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Author: Aatu KoskensiltaAatu Koskensilta
Date: Dec 21, 2006 23:18
Charlie-Boo wrote:
> Well, you're jumbling things again. The inference is that whoever said
> these words is saying that he took a poll (to determine what everyone
> expects) and that the poll results are being used to establish a
> mathematical concluson.
What mathematical statement are you talking about? The words you refer
to were written by me, as I already said. The only statement I made (in
those words) is "everyone expects amending the proof so as to through in
ZFC to be routine" which is not a mathematical statement or conclusion.
Of course, to avoid spurious pedantry, "everyone" needs to be suitable
qualified to refer to the majority of competent people who have voiced
their opinion on this issue.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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Author: Aatu KoskensiltaAatu Koskensilta
Date: Dec 21, 2006 22:58
Charlie-Boo wrote:
> Jesse F. Hughes wrote:
>> But that has little to do
>> with the foundational status of ZFC.
>
> How do you define foundational status? How is ZFC's "foundational
> status" demonstrably different from that of Noodle Theory (whose model
> is a bowl of noodles)?
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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Author: herbzetherbzet
Date: Dec 21, 2006 22:54
Nam Nguyen wrote:
> herbzet wrote:
>> Nam Nguyen wrote:
>>>
>>> A formula's validity in a T will *depend* on it being valid (true)
>>> in all models (interpretations) of T, which I think is George's point.
>>> (That's the definition of validity!)
>>
>>
>> Thanks for this clarification.
>>
>> Hmm, given a formal theory T, and a formula X (in the language
>> of T), if I ask "Is X true in T?" this is different from asking
>> "Is X valid in T?" ?? Seems a little odd. Actually, the second
>> question sounds a little odd to me in itself.
>
> Actually I don't think we'd ask "Is X true in T?". Instead,
> we should ask "Is X true in a model M of T?", which is different
> from "Is X valid in T?" which means "Is X true in all models of T?".
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Author: Nam NguyenNam Nguyen
Date: Dec 21, 2006 22:39
Aatu Koskensilta wrote:
> Nam Nguyen wrote:
>> Charlie-Boo wrote:
>>
>>> But there are always theorems that any Logic does not prove
>>
>> Huh??? Why call them "theorems" then?
>
> Charlie is probably referring to the well-known "inexhaustibility" of
> mathematics following from the incompleteness theorem. Gödel himself
> observed, in the famous Gibbs lecture, that given any formal theory T we
> accept as correct, there is a (arithmetical) truth not contained in T,
> namely the consistency of T. Thus there is no formal theory we accept -
> or could accept in some idealised sense - as correct in which all
> (arithmetical) truths we accept - or could accept in some idealised
> sense - are provable. What this has with his queer ideas about our being
> able to prove uncountably many mathematical...
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Author: Charlie-BooCharlie-Boo
Date: Dec 21, 2006 22:32
Aatu Koskensilta wrote:
> Charlie-Boo wrote:
>> Aatu Koskensilta wrote:
>>> How would this establish that I have never proved anything?
>>
>> You wouldn't have to - CBL does it automagically.
>
> How does CBL automagically establish that I have never proved anything?
Using its axioms and rules - you wouldn't have to prove anything (if
you knew any theorems) - see? You just say the theorem and it proves
it - if you know how to use CBL, of course. (That's why I said you'd
be better off if you knew CBL better than the limited use that you said
that you have made of Computationally Based Logics.)
C-B
> --
> Aatu Koskensilta (aatu.koskensilta@xortec.fi)
>
> "Wovon man nicht sprechen kann, daruber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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Author: Aatu KoskensiltaAatu Koskensilta
Date: Dec 21, 2006 22:23
Nam Nguyen wrote:
> Charlie-Boo wrote:
>
>> But there are always theorems that any Logic does not prove
>
> Huh??? Why call them "theorems" then?
Charlie is probably referring to the well-known "inexhaustibility" of
mathematics following from the incompleteness theorem. Gödel himself
observed, in the famous Gibbs lecture, that given any formal theory T we
accept as correct, there is a (arithmetical) truth not contained in T,
namely the consistency of T. Thus there is no formal theory we accept -
or could accept in some idealised sense - as correct in which all
(arithmetical) truths we accept - or could accept in some idealised
sense - are provable. What this has with his queer ideas about our being
able to prove uncountably many mathematical truths is more difficult,
possibly impossible, to figure out.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
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Author: Nam NguyenNam Nguyen
Date: Dec 21, 2006 22:02
Charlie-Boo wrote:
> But there are always theorems that any Logic does not prove
Huh??? Why call them "theorems" then?
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Author: Michael GrayMichael Gray
Date: Dec 21, 2006 21:54
On Thu, 21 Dec 2006 15:03:41 -0800, stoney the.net> wrote:
- Refer: <1m4mo2dbsbsvrurhplfagf3l9n4dqkrvu1@4ax.com>>On Tue, 19 Dec 2006 07:48:03 +1030, Michael Gray newsguy.com>
>wrote in alt.atheism
>>>On Mon, 18 Dec 2006 11:17:56 -0800, stoney the.net> wrote:
>> - Refer: 4ax.com>>>>On 14 Dec 2006 14:19:43 -0800, j_hawk1979@ yahoo.com wrote in alt.atheism
>>> >>>>
>>>>just a question: So no one believes that these something higher..... it
>>>>doesn't matter if it's someone or just something...
>>>>
>>>>You don't believe that something or someone made us?
>>>
>>>If something 'made us' what made that something?
>>
>>The boogy-man under this mental 4 year old's bed.
>
>You're a generous man, Mike. ...
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Author: Michael GrayMichael Gray
Date: Dec 21, 2006 21:52
>
>Panpharmacon wrote:
>> "Richo" utas.edu.au> wrote
>>>>> - I am not a believer in gods - but I am not particularly concerned
>>> with thier existence - that is their least interesting aspect for me.
>>> It's the *power* that they have ...
>>
>> How can something that doesn't exist have power,
>
>How can Sherlock Holmes have a hat, Septic?
Bingo.
Perhaps you understand it all now.
But I expect that moment of clarity was a slip-up.
--
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Author: Aatu KoskensiltaAatu Koskensilta
Date: Dec 21, 2006 21:13
Charlie-Boo wrote:
> Aatu Koskensilta wrote:
>> Where do you get this idea of deciding mathematical questions by taking
>> a poll?
>
> You forget you said, "everyone expects amending the proof so as to go
> through in ZFC to be routine".
I recall writing those words, as if it was just yesterday. Do you
propose to infer from them that some mathematical question should be
decided by taking a poll?
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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