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

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From: Nam Nguyen on 6 Mar 2010 12:00

Jesse F. Hughes wrote:
> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>
>> David Bernier wrote:
>>> Nam Nguyen wrote:
>>>> Aatu Koskensilta wrote:
>>>>> Marshall <marshall.spight(a)gmail.com> writes:
>>>>>
>>>>>> For me, Nam has mostly moved into the same category as AP.
>>>>> Come now, even if you don't find Nam's posts worth reading comparing him
>>>>> to Archimedes Plutonium is surely excessively harsh.
>>>>>
>>>> Thanks. But it's ok Aatu. I've been"blasted" by both the "orthodox" and
>>>> the "crank" for years; nothing is new.
>>>>
>>>> It's hard to be in a 3rd party isn't it? In the past one "crank" alluded
>>>> that I wasn't "liberal"/"open-minded" enough in my critique of the
>>>> current
>>>> regime of reasoning, and recently AP "lumped" me together with the
>>>> "standard theorists".
>>> [...]
>>>
>>> I respectfully disagree with your view that mathematicians should be
>>> concerned with what Branson (who, it seems, debated "denotation"
>>> or something with Russell) thought, when math. questions are
>>> what's being discussed.
>>>
>>> I think you and I are in a stalemate position here on the point above.
>>> I offer to make peace, in the following form:
>>>
>>> That you and I agree to disagree on Branson vs Russell,
>>> when limited to math. questions.
>>>
>>>
>>> David
>> I think you accidentally mistook me for another poster. I've never
>> mentioned Branson or Russell here. (In fact I haven't heard of Branson
>> before!)
>
> I think he mistook you for Newberry and used the name Branson where he
> meant Strawson.
>
> Aside from those little errors, his post was spot on, I'm sure.
>

Perhaps. But since I didn't quite follow that part of thread I'm not
sure what is sure there. :-)

From: David Bernier on 6 Mar 2010 12:47

Jesse F. Hughes wrote:
> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>
>> David Bernier wrote:
>>> Nam Nguyen wrote:
>>>> Aatu Koskensilta wrote:
>>>>> Marshall <marshall.spight(a)gmail.com> writes:
>>>>>
>>>>>> For me, Nam has mostly moved into the same category as AP.
>>>>> Come now, even if you don't find Nam's posts worth reading comparing him
>>>>> to Archimedes Plutonium is surely excessively harsh.
>>>>>
>>>> Thanks. But it's ok Aatu. I've been"blasted" by both the "orthodox" and
>>>> the "crank" for years; nothing is new.
>>>>
>>>> It's hard to be in a 3rd party isn't it? In the past one "crank" alluded
>>>> that I wasn't "liberal"/"open-minded" enough in my critique of the
>>>> current
>>>> regime of reasoning, and recently AP "lumped" me together with the
>>>> "standard theorists".
>>> [...]
>>>
>>> I respectfully disagree with your view that mathematicians should be
>>> concerned with what Branson (who, it seems, debated "denotation"
>>> or something with Russell) thought, when math. questions are
>>> what's being discussed.
>>>
>>> I think you and I are in a stalemate position here on the point above.
>>> I offer to make peace, in the following form:
>>>
>>> That you and I agree to disagree on Branson vs Russell,
>>> when limited to math. questions.
>>>
>>>
>>> David
>> I think you accidentally mistook me for another poster. I've never
>> mentioned Branson or Russell here. (In fact I haven't heard of Branson
>> before!)
>
> I think he mistook you for Newberry and used the name Branson where he
> meant Strawson.

My memory failed me. I'm now pretty sure it was
Strawson, just like you say.

< http://en.wikipedia.org/wiki/P._F._Strawson > .

And someone in this thread referred to a scribd.com (spelling?)
image of a document where the poster cited Strawson's book.

Maybe I'll be second time lucky; otherwise, I'll be second
time wrong.

