donald (04/17/83)
Well, okay, now we're down to brass tacks. My definition is
D1: Determinism in a system S means there exists a specification of
all states of S over all time. i.e. there exists a function f
mapping times to states, such that f(t) is the state of S at time t.
Ralph's stated definition is:
... I think the word
determinism implies that the transition between states must be specifiable
in rules which have only the current state of the system as input. I.e.
time should be excluded as an input, to bar trivial rule concoctions like
at time t the system will go into the state that I know it will be in at
time t+1.
Formally this is (I think):
D2: Determinism in a system S means for any state A of S, there exist rules
by which A may be transformed to the next state B that S will assume.
[ note: Ralph has implicitly assumed that time moves in discrete jumps;
otherwise one would have to have a time delta as input into the
rules so that A is transformed into B at time+delta. Minor point. ]
If we are given the initial state of the system, D2 is equivalent to D1!
For any system S, if S0 is the state at time zero, we can fully specify
the function of D1 merely by applying the rules of D2 to S0 for all times.
And also, therefore, although the states can be KNOWN by God, He did not
choose them; we did.
But he DID choose them because he set up the initial state, knowing exactly
how it would evolve! Under D1 or D2, the universe is still deterministic.
Thusly, in this context, I would say that the existence of free will is
equivalent to the non-existence of such rules.
I think the confusion arises because this whole discussion is taken from
the omniscient viewpoint. To us, the functions of D1 or rules of D2 are
not findable or not computable. To god presumably they are. In particular,
the rules of D2 ALWAYS EXIST: they consist of the trivial rule "ask myself"!
Given an omniscient being, our perception of free will is solely a result
of our ignorance. But He knows better.
Don Chan