The chaos argument is a philosophical argument. It argues that determinism is an idealistic mathematical construction whose mapping onto reality is untestable in the real world, and that this is an essential precondition for the existence of free will.
The chaos argument asserts that given any description of position and momentum (of all particles in the universe) approaching completeness, long-term prediction is impossible, because variances from completeness multiply over even short periods of time.
Due to the uncertainty principle of quantum mechanics, we as observers can never have access to a complete description and therefore can never close the debate on free will versus determinism.
Also, the electrodynamics of the human brain are chaotic in nature; accordingly there is also no way to prove, in the event that free will does exist in the universe, whether the human has none.
One common objection to drawing conclusions about free will from the chaos argument is that it seems unclear how quantum uncertainty, whether reducible or irreducible, could provide a basis for any kind of free will. The philosopher J. J. C. Smart observed, "Indeterminism does not confer freedom on us: I would feel that my freedom was impaired if I thought that a quantum mechanical trigger in my brain might cause me to leap into the garden and eat a slug".
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