Hi Tom,
Your post has inspired a thought for me that I have been struggling for years to generate! Where is Intensionality instantiated in Arithmetic Realism, or any form of Platonism? To re-phrase in folk-speak: How is "to whom-ness" present in a number?
I find in
http://en.wikipedia.org/wiki/Intension the idea that "refers to the set of all possible things which a word could describe.", thus intensionality for a number would be the set (???) of all possible other numbers that it could encode, which has a nice algorithmic flavor; but let's go to extensionality: "extension (or denotation) refers to the set of all actual things which the word actually describes".
How do numbers *distinguish* (if I am permitted to use that word) between *possibility* and *actuality*? Is the "bush" what Bruno is "beating around"?
Onward!
Stephen
----- Original Message -----
From: <daddycaylor.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Cc: <quentin.anciaux.domain.name.hidden>
Sent: Monday, April 03, 2006 5:20 PM
Subject: Re: The Riemann Zeta Pythagorean TOE
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. 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.
Tom
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Received on Mon Apr 03 2006 - 22:36:37 PDT