'When Are Relations Neither True Nor False?
in [Math]
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From: Nam Nguyen on 20 Feb 2010 02:39 Marshall wrote: > On Feb 18, 8:09 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Look, there's a false relation, e.g. the empty set {} for a 1-ary relation >> symbol, right? > > Wrong. Like you knew how to show it's impossible to define such a relation!
From: Nam Nguyen on 20 Feb 2010 02:59 Alan Smaill wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Aatu Koskensilta wrote: > >>> "Philosophical" is not a term of derision. Musings about absolute >>> undecidability are most assuredly philosophical. It seems you think I >>> have said something about the validity of such musings. Why? >>> >> You summarily dismissed Calvin's appropriately mentioning of CH in this >> thread topic, on the ground that it's philosophical, which I don't see >> as justified at all. > > As Aatu just said, saying that something is philosophical is *not* > dismissing it, summarily or otherwise. Why do you think it is? First of all that's not what Aatu said. What he said: "Philosophical" is not a term of derision. I'm the one who said he "summarily dismissed Calvin's appropriately mentioning of CH". And I said that based on a very short conversation between him and Calvin. Iirc, Calvin had *only 1 short post* in this thread: >> The 'continuum hypothesis' is neither true nor false, for example. to which Aatu had a terse response: >> This piece of philosophical reflection -- which stands in need of some >> argument -- has no apparent relevance to Newberry's original post. If one responds for the very first time with a short _commandment-like_ telling people their writing "has no apparent relevance to ..." _without_ a courtesy of explaining to the writer then that's very dismissing to me for no good reason (not to mention that it's rather rude).
From: Nam Nguyen on 20 Feb 2010 03:16 Nam Nguyen wrote: > Alan Smaill wrote: >> Nam Nguyen <namducnguyen(a)shaw.ca> writes: >> >>> Aatu Koskensilta wrote: >> >>>> "Philosophical" is not a term of derision. Musings about absolute >>>> undecidability are most assuredly philosophical. It seems you think I >>>> have said something about the validity of such musings. Why? >>>> >>> You summarily dismissed Calvin's appropriately mentioning of CH in this >>> thread topic, on the ground that it's philosophical, which I don't see >>> as justified at all. >> >> As Aatu just said, saying that something is philosophical is *not* >> dismissing it, summarily or otherwise. Why do you think it is? > > First of all that's not what Aatu said. What he said: > > "Philosophical" is not a term of derision. I might add: he said this to me, _after_ the fact (i.e. after he had dismissed Calvin's short and only note). For the record, I didn't "see" his caveat about 'derision' then. Without further information I had no choice but thinking his dismissing was based on the word "philosophical", which is a bad term about reasoning, without any qualifying caveat. > > I'm the one who said he "summarily dismissed Calvin's appropriately > mentioning of CH". And I said that based on a very short conversation > between him and Calvin. Iirc, Calvin had *only 1 short post* in this > thread: > > >> The 'continuum hypothesis' is neither true nor false, for example. > > to which Aatu had a terse response: > > >> This piece of philosophical reflection -- which stands in need of some > >> argument -- has no apparent relevance to Newberry's original post. > > If one responds for the very first time with a short _commandment-like_ > telling people their writing "has no apparent relevance to ..." _without_ > a courtesy of explaining to the writer then that's very dismissing > to me for no good reason (not to mention that it's rather rude). >
From: Newberry on 20 Feb 2010 11:09 On Feb 19, 9:15 pm, OP <facetious_nickn...(a)hotmail.com> wrote: > Newberry wrote: > > On Feb 19, 7:30 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > >> Why then go on about such matters? > > > I do not have a clue. > > Well it's settled then. What gave you that peculiar idea?
From: Frederick Williams on 20 Feb 2010 11:53
Aatu Koskensilta wrote: > As usually understood it makes no sense to say of a relation that it is > or is not true. It seems ok to me to take "such and such a relation is false" to mean that no objects in the domain of discourse have the relation to one another. For example "x is the mother of y" could be called false in the domain {Aatu, Fred}. Ok, you might say "not satisfiable" but so what? -- ..... A lamprophyre containing small phenocrysts of olivine and augite, and usually also biotite or an amphibole, in a glassy groundmass containing analcime. |