The Virgin Birth of Points
in [Physics]
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From: G. Frege on 2 Dec 2007 11:29 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. F. -- E-mail: info<at>simple-line<dot>de
From: G. Frege on 2 Dec 2007 11:40 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. Still geometrical objects are neither true nor false. :-) Hint: What would it mean for a certain circle to be true or to be false? :-o F. -- E-mail: info<at>simple-line<dot>de
From: Lester Zick on 2 Dec 2007 13:03 On Sun, 02 Dec 2007 17:16:56 +0100, G. Frege <nomail(a)invalid> wrote: >>> 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 So "square circle" was your phrase? ~v~~
From: Lester Zick on 2 Dec 2007 13:06 On Sun, 02 Dec 2007 17:16:56 +0100, G. Frege <nomail(a)invalid> 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. Whereupon a moronic exchange of pleasantries reminiscent of childhood might ensue except you can't demonstrate the truth of what you say, at least according to Bertie. >> if their definitions are true or false. >> >Definitions aren't true ore false. Sure they are. Any combination of predicates is. Unless you're seriously suggesting definitions aren't combinations of predicates. ~v~~
From: Lester Zick on 2 Dec 2007 13:11
On Sun, 02 Dec 2007 17:40:10 +0100, 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. > >Still geometrical objects are neither true nor false. :-) > > Hint: What would it mean for a certain circle > to be true or to be false? :-o It would mean the combination of predicates used to defined the circle were mutually contradictory as in "the set of all points equidistant from any point" which actually defines a sphere and not a circle and assumes concepts such as "points" and "equidistance" which can't be defined without prior reference to geometry and geometric concepts such as lines, planes, intersection, and so on. ~v~~ |