do you know laplace's demon?
it's a classic determinist presentation by mathematician and physicist pierre simon laplace, in his philosophical essays on probabilities:
We may regard the present state of the Universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the Universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.let's suggest it as: ∀s ∈U, η su
i.e., every state "s" in the Universe is necessary (i.e., determined by a set of initial conditions plus the laws of physics).
a terse conclusion, but there is a problem. theorems apply to mathematical objects*, not to reality. though we have reasons to believe that the universe is structurally mathematical, not all our representations of the the universe are, well, mathematical. for instance, the existence of solutions to some equations that represent physical laws does not imply physical existence (see my previous post).
laplace's demon is incompatible with quantum mechanics. said differently physical phenomena cannot be -completely- reduced to strict deterministic laws.
*what is a mathematical object? o is mathematical if it exhibits mathematical properties, i.e., nullity, identity, commutativity, associativity, distributivity, etc.