The Virgin Birth of Points
in [Physics]
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From: G. Frege on 1 Dec 2007 14:28 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_. F. -- E-mail: info<at>simple-line<dot>de
From: G. Frege on 1 Dec 2007 14:30 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. :-) F. -- E-mail: info<at>simple-line<dot>de
From: Nam D. Nguyen on 1 Dec 2007 15:33 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? > > > F. >
From: Wolf Kirchmeir on 1 Dec 2007 16:53 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.
From: Wolf Kirchmeir on 1 Dec 2007 16:57
G. Frege 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_. > > > F. > Actually, IIRC Russell said: "Mathematics may be defined as the subject in which we never know what we are talking about, but we know whether what are saying is true. Poetry is the subject in which we always know what we are talking about but we never know whether what we are saying is true." Or words to that effect. HTH |