The Definition of Points
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From: Lester Zick on 17 Mar 2007 15:01 On 17 Mar 2007 11:09:55 -0700, "Hero" <Hero.van.Jindelt(a)gmx.de> wrote: > Bob Kolker wrote: >> 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. >> >> Point is a place holder for an intuition about space. Nothing more. >> Along with line, plane and a few other place holders they constitute the >> undefined terms of geometry. Intuitive notions are useful guides for >> finding logical proofs, but they have not probatory or logical standing. >> > >Referring to .." they have not probatory...standing". >This associates: If You want to put down a glass onto a table and You >are holding it's base a bit skew it might get a standing, but being >pushed by someone at this moment it might tumble - and this has to do >with it's point of gravity. In other words for a glass to have probative value it can't be probitive. >With friendly greetings >Hero >PS. I just wonder, if a point relates to the word "pointing"? I'm convinced the phrase "pointing out" is definitely related to "point". You can easily enough "point out" an irrational on a straight line using rac construction but you can't "point out" a transcendental on a straight line at all. ~v~~
From: Bob Kolker on 17 Mar 2007 15:01 Lester Zick wrote: > > Geometric figures are boundaries not physical entitities. They're more How is the interior of a sphere a boundry? Bob Kolker
From: Lester Zick on 17 Mar 2007 15:36 On Sat, 17 Mar 2007 11:27:48 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >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.... Hey, Tony. Good to hear from you as always. The point is that any self contradictory predicate is perforce false.Therefore any alternative to self contradictory predicates must be perforce true. However you need to be very careful here. It is certainly possible to combine predicates in various ways such that showing the combination is self contradictory and perforce false doesn't make it exactly clear what the tautological alternative may be that is true. This is why I invariably reduce consideration of such self contradictory predicates to"not not" or the "contradiction of contradiction" whose tautological alternatives are the clear and unambiguous "not" or "contradiction". On the other hand if we complain "blue ideas" are self contradictory it's not really clear at all just what the tautological alternative to "blue ideas" might be. We could just say "not blue ideas" but that doesn't tell us what exactly "not blue ideas" might mean. Obviously both "blue" and "ideas" are true in some ways but their combination is not for reasons which are not clear just from their combination. The same would be true for "one sided triangles" except that here we can see the self contradiction in "one" versus "tri-" and recognize the alternative "three sided triangle". But most self contradictory predicate combinations do not have such clear cut tautological alternatives whose reduction to "truth" is so readily apparent. It's a fascinating area of science, Tony, because it represents the way we actually think and mechanize ideas whether true or false. In other words conventional approaches to truth in empiricism and empirical mathematics emphasize truth by axiomatic assumption or reduction to such simple circumstances that the "truth" is readily apparent. But in point of fact "truth" has to be demonstrated in mechanical terms and cannot just be assumed regardless of how "intuitively obvious to the casual observer" an axiomatic reduction might appear. I don't know if you caught my recent post "Epistemology 401: Tautological Mechanics" which illustrates the tautological reduction of conjunctions to compoundings of "contradiction" or "not" but that represented the last major hurdle in my efforts to reduce the origin of all things to finite tautologically true regressions in mechanical terms and its well worth checking out. ~v~~
From: SucMucPaProlij on 17 Mar 2007 15:54 "Bob Kolker" <nowhere(a)nowhere.com> wrote in message news:562nt9F2625ppU1(a)mid.individual.net... > SucMucPaProlij wrote: >> >> >> Can you define a difference between intuitive point and real apple? >> How matematikers handle reality? > > You can make apple sauce from an apple. You can't make point fritters. > And you can make a line made out of apples :))))
From: Math1723 on 17 Mar 2007 16:15
On Mar 13, 5:44 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 13 Mar 2007 11:20:47 -0700, "Ross A.Finlayson" > > >You should ask me. > > Why? Perhaps he could use a good laugh? |