'When Are Relations Neither True Nor False?
in [Math]
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From: MoeBlee on 1 Mar 2010 16:36 On Mar 1, 4:34 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > I suggest you > consult a standard text such as Girard's _Proof Theory and Logical > Complexity_. Oh great, a book that costs $1,417.06 online! (Wait till the poster TransferPrinciple hears about that!) MoeBlee
From: Aatu Koskensilta on 1 Mar 2010 16:45 MoeBlee <jazzmobe(a)hotmail.com> writes: > On Mar 1, 4:34�am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > >> I suggest you consult a standard text such as Girard's _Proof Theory >> and Logical Complexity_. > > Oh great, a book that costs $1,417.06 online! Ouch! This is truly appalling. A reprint is in order, surely. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Daryl McCullough on 1 Mar 2010 21:03 Newberry says... > >On Mar 1, 2:25=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: >> Newberry says... >> >What if you derive counterintuitive consequences from these axioms that >> >seemed manifestly true at first? >> >> I would be disappointed if that didn't happen. > >How does manifest truth morph into counter-intuition? I'm not exactly sure what the process is, but every nontrivial field has counter-intuitive results. I guess that's true by definition; if every result were intuitive, then it would be a trivial theory. -- Daryl McCullough Ithaca, NY
From: Newberry on 2 Mar 2010 00:36 On Feb 28, 3:54 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Newberry <newberr...(a)gmail.com> writes: > > a) Do you know that my distinction between > > > ~(Ex)(Ey)(P'xy & Q'y) > > > and > > > ~(Ex)P'xm' > > > corresponds to Gaifman/Goldsten's solution of the Liar paradox? > > I'm afraid your formalism is obscure to me. What's the significance of > all these primes? > > > b) Is this > > > (x)((2 > x > 4) -> ~(x < x + 1)) > > > "ordinary mathematical reasoning"? > > It isn't reasoning at all. It's a formula that doesn't formalize any > statement we would ordinarily meet in mathematical reasoning. So why do you exhort people that it is true? > > It does not even occur to anybody until they are thoroughly > > brainwashed by classes in classical logic and lectures about empty > > sets. > > You may of course choose to describe ordinary mathematical education > "brainwashing" if you wish. It remains that in ordinary mathematical > reasoning there is no distinction between > > There are no counterexamples to GC less than 27. > > and > > It's not true that there are counterexamples to GC less than 27. > > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Marshall on 2 Mar 2010 01:17
On Mar 1, 9:36 pm, Newberry <newberr...(a)gmail.com> wrote: > On Feb 28, 3:54 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > > b) Is this > > > > (x)((2 > x > 4) -> ~(x < x + 1)) > > > > "ordinary mathematical reasoning"? > > > It isn't reasoning at all. It's a formula that doesn't formalize any > > statement we would ordinarily meet in mathematical reasoning. > > So why do you exhort people that it is true? I don't speak for Aatu of course, but one possible reason to assert that the above is true is because it is, in fact, true. Marshall |