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From: Nam Nguyen on 14 Apr 2010 23:26
David Bernier wrote:

>
> Somebody referred to Strawson, the logician/philosopher.
> Would you know if Strawson thought of a "Principle of Symmetry"
> similar to yours?

I read briefly the first few sections of his writing from the
link you gave but didn't see anything about any "Principle of
Symmetry". Iirc, what I read is in PS form so I couldn't search
for the phrase. If anyone knows the page number (if he actually
wrote something about it), much appreciated if you could let me
know.

>
> Presumably, this "Principle of Symmetry" you mention has been
> discussed in some book or article. Would you know
> of some reference for this?

I actuallly came up with that in an impromptu way, though I might
have unconsciously remembered a similar phrase "Symmetry Breaking"
in some kind of physics book (perhaps QM) I had read years ago.

I've googled "Principle of Symmetry" but found nothing directly
for mathematical logic, in the way I stipulated it. I don't think
anyone has thought of the term in conjunction with mathematical
reasoning, since the phrase implies a high degree of "relativity"
but our mathematical reasoning has been (rather wrongly) based
in absolutism (Platonism).
From: Nam Nguyen on 14 Apr 2010 23:43
Alan Smaill wrote:
> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>
>> Alan Smaill wrote:
>>> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>>>
>>>> Alan Smaill wrote:
>>>>> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>>>>>
>>>>>> To claim some formula being
>>>>>> absolutely true (or false) is to destroy the notion of such symmetry.
>>>>> Do you agree that symmetry is only
>>>>> broken if the cases "P" and "not P" are treated differently?
>>>> Of course I'd not agree. Even in relativity, given an appropriate context,
>>>> P and ~P must necessarily be treated differently because of LEM.
>>> Now you've really lost me.
>>> LEM *is* symmetric itself, isn't it?
>> I have no idea what you meant here by "LEM *is* symmetric itself".
>> You have to explain what you meant by that.
>>
>> The word "symmetry" I've used here is in the context of the Principle
>> of Symmetry I articulated before with some clear examples and are about
>> concepts, formulas - but not about LEM].
>
> LEM can be expressed by all formulae of a certain syntactic shape
> (P v not P) in the language to hand.
> Whether you take P as true or P as false makes no difference to
> LEM. In that sense, swapping P with not P makes no difference,
> LEM will apply in either case.
>
> Perhaps you can explain why "P and ~P must necessarily be treated
> differently because of LEM"? (Are you maybe thinking of what
> is called the law of non-contradiction, rather than the excluded middle?)

I think you misunderstood the context in which I've been talking.
The point I've been making is that a formula (other that those that
are tautologous or contradictory) would never have an absolute truth.
For example Ax[~(Sx=0)] cann't be absolutely true or false: there must
always be a context when we say it's true, or false. So without a context
the formula is neither true nor false, seemingly violating LEM.

But once we choose a context, say a model of a language, then the formula
must conform to LEM: it must either true or false and its negation must
be opposite (hence different); and there's no violation of LEM whatsoever.
And that's what I meant in "given an appropriate context, P and ~P must
necessarily be treated differently because of LEM".

>
>>>> The Principle addresses a different issue: P or ~P can't be uniformly
>>>> treated as true or false in _all_ contexts. That's all the Principle of
>>>> Symmetry would stipulate, and all I've really said (as above).
>>> So how do you know it is relevant to the particular context at hand,
>>> that of assuming "not P" hypothetically (ie for sake of argument), deriving
>>> a contradiction, and concluding "P". And also in the context where "P"
>>> and "not P" are switched systematically in such an argument?
>> I'm not sure what you're trying to argue here. My argument only concerns
>> the alleged "absolute" truths that DB tried to suggest, and in which I
>> counter claimed any such absolute truth would break the Principle of
>> Symmetry. That's all I've really argued in this conversation!
>
> Still not convinced on my side.
> I think we've gone as far as we can productively go, however.
>
From: Nam Nguyen on 15 Apr 2010 00:34
Marshall wrote:
> On Apr 12, 9:18 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>> Marshall wrote:
>>> On Apr 11, 7:51 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>>>> Marshall wrote:
>>>>> On Apr 11, 5:09 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>>>>>> Marshall wrote:
>>>>>>> On Apr 11, 3:54 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>>>>>>>>> I reject your claim that intuition, of whatever kind, plays
>>>>>>>>> any part in our thinking about the naturals.
>>>>>>>> So is the naturals collectively a finite syntactical notion *to you*,
>>>>>>>> since you'd reject the idea they're an intuition notion?
>>>>>> Can you share with us your resounding, firm, answer to that simple
>>>>>> question?
>>>>> You mean, again? You want me to say "yes" again? Okay:
>>>>> Yes.
>>>> So your resounding answer is "yes" that the notion of the naturals
>>>> is based on an intuition but is a notion of syntactical formal system.
>>> Not a "formal system" in this sense:
>>> http://en.wikipedia.org/wiki/Formal_system
>>> The naturals and their operators are a model, not a theory.
>> Not only you're clueless as to exactly what the natural numbers be,
>> you also don't use the technical terms correctly.
>
> One of the things that makes you so amusing is the way
> you thrash around any time anyone speaks of something
> with which you are unfamiliar. It's hilarious how huffy you
> get whenever anyone uses a term in a way you don't
> like, yet at the same time you always feel free to change
> the meaning of your own symbols in capricious ways.

There's no "like" or "dislike" on my part, here. You clearly claimed
the "naturals and their operators are a model" but you haven't
proved they satisfy the technical definition of model, have you?
And since you didn't prove the naturals are model theoretical and
yet wrongly assert rejected they are of an intuitive notion, I just
pointed out whatever you said about them including your rejection
are incorrect. That's all.

So again, how did you arrive at the conclusion that the naturals
meet the definition of language model? Did you, as I mentioned
before, define all the n-ary relations (sets) required by model-
definition?

Also, did you now realize that the naturals are of intuitive notion?

These are technical matters and questions. Either you have some clues
what they're or you don't but there's no "like" or "dislike" in these
matters.
From: Marshall on 15 Apr 2010 22:55
On Apr 14, 9:34 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
> Did you, as I mentioned
> before, define all the n-ary relations (sets) required by model-
> definition?

Listing out all the tuples is only part of the buffoon-theoretic
version of the definition of model. So really that requirement
is only binding on you.


Marshall
From: Nam Nguyen on 15 Apr 2010 23:14
Marshall wrote:
> On Apr 14, 9:34 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>> Did you, as I mentioned
>> before, define all the n-ary relations (sets) required by model-
>> definition?
>
> Listing out all the tuples is only part of the buffoon-theoretic
> version of the definition of model. So really that requirement
> is only binding on you.

Ah! So you'd ignore technical definition! No wonder why your arguments
are cohesiveness and incorrect!

In the theory T = {Ax[x=a]} I know we could have a model because
we could establish the 2-ary relation = which is the set {(a0,a0)}
where a0 = {} by definition. So, T has a model, _by definition of model_ .

That's how proofs, reasoning, and arguments are done, Marshall.
By technical definitions, not by idiotic rambling and attacks!

Naturally.
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