Galileo's Paradox
in [Math]
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From: Virgil on 1 Dec 2006 15:50 In article <45700139.40908(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 11/30/2006 1:34 PM, Bob Kolker wrote: > > > > Giants, such as Hilbert, welcomed Cantorian mathematics. > > It was David Hilbert who declared Cantor's CH the first out of 23 > problems of mathematics, and he did so in 1900 at 2nd International > Congress of Mathematicians when he was 38 years old, full professor for > 7 years and chair of mathematics at U of Goettingen for 5 years. > Cantor was founder and president of the Society. Both Hilbert and Cantor > benefitted from their close friendship with Hurwitz. > Because Hilbert successfully applied axioms to geometry in 1999, and set > theory did not have a reliable basis, he may have felt in position and > was perhaps invited to provide axioms for set theory, too. > However, despite of beeing desined for this task, he did lower his > standard and invent the masterpiece of delusion which has been ascribed > to Zermelo: claiming the existence of infinite sets. The claim of existence of points and lines, etc. in Hilbert's axiomatization of geometry relies on making equally unverifiable assumptions of infiniteness.
From: Virgil on 1 Dec 2006 15:52 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.
From: Virgil on 1 Dec 2006 15:59 In article <45704f2b(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Eckard Blumschein wrote: > > On 11/29/2006 6:37 PM, Bob Kolker wrote: > >> Tony Orlow wrote: > >>> It has the same cardinality perhaps, but where one set contains all the > >>> elements of another, plus more, it can rightfully be considered a larger > >>> set. > >> Not necessarily so, if it is an infinite set. > >> > >> Bob Kolker > > What, is it not necessarily so that it CAN rightfully be considered a > larger set, with some justification? It doesn't have a right to be > considered that way? Why? Because it contradicts theoretical > transfinitology? Depends on one's standard of "size". Two solids of the same surface area can have differing volumes because different qualities of the sets of points that form them are being measured. Sets can have the same cardinality but different 'subsettedness' because different qualities are being measured. > You do? Do you mean that the addition of elements not already in a set > doesn't add to the size of the set in any sense? In the subsettedness sense yes, in the cardinality sense, not necessarily. In the sense of well-ordered subsettedness, not necessarily. TO seems to want all measures to give the same results, regardless of what is being measured.
From: Virgil on 1 Dec 2006 16:02 In article <457059e6(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Lester Zick wrote: > > On Thu, 30 Nov 2006 09:52:49 +0100, Eckard Blumschein > > <blumschein(a)et.uni-magdeburg.de> wrote: > > TO verus LZ versus EB. It only wants WM to become the ultimate battle of the pigmies
From: Virgil on 1 Dec 2006 16:06
In article <45705ad3(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Huh! So, what happens if I declare a number, Big'un, and say that that > is the number of reals in (0,1]? What if I say the real line is > homogeneous, so every unit interval contains the same number of points? > And then, what if I say the positive number line is going to include > Big'un such unit intervals, so it has Big'un^2 reals up to Big'un? Does > the universe collapse, or all tautologies suddenly become false? As long as it is only TO playing his silly games, nobody much cares. If TO were ever to produce anything like a coherent system with actual proofs, we might actually have to pay some attention. |