The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 2 Dec 2007 13:13 On Sun, 02 Dec 2007 17:29:09 +0100, G. Frege <nomail(a)invalid> wrote: >On Sun, 02 Dec 2007 09:21:09 -0700, Lester Zick <dontbother(a)nowhere.net> >wrote: > >>> >>> To avoid misunderstandings, I would like to add an 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. >> >Ok. The irony is apparently wasted since I had no idea what you were trying to describe to begin with and less so how you changed it or how the changes were supposed to avoid misunderstandings. ~v~~
From: Lester Zick on 2 Dec 2007 13:17 On Sun, 02 Dec 2007 17:25:52 +0100, G. Frege <nomail(a)invalid> wrote: >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_.) Except you didn't say "all axioms of a certain theory" and you certainly didn't specify which "certain" theory you might be talking about but made a blanket statement covering "all axioms (and theorems)" of any world which might exist (in a modal sense . . .) which would presumably include any theory like square circles. ~v~~
From: Lester Zick on 2 Dec 2007 16:13 On Sun, 2 Dec 2007 10:54:45 -0800 (PST), Marshall <marshall.spight(a)gmail.com> wrote: >On Dec 2, 8:40 am, G. Frege <nomail(a)invalid> wrote: >> On Sun, 02 Dec 2007 17:16:56 +0100, G. Frege <nomail(a)invalid> wrote: >> >> Typos corrected... >> >> >> >> >>> 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 or false. >> >> At least this is "general wisdom". Though if we formally introduce >> definitions as some sort of "ad hoc axioms", well, things are different >> --- in this case the model also makes those "ad hoc axioms" true. > >I was reading a book just the other day that described rules for >forming >definitions and gave a formal description of "non-creative" >definitions: >ones that do not add any strength to the system. It was interesting. 'Tis a mystery what "non creative" and "strength to the system" mean. They don't sound very true but they do sound very false. ~v~~
From: Lester Zick on 2 Dec 2007 16:15 On Sun, 2 Dec 2007 12:12:53 -0800 (PST), Ace0f_5pades <m4deep_(a)hotmail.com> wrote: >On Nov 13, 2:03 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Mon, 12 Nov 2007 13:01:17 -0800, lwal...(a)lausd.net wrote: >> >> On Nov 12, 6:21?pm, "Robert J. Kolker" <bobkol...(a)comcast.net> wrote: >> >> > Once again you do not distinguish between objects and the sets of which >> >> > the objects are elements. Another evidence that you cannot cope with >> >> > mathematics. >> >> A line is not a set of points because sets are indifferent to order. >> >> However, if you care to order points we still do not have a minimal >> >> definition of a line. >> >> >I've been thinking about the links to Euclid's and Hilbert's >> >axioms presented in some of the other geometry threads: >> >> Guesswork gives me a headache. Please spare us undemonstrated >> assumptions of truth. >> >> ~v~~ > >let me help you. As you're only proving yourself as limited and base, >and need to approach this with an open and enquiring mind. > >for R = AxAy where Ax=n>0, Ay=n<0 > >when x=0 then Ay=(n<0)*1 > >therefore >if l=0 >then "!l : !1?l" states the boudary of the 2nd dimension, that 0 and >A(R) can exist at one moment in the 2nd dimensional sense only as a >boundary or limit. > >where l = length >where !l = exceptional length. > >I haven't yet read through all of the discourses here, but I just >wanted to help you to decide to stop making a fool of yourself hence >forth. Well as I have a very limited knowledge of sign language you haven't helped very much. ~v~~
From: Lester Zick on 2 Dec 2007 16:16
On Sun, 2 Dec 2007 12:20:22 -0800 (PST), Ace0f_5pades <m4deep_(a)hotmail.com> wrote: >> I haven't yet read through all of the discourses here, but I just >> wanted to help you to decide to stop making a fool of yourself hence >> forth.- Hide quoted text - >> >> - Show quoted text - > >if you don't believe me, then plot a line along the x axis =0 and y >axis = n>0 Ah, the plot thickens. ~v~~ |