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

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From: Transfer Principle on 16 Mar 2010 16:40

On Mar 15, 2:25 pm, MoeBlee <jazzm...(a)hotmail.com> wrote:
> On Mar 11, 12:44 am, Transfer Principle <lwal...(a)lausd.net> wrote:
> > Conversely, they shouldn't ridicule _every_single_ model just because
> > the person who mentions it has been labeled a "crank." I'd be glad
> > if standard theorists just gave _some_ constructive discussion of the
> > alternate models.
> Who ridicules MODELS? What an insane idea! A model is a mathematical
> object. How would one ridicule a mathematical object?

If one can't use the model to perform enough math for the sciences, or
one can perform scientific math in the model only by using ad hoc or
inelegant methods, then the model is ridiculed by standard theorists.

> And if you want to find discussion about all kinds of models
> (standard, non-standard, schmandard, non-schmandered, whatever!) then
> just look in a book
(...that I can't afford, of course, but let's not dwell on that issue
again).
> on mathematical logic, model theory, or any of
> probably THOUSANDS of journal articles about the subject.

> > Actions speak louder than words. Repeating that people aren't called
> > "cranks" for proposing alternate theories doesn't erase the numerous
> > times I've seen people who post alternate theories called "cranks,"
> > right here on sci.math, with my own eyes.
> YOU DID IT AGAIN!!! You just SKIPPED the VERY point I just made.
> Would you please LISTEN this time?:
> The cranks weren't called 'cranks' MERELY for proposing an alternative
> theory

....but rather, as MoeBlee claims in another post:

> the WAY in which they argued along
> with certain other behaviours reflecting irrationality, ignorance, and
> intellectual dishonesty.

OK, so right I'm not _skipping_ the point MoeBlee's making -- to
repeat,
his point that the label "crank" isn't necessarily given to those who
simply
propose alternate theories, but to those who are irrational, ignorant,
or
intellectually dishonest in their arguments.

But the issue is, should I _believe_ MoeBlee's claim? My counterclaim
is that posters _are_ labeled "crank" for making the specific
statement
that I made in my post -- namely, 0.999...<1. And if they aren't
actually
labeled "cranks," they're at least criticized for either having a
theory
that doesn't axiomatize for the sciences (even though almost 40% of
physicists believe that 0.999...<1), or -- one of the standard
theorists'
favorite criticisms -- using an undefined ellipsis symbol.

(In another thread, I once tried to come up with a rigorous theory in
which
the ellipsis symbol actually is a primitive, with axioms to show how
the
ellipsis corresponds to "crank" notions. But that theory had over 20
axioms, which is obviously too ad hoc for the standard theorists. I'd
love
to give a theory with only a handful of axioms/schemata, yet describes
the ellipsis as adhering to "crank" notions, if such a theory is
possible.)

Every single time someone posts 0.999...<1, the "crank"-busters come
out in full force. I use this as evidence for my counterclaim that
it's
0.999...<1 itself that leads to the "crank" label in this case. So I'm
not
_skipping_, but _doubting_ MoeBlee's claim that it's all about the
"ignorance" and "intellectual dishonesty" in the arguments.

> NO. It refers to virtually complete woozy ambiguity. It refers to
> using suggestive CONNOTATIONS of mathematical terminology in
> deductions (formal or informal deductions). It refers to using the
> metaphorical suggestiveness of terms such as 'line' or whatever in
> deductions as opposed to confining to the actual deductive capability
> wrought from axioms and definitions. Also to ersatz terminology that
> is not declared either primitive or defined but is used merely at the
> whim of the creator of the terminology. ETC. with a bunch of points
> I've made in numerous posts.
> Wonderful. I have no problem with "<= is a total order" when spoken by
> someone who is using that terminology in its ordinary sense or is
> using that terminology in some special sense but with alternative
> definitions back to some alternative or standard primitives.

OK, I'll try to keep this in mind when trying to resolve arguments
about "cranks" in order to make them more rigorous.

From: Alan Smaill on 17 Mar 2010 08:22

Transfer Principle <lwalke3(a)lausd.net> writes:

> But I won't focus on that example, since it focuses on politics rather
> than mathematics or science -- and besides, I'd be hardpressed to call
> "deadrat" a "standard theorist," since it appears that he doesn't post
> too often about math or science anyway (though it's hard to tell,
> since
> he's a frequent nym-shifter). It may be still appropriate to call
> "deadrat"
> an anti-"crank" or "crank"-buster, though. (AP crossposted his claim
> to both sci.math and a non-scientific newsgroup.)

A paragraph like this suggests that your terminology is getting
in the way of discussing whatever it is you want to be talking about.

Might it be more productive to make your point without labelling
posters into classes which even you have trouble distinguishing?

--
Alan Smaill

From: Alan Smaill on 17 Mar 2010 08:27

Transfer Principle <lwalke3(a)lausd.net> writes:

> (even though almost 40% of
> physicists believe that 0.999...<1)

Do I get labelled as a bully if I ask for some evidence for your claim?

--
Alan Smaill

From: Transfer Principle on 19 Mar 2010 18:20

On Mar 17, 5:27 am, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote:
> Transfer Principle <lwal...(a)lausd.net> writes:
> > (even though almost 40% of
> > physicists believe that 0.999...<1)
> Do I get labelled as a bully if I ask for some evidence for your claim?

