FOM: RE: RE: Proper Names and the Diagonal Proof

[Dennis E. Hamilton]

This resonates with me (it is an interpretation of the consequences of the
formal theory, of course), because it provides a really powerful analogy for
me.

They way it has looked to me has been from the lower half (not thinking
about what it would be like in the next level above).  That is, putting
myself in the place of the computerist, I notice that I am always operating
below N and that no matter what I do, I can't reach it.  Furthermore, I must
be careful and be content with operating only where I do not depend on
transcending the finite.  Anytime where I undertake anything that is
tantamount to brining N into my grasp, my theory is busted or my computer
doesn't stop.  I have no access to N as an graspable aggregate (and PA
doesn't give me any, of course).

I have wanted to motivate that in my work and also demonstrate how much
power we get *anyhow*, but not *that* *much*!

So I love it.  I just love it, as I said.  Thank you.

OH, and I see that this did go to the list (I missed the CC: before), so
forget my off-list request.  Thanks.

-- orcmid

------------------
Dennis E. Hamilton
http://orcmid.com/
mailto:dennis.hamilton at acm.org
tel. +1-206-932-6970
cell +1-206-779-9430
     The Miser Project: http://miser-theory.info

-----Original Message-----
From: Insall [mailto:montez at rollanet.org]
Sent: Wednesday, June 26, 2002 13:21
To: dennis.hamilton at acm.org
Cc: Foundations of Mathematics
Subject: RE: RE: Proper Names and the Diagonal Proof


Dennis Hamilton wrote:
``I had thought he used the proof to show that there are more of the things
he wanted to name than the available supply of names.''

and

``I don't think duplicates are the issue.''



I once believed the same thing you suggest in your first statement above.
Your second statement above is quite clearly on target, IMO.

[ ... ]

The fact that McNulty did not convince me on the spot suggests to me that I
was at the time such a pedanticist.  But, I must have been struck in a
beneficial way by George's multitude of comments about the situation, for I
have come to learn some bit from it, and I have come to realize there was a
connection between all these facts.


Matt Insall