Re: The modern mathematical concept of infinity is indefensible
Nam Nguyen
> Nam Nguyen <namduc...@shaw.ca> writes:
>
>> If an axiom codifies an important truth, so would its negation!
>> [Unless they conflict with each other, axioms (which are formulas)
>> are born independent and equal, at least in term of importance,
>> naturally].
>
> Since you can't possibly be suggesting that both "the successor of
> zero is not zero" and "the successor of zero is zero" (or their
> formalisations) are true
I simply suggested that if an axiom A codifies a truth, so would ~A
codify a[nother] truth. It's that simple. (Note: I never mentioned
"both"!).
> it's difficult to make anything of this rather baffling doctrine.
Only if you made it more difficult than what it really is.
For instance, let A1 df= "Obama is the 1st African US President".
If A1 represents a truth, so would ~A1. (Note: genetically Obama
is only 50% African).
For another instance, let A2 df= (S0=0). If there's a context that A2 is
true, so would there be one in which ~A2 is true. Don't you think so.
In brief, mathematical truth is subjective - is context sensitive.
If I were wrong, could you then prove the counter-thesis?
--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")
herbzet
Nam Nguyen wrote:
> Aatu Koskensilta wrote:
> > Nam Nguyen <namduc...@shaw.ca> writes:
> >
> >> If an axiom codifies an important truth, so would its negation!
> >> [Unless they conflict with each other, axioms (which are formulas)
> >> are born independent and equal, at least in term of importance,
> >> naturally].
> >
> > Since you can't possibly be suggesting that both "the successor of
> > zero is not zero" and "the successor of zero is zero" (or their
> > formalisations) are true
>
> I simply suggested that if an axiom A codifies a truth, so would ~A
> codify a[nother] truth. It's that simple. (Note: I never mentioned
> "both"!).
>
> > it's difficult to make anything of this rather baffling doctrine.
>
> Only if you made it more difficult than what it really is.
>
> For instance, let A1 df= "Obama is the 1st African US President".
> If A1 represents a truth, so would ~A1. (Note: genetically Obama
> is only 50% African).
>
> For another instance, let A2 df= (S0=0). If there's a context that A2 is
> true, so would there be one in which ~A2 is true. Don't you think so.
>
> In brief, mathematical truth is subjective - is context sensitive.
> If I were wrong, could you then prove the counter-thesis?
Did I call it, or not?
--
hz
Nam Nguyen
I don't understand your question.
>
> --
> hz
Aatu Koskensilta
> For another instance, let A2 df= (S0=0). If there's a context that A2 is
> true, so would there be one in which ~A2 is true. Don't you think so.
Whether "S0=0" is true or false obviously depends on what S and 0
mean, and we can certainly find a way of arbitrarily assigning meaning
to 0 and S so as to render "S0=0" false and also a way go render it
true. Is there some point to expressing this triviality in a
misleading and bizarre way? Whatever value there is to your rumination
on the subjectivity of this or that is not made more apparent to
anyone by such silliness.
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Nam Nguyen
> Nam Nguyen <namduc...@shaw.ca> writes:
>
>> For another instance, let A2 df= (S0=0). If there's a context that A2 is
>> true, so would there be one in which ~A2 is true. Don't you think so.
>
> Whether "S0=0" is true or false obviously depends on what S and 0
> mean, and we can certainly find a way of arbitrarily assigning meaning
> to 0 and S so as to render "S0=0" false and also a way go render it
> true.
> Is there some point to expressing this triviality in a
> misleading and bizarre way?
You got to calm down and be consistent in your arguing with people.
If your previous paragraph agrees with what I said then how come
now it becomes "misleading and bizarre"? Besides, and to be honest
with you, you're just venting out your subjective feelings
("misleading and bizarre") and not offering any technical argument
here, which is quite unexpected!
> Whatever value there is to your rumination
> on the subjectivity of this or that is not made more apparent to
> anyone by such silliness.
Why is it that you tend to offer subjective mumbling such as this
paragraph, instead of real technical argument?
Aatu Koskensilta
> If your previous paragraph agrees with what I said then how come now
> it becomes "misleading and bizarre"?
What was misleading and bizarre was your expressing the triviality,
that in case of statements that aren't logical truths or falsehoods we
can find a way of assigning meaning to the non-logical terms so that
the statement comes out true and also so that it comes out false, by
saying that the negation of the codification of an important truth
also codifies an important truth.
> Why is it that you tend to offer subjective mumbling such as this
> paragraph, instead of real technical argument?
