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

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From: MoeBlee on 8 Mar 2010 11:33

On Mar 8, 10:22 am, MoeBlee <jazzm...(a)hotmail.com> wrote:

> he hasn't said WHAT system of
> reasoning he would accept as proving the incompleteness theorem IF he
> doesn't already accept reasoning in the system that Koskensilta
> mentioned, which is an even MORE restricted version of PRA.

To be fair, he does discuss some general principles later in his post
and in later posts. However, I don't find anything in his principles
that supply or even suggest a system that has any potency at all while
embodying premises and principles of reasoning as modest as the
limited version of PRA mentioned by Koskensilta. Moreover, for each
principle that Nam announces (including those I may agree with), I
don't see that he's provided a basis for THEM that is any less based
on "intution" than is the basis for adopting the logical and very
modest mathematical principles employed in the limited version of PRA
mentioned by Koskensilta.

MoeBlee

From: Nam Nguyen on 8 Mar 2010 23:52

MoeBlee wrote:
> On Mar 8, 10:22 am, MoeBlee <jazzm...(a)hotmail.com> wrote:
>
>> he hasn't said WHAT system of
>> reasoning he would accept as proving the incompleteness theorem IF he
>> doesn't already accept reasoning in the system that Koskensilta
>> mentioned, which is an even MORE restricted version of PRA.

>
> To be fair, he does discuss some general principles later in his post
> and in later posts. However, I don't find anything in his principles
> that supply or even suggest a system that has any potency at all while
> embodying premises and principles of reasoning as modest as the
> limited version of PRA mentioned by Koskensilta.

Of course by presenting those principles I already had in my mind
the kind of potency a reasoning system (edifice) conforming to these
4 principles would have. And I think I've expressed that before in
some forms. For one thing, such a system could be conducive to
relativity in mathematical reasoning, which is more _realistic_
than the "absoluteness" kind of reasoning we'd see in PRA or what
Godel used to prove his meta proof. For another, it'd make our
reasoning _more conservative_ in the sense that if we can't possibly
know some "truth" then we have to acknowledge that impossibility,
rather than acting as if we could know; this is nothing more than
the principle of "conservation of knowledge" in mathematical
reasoning, so to speak.

The knowledge of the naturals (which Godel's work and PRA is based
on, via recursion and truth of the relations of numbers) is uncertain,
not conservative, and too intuitive to be rigorous for reasoning
sake, which is why my 4 principles don't suggest or support it.
In fact, the 4 principles basically "dismantle" any foundation based
on knowledge of the natural numbers. The naturals then is just one
of infinitely models (if at all), nothing more nothing less, nothing
special, _nothing preferential_.

> Moreover, for each
> principle that Nam announces (including those I may agree with), I
> don't see that he's provided a basis for THEM that is any less based
> on "intution" than is the basis for adopting the logical and very
> modest mathematical principles employed in the limited version of PRA
> mentioned by Koskensilta.

As I've mentioned above, any principles based on the knowledge of the
naturals would *not* be "modest" at all. For one thing, this knowledge
is rooted in intuition and however appealing as a "suggestion" force,
intuition should never be a foundation of reasoning. The whole reason
why today we have (Hilbert style) rules of inference is because we've
never been able to completely 100% trust intuition. Intuition and
reasoning as as different as the heart and the mind: one should not
replace the other as far as "role" is concerned.

For another thing, there are very strong indications that there are
formulas in L(PA) that we can't assign truth value to them, hence a
reasoning foundation based on the natural numbers would most likely
incomplete.

From: Transfer Principle on 9 Mar 2010 01:21

On Mar 5, 7:17 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
> Marshall wrote:
> > On Mar 5, 2:01 am, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote:
> >> Nam Nguyen <namducngu...(a)shaw.ca> writes:
> >>> The "crank" tends to assert Goedel's theorem is false.
> >>> The "standard theorist" would insist GIT is true.
> >>> That leaves the "rebel" the only side who observes the
> >>> method in Godel's work is invalid.
> >>> Except for the relativists, why should we care about invalid
> >>> truth or falsehood?
> >> Because the notions of "truth" and "validity" are not beyond dispute, and
> >> maybe we/you/I have got those wrong.

