Le 26-juin-06, à 23:09, Tom Caylor a écrit :


> I also agree that the "subject" to which the Forms have meaning cannot
> be a Form itself.  But as my previous post(s) on this thread mentioned,
> I see it as a "recognition" of what "is there".  I like to use the word
> "re-cogn-ize" ("again know").  A year ago in a meeting of fathers and
> sons, the question was asked, "What does the word recognize mean?"  My
> son, who was 8 years old, said, "It's when you know something, and you
> know that you know it."  Jesus said, "Unless you become like children,
> you will not enter the kingdom of God."  Bruno, you have brought up
> examples of children being able to see simple truths, like the
> 7+7+7+7+7+7 in your fairy-riddle introduction to diagonalization.
> (Along those lines, there's the classic objection to the Penrose
> argument, objecting that it shouldn't require the ability see the truth
> of the Godel statement in order to qualify for having consciousness.  I
> agree, but think the objection portrays a misunderstanding of Penrose's
> argument, even though I don't necessarily agree with all of Penrose's
> conclusions.)
>
> Anyway, I think this is a pretty good definition of recognize, "to know
> something, and to know that you know it".  Now people object that this
> just produces an infinite regression, but this is assuming that we
> never can have any direct contact with truth.  I think Bruno is partly
> right in that the key lies in the infinite.  I think we adults have
> gotten so caught up in building our own empire (science), in a
> computational step-by-step manner, that we often blind ourselves from
> simple truth.



I agree with you. Most theories of knowledge (or "knowledgeability") 
accept the axiom named "four":

4:  Kp -> KKp  (knowable p entails knowable knowable p; or "if I can 
"cognize" the truth of p, then I can (re)cognize that I can "cognize" 
the truth of p). Of course we will come back on this. the "K" here will 
be defined through the Theaetetical variant of the Godel beweisbar "B", 
which hides many diagonalizations.




> My comment about math being about invariance was not meant to be a
> global definition of math.  "Math is about invariance" was meant to
> imply "math is about looking for invariance".  This is something that
> children understand even more naturally than numbers.


Invariance is for me mainly the subject matter of group theory or 
geometry, and I would argue that numbers are more elementary. I am 
happy because I will have the opportunity this summer to teach math to 
very little children (6 year old), so I will have perhaps a better 
idea. I have not so much experience with so young students except a 
long time ago when I worked with highly mentally disabled one. You 
could be right in some sense. Piaget wrote about this and I should 
perhaps reread it. But then this question is also a little bit out of 
topic given that you seem already agreeing with AR, if only for the 
sake of the comp argumentation.

BTW, I will send asap the solution of the four diagonalization 
questions. Thanks to you and George for your patience,

Bruno


http://iridia.ulb.ac.be/~marchal/


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