Galileo's Paradox
in [Math]
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From: Tony Orlow on 2 Dec 2006 23:37 Virgil wrote: > 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. We can treat it as if each dimension were ordered, because each is. Yeah.
From: Virgil on 2 Dec 2006 23:40 In article <45724bde$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Lexicographic ordering corresponds to some multidimesnional ordering, > such as is obvious here. :) Then what is the dimensionality of one's handy dandy Webster's Unabridged, TO?
From: Virgil on 2 Dec 2006 23:47 In article <45724dc2(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Dribble bubble boil down.... okay. Here's the issue. You add elements, > you get a "bigger" set, with a "greater count". You take them away, and > the set becomes a smaller set, with a lesser count. TO conflates "ordering by subset" with "ordering by count". They are not the same thing. To insist that they are is foolish.
From: Virgil on 2 Dec 2006 23:56 In article <4572510c(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > 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. > > > > Absolutely true. I agree. > > A formula relating the surface area s to volume v of a given scalable 3D > figure would boil down to a s=y^(2/3), given any linear unit of measure. So is TO claiming that all sets are "scalable figures", each of which can be scaled to every other set using some ingeneous formula. > > > > Sets can have the same cardinality but different 'subsettedness' because > > different qualities are being measured. > > > > True. > >> 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. > > Well, Virgilium, what I want, and I don't really think this is > unreasonable or even unrealistic, is to have mathematics become a single > cohesive system of knowledge, with respect to facts and rules, with > respect to measure and the real world, such that there exists no > contradiction within this "entire" "system". I guess that makes it sort > of a science, and I apologize for how distasteful that may seem to you. :) What TO wants, TO has repeatedly shown that he not have the capacity to get, at least in mathematics. Nor has he shown that anyone else has the capacity to get those things, nor even that those things are worth striving for.
From: Virgil on 2 Dec 2006 23:58
In article <45725169(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > 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 > > Isn't that spelled "pygmies"? Would you like to take a walk on my vine > bridge, oh Tall One? Those 4 strike me as being as much piggish as pygmy-ish, with a number of the least attractive properties of both. |