Galileo's Paradox
in [Math]
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From: Virgil on 1 Dec 2006 19:54 In article <4570848f(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Bob Kolker wrote: > > Tony Orlow wrote: > > > >> Are x and y ordered? The Cartesian plane is ordered in two dimensions, > >> not a linear order, but a 2D ordered plane with origin. > > > > > > The plane is not a linearly ordered set of points. > > > > Bob Kolker > > That's what I just said. And then you went on to say that because parts of it are ordered, we can treat it as if it were ordered.
From: cbrown on 2 Dec 2006 00:00 Tony Orlow wrote: > Eckard Blumschein wrote: <snip> > > Actually the continuum is a concept that complements the concept of > > discrete numbers and complements it at a time. A genuine continuum > > cannot at all be resolved into single points. > > Oh, I don't know about that. It depends on whether you allow actual > infinity. Take the H-riffic number generator: > E 1 > E x -> E 2^x ^ E 2^-x > > This produces all positive real numbers. Just to be picky, could you demonstrate how this generator, using only the above two rules, can be used to produce the number 3? Cheers - Chas
From: cbrown on 2 Dec 2006 00:24 Tony Orlow wrote: <snip> > Anyway, ala Leibniz, each object IS the set of properties which it > possesses, so any two objects with the exact same set of properties are > the same object. But this begs the question: what do we mean, exactly, by a SET of properties? What exactly are we trying to say when we say "This set of properties is the same as this other set of properties"? Cheers - Chas
From: Lester Zick on 2 Dec 2006 12:38 On Fri, 01 Dec 2006 13:52:03 -0700, Virgil <virgil(a)comcast.net> wrote: >In article <45701F81.8050901(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > Mathematics will survive >> set theory. > >Set Theory will survive Eckard. But it still won't be true. ~v~~
From: Lester Zick on 2 Dec 2006 12:40
On Fri, 01 Dec 2006 13:46:17 -0700, Virgil <virgil(a)comcast.net> wrote: >In article <456FEEEF.5070409(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 11/30/2006 1:32 PM, Bob Kolker wrote: >> > Eckard Blumschein wrote: >> > >> >> >> >> >> >> I consider Dedekind wrong, and he admitted to have no evidence in order >> >> to justify his basic idea. >> > >> > What sort of evidence? Surely not empirical evidence. Mathematics done >> > abstractly has no empirical content whatsoever. >> > >> > Bob Kolker >> >> Serious mathematicans have to know the pertaining confession. Dedekind >> wrote: "bin ausserstande irgendeinen Beweis f�r seine Richtigkeit >> beizubringen". In other words, he admitted being unable to furnish any >> mathematical proof which could substantiate his basic assumption. > >That conclusion assumes something not in evidence, that no one else has >been able to do what Dedekind said he had not done. > >> Consequently, any further conclusion does not have a sound basis. >> Dedekind's cuts are based on guesswork. > >So are everyone else's equally based on "guesswork", as without ASSUMING >something, one cannot deduce anything. Especially when one can assume the truth of ones assumptions. ~v~~ |