The Definition of Points
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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?
From: Hero on 17 Mar 2007 16:27 Bob Kolker wrote: > Hero wrote: > > > Left and right are geometrical concepts. > > When You write down ( 3, 4 ) 3 is left in Your view and 4 is right. > > 'scuse me. That could be first and second which are temporaal concepts. > So Hamilton, who invented calculation with these ordered pairs, was right about his "science of pure time"? http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/PureTime/ > The Left and Right refer to printing or writing conventions, not to > something intrinsically geometric. > So with Your kind of geometry You can or You can not tell, that DNA is a right screw? With friendly greetings Hero
From: Hero on 17 Mar 2007 16:57
Lester Zick wrote: > Hero wrote: > >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. Using only rac construction ( ruler and compass) results in a geometric handicap. Already before Euclid Hippias of Elis did his quadratrix with other tools. Actually a transcendental, as well as an rational, is a mutual relation to a one, a measure. A point can live an egocentric life, a real number ( not natural number) arises out of a minimum of three points. With friendly greetings Hero |