The Definition of Points
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From: Randy Poe on 17 Mar 2007 11:51 On Mar 17, 10:22 am, "SucMucPaProlij" <mrjohnpauldike2...(a)hotmail.com> wrote: > "Bob Kolker" <nowh...(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" What was called "Natural Philosophy" in Newton's time is what is now called "physics" and is not what is currently called "philosophy". - Randy
From: Bob Kolker on 17 Mar 2007 11:57 SucMucPaProlij wrote: > > > Isaak Newton: Philosophiae Naturalis Principia Mathematica Natural Philosophy, the old name for Science. It was not metaphysics. "When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume of divinity or school metaphysics, for instance, let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion." An Inquiry Concerning Human Understanding by David Hume, one of the few philosophers that ever made any sense. Bob Kolker
From: Bob Kolker on 17 Mar 2007 11:59 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. Bob Kolker
From: Bob Kolker on 17 Mar 2007 12:01 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. >> > > > Reality check: > > If I say "This is math" does it make it math just because I say so? > If I say "This is physics" does it make it physics just because I say so? > If I say "This is philosophy" does it make it philosophy just because I say so? > > How can you tell if something is math, physics or philosophy if you never saw > this thing I talk about? First of all you are talking about abstractions so you cant literally see them. Second if you have learned some geometry or physics you will know it when you encounter it (as in thinking about it). > > > Introduce yourself with Shakespeare! Your posts are full of Sound and Fury. A Tale told by an Idiot. Bob Kolker > >
From: Bob Kolker on 17 Mar 2007 12:03
Tony Orlow wrote: > Yes, the relationship between points and lines is rather codependent, > isn't it? I looked at some of the responses, and indeed, one can define > points as tuples of coordinates, but of course, that all depends on > defining a set of dimensions as a space to begin with, each dimension > constituting an infinite line along which that coordinate is defined. In > language, both points and lines are taken as primitives, since their > properties are not rooted in symbols and strings, but geometry. So, we > may be left with the question as to what the primitives of geometry > really are, sets of points, or sequences of lines. That's the conundrum > right, that differences and differences between differences are lines, > and not points? :) You can develop geometry based purely on real numbers and sets. You need not assume any geometrical notions to do the thing. One of the triumphs of mathematics in the modern era was to make geometry the child of analysis. Bob Kolker |