What is missing from Vaughan's account is the "Principle of Asymptotic Omnipotence". Of course the supreme being can create a stone it cannot lift. But being omnipotent it can grow its strength to the point where it can now lift it. Omnipotence allows it to create a more massive stone that it currently could not lift. But then.... It makes no more sense to ask what happens in the limit than it does to ask which way the fly was flying when it was crushed between the two locomotives. Michael On Fri, 19 Dec 2008, Vaughan Pratt wrote:
In The Reasoner 2:12 (December 2008), freely downloadable as
http://www.kent.ac.uk/secl/philosophy/jw/TheReasoner/vol2/TheReasoner-2(12)....
from
editor David Corfield writes about n-categories, giving an impressively accessible short overview of the concept and then interviewing Tom Leinster about his experience with n-categories.
The interview is followed by an article on the Paradox of Omnipotence by Alex Blum, which addresses the frustration any omnipotent being must surely experience at being unable to create a stone that she cannot lift. (Imagine the applications, such as blocking the fridge door when on a diet: one paradox helping another.) Many of us in moments of temporary perceived omnipotence have experienced this accompanying sense of impotence, which can occur so frequently in life that one learns to suppress it subliminally in microseconds, becoming completely unconscious of it at an early age (but not without much screaming before then).
Properly understood, this so-called Paradox of Omnipotence is, as often happens, really a principle, the Principle of Omniimpotence. Paradoxical origins tend to potentize principles to a remarkable degree, with potencies upwards of 200C (the fourth power of a googol). As a case in point the omniimpotence principle forms the basis of a useful diagnostic. Using all available tools, how would you go about creating a stone you cannot lift? If it seems impossible you may be suffering from omnipotence.
The principle is modeled at a very elementary level by 0-1 matrices, which cannot simultaneously contain a row of all 1's and a column of all 0's. This is the zeroary case of a more general interference or "uncertainty principle," the binary case of which is that any proper meet in the rows of such a matrix precludes a proper join in the columns. (For this purpose a meet or join is held to be *proper* when it is neither of its arguments.) From this it follows that if a matrix represents a semilattice by virtue of its rows having all meets then its columns cannot have any proper join.
This and more can be found at
http://boole.stanford.edu/pub/coimbra.pdf
as the dry edition of the notes from the course on Chu spaces I gave at the School on Category Theory and Applications held at the University of Coimbra in 1999. (The wet edition, under the slogan "All wet all the time," would have included the above wisdom on omniimpotence but wiser heads prevailed, both mine.)
It is not immediately obvious to the untrained eye that there should be any connection between the omnipotence of god and category theory. It should therefore be of some interest to both category theorists and theologians that a more formal connection could exist beyond this mere juxtaposition of articles in The Reasoner.
Vaughan