The End of an Era - That of The Natural Numbers
in [Math]
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From: Aatu Koskensilta on 1 Jun 2010 16:05 stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > If we understand the logical form of this syllogism, we know > that it is valid, even if we have no idea what "mortal" means, > or what "men" are, or who Socrates is. In particular, we don't > need to know whether there *are* any men. I seem to recall universal statements have existential import in Aristotle's logic. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Jun 2010 16:12 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > (Be careful here: you might run into conflict with Aatu's belief that > logic is just a branch of mathematics, or that logic provability can > be guided [or even "dictated"] by the mathematics of the naturals, > iirc). There's nothing controversial in the observation that mathematical logic is a branch of mathematics. The view that "logic provability" can be "guided" or "dictated" by the "mathematics of the naturals" that you ascribe to me I can't make anything of. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Jun 2010 16:19 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Sigh. I don't know why people just don't understand simple things! I too often wonder about that. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Jun 2010 16:24 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Suppose someone says to you "Marshall you're not couch potato", would > you think they "mean" you aren't a couch or aren't a potato? Uh, come again? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Jun 2010 17:19
Marshall <marshall.spight(a)gmail.com> writes: > There's a minor typo here: you said "authors" when in fact he just > quotes endlessly from the one book by the one guy. Well, it is a swell book. Quoting from page 160: We have already seen that the use of quantifiers in explicit definitions leads outside of the class of recursive relations. We are going to study the relations which may be obtained by applying quantifiers to recursive relations. In this section, we consider only quantifiers on number variables; quantifiers on function variables will be considered later. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |