The Virgin Birth of Points
in [Physics]
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From: Robert J. Kolker on 1 Dec 2007 13:15 Lester Zick wrote: > > Well of course the objective of mathematics are demonstrations of > truth and not merely hypothetical assumptions. And this is one of the > main themes I've been trying to stress throughout these threads. Wrong. The objective of mathematics is to show that the theorems follow from the basic postulates logically. Truth has little to do with it. The collection of postulates do not have to be (jointly) true. They only have to be consistent. Euclidean geometry and the various non-euclidean geometries are all equally true, in the sense that they are consistent systems. Bob Kolker
From: G. Frege on 1 Dec 2007 13:22 On Sat, 01 Dec 2007 13:15:11 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> wrote: > > The collection of postulates do not have to be (jointly) true. They only > have to be consistent. > On the other hand, _if_ they are consistent, then a model for that theory [assuming we are talking about first-order theories] exists; i.e. an interpretation that makes all axioms (and hence all theorems) true. With other words, there might exist a "world" (in the "modal" sense of the word) where all those axioms (and theorems) actually are true. F. -- E-mail: info<at>simple-line<dot>de
From: Quint Essential on 1 Dec 2007 14:14 On Sat, 01 Dec 2007 10:33:44 -0700, Lester Zick <dontbother(a)nowhere.net> wrote: >On Fri, 30 Nov 2007 22:46:35 -0700, Quint Essential <QT(a)archangel.net> >wrote: > >>On Fri, 30 Nov 2007 11:33:50 -0700, Lester Zick >><dontbother(a)nowhere.net> wrote: >> >>>On Sun, 11 Nov 2007 14:40:29 -0700, Lester Zick >>><dontbother(a)nowhere.net> wrote: >>> >>>> >>>> The Virgin Birth of Points >>>> ~v~~ >>>> >>>>The Jesuit heresy maintains points have zero length but are not of >>>>zero length and if you don't believe that you haven't examined the >>>>argument closely enough. >>> >>>The epistemological problem for modern math is where do an infinite >>>number of points required to unionize points into lines come from? >>> >>>Only one solid is needed to produce one surface and one surface >>>required to produce one line but an infinite number of points are >>>required to produce one line. And the difficulty is that we can only >>>produce finite numbers of points through tangency or intersection. So >>>where are all the points supposed to come from? Imagination? Otherwise >>>we can only be left with a finite number of straight line segments >>>defined between points. >>> >>>~v~~ >> >>So let me give you a hypothetical. What's wrong with assuming an >>infinite number of points from which we construct lines and so on? > >Well of course the objective of mathematics are demonstrations of >truth and not merely hypothetical assumptions. And this is one of the >main themes I've been trying to stress throughout these threads. > >However even hypothetically the problem is that lines have direction >and points don't. Consequently any infinity of points that might be >assumed couldn't also be assumed to lie on any line in any direction. > >In other words given some line, infinite subdivision is possible but >those results would not be points; they would be line segments defined >by points of intersection. And given any infinity of points all you >could produce are various line segments not lying along any line >unless the line itself is defined first regardless of the points. > >~v~~ Well then why not just hypothetically assume space is filled with infinities of points. Since points would be everywhere wouldn't that circumvent the problem of directionality?
From: Lester Zick on 1 Dec 2007 14:19 On Sat, 01 Dec 2007 18:46:39 +0100, G. Frege <nomail(a)invalid> wrote: >On Sat, 01 Dec 2007 10:33:44 -0700, Lester Zick <dontbother(a)nowhere.net> >wrote: > >> >> Well of course the objective of mathematics are demonstrations of >> truth and not merely hypothetical assumptions. And this is one of the >> main themes I've been trying to stress throughout these threads. >> >Of course you just don't know what you are talking about. Of course I just don't know what a lot of other people are talking about because they talk nonsense. > "Mathematics may be defined as the subject in which we never > know what we are talking about, nor whether what we are saying > is true." > > (Bertrand Russell) Is that true? I don't mean whether Russell said it but whether we may define mathematics any way we want because we're too lazy or stupid to understand what we're talking about. ~v~~
From: Lester Zick on 1 Dec 2007 14:20
On Sat, 01 Dec 2007 19:22:12 +0100, G. Frege <nomail(a)invalid> wrote: >On Sat, 01 Dec 2007 13:15:11 -0500, "Robert J. Kolker" ><bobkolker(a)comcast.net> wrote: > >> >> The collection of postulates do not have to be (jointly) true. They only >> have to be consistent. >> >On the other hand, _if_ they are consistent, then a model for that >theory [assuming we are talking about first-order theories] exists; i.e. >an interpretation that makes all axioms (and hence all theorems) true. >With other words, there might exist a "world" (in the "modal" sense of >the word) where all those axioms (and theorems) actually are true. So square circles are true after all? ~v~~ |