What source and at what part does it mention hard determinism being restricted to linear math?
The Newtonian view of our universe,
If you go beyond linear math to fractal math with the possible internal conscious variables hard determinism no longer applies. In our ability to make limited free will decisions that hard determinism excludes the influence of possible influence of rational self motivation in the decision making process.
I propose Potential limited Free Will, which is more limited than soft determinism or compatibilism.
Class Four: Soft Determinism and Indeterminism
According to hard determinism, environment, heredity, unconscious impulses, defense mechanisms, and other influences determine people to act the way they do; and because of that, they are not responsible for their actions. But if people are not free and thus responsible for their actions, then how can we be justified in holding people responsible? Perhaps, as the hard determinist suggests, we are justified in holding people responsible only in order to influence future behavior.
However, there are a number of theories that support the claim that human beings are free and can thus be justifiably held responsible for their actions. We will consider four of them (soft determinism, pragmatism/indeterminism, existentialism, and rational-agent theory).
Soft Determinism (also called Compatibilism and Self-determinism):
Though determinism is true, that does not rule out freedom and responsibility.
In contrast to hard determinism (which claims that determinism is incompatible with freedom), soft determinism says that we are determined and are nonetheless still free. According to the soft determinist, when the individual is the cause of his or her actions, he or she is said to act freely.
There are two versions of this view: passive self-determinism and active self-determinism. Augustine, Spinoza, and Hume are proponents of the first version; Aristotle is a proponent of the second.
(I) According to
passive self-determinism, freedom means being able to do what one wants to do, without (external) coercion or interference from anyone else. What one wants (as expressed by one's personality or character) is determined by external events (e.g., genetics, culture, upbringing), but as long as one is able to act consistent with the choices he/she makes, he/she is free. This position is called
Compatibilism or
soft determinism because it (like hard determinism) acknowledges that all events, including human actions, have causes; but it allows for free actions when the actions are caused by one's choices rather than external forces.