On 14 Feb 2011, at 11:17, Stephen Paul King wrote:

From: Bruno Marchal
Sent: Monday, February 14, 2011 4:49 AM
To: everything-list@googlegroups.com
Subject: Re: Plato's Heaven

On 14 Feb 2011, at 09:40, Stephen Paul King wrote:


Allow me to add a comment to this brilliant argument. Following Jason’s description of Platonia, Plato’s heaven, it would seem to include all possible descriptions of itself and thus is in a way like a set that contains all subsets of itself including at least one subset that is identical to itself. Is this not a paradox?

>Not at all. UD* contains many UD* which contains many UD* ad infinitum. There is no paradox because UD* is infinite. It is no more paradoxical than the Mandelbrot set, which is "made of" Mandelbrot sets.

    OK, how does the UD* relate to Numbers?

By the UD, which can be seen as a number, which, in relation with other number, does emulate the computations.

Is the UD* like an inch worm that travels Platonia measuring them?

UD* is the same as the truth an d falsity of the arithmetical sentences having the simple existential form ExP(x, y) P decidable (the Sigma_1 sentences). UD* is the tiny effective part of the arithmetical truth.

Seriously, how is the difference between one number and another knowable to the UD* if the UD* is almost every where in Platonia. This UD* seems remarkably similar to an eternal, omniscient and omnipotent being!

It is as eternal as the number 7.
It is not omniscient, nor omnipotent. It is less "scient" and less "potent" than any Löbian machine, and of course a fortiori much less so than the divine hypostases (the G* part of the G/G* variant).

UD* is just the collection of all computations. I suspect it to be coded by the rational Mandelbrot set, which is a good illustration for it. But some Penrose pavage will, do, or you can write it in Lisp, as I did. I mean it is a very concrete and specific object, which, assuming comp, can play the role of the effective (computably generable) part of arithmetical Platonia (which is non computable).



You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
For more options, visit this group at 

Reply via email to