'When Are Relations Neither True Nor False?
in [Math]
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From: Aatu Koskensilta on 18 Feb 2010 09:23 Newberry <newberryxy(a)gmail.com> writes: > You are a smart guy. Surely you can come up with a more substantive > objection than "As usually understood it makes no sense to say of a > relation that it is or is not true." This trivial observation is not in any apparent sense an objection. Why do you think it is? Objection against what? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Marshall on 18 Feb 2010 10:42 On Feb 18, 6:23 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Newberry <newberr...(a)gmail.com> writes: > > You are a smart guy. Surely you can come up with a more substantive > > objection than "As usually understood it makes no sense to say of a > > relation that it is or is not true." > > This trivial observation is not in any apparent sense an objection. Why > do you think it is? Objection against what? > > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus Yeah, smart guy. You ought to be able to come up with a reply that not only points out how he's using the term wrong, but immediately causes him to see the error of his ways. Also, the first letter of each line should spell out his name. And it should also inspire the reader to devote more time to his or her family. And it should have a clean, fresh scent. Maybe you're not such a smart guy after all.<sob> Marshall
From: Aatu Koskensilta on 18 Feb 2010 11:31 Marshall <marshall.spight(a)gmail.com> writes: > Maybe you're not such a smart guy after all.<sob> Sobbity-sob. But don't cry for me, Marshall! I recently learned, in an episode of Bones, that we can't help it if we aren't as intelligent as others. I was greatly consoled by this, even though it wasn't Angel himself who said it. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Nam Nguyen on 18 Feb 2010 23:09 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Am I exaggerating to cover a not-so-clear-cut thread-title? > > Thread titles are irrelevant. Huh? So "On formally undecidable propositions of Principia Mathematica and related systems" is irrelevant to what Godel wrote in his 1931 paper? This is a very strange idea you have there! > >> Hardly. You could google on "absolute undecidability" to see some >> links about Godel's view on the subject together with some related >> mentioning of CH. (It's these information that I think Calvin's >> mentioning CH in this thread is valid, not "philosophical" as AK >> suspected." > > "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. Look, there's a false relation, e.g. the empty set {} for a 1-ary relation symbol, right? There's also a true relation, a non-empty Universe U for a 1-ary relation symbol, right? There are also relations that are in between. So discussing the possibility of a relation in which there are formulas that are neither true nor false, is within the inquiry suggested by the thread title. And I already explained such scenarios (i.e. incomplete relations/models). In the first and subsequent dialogs with Jesse, what Newberry discussed is one technical possibility for such scenarios. But what they discussed there is very relevant about when a relation would be neither true nor false for some formulas. I hope that you'd now see that point.
From: Nam Nguyen on 18 Feb 2010 23:22
Marshall wrote: > > Yeah, smart guy. You ought to be able to come up with a reply > that not only points out how he's using the term wrong, Look guys, you and AK, there's nothing wrong with the title question "When Are Relations Neither True Nor False?". And this has been explained already. Your guys just desired to ignore it. That's all. |