Thank you for contributing, I thought this thread would die of neglect.
What you say is very interesting. Indeed, certain advances in maths, for example category theory, have had great rebound on philosophy, in lots of different areas (logic, but also ontology!). But I'd develop this on a more maths-specific thread.
I would like to stress on the fact that chaos is not only quantum. Actually, since quantum physics has a hard foundations problem, more mathematically-flavored accounts of chaos are realized in the realm of classical mechanics.
But the determinism hard coded in classical mechanics is nothing to be against. In fact, chaotic systems are, in a certain sense, ultradeterministic
What I mean with this is that you may chose a property you want a solution to realize, and a chaotic system always has at least one such solution
. So the dynamics in the chaotic realm is so rich it is akin to random processes: you may flip a coin and decide from the outcome that some solution should have some property, and the chaotic system will
have such solution. This is a twisted version of determinism, where the possibilities, whose evolution along their "worldlines" is perfectly causal
, are so many that the result is non-causal, entropic.
To expand, there always is a sort of "microdeterminism" in classical systems: the dynamics of one single point
are totally determined by its equations of motion, well in contrast to the equations that govern quantum mechanics, which determine probability distributions.
So determinism is still there, but to really experience it, you must restrict yourself to an insignificant part of the system. Globally, or even locally (in the topology sense), determinism is not true: the evolution of a set of points is not guaranteed to mimic the evolution of a single point, and this is true also for non-chaotic systems (Gromov's non-squeezing theorem)!
For example we may take the single points of the set very close (small initial uncertainty), but the dynamics can separate them exponentially in time. As a result, the small initial uncertainty is propagated, deterninistically
, to an enormous uncertainty at a further time.
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