 13, 1:52 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > The Definition of Points > ~v~~ > > In the swansong of modern math lines are composed of points. But then > we must ask how points are defined? However I seem to recollect > intersections of lines determine points. But if so then we are left to > consider the rather peculiar proposition that lines are composed of > the intersection of lines. Now I don't claim the foregoing definitions > are circular. Only that the ratio of definitional logic to conclusions > is a transcendental somewhere in the neighborhood of 3.14159 . . . > > ~v~~ My impression is that Euclid defined a line, not in terms of points, and never claimed a line was made up of points, but defined a line as a geometrical object that has only the property of extensibility (length, where length can be infinite). He uses points in his proofs specifically as intersections of lines, if I remember correctly, and makes no attempt at describing or explaining their density in a line. (You gotta lot of 'splainin to do, Euclid!).
From: Lester Zick on 16 Mar 2007 14:27
On Fri, 16 Mar 2007 16:18:53 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >"Lester Zick" <dontbother(a)nowhere.net> wrote in message >news:1ukbv2hq1fo7ucv8971u9qo37b48bj6a5h(a)4ax.com... >> >> The Definition of Points >> ~v~~ >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> ~v~~ > >Can you prove that non-circular definition of existence exists? Well that depends on what you and others mean by "existence exists". On the face of it the phrase "existence exists" is itself circular and no more demonstrable than a phrase like "pointing points". It's just a phrase taken as a root axiomatic assumption of truth by Ayn Rand in my own personal experience whether others have used it or not I don't know. On the other hand if you're asking whether anything exists and is capable of being unambiguously defined the answer is yes. I've done exactly that on more than one occasion first in the root post to the thread "Epistemology 201: The Science of Science" of two years ago and more recently in the root post to the thread "Epistemology 401: Tautological Mechanics" from a month ago. The technique of unambiguous definition and the definition of truth is simply to show that all possible alternative are false. Empirics and mathematikers generally prefer to base their definitions on undemonstrable axiomatic assumptions of truth whereas I prefer to base definitions of truth on finite mechanical tautological reduction to self contradictory alternatives. The former technique is a practice in mystical insight while the latter entails exhaustive analysis and reduction in purely mechanical terms. ~v~~ |