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Chaos Theory is often cited as a way out of the determinsim-free will paradox. The explanation usually goes like this: OK, everything is determined by physical law, but the laws themselves are non-linear and the output of a particular equation that codifies a law often leads to a pseudo-random process and/or sensitive dependence on initial conditions. Ergo while we are governed by strict physical laws, our behavior - and by implication our decisions - do not give the appearance of being constrained in any way.
The philosophical position that free will can co-exist with determinism pre-dates chaos theory, with Hume and Hobbes early proponents. Known as compatibilism, it stands on its own without chaos theory. Much of the compatibilist argument rests on a careful definition of what it means to act freely, leading to a so-called category error.
The compatibilist definition of free will states that free will is not the ability to choose as an agent independent of prior cause, but as an agent who is not forced to make a certain choice. Determinists argue that all acts that take place are predetermined by prior causes. Because human decision is an act that is not exempt from prior cause, by this definition, some determinists known as hard determinists believe that free will thus becomes an illusion.
A compatibilist, or soft determinist, in contrast, will define a free act in a way that does not hinge on causal necessitation. For them, an act is free unless it involves compulsion by another person. Since the physical universe and the laws of nature are not persons, they argue that it is a category error to speak of our actions being forced on us by the laws of nature, and therefore it is wrong to conclude that universal determinism would mean we are never free.
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