The Definition of Points
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From: SucMucPaProlij on 17 Mar 2007 19:43 "Lester Zick" <dontbother(a)nowhere.net> wrote in message news:ilrov2l07utt9j1ma26lm7stptkh28a9rg(a)4ax.com... > On 17 Mar 2007 09:40:22 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> > wrote: > >>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. > > What does the space concepts take up have to do with their truth? > Every idea/concept/definition/axiom must be expressed in some physical form - it must be formulated. You can't express concept that has more elements/parts/whatever than number of atoms in universe. If you have concept that takes all but one atom then you can't tell if it is true or not - you don't have enough resources to do so but you still have one extra atom that you probably can't use for anything :)))))
From: Bob Kolker on 17 Mar 2007 20:06 Tony Orlow wrote:> > Except that linear order (trichotomy) and continuity are inherent in R. > Those may be considered geometric properties. They can be defined in a purely analytic and algebraic manner starting with the Peano axioms. While linear order is suggestive of geometric notions, one can define such order without any geometric content whatsoever. The order of the postive integers is more temporal than spatial. Fist comes an integer -then- comes its successor. Etc. Etc. Bob Kolker
From: Wolf on 17 Mar 2007 22:40 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." -- Wolf "Don't believe everything you think." (Maxine)
From: Tony Orlow on 17 Mar 2007 21:51 Bob Kolker wrote: > Tony Orlow wrote:> >> Except that linear order (trichotomy) and continuity are inherent in >> R. Those may be considered geometric properties. > > They can be defined in a purely analytic and algebraic manner starting > with the Peano axioms. While linear order is suggestive of geometric > notions, one can define such order without any geometric content > whatsoever. The order of the postive integers is more temporal than > spatial. Fist comes an integer -then- comes its successor. Etc. Etc. > > Bob Kolker > They can be defined as certain rules regarding the manipulation of certain symbols and strings thereof, such that the resulting strings translate back into geometric statements that still make sense, but the root meanings of those symbols and strings lie in geometry. The axioms concerning points and lines may be stated without explaining what points and lines are within the theory, but that doesn't mean the theory isn't about what points and lines are, as defined by their properties. As far as your idea that the order of integers is "more temporal than spatial", all I can say is that time is a dimension like the spatial ones, except that it always goes forward. It's a moving point. The integers exist all at once, and can be traversed backwards or forwards. So, they're really more spatial than temporal. You're only thinking in the manner that makes Zeno's paradox a mystery. Tony Orlow
From: Virgil on 18 Mar 2007 02:23
In article <45fc6fd6(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Except that linear order (trichotomy) and continuity are inherent in R. > Those may be considered geometric properties. If one defines them algebraically, as one often does, are they still purely geometric? > > Tony Orlow |