Science can make predictions that are extremely accurate (think ten significant digits) and the uncertainty on that prediction (i.e. the eleventh significant digit) does not have anything to do with neural networks or us being "probabilistic creatures", whatever that means.
We learn by experience, and we build weightings, and both our gut reactions and careful conclusions are simply the ones which win the confidence ratings. Logic may be an exception by virtue of it's mathematical nature, but any facts involved are not, and we fall back on judgement calls most of the time even when we think we're being logical.
And yet by means of statistics one can model the errors, and obtain an experimental measurement with 10 significant digits.
And, guess what, it agrees with the theory! Ten. Significant. Digits.
> Logic may be an exception by virtue of it's mathematical nature, but any facts involved are not, and we fall back on judgement calls most of the time even when we think we're being logical.
That's not how Science works.