Re: Incompleteness vs. Mechanical Reasoning

On 2008-04-06, in sci.logic, R. Srinivasan wrote:
Consider a proposition P about a future contingency that is based on
the decision taken by a human being X. A human being has free will if
and only if that proposiiton is fundamentally undecidable right now,
in the sense that we human beings (including X) cannot ever hope to
have a theory (right now) that correctly decides P.

(I presume you don't mean the question of free will hinges on our
ability to predict a particular choice P). If this is all that is
meant by our having free will I'm perfectly happy to agree we have
absolutely and utterly free will. That is, I'm perfectly willing to
accept that with regards to future contingencies about human decisions
we can't ever hope to have a theory that, with any practical success,
predicts what we will or will not decide in all but the most trivial
cases.

Alas, on this conception it's difficult to see what relevant
difference there is between computers and humans. For all we know it's
perfectly possible future computers have free will in this sense. It
wouldn't be much of a stretch to say they have free will at this very
moment.

At this point you would say "Right now we do have a theory T1 which
proves P and another theory T2 which proves ~P and one of these has to
correctly predict the truth or falsity of P; but we human beings have
no way of predicting which of these is the correct theory". This is
exactly equivalent to asserting that "Right now P is either true or
false, but we human beings have no way of saying which of these is the
case".

But just what does our having or failing to have free will have to do
with claims about future being true or false? On the face of it, it's
perfectly compatible with the freeness of my will that it's true that
I will, in fact, freely choose to eat an ice-cream cone tomorrow at
10am.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.