Le 03-avr.-06, à 23:20, daddycaylor.domain.name.hidden a écrit :
>
> Quentin:
>
> I don't know from your wink at the end whether you are half-serious or
> not.
> But just in case (and Bruno can do better than I can on this), I think
> I can correctly appeal to Peano's distinction between mathematical and
> linguistic paradox. The meaning of the symbols is defined at a higher
> level than the encoding itself.
Yes, and the "gone with the wind" seemingly paradoxical statement does
not depend of the encoding chosen. If you write the number with the
base <keyboard>, it means that any humans looking at arbitrary big
numbers will see the "usual english version of "gone with the wind".
But the reasoning to show this does not depend of the base nor on any
particular encodings.
I take the opportunity to recall a universal dovetailer is not
equivalent with set of finite or even infinite strings. I will come
back on this in a post "the heart of the matter" where I will try to
make more precise what is the UD and what is the relation between the
UD and the type G reasoner (and then the "hypostases" will appear by
themselves, including a Plotinus-like theory of matter.
> Your statement turns on the word
> "chosen", which is a verb. This goes back to my other post in this
> thread that, in order to keep from going into an infinite regress of
> meaninglessness, defining meaning ultimately requires a person.
I agree with you. Now, in order of *defining* meaning through the
notion of person, well, you need to *define* the notion of person. And
this can be done with the comp hyp. At an informal level it can be done
by the notion of transportable diary, like the one of the candidate for
the self-duplication experiment which is supposed to be destroyed in
teleportation experiment. At a formal level it can be done trough the
modal variant which are forced by the incompleteness argument (this
leads to the arithmetical interpretation of Plotinus notion of "person"
called "hypostase".
But all this has quasi noting to do with the fact that all finite
strings appears in almost all big numbers. We don't need any notion of
meaning for stating this. I give a hint for the proof: show first that
in the usual base "10", the absence of "9" is rare. Then generalize.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Apr 04 2006 - 05:20:43 PDT