'When Are Relations Neither True Nor False? [Logic]

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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