determinism versus indeterminism

[DD_8630]

Here is a quotation from Stephen Hawking's book A brief history of time, chapter The uncertainity principle:
" In general quantum mechanics does not predict a single definite result
for an observation.Instead it predicts a number of different possible outcomes and tells us how likely each of these is".( unquote)

So quantum mechanics does predict outcomes but they are fuzzy as you put it.
May I ask on what base is this prediction done if not on physical laws which are per se an expression of determinism.The fuzzyness or the randomness of the outcomes is the second part of this equation expressed statistically or as Hawking puts it "how likely each of these is".

Correct, but the subtlety is that the outcome is truly probabilistic: the universe doesn't 'know' what's going to happen until it does. It's not that particles have an unknown position, but rather that they don't have a position.

One can express that duality of determinism and indeterminism in many philosophical forms but one can not deny their simultaneous coexistence in the most basical laws of nature.

Sure we can: determinism does not exist, insofar as quantum mechanics is concerned. You cannot determine the future with absolute accuracy because the fundamental rules that govern the behaviour of the universe and its contents are inherently probabilistic.

We can use mathematical formulae to describe probability distributions, but we still do not know the outcome of a trial until we run it.

Here is another quotation from the same book ,the same chapter:
"We could still imagine that there is a set of laws that determines events completely for some supranatural being,who could observe the present state of the universe without disturbing it.However such models of the universe are not of much interest to us ordinary mortals.It seems better to employ the principle of economy known as Occam's razor and cut out all the features of the theory that cannot be observed.(unquote)

In his concise scientifical but also popular style Hawking cuts the limits of determinism and throughs the remainig features away to randomness.

In that case, I humbly disagree with Hawking's conclusion.

That's,in other words, just the characteristics of statistical laws.
Let's take for instance a law which says :A+B =C, but where C has not a definite value but a statistical one of let's say 60%.
Now if we will repeat the experiment A+B for a 100 times we will get only in 60 cases the result C in at least 2 conditions:
- before each experiment we will not know if the result is exact C for the reason as put by Hawking ( in generally, not in the particular case of quantum mechanics)
-after achieving the value C in 60 experiments before the number of 100 the next results will be highly random.
Here we see the same dualty :the value C is predictable (say determined) for a certain number of experiments but is in the same time random for all the others.

Ah, no, that's not what 'determine' means. We can calculate the likelihood that a given outcome will occur, but we cannot determine whether it will actually occur or not (until we run the trial, of course).

We can say where an electron in a potential well is likely to be at some time t, but not where it will be. This is not because we don't have enough information, but rather the position of the electron is 'spread out' over all of space. Instead of it being at one particular place, it exists as a superposition of all possible positions. Until we measure it, whereafter things get complicated :p