The Definition of Points
in [Math]
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From: Bob Kolker on 17 Mar 2007 12:01 SucMucPaProlij wrote: > "Bob Kolker" <nowhere(a)nowhere.com> wrote in message > news:5629arF26ac36U1(a)mid.individual.net... > >>SucMucPaProlij wrote: >> >>>I don't want you to expect too much because this is not mathematical proof, >>>it is philosophical proof (or discussion). This is just the way how I explain >>>things to myself. >> >>If it ain't mathematics and it ain't physics, it is bullshit. Philsophy, by >>and large, is academic style bullshit. >> > > > Reality check: > > If I say "This is math" does it make it math just because I say so? > If I say "This is physics" does it make it physics just because I say so? > If I say "This is philosophy" does it make it philosophy just because I say so? > > How can you tell if something is math, physics or philosophy if you never saw > this thing I talk about? First of all you are talking about abstractions so you cant literally see them. Second if you have learned some geometry or physics you will know it when you encounter it (as in thinking about it). > > > Introduce yourself with Shakespeare! Your posts are full of Sound and Fury. A Tale told by an Idiot. Bob Kolker > >
From: Bob Kolker on 17 Mar 2007 12:03 Tony Orlow wrote: > Yes, the relationship between points and lines is rather codependent, > isn't it? I looked at some of the responses, and indeed, one can define > points as tuples of coordinates, but of course, that all depends on > defining a set of dimensions as a space to begin with, each dimension > constituting an infinite line along which that coordinate is defined. In > language, both points and lines are taken as primitives, since their > properties are not rooted in symbols and strings, but geometry. So, we > may be left with the question as to what the primitives of geometry > really are, sets of points, or sequences of lines. That's the conundrum > right, that differences and differences between differences are lines, > and not points? :) You can develop geometry based purely on real numbers and sets. You need not assume any geometrical notions to do the thing. One of the triumphs of mathematics in the modern era was to make geometry the child of analysis. Bob Kolker
From: Tony Orlow on 17 Mar 2007 12:27 Lester Zick wrote: > 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~~ So, essentially, anything that's not self-contradictory exists, or is "true"? In an infinite universe, perhaps.... 01oo
From: Randy Poe on 17 Mar 2007 12:40 On Mar 17, 12:27 pm, Tony Orlow <t...(a)lightlink.com> wrote: > Lester Zick wrote: > > On Fri, 16 Mar 2007 16:18:53 +0100, "SucMucPaProlij" > > <mrjohnpauldike2...(a)hotmail.com> wrote: > > >> "Lester Zick" <dontbot...(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~~ > > So, essentially, anything that's not self-contradictory exists, or is > "true"? In an infinite universe, perhaps.... Every abstract concept exists as a concept. What does the size of the universe have to do with that? They don't take up any space. - Randy
From: SucMucPaProlij on 17 Mar 2007 12:47
"Bob Kolker" <nowhere(a)nowhere.com> wrote in message news:562hj4F2673reU3(a)mid.individual.net... > SucMucPaProlij wrote: >> >> >> And I agree but can you tell me does point exist? >> How do you explain it? > > Point is an idea or a notion. It has no physical existence. Neither does the > integer 1. > If idea has no physical existence then what type of existence it has? Metaphysical? Are you sayng that there are parallel universes? And when you die your soul goes to heaven........ > Point is a place holder for an intuition about space. Nothing more. Wrong. Point is real just as you and it is also egocentric hahahahhahaha > Along with line, plane and a few other place holders they constitute the > undefined terms of geometry. Good for geometry. > Intuitive notions are useful guides for finding logical proofs, but they have > not probatory or logical standing. > Can you define a difference between intuitive point and real apple? How matematikers handle reality? |