The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 1 Dec 2007 16:58 On Sat, 01 Dec 2007 20:28:04 +0100, G. Frege <nomail(a)invalid> wrote: >On Sat, 01 Dec 2007 12:19:32 -0700, Lester Zick <dontbother(a)nowhere.net> >wrote: > >>> >>> "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 know. But imho it's at least _reasonable_. "Reasonable"? That we never know what we're talking about? Nor whether what we're saying is true? Sounds reasonable to philosophers I expect. What is it you're paid to do anyway? Expostulate on stuff you don't know what you're talking about that you don't know is true? Probably why Nature abhors philosophers. ~v~~
From: Lester Zick on 1 Dec 2007 17:03 On Sat, 01 Dec 2007 20:30:56 +0100, G. Frege <nomail(a)invalid> wrote: >On Sat, 01 Dec 2007 12:20:22 -0700, Lester Zick <dontbother(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. :-) Oh, so you're only talking about Euclidean geometry? Funny, from your words "all axioms (and theorems) are actually true" I might just have concluded something besides Euclidean geometry. Silly me. But then I obviously don't know what I'm talking about whereas you do. ~v~~
From: Lester Zick on 1 Dec 2007 17:04 On Sat, 01 Dec 2007 20:33:04 GMT, "Nam D. Nguyen" <namducnguyen(a)shaw.ca> 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. > >How would "there _might_ exist" and "_actually_ are true" rhyme together? Don't ask, don't tell. ~v~~
From: G. Frege on 1 Dec 2007 17:31 On Sat, 01 Dec 2007 15:03:54 -0700, Lester Zick <dontbother(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) >>> of this theory [of course, *sigh*] >>> >>> 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? >> Note that geometrical OBJECTS can't be true or false. Only proposition and/or statements (sentences) can be true or false. So I take your question to mean So the claim that there are square circles is true after all? >> >> Huh? 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. > > Oh, so you're only talking about Euclidean geometry? > Right. Since concerning Euclidean Geometry I know for sure that we can disprove the existence of square circles. (So if Euclidean Geometry is consistent, we _can't_ prove the existence of square circles in it. Moreover then there is a interpretation of this theory which makes the statement/theorem that there isn't a square circle true.) > > Funny, from your words "all axioms (and theorems) > of the theory in question > > are actually true" > Are you on drugs, or what? F. -- E-mail: info<at>simple-line<dot>de
From: G. Frege on 1 Dec 2007 17:42
On Sat, 01 Dec 2007 23:31:42 +0100, G. Frege <nomail(a)invalid> 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. >>>>> >>>> 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. :-) >>> >> Oh, so you're only talking about Euclidean geometry? >> Actually, _any_ theory would do where we can prove that the assumption that an object is a square and also a circle leads to a contradiction. *sigh* F. -- E-mail: info<at>simple-line<dot>de |