It is a horrible flaw in my character. In so far as your peculiar
doctrine amounts to merely stipulating that a statement is to be said
to be subjective whenever it is not a logical truth or falsity there
is no "real technical argument" to be offered against it. One may
merely observe that this stipulation is, on the face of it, entirely
unrelated to any subjectivity in the usual sense of the word. If, on
the other hand, you mean to make a substantial claim, about
subjectivity as it is usually understood, a special argument is
needed, an argument which might then be subjected to technical logical
and philosophical scrutiny.
Nam Nguyen
> Nam Nguyen <namduc...@shaw.ca> writes:
>
>> If your previous paragraph agrees with what I said then how come now
>> it becomes "misleading and bizarre"?
>
> What was misleading and bizarre was your expressing the triviality,
In logics arguments misleading would lead to error and "bizarre"
would mean contradiction/inconsistency. How you ended up believing
being trivial is the same as being misleading or bizarre is really
beyond typical understanding.
> that in case of statements that aren't logical truths or falsehoods we
> can find a way of assigning meaning to the non-logical terms so that
> the statement comes out true and also so that it comes out false, by
> saying that the negation of the codification of an important truth
> also codifies an important truth.
>
>> Why is it that you tend to offer subjective mumbling such as this
>> paragraph, instead of real technical argument?
>
> It is a horrible flaw in my character.
If you say so!
> In so far as your peculiar
> doctrine amounts to merely stipulating that a statement is to be said
> to be subjective whenever it is not a logical truth or falsity there
> is no "real technical argument" to be offered against it.
This isn't the 1st time my subjectiveness/relativity "doctrine"
of FOL reasoning is stipulated - in your presence/participation.
In the last time, the talk about GC as potential "absolute undecidable"
formula *could have lead to a highly technical illustration* of what
subjectiveness means. But what did you do, beside a subjective silence?
Nothing!
So now when I presented a very _simple_ illustration of subjectiveness,
you decried "silly", "bizarre", "unrelated ... [to what's] usually understood",
... I feel like being in an intellectual guerrilla-warfare!
> One may
> merely observe that this stipulation is, on the face of it, entirely
> unrelated to any subjectivity in the usual sense of the word.
Really? I'm sure you know the 'R' in SR means relativity, which in this
context means the same as "subjectivity".
> If, on
> the other hand, you mean to make a substantial claim, about
> subjectivity as it is usually understood, a special argument is
> needed, an argument which might then be subjected to technical logical
> and philosophical scrutiny.
In *any* relativity/subjectivity, there are 2 indispensable components:
- what's *the same* for any 2 observers/reasoning-beings/individuals
- what will vary from the perspective's one individual to the that
of the other.
In so far as FOL doesn't 100% exclude the existence of an "absolute
undecidable" formula F, w.r.t. a collection K of formal systems, then K's
(syntactical) description becomes the "the same" component; and the
assertion F is provable or ~F is provable is entirely subjective: it
would "vary from the perspective's one individual to the ... other".
(That's as far as I could introduce my "doctrine" of mathematical
relativity, without converting the whole post into a dissertation!)
MoeBlee
> This isn't the 1st time my subjectiveness/relativity "doctrine"
> of FOL reasoning is stipulated - in your presence/participation.
> In the last time, the talk about GC as potential "absolute undecidable"
> formula *could have lead to a highly technical illustration* of what
> subjectiveness means. But what did you do, beside a subjective silence?
> Nothing!
>
> So now when I presented a very _simple_ illustration of subjectiveness,
> you decried "silly", "bizarre", "unrelated ... [to what's] usually understood",
> ... I feel like being in an intellectual guerrilla-warfare!
No poster is obligated to comment on your previous posts just to
excercise his or her prerogative to comment on any other of your
posts. Aatu might have not read the thread your'e talking about, or
might have been not interested, for whatever his own reasons, in
commenting at that time or later time even though he read it. That's
entirely his own prerogative and his prerogative to change his mind as
to what interests or motivates him to comment at any time, and
exercise of such prerogative is not the least bit inappropriate.
MoeBlee
Nam Nguyen
Yeah. I forgot this forum is really "sci.prerogative".
MoeBlee
> Yeah. I forgot this forum is really "sci.prerogative".
No, but here are some other options:
sci.smartass.rejoinders.notsubstantive.namnguyen
sci.itsallsubjective.sez.namnguyen
alt.rants.misinformed.namnguyen
alt.philosopy.mathematics.sheersilliness.namnguyen
MoeBlee