[net.misc] Can determinism be proven?

portegys (08/09/82)

I think that it is not possible for a being contained in
a system to ever know the system completely.  Because, to
know the system completely would be to also understand
itself within the system completely, which would be a model
of itself contained within a model of itself contained within
a model of itself ... an infinite regress.

This bears on determinism vs free will in that I think in
order to show one vs the other, it is necessary to have
a perfect knowledge of the world, which cannot be done.

So, if you can't choose conclusively between them, why
not just use the one that fits the situation best? For
science, determinism seems to be most appropriate. For
accounting for a person's responsibilities within society,
I think a free will model works better.

                                   Tom Portegys

davidson (08/23/82)

Interestingly, it does not necessarily involve an infinite regress to
have part of a system completely model the whole system.  It does, however,
require that the system be describable with less information than it
contains (and there are other requirements too).  An analogous situation
is with the common programming exercise of writing a program which prints
itself out.  Indeed, a deterministic universe with simple physical laws
and a simple initial state is easily modelled completely from within.  A
non-deterministic universe, on the other hand, can not be completely modeled
at all.

This brings up one of my favorite speculations about the universe:  assuming
that the universe is finite in extent, or taking a finite subset of it, does
the universe or that subset contain a finite or an infinite amount of
information?  That is, could one completely specify an instantaneous time
slice with a finite amount of information?  The answer to this question
depends, I think, on whether space, as well as everything else, is quantized.