virus: Godel vs. Axiom of Choice Re. Freewill
Tue, 17 Dec 1996 16:39:12 -0600 (CST)

David Pape,
Since truth-values are [hopefully] deterministic, I wouldn't
consider Godel's incompleteness theorems a major loophole for freewill,
or absence thereof. Also, randomness doesn't generate freewill, although
it may be effective at emulation.
The highly controversial Axiom of Choice [from Set/class theory] is
much more interesting as a loophole--or possibly outright assertion.
Several schools of mathematics outright forbid its use, not including the
more common ones.
A "proof" using the Axiom of Choice explicitly (and critically, no
rewriting to avoid it possible) is the ultimate in nonconstructive
proofs: not only does it fail to explicitly construct the
example, the proof *cannot* be patched to allow explicit construction.
It could be argued that the Axiom of Choice is usable (on infinite sets,
the finite sets are not as controversial) iff freewill is usable.
[Yes, the Axiom of Choice has a perfectly well-formed
expression in Predicate Calculus. That's not why it does strange stuff.]

/ Towards the conversion of data into information....
/ Kenneth Boyd