Incompatibilism is the position that determinism is incompatible with human freedom.
There are two kinds of incompatibilists, those who deny human freedom (usually called "hard" determinists), and those who assert it (often called voluntarists, free willists, or metaphysical libertarians - to distinguish them from political libertarians).
A corollary is that indeterminism is also incompatible with human freedom, or at best an incoherent and unintelligible account of freedom. Incompatibilists feel (correctly) that there must be a deterministic or causal connection between our will and our actions. This allows us to take responsibility for our actions, including credit for the good and blame for the bad.
If the proximate cause of our actions was undetermined, the result of an uncaused quantum mechanical event in the mind, it would not be freedom of a kind worth having and we should disavow responsibility.
Most incompatibilists accept the view of a causal chain of events going back indefinitely in time, consistent with the laws of nature, with the plan of an omniscient God, or with other determinisms. As long as our own will is included in that causal chain, we are free, they say. And they think causality in nature is related to the very possibility of reason and logic. Without causality, we could not be certain of the truths of our arguments.
Compatibilists, sometimes reluctantly, also accept the view that random quantum mechanical events occur in the world. Whether in the physical world, in the biological world (where they are a key driver of genetic mutations), or in the mind, randomness and uncaused events are real. They introduce the possibility of accidents, novelty, and human creativity.
Our Cogito model places causality and determinism in the critical apparatus of the Macro Mind. From the Micro Mind, and from the external world including other minds, come surprising and unpredictable events to feed the Agenda of possible thoughts and actions. The Cogito is compatibile with both determinism and uncertainty. It lives in Eddington's "halfway house."
The old compatibilism explains the will. It cannot explain free. The new compatibilism gets us both free (random) and will (adequately determined). The Cogito is genuine free will.
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Chapter 3.7 - The Ergod Chapter 4.2 - The History of Free Will
Part Three - Value Part Five - Problems