No -- at least, not yet, anyway.

First of all, keep in mind that I don't -- repeat, _don't_ -- dispute
that
there is a proof in ZFC of "0.999...=1." Indeed, the Metamath website
gives a link to the ZFC proof:

http://us.metamath.org/mpegif/0.999....html

The proof obviously doesn't require AC, nor is Foundation/Regularity
required either. So the proof works in ZF-Foundation/Regularity (i.e.
Z+Replacement Schema).

But there's a huge difference between "ZF proves 0.999...=1" and
"physicists believe that 0.999...=1." The former isn't up to debate,
whereas the latter can be determined in a poll.

We notice at the top of the Metamath page, it reads:

"Interestingly, about 40% of the people responding to a poll at
http://forum.physorg.com/index.php?showtopic=13177 disagree."

This is where I found that poll I mentioned in the last post. When we
click on it, we see that out of 183 respondents, 99 agreed with the
ZF conclusion, 66 disagreed, and 18 responded with the third, joke
option "Don't ask me or I'll hurt you." The number of respondents
(and keep in mind that this is a _physics_ forum) who disagreed with
the ZF conclusion amounts to about 36%.

The first poster in this thread who disagreed with 0.999...=1 wrote
the
following message:

"Let's do it like this:
1-.9=.1
1-.99=.01
1-.999=.001
....
1-.999...999=.000...001
At no step of this recursion are the two values equal, so unless you
can
pick some magic number at infinity, they're never precisely equal
..000...001 != .000...000
"A number ending in 1 never exactly equals the same number ending in
zero,
unless you're willing to weight the digits down to the point where you
can
close your eyes and ignore the difference. So, yes, for real world
applications
with successly [sic] smaller and smaller weighted digits it might be
close
enough but technically they aren't identical and can't be manipulated
arbitrarily and see the same result apply.
"If we could treat them indentically [sic] then we couldn't do this:
x=10^y
1-.9r = (1-.9)/x (where y is the number of 9 digits) = 0
But:
x*(1-.9)/x = x*0
1-.9=0
Is obviously incorrect.
Another way to see this is that it's a process continually approaching
1, but
never reaching it. If it could actually reach 1 then no more 9s would
be
needed ... but that violates the repetition."

The poster then goes on to argue that the usual proof of 0.999...=1 is
"circular" and thus invalid.

Of course, the standard theorists are free to dispute the validity of
the poll
that I gave here. They might point out that this online poll was too
informal
to be truly representative of those who are knowledgeable in physics.

If the standard theorists would like to convince me that a
supermajority of
physicists do accept 0.999...=1, then I'd like to see another, perhaps
more
valid poll that demonstrates this. If desired, we can start that poll
right here
by crossposting to, say, sci.physics, and then have the posters there
state whether they believe that 0.999...=1 or not.

Or perhaps the standard theorists might disagree with all online polls
altogether -- but in that case, how can we ever see the results? I'll
accept
the results of any poll as long as the posters are knowledgeable about
physics and I can see the results.

But if they fail to convince me that a supermajority of physics people
accept 0.999...=1, then that weakens the standard theorists'
insistence
that "crank" theories can't provide an axiomatization for the
sciences. For
what theory provides an axiomatization for the 40% (or whatever
percentage
comes out of a valid poll, as long as it's not minuscule) of
physicists who
believe that 0.999<1?

From: Nam Nguyen on 19 Mar 2010 21:04

Daryl McCullough wrote:
> Nam Nguyen says...
>> MoeBlee wrote:
>
>>> What you did is to give an example of an uninteresting theorem in Q.
>> Apparently you didn't understand the short conversation. First, Daryl
>> asked me to give an example of a _nontrivial_ theorem. I gave him
>> just that.
>
> The theorem was: ExAy[~(Sy=x)].
>
> It doesn't seem nontrivial to me. It's a one-step proof from
> Ay ~(S(y) = 0)

Whether or not you used "nontrivial" in technical sense, you were
still wrong on multiple level here. If your "nontrivial" was technical
then Ay ~(S(y) = 0) is a trivial theorem in Q but ExAy[~(Sy=x)] isn't.
If your "nontrivial" was non-technical then you were asking me for
an "interesting" example which is *subjective* and as such my example
satisfied your small challenge here because it was interesting to me
(and I already gave a reason why and I don't mind giving more
reasons if you'd care to hear).

In any case that you (and MoeBlee) thought ExAy[~(Sy=x)] weren't
nontrivial to you is a mistake: either you didn't use the technical
term "nontrivial" appropriately, or you asked for a *subjective* opinion
in a technical challenge!

>
>> Secondly, _he said even I wouldn't interested_ in it and that is wrong,
>> because _to me_ non-trivial theorems should reflect something new that
>> axioms have not reflected and in this case the theorem does remind me
>> certain uni-directional flow in provability.
>
> It's not the sort of fact about numbers that would lead anybody
> to care about number theory. You say you find it interesting,
> and I certainly can't know that you don't, but I don't find it
> interesting.

Remember you challenge _me_ as in "even you [Nam]" couldn't find it
interesting. So whether you find it interesting or not is *irrelevant*
in my example response to you challenge!

In summary, your challenge would never make sense, because "interesting"
and non-technical "nontrivial" is a *subjective* terminologies, but we
were talking about _technical_ merits of the 4 principles.