> Aside from those little errors, his post was spot on, I'm sure.
>

From: David Bernier on 6 Mar 2010 13:13

Nam Nguyen wrote:
> Alan Smaill wrote:
>> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>>
>>> Jesse F. Hughes wrote:
>>>
>>>> So, you want to deny that Goedel's theorem is true.
>>> 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.
>
> In a high level that makes sense, imho. But I'm not after the "absolute"
> truth, validity, or correctness. It's the _process and methods_ of
> reasoning that I'm really ... really after.
>
> My posting in threads after threads is a means to re-examine, evaluate,
> and revise the current methods of reasoning in FOL in general and in
> Incompleteness in particular. And my motivation of the re-examination
> is basically a following of what Shoenfield said about mathematical logic:
>
> "Logic is the study of reasoning; and mathematical logic is the study
> of reasoning done by the mathematicians.
>
> To _discover proper approach to mathematical logic_, we must therefore
> _examine the methods of the mathematicians_."
>
> [The highlights are mine].
>
> For what it's worth, the long and short of it is what I've been doing for
> years is simply trying to evaluate, for possible shortcomings, of the
> current
> FOL regime and of anyone's reasonings I've come across in some way: myself,
> posters in this and other fora, Torkel Franzen, Godel, Hilbert, etc...
>
> I'm less interested for example whether or not, say, PA is consistent
> but I'm interested in based from what existing and historical reasoning
> backgrounds and by what methods one would logically conclude - with no
> emotion or "belief" - PA is consistent - or not.

There's an ultrafinitist named Nelson, who rose
in professorial (USA) ranks to Associate Professor
of Mathematics or higher. That's a sign
of a definitely competent mathematician, generally
speaking. For years, PA and/or ZFC were ok
for him. Now, his belief is that PA *might*
be inconsistent.

With mathematicians, there's a method to
their "madness" (English saying), and, hopefully,
no "madness" to their methods.

> For instance, here's what MoeBlee said earlier:
>
> >> at least we do know how to formalize PRA. And if we cannot be
> >> confident that PRA is consistent then I don't know what substantive
> >> mathematical theory we could be confident as to consistency.
>
> This passage, imho, is a typical example of where one would forget that
> reasoning is a _process_ (as Shoenfield alluded to above), _not_ a mixture
> of intuitive and religious-like _beliefs_. If we agree what "formalize"
> means, what methods of reasoning are, what consistency and inconsistency
> means, then as a fact it's either PRA is or isn't inconsistent strictly
> based on the definitions and the methods, and it's either we do know *or*
> don't know about the fact. Period. "Confidence" isn't an issue nor does
> it have a role here, in the process of reasoning.
>
> The long and short of it is from what I've gathered, Godel's "proof" is
> invalid as a meta proof, because the methods used in reasoning failed
> in one of the few intuitive principles about the methods of logical
> reasonings. Let me cite the 2 obvious principles:
>
> (1) Principle of Consistency:
>
> No methods shall lead to contradictory conclusions.
>
> (2) Principle of (Method) Compatibility:
>
> If each of any 2 equivalent conclusions is expressed in an independent
> method then it shall not be the case that one method would lead to
> its perspective conclusion, while the other method wouldn not lead to
> the other counterpart conclusion.
>
> In Godel's work, the knowledge of the natural numbers as a sheer intuition
> or as a model of a FOL formal system is incompatible with rules of
> inference
> in so far as both of them are methods of reasonings (and they are).
>
> The reason being is "undecidability" of formal systems is purportedly
> "equivalently" defined by both methods, but the natural number would lead
> to proof of consistency while the rules of inference method would not!

From: Jesse F. Hughes on 6 Mar 2010 16:13

Newberry <newberryxy(a)gmail.com> writes:

> So here is the problem. We can have semantics such that a) vacuous
> sentences are true, or we can have semantics such that b) vacuous
> sentences are ~(T v F). Whether a) or b) does not depend on the model
> or any model. People then forget that it is the logic that generates
> the truth result for vacuous sentences. Then they claim that in any
> model this and any model that. They talk about truth preservation, but
> it is not the axioms that inject the untruths.

Sorry, I haven't any clue what you're trying to say here.

--
"All that 'shock and awe' stuff we've just dumped onto the Asian part of this
earth - could we have fractured something? Perhaps the earth was just reacting
to something that man has done to injure it. The earth is organic, you know. It
can be hurt." -- A chatroom explanation of the Dec. 2004 tsunami.

From: Newberry on 6 Mar 2010 17:23

On Mar 6, 2:26 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Newberry <newberr...(a)gmail.com> writes:
> > But in any case why is quoting G del's original statement pointless
> > obscurantism?
>
> The notation and terminology of G del's original statement is
> impenetrable to anyone who doesn't have the paper in front of
> them. There's no reason not to state it in standard terminology and
> notation.

Which is the standard formulation?

> --
> Aatu Koskensilta (aatu.koskensi...(a)uta.fi)
>
> "Wovon man nicht sprechan kann, dar ber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus