The Definition of Points
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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?
From: SucMucPaProlij on 17 Mar 2007 12:51 >> 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. > Wrong! If idea doesn't have any material form and it is not even energy, magnetic field of enything else, then you have Altzhaimer and idea is lost :)))))
From: SucMucPaProlij on 17 Mar 2007 12:54
> > 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. > And it means that lines, planes and points are defined in geometry. Make up your mind, Bob! |