As I've said, there are times when knowing all relevant information isn't possible, even in theory. Even if it were possible, that information would also have to be processed in order to make a prediction. — T Clark
If we flip one coin, we know zero, nada, not-a-fucking-thing about the outcome (unless the system is rigged or we have Laplace's demon on hand.) I'm sure you agree with that? — frank
You actually know quite a lot about the outcome. It's described as 50% heads 50% tails. We don't know
what the outcome is but we have a complete specification of the system; all relevant info is encoded there, right? Anyway.
Let's look at determinism as captured in Wayfarer's quote of Laplace.
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... — Wayfarer
From which you can distill two principles.
(1) If you have a complete specification of a system at some time t, then it is specified for all times before t and after t. Positions, momenta, orientations, that kind of thing.
(2) The specification procedure for all preceding and following states can be obtained by 'submitting the data to analysis'. Presumably this is a codification of all relationships of the basic variables of nature that entail everything about everything else given sufficient manipulation.
and from the remainder of the quote.
for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
(3) In such a description, nothing would be uncertain (for the subject of 1 which has the specification procedure in 2).
I wanna say that (1) is purely an ontological claim; it concerns the nature of nature/being/One/All/Many/process/stuff/whatever. (2) is talking about a
codification of the information in (1), if it can all be distilled into some placeholder. It is how the 'complete' specification' in (1) would be articulated. Then we have that if (1) is true and (2) exists, nothing would be uncertain
for that intellect.
So there's a lot going on there. (1) and (2) together still look like determinism, and don't have any epistemic valences. But (3) uses 'uncertain' in a colloquial sense, as in 'there is nothing which could not be known/predicated/anticipated' by the intellect.
We know that (1) is false, so long as we take a
realist interpretation of the wavefunction in quantum mechanics. It might fail for
other reasons too, but this suffices. There's randomness in nature.
Interestingly (2) also seems to be
false, at least if we make the assumption that the grand complete specification in Laplace's formulation is the result of an algorithm, anyway. And not some divine act of comprehension.
I know this doesn't really clear up much of the relationship between uncertainty and determinism, or randomness and determinism, but hopefully it provides a useful distinction between what's going on in (1), (2) and (3).