The Definition of Points
in [Math]
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From: Tony Orlow on 17 Mar 2007 19:01 Lester Zick wrote: > 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. I think that's what I said. > > 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". If x is false, then not(x) is true, but not(x) doesn't define a true y. > > 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. That seems to be an example, not of logical contradiction, but of inappropriate context for the attribute. Ideas are not generally considered to have the attribute of color, but that doesn't contradict the notion that color may be associated with some ideas. For instance, "blue ideas" may be sad thoughts, or concepts regarding shades of blue, or maybe even plans to go to the beach. So, I wouldn't say "blue ideas" is self-contradictory, or that it has any particular negation. > > 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. I think if they are truly self-contradictory, that could be determined logically. In this case, since 1<3, and triangles are defined to have 3 sides, the contradiction is clear. > > 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. Yes, I think what you're advocating is the more inductive side of discovering the rules, by analyzing evidence, rather than assuming rules, and following them to their deductive conclusions. Both are necessary for science, wouldn't you say? > > 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~~ I'll try to take a look. I've kinda been on a hiatus lately. Have a good one. 01oo
From: Tony Orlow on 17 Mar 2007 19:05 Hero wrote: > On 17 Mrz., 22:13, Bob Kolker <nowh...(a)nowhere.com> wrote: >> Hero wrote: >> >>> So with Your kind of geometry You can or You can not tell, that DNA is >>> a right screw? >> >> You can tell that right and left are differnt. > > Can You please give me a hint, where in Your geometry or in which of > Your geometries this is axiomized or where it follows from axioms? > Or where the plane-reflection is possible? > > Thanks > Hero > > > > A<B -> ~B<A A<B ^ B<C -> A<C Tony
From: Lester Zick on 17 Mar 2007 19:07 On Sat, 17 Mar 2007 12:19:48 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> >> And I think you're making a little too much out of nominal circular >> regressions. All you really have to do to define definition is prove >> it satisfies it own definition. >> > > >1) Definition for definition: >"Definition is anything" So definition is undefintion? >2) All you really have to do to define definition is to prove it satisfies its >own definition. >"Definition is anything" satisfies itself (it masturbates). > >Did I miss something? Is there anything you didn't miss? >Second attempt > >1) Definition is sentence that is always true. Very good. What is always true? >2) Is sentence "Definition is sentence that is always true" always true? >For mathematikers definition is sentence that is always true but there are other >sentences that are always true ("two is more that one", "it is better to live >100 years as a rich man that one day as a poor woman") and you can hardly called >them definitions. > >What will happened if I define definition as something that is not always true? >It changes math altogether. If definition is not always true you can't use >definition for point to tell if something is point. > > >Mathematikers are strange liberals. They even give you right to destroy >everything they believe in :)))) You mean the catholic church is in jeopardy? ~v~~
From: Lester Zick on 17 Mar 2007 19:09 On Sat, 17 Mar 2007 12:23:28 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >>>How do you define "definition"? >> >> Well actually this is at least several years old. I don't claim my own >> question in that regard was necessarily original but I did raise this >> issue at least several years ago and have routinely continued to raise >> it. Quite possibly the silliest definition of definition I noted was >> David Marcus's comment that a definition is only an abbreviation. >> > >I think that "existence", "definition" and "number one" are equal terms. So what? No one cares what you think. They may or may not care what you can prove. >Proof is based on a fact that you can't tell a difference between them. Obviously you can't. >I don't expect anyone to accept my proof (just as nobody takes you seriously). What proof? ~v~~
From: Lester Zick on 17 Mar 2007 19:11
On Sat, 17 Mar 2007 12:34:44 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: > >"Lester Zick" <dontbother(a)nowhere.net> wrote in message >news:fdnlv2d3t3vmaht79o2trmqtfq4halm5t8(a)4ax.com... >> 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. >> > > >I think that there is no such thing as "don't exist". It means that everything >exists and negation of existence is impossible. Problem is that word "existence" >is ambiguous and to explain my theory one must first resolve ambiguousness. > >Yes, I don't expect anyone to believe me nor to agree with me. You certainly won't be disappointed. >> 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. >> > >It is interesting but I didn't define my opinion about truth so I choose to say >nothing. So I've noticed. ~v~~ |