OK, I've resisted posting in this thread long enough. Although
I'm not posting in the main Newberry subthread, I do post here
in the Nam Nguyen subthread.

> > On usenet, nothing is beyond dispute.
> > For example, try to get
> > Nam to agree that the sky is blue.
> > He has contested this in
> > the past, sometimes with the argument that aliens might use
> > the word "blue" to mean red.
> The aliens might. Who knows? Would you be able to "know" that, Marshall?

But on the other hand, if a known so-called "crank," let's say
JSH, were to state that the sky is blue, the _standard theorists_
would be the ones to start coming up with obscure counterexamples
such as the Doppler effect at velocities approaching c, alien
languages in which "blue" means "red," and so forth.

Case in point -- in a thread in which the standard theorists
demanded that a "crank" accept Cantor's theorem as beyond dispute,
I mentioned that there are some statements, such as 2+2=4, which,
unlike Cantor's theorem, I do accept as unequivocally true. Then
a standard theorist immediately brought up 2+2 == 1 (mod 3).

Case in point -- spelling errors. Some standard theorists call
out "cranks" who make spelling errors in their posts. They rarely
point out such errors when fellow non-"cranks" are the ones who
are misspelling.

The truth is, most people -- standard theorists and "cranks"
alike -- point out errors or obscure counterexamples only when an
opponent makes the statement, even though the same statement would
go unchallenged if an ally makes the statement. It's simply human
nature -- I admit that I am guilty of the same. I, like both the
standard theorists and Nguyen, point out errors and obscure
counterexamples made by opponents all the time. (Indeed, I'm doing
so right here, right now, in this very post.)

So the standard theorists, no matter how much they may claim
otherwise, don't avoid the natural human reaction of searching for
errors and obscure counterexamples in their opponents' posts.

And so, my own opinion of Spight's statement is:

> > On usenet, nothing [written by an opponent] is beyond dispute
[whether a standard theorist or a "crank"].

From: OP on 9 Mar 2010 01:27

Transfer Principle wrote:
> On Mar 5, 7:17 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>> Marshall wrote:
>> > On Mar 5, 2:01 am, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote:
>> >> Nam Nguyen <namducngu...(a)shaw.ca> writes:
>> >>> The "crank" tends to assert Goedel's theorem is false.
>> >>> The "standard theorist" would insist GIT is true.
>> >>> That leaves the "rebel" the only side who observes the
>> >>> method in Godel's work is invalid.
>> >>> Except for the relativists, why should we care about invalid
>> >>> truth or falsehood?
>> >> Because the notions of "truth" and "validity" are not beyond dispute, and
>> >> maybe we/you/I have got those wrong.
>
> OK, I've resisted posting in this thread long enough. Although
> I'm not posting in the main Newberry subthread, I do post here
> in the Nam Nguyen subthread.
>
>> > On usenet, nothing is beyond dispute.
>> > For example, try to get
>> > Nam to agree that the sky is blue.
>> > He has contested this in
>> > the past, sometimes with the argument that aliens might use
>> > the word "blue" to mean red.
>> The aliens might. Who knows? Would you be able to "know" that, Marshall?
>
> But on the other hand, if a known so-called "crank," let's say
> JSH, were to state that the sky is blue, the _standard theorists_
> would be the ones to start coming up with obscure counterexamples
> such as the Doppler effect at velocities approaching c, alien
> languages in which "blue" means "red," and so forth.
>
> Case in point -- in a thread in which the standard theorists
> demanded that a "crank" accept Cantor's theorem as beyond dispute,
> I mentioned that there are some statements, such as 2+2=4, which,
> unlike Cantor's theorem, I do accept as unequivocally true. Then
> a standard theorist immediately brought up 2+2 == 1 (mod 3).
>
> Case in point -- spelling errors. Some standard theorists call
> out "cranks" who make spelling errors in their posts. They rarely
> point out such errors when fellow non-"cranks" are the ones who
> are misspelling.
>
> The truth is, most people -- standard theorists and "cranks"
> alike -- point out errors or obscure counterexamples only when an
> opponent makes the statement, even though the same statement would
> go unchallenged if an ally makes the statement. It's simply human
> nature -- I admit that I am guilty of the same. I, like both the
> standard theorists and Nguyen, point out errors and obscure
> counterexamples made by opponents all the time. (Indeed, I'm doing
> so right here, right now, in this very post.)
>
> So the standard theorists, no matter how much they may claim
> otherwise, don't avoid the natural human reaction of searching for
> errors and obscure counterexamples in their opponents' posts.
>
> And so, my own opinion of Spight's statement is:
>
>> > On usenet, nothing [written by an opponent] is beyond dispute
> [whether a standard theorist or a "crank"].

