Brian, call me slow (please, in private mail ;^>), but I don't see how any
of these contradict what I was saying.
Sure if one -assumes- that conscious agents can -freely- affect the physical
world, then of course there will be potentially enormous changes from even
small amounts of freedom for the reasons that you spell out an order of
magnitude better than I could.
But why, in a scientistic (science plus rejecting non-science based reasons)
view, would one think that agents had any freedom whatever?? No doubt, in
such a view, agents do have such causal impact (they are material objects,
after all) -- but in the relevant sense, -freely-?
> The last thing I would like to mention is Chaitin's fairly recent
> work on undecidability. Kevin asked me a long time ago for a
> definition of this term. Unfortunately, I was unable to follow
> through with that thread due to time restraints. Actually, there
> have been quite a few threads lately where I haven't followed
> through as I should. Apologies to those I should have answered
> but didn't.
>
> Well, for a thorough understanding of Chaitin's work, the best
> place to go is his web page at:
>
> http://www.umcs.maine.edu/~chaitin/
>
> This seems to contain all of his papers in electronic form
> (either html or postscript) as well as many of his books.
>
> In a nutshell, undecidable has the same meaning as random,
> provided (!!!) you use the definition of random found
> in algorithmic information theory. Random means incompressible,
> without pattern. We can say, for example, that the toss of
> a fair coin is undecidable.
>
> Since many have perhaps not heard of Chaitin, let me just
> mention that Casti (in one of his books) referred to
> Chaitin's undecidability as one of the greatest achievements
> in modern mathematics. It is comparable in significance to
> Godel's incompleteness and to Turing's uncomputability.
>
> Basically, what Chaitin showed is that there are mathematical
> facts that are true for no reason. Maybe I should let
> Chaitin speak for himself. Here is a short quote from one
> of his papers:
>
> ======================================================
> The most important application of algorithmic information
> theory is to show the limits of mathematical reasoning. And
> in particular what I've constructed and exhibited are mathematical
> facts which are true for no reason. These are mathematical facts
> which are true by accident. And since they're true for no reason you
> can never actually prove logically whether they're true or not. They're
> sort of accidental mathematical facts which are analogous to
> the outcome of a coin toss, because the independent toss of a
> fair coin has got to come out heads or tails but there's no reason
> why it should come out one or the other. And I've found mathematical
> facts that mirror this very precisely.
> -- Gregory Chaitin, "How to Run Algorithmic Information Theory
> on a Computer," <Complexity>, 2(1):15-21.
> =======================================================
>
> OK, to tie this back in. The language of physics is mathematics.
> If there are facts that are true for no reason in mathematics
> then wouldn't we at least expect that there may be things that
> happen in the world for no reason?
>
While I don't necessarily like the phrasing "for no reason", and I haven't
read Chaitin, it is easy to see vaguely how it would be an implication of
Gšdel's incompleteness theorem. (Maybe that shows I don't understand it!)
Indeed, something -really vaguely- like this is the one way I can see to
have determinism combined with a real sense of freedom and moral
responsibility: our choices are ultimately rigidly determined by ourselves,
flowing deterministically from our character, or minds, or souls, or
something like that, BUT said character, etc., is NOT (completely)
determined in turn by something else beyond our control. Maybe it
just -is-, or ...?
This is a long way from Chaitin, I imagine. And it's hard to spell out in
anything but the purest speculation just how it would work out. (E.g.,
something like eternally existing Platonic souls?) But it seems possible
and maybe rational (um....), if not at all scientific just now.
John