"Hard" and "soft" determinism are terms invented by William James, who lamented the fact that some determinists were co-opting the term freedom for themselves. He called them "soft" determinists, because, abhoring harsh words like fatality, necessity, and even predetermination, they say determinism’s "real name is freedom; for freedom is only necessity understood, and bondage to the highest is identical with true freedom."

"Hard" determinists deny the existence of free will. "Soft" determinists co-opt the term.

Compatibilism is the most common name used today for James' category of soft determinism. For compatibilists, free will is compatible with determinism.

Semicompatibilists are agnostic about free will and determinism, but claim that moral responsibility is compatible with determinism. Narrow incompatibilism is a similar concept.

Hard incompatibilists think both free will and moral responsibility are not compatible with determinism (they mean pre-determinism).

Illusionists are hard incompatibilists, who say that free will is an illusion. They usually deny moral responsibility, but some say we can preserve responsibility by maintaining the illusion.

Impossibilists are also hard incompatibilists. They say moral responsibility is impossible.

Incompatibilism is the idea that free will and determinism are incompatible. Incompatibilists include both hard determinists and libertarians. Incompatibilists include both hard determinists and libertarians (both yellow in the taxonomy). This confuses the debate by analytic language philosophers - who are normally committed to clear and unambiguous concepts - and adds difficulties for students of philosophy.

Soft incompatibilists says that free will is incompatible with pre-determinism, and that pre-determinism is not true. Using "soft" is preferable to the loose usage of the term "incompatibilist" to describe a libertarian, since "incompatibilist" is ambiguous and also used for determinists, the "hard" incompatibilists.

Source and Leeway Incompatibilism locate indeterminism in the Actual Sequence or Alternative Sequences. The first in each pair breaks the causal chain in the actual sequence, the last pair provide alternative possibilities in alternative sequences.

Indeterminism is the position that there are random (chance) events in a world of possible futures. The irreducible indeterminism is quantum indeterminacy.

Libertarians believe that indeterminism makes free will possible. Note that there many philosophers who admit indeterminism may be true but that it does not really explain free will ("hard" indeterminists?). See the standard argument against free will - If our actions are determined, we are not free. If they are random, we are not responsible for them. So indeterminism is not enough. We need a limited indeterminism in the first stage and also "adequate determinism" in the second stage of a two-stage model.

Agent-causal indeterminists are libertarians who think that agents have originating causes for their actions that are not events. Actions do not depend on any prior causes. Some call this "metaphysical" freedom.

Non-causal indeterminists simply deny any causes whatsoever for libertarian free will.

Event-causal indeterminists generally accept the view that random events (most likely 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.

Soft Causality is the idea that most events are adequately determined by normal causes, but that some events are not precisely predictable from prior events, because there are occasional quantum events that start new causal chains with unpredictable futures. These events are said to be causa sui.

Soft Libertarians accept some indeterminism in the Actual Sequence. They are source incompatibilists.

While microscopic quantum events are powerful enough to deny strict determinism, the magnitude of these events is generally so small, especially for large macroscopic objects, that the world is still overwhelmingly deterministic. We call this "adequate determinism."

Although random quantum mechanical events break the strictly deterministic causal chain, which has just one possible future, random events are probable causes for later events. They start new causal chains with unpredictable futures. They are said to be causa sui. They need not be the direct cause of human actions, which would make the actions random, but simply provide alternative possibilities for willed actions.

Two-stage models for free will have been discussed by many thinkers including William James, Henri Poincaré, Arthur Holly Compton, Karl Popper, Daniel Dennett (Valerian Model), Henry Margenau, Robert Kane, John Martin Fischer, Alfred Mele(Modest Libertarian), Stephen Kosslyn, Bob Doyle (Cogito Model), and Martin Heisenberg.

These models are a combination of "adequate determinism" and indeterminism limited to generating alternative possibilities for action.

It is only pre-determinism that is incompatible with free will.

Thoughts come to us freely. Actions go from us willfully.

First chance, then choice. First "free," then "will."