The idea of something more than just chance and necessity was clearly understood in antiquity. It gave rise to the idea of agent-causality.

Enlightment thinkers who held a libertarian view, such as Immanuel Kant, and the Scottish Naturalists following Thomas Reid, had a metaphysical view of free will. The tertium quid was non-physical, outside of science. Few modern agent-causalist libertarians now accept the idea of a non-physical substance like Kant's noumenal world, and some have given up their agent-causal libertarian views as a result (Randolph Clarke, for example).

For theologians, the tertium quid is a gift from God and inexplicable in the purely physical terms of chance and necessity. In recent years, religious libertarians like Peter van Inwagen say that "Free Will Remains A Mystery" and inexplicable because of his Consequence Argument and Mind Argument. The "New Mysterians" following Colin McGinn share this view.

Aristotle was the first major philosopher to argue convincingly for some indeterminism. First he described a causal chain (ἄλυσις) back to a prime mover or first cause, and he elaborated the four possible causes (material, efficient, formal, and final). Aristotle's word for these causes was ἀιτία, which translates as causes (or explanations) in the sense of the multiple factors responsible for an event. Aristotle did not subscribe to the simplistic "every event has a (single) cause" idea that was to come later.

Then, in his Physics and Metaphysics, Aristotle also said there were "accidents" caused by "chance (τύχη)." In his Physics, he clearly reckoned chance among the causes. Aristotle might have added chance as a fifth cause - an uncaused or self-caused cause - one he thought happens when two causal chains come together by accident (συμβεβεκός). He noted that the early physicists had found no place for chance among their causes.

Aristotle opposed his accidental chance to necessity:

Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause.
(Metaphysics, Book V, 1025a25)^2a

It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not.
(Metaphysics, Book VI, 1027a29)

Tracing any particular sequence of events back in time will usually come to an accidental event - a "starting point" or "fresh start" (Aristotle calls it an origin or arche (ἀρχῆ) - whose major contributing cause (or causes) was itself uncaused, e.g., it involved quantum indeterminacy.

Whether a particular thing happens, says Aristotle, may depend on a series of causes that

goes back to some starting-point, which does not go back to something else. This, therefore, will be the starting-point of the fortuitous, and nothing else is the cause of its generation.
(Metaphysics Book VI 1027b12-14)

Beyond causal sequences that are the result of chance or necessity, Aristotle felt that some breaks in the causal chain allow us to feel our actions "depend on us" (ἐφ' ἡμῖν). These are the causal chains that originate within us (ἐv ἡμῖν).

Aristotle was the first philosopher to identify the tertium quid beyond chance and necessity as an autonomous agent power.

Aristotle knew that many of our decisions are quite predictable based on habit and character, but they are no less free nor we less responsible if our character itself and predictable habits were developed freely in the past and are changeable in the future.

One generation after Aristotle, Epicurus argued that as atoms moved through the void, there were occasions when they would "swerve" from their otherwise determined paths, thus initiating new causal chains. Epicurus argued that these swerves would allow us to be more responsible for our actions, something impossible if every action was deterministically caused. For Epicurus, the occasional interventions of arbitrary gods would be preferable to strict determinism.

Epicurus did not say the swerve was directly involved in decisions. His critics, ancient and modern, have claimed mistakenly that Epicurus did assume "one swerve - one decision" and that "free " actions are uncaused. But following Aristotle, Epicurus thought human agents have the autonomous ability to transcend necessity and chance (both of which destroy responsibility), so that praise and blame are appropriate.

...some things happen of necessity, others by chance, others through our own agency. ...necessity destroys responsibility and chance is inconstant; whereas our own actions are autonomous, and it is to them that praise and blame naturally attach.

Parenthetically, we now know that atoms do not occasionally swerve, they move unpredictably whenever they are in close contact with other atoms. Everything in the material universe is made of atoms in unstoppable perpetual motion. Deterministic paths are only the case for very large objects, where the statistical laws of atomic physics average to become nearly certain dynamical laws for billiard balls and planets.

This challenge can be met by two-stage models of free will.

Conservative Libertarians believe that one's actions are adequately determined by events prior to a decision, including one's character and values, and one's feelings and desires, in short, one's reasons and motives. Their model of free will is "reasons responsive."

The role of pure chance, irreducible randomness, or quantum indeterminacy, is limited to generating alternative possibilities for action. Chance events are not direct causes of our thoughts and actions, as "radical" libertarians believe.

"Conservative" - or "Adequate" or "Modest" - Libertarians believe that humans are free from strict physical determinism - or pre-determinism, and all the other diverse forms of determinism. They accept the existence of chance, but believe that if chance were the direct cause of actions, it would preclude control of the agent's actions and deny moral responsibility.

Note that information philosophy and its value theory separate free will from moral responsibilty.

The existence of free will is a scientific question for physics, biology, and psychology.
Moral responsibility is a cultural question for sociology and the law.

Information philosophy also separates responsibility from the ideas of retributive punishment, which is still another social and cultural question.

Critics of libertarianism (determinists and compatibilists) attack the view of radical libertarians that chance is the direct cause of actions. If an agent's decisions are not connected in any way with character and other personal properties, they rightly claim that the agent can hardly be held responsible for them.

Many determinists and compatibilists now accept the idea that there is real indeterminism in the universe. Conservative libertarians can agree with them that if indeterministic chance were the direct direct cause of our actions, that would not be freedom with responsibility.

But determinists and compatibilists might also agree that if chance is not a direct cause of our actions, it would do no harm to responsibility. In which case, conservative libertarians should be able to convince some determinists of their position. Galen Strawson agrees that conservative libertarianism is a "kind of freedom that is available" to us.

If chance is limited to providing real alternative possibilities to be considered by the adequately determined will, it provides an intelligible freedom and can explain both freedom and creativity.

Conservative libertarians can give the determinists, at least the compatibilists, the kind of freedom they say they want, one that provides an adequately determined will and actions for which we can take responsibility

Even the current chief spokesman for libertarianism, Robert Kane, admits that "radical" libertarian accounts of free will are unintelligible. No coherent idea can be provided for the role of indeterminism and chance, he says.

But Kane's radical libertarianism doggedly insists that "something more" is needed beyond simple determination of our thoughts and actions by our desires and feelings, our character and values, and our motives and reasons.