The Definition of Points
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From: Lester Zick on 18 Mar 2007 14:01 On Sat, 17 Mar 2007 14:57:02 -0700, Bob Cain <arcane(a)arcanemethods.com> wrote: >Sam Wormley wrote: > >> May I suggest: >> >> "Newton's Principia for the Common Reader" by S. Chandrasekhar (1995) >> Clarendon Press . Oxford >> ISBN 0 19 851744 0 > >Yikes! $114 new and $82 used in paperback from Amazon. Wonder what >he means by common. Is that the Latin edition? ~v~~
From: Lester Zick on 18 Mar 2007 14:04 On Sat, 17 Mar 2007 21:40:51 -0500, Wolf <ElLoboViejo(a)ruddy.moss> wrote: >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. >>> >> >> Isaak Newton: Philosophiae Naturalis Principia Mathematica >> >> or "academic style bullshit" >> >> >> Think first, reply latter, Bob! >> >> > > >In those days, "philosophy" meant what we now mean by "science." Well I'd agree with you here, Wolf, except it's never really been clear what science is supposed to be. The only thing really even close in ancient times was Aristotle's organon or syllogism. ~v~~
From: VK on 18 Mar 2007 14:12 On Mar 18, 8:33 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > Oh I don't actually disagree; I just can't tell exactly what all these > qualifications amount to and mean. You've got "abstraction" and > "perception" and "equivalence" and all sorts of terms mixed up in here > that make me suspect none of us including you knows exactly what > you're talking about in mechanically exhaustive terms. If anyone of rivals (mathematics, philosophy, religion) would knew one day "in mechanically exhaustive terms" what is a "thing without sides" or say what is "infinity" - wow, the rest would come begging to clean their shoos :-) <snip> > Well maybe that would be true if your initial predicates had any > specific and exhaustive value. But lots of things may be true of > points without being essential to their definition. I don't understand > what "ti en einai of infinity" is supposed to mean nor a "reversed > infinity". That was not a question which one of definition is correct, neither "in mechanically exhaustive terms" nor even by some intuitive feeling; well probably neither one. I was asking: do you believe that there is one and only one correct definition of the point (a point on a line) implied by the very nature of this entity? The fact that maybe no one can bring it in some mechanically exhaustive terms right in this second does not change anything in the question. After all there is a number of unresolved problems not because they don't have any solution but simply because they are not solved yet due to different obstacles. But as long as we arrived to such entities as "point", "line", "infinite set", "natural number", "real number", "irrational number" etc. - as long that: do you believe that each of them there is one and only one proper mechanically exhaustive definition to find - coming from the very nature of these entities? So once found we may expect them universally correct, so even for some civilization from another star they will be necessary either the same or wrong (so the said civilization did not find the proper definition yet)?
From: Lester Zick on 18 Mar 2007 14:12 On Sat, 17 Mar 2007 15:01:10 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Lester Zick wrote: > >> >> Geometric figures are boundaries not physical entitities. They're more > >How is the interior of a sphere a boundry? The interior of a sphere is not a boundary any more than the exterior is. The surface of a sphere is the boundary dividing the interior from the exterior. The interior and exterior are just spaces whatever that may turn out to mean. You can't have one without the other and the boundary is what divides them and defines both in relation to each other. ~v~~
From: Lester Zick on 18 Mar 2007 14:16
On 17 Mar 2007 13:57:16 -0700, "Hero" <Hero.van.Jindelt(a)gmx.de> wrote: > 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. Well to the best of my knowledge rac construction is the only mechanically exhaustive method of construction that actually specifies or defines some point. >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. Not sure what this comment is in aid of. Transcendentals are defined on curves not straight lines. ~v~~ |