Creepy, man. You paint yourself as the defender of the weak and
downtrodden but in fact all you ever do is attack people. It's
classic bully behavior - really vile. This "crank" thing is just
100% bullshit.

From: Don Stockbauer on 9 Mar 2010 01:27

On Mar 9, 12:21 am, Transfer Principle <lwal...(a)lausd.net> wrote:
> On Mar 5, 7:17 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>
> > Marshall wrote:
> > > On Mar 5, 2:01 am, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote:
> > >> Nam Nguyen <namducngu...(a)shaw.ca> writes:
> > >>> The "crank" tends to assert Goedel's theorem is false.
> > >>> The "standard theorist" would insist GIT is true.
> > >>> That leaves the "rebel" the only side who observes the
> > >>> method in Godel's work is invalid.
> > >>> Except for the relativists, why should we care about invalid
> > >>> truth or falsehood?
> > >> Because the notions of "truth" and "validity" are not beyond dispute, and
> > >> maybe we/you/I have got those wrong.
>
> OK, I've resisted posting in this thread long enough. Although
> I'm not posting in the main Newberry subthread, I do post here
> in the Nam Nguyen subthread.
>
> > > On usenet, nothing is beyond dispute.
> > > For example, try to get
> > > Nam to agree that the sky is blue.
> > > He has contested this in
> > > the past, sometimes with the argument that aliens might use
> > > the word "blue" to mean red.
> > The aliens might. Who knows? Would you be able to "know" that, Marshall?
>
> But on the other hand, if a known so-called "crank," let's say
> JSH, were to state that the sky is blue, the _standard theorists_
> would be the ones to start coming up with obscure counterexamples
> such as the Doppler effect at velocities approaching c, alien
> languages in which "blue" means "red," and so forth.
>
> Case in point -- in a thread in which the standard theorists
> demanded that a "crank" accept Cantor's theorem as beyond dispute,
> I mentioned that there are some statements, such as 2+2=4, which,
> unlike Cantor's theorem, I do accept as unequivocally true. Then
> a standard theorist immediately brought up 2+2 == 1 (mod 3).
>
> Case in point -- spelling errors. Some standard theorists call
> out "cranks" who make spelling errors in their posts. They rarely
> point out such errors when fellow non-"cranks" are the ones who
> are misspelling.
>
> The truth is, most people -- standard theorists and "cranks"
> alike -- point out errors or obscure counterexamples only when an
> opponent makes the statement, even though the same statement would
> go unchallenged if an ally makes the statement. It's simply human
> nature -- I admit that I am guilty of the same. I, like both the
> standard theorists and Nguyen, point out errors and obscure
> counterexamples made by opponents all the time. (Indeed, I'm doing
> so right here, right now, in this very post.)
>
> So the standard theorists, no matter how much they may claim
> otherwise, don't avoid the natural human reaction of searching for
> errors and obscure counterexamples in their opponents' posts.
>
> And so, my own opinion of Spight's statement is:
>
> > > On usenet, nothing [written by an opponent] is beyond dispute
>
> [whether a standard theorist or a "crank"].

Gives people something to do.