The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 2 Dec 2007 11:11 On Sat, 1 Dec 2007 16:26:51 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Dec 1, 2:30 pm, G. Frege <nomail(a)invalid> wrote: >> On Sat, 01 Dec 2007 12:20:22 -0700, Lester Zick <dontbot...(a)nowhere.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? >> >> Huh? Show me a _consistent_ theory of Euclidean Geometry where you can >> prove the existence of square circles. :-) > >You're addressing the statement "there exists a square >circle" which can have a truth value of T or F. > >Lester believes that definitions have truth value, and >insists on us telling whether any given definition is >"true". Well, Randy, the last time I checked definitions are combinations of predicates and combinations of predicates don't have truth values because no one seems to know what truth values are but combinations of predicates can be true or false. ~v~~
From: G. Frege on 2 Dec 2007 11:16 On Sun, 02 Dec 2007 09:06:10 -0700, Lester Zick <dontbother(a)nowhere.net> wrote: >>>> >>>> So square circles are true after all? [Lester Zick] >>>> >> Note that geometrical OBJECTS can't be true or false. >> > Sure they can ... > No they can't. > > if their definitions are true or false. > Definitions aren't true ore false. Now *I* said: >>>> >>>> Show me a _consistent_ theory of Euclidean Geometry where you can >>>> prove the existence of square circles. :-) >>>> >> Which actually means: ...where a statement stating the existence of a >> square circle can be proved. >> > Well you're certainly welcome to rephrase what I said any way you feel > like that makes you feel comfortable trying to explain what I said but > that doesn't make it what I said. > ??? I guess you REALLY are on drugs. I commented MY OWN statement, NOT something YOU wrote/said... :-o F. -- E-mail: info<at>simple-line<dot>de
From: Lester Zick on 2 Dec 2007 11:19 On Sat, 01 Dec 2007 16:53:21 -0500, Wolf Kirchmeir <ElLoboViejo(a)RuddyMoss.com> wrote: >G. Frege 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. >> >> >> F. >> > > >Sure, but that concept is beyond Zick's ability to comprehend. He'd >insist that this world must "exist in mechanical terms." Whatever that >means. Wherein Wolf departs from his own maxim of self healing and mental health of leaving Lester to his own devices to announce this world must not "exist in mechanical terms". The alternative to mechanical terms presumably being some form of magic and mystery. Whatever that means. ~v~~
From: Lester Zick on 2 Dec 2007 11:21 On Sat, 01 Dec 2007 23:47:30 +0100, G. Frege <nomail(a)invalid> wrote: >On Sat, 01 Dec 2007 19:22:12 +0100, G. Frege <nomail(a)invalid> wrote: > >To avoid misunderstandings, I would like to ad a n additional clause... > >>> >>> 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) >> of this theory 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. >> > >One might think that this should be clear from the context. But Lester >Zick proved me wrong! :-) Well that certainly clears things up. ~v~~
From: G. Frege on 2 Dec 2007 11:25
On Sun, 02 Dec 2007 09:07:51 -0700, Lester Zick <dontbother(a)nowhere.net> wrote: "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) of this theory 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." > > ... where all axioms (and theorems) ... > Please read again what I've written above. (Note that it doesn't make much sense to talk about "all axioms" [in general] in this context, since there are many theories with axioms that would contradict each other. What we are interested in -and what is addressed here- are all axioms _of a certain theory_.) F. -- E-mail: info<at>simple-line<dot>de |