24 Oct
2006
24 Oct
'06
4:24 p.m.
On Mon, Oct 23, 2006 at 11:15:04PM -0700, Vaughan Pratt wrote:
In your Week 240 post to categories, you said
The moral of this game is that all systematic methods for picking an element of (X^X)^(X^X) for an unknown set X can be written using the lambda calculus.
What is unsystematic about the contagious-fixpoint functional? This is the functional that maps those functions that have any fixpoints to the identity function (the function that makes every element a fixpoint) and functions without fixpoints to themselves (thus preserving the absence of fixpoints).
Whoops. I got carried away there. Later I admitted that by "systematic method" I just meant "definable using the lambda calculus". I'll have to fix this. Thanks! Best, jb