Chance is closely related to the ideas of uncertainty and indeterminacy. Uncertainty today is best known from Werner Heisenberg's principle in quantum mechanics. It states that the exact position and momentum of an atomic particle can only be known within certain (sic) limits. The product of the position error and the momentum error is equal to a multiple of Planck's constant of action. This irreducible randomness in physical processes established the existence of chance and indeterminism in the world.

But real chance and uncertainty had already entered physics fifty years earlier than Heisenberg, when Ludwig Boltzmann showed in 1877 that random collisions between atomic particles in a gas could explain the increase in entropy that is the Second Law of Thermodynamics.

In 1866, when Boltzmann first derived Maxwell's velocity distribution of gas particles, he did it assuming that the physical motion of each particle (or atom) was determined exactly by Newton's laws. In 1872, when he showed how his kinetic theory of gases could explain the increase in entropy, he again used strictly deterministic physics. But Boltzmann's former teacher Josef Loschmidt objected to his derivation of the second law. Loschmidt said that if time was reversed, the deterministic laws of classical mechanics require that the entropy would go down, not up.

So in 1877 Boltzmann reformulated his derivation, assuming that each collision of gas particles was not determined, but random. He assumed that the directions and velocities of particles after a collision depended on chance, as long as energy and momentum were conserved. He could then argue that the particles would be located randomly in "phase space" based on the statistical assumption that individual cells of phase space were equally probable. His H-Theorem produced a quantity which would go only up, independent of the time direction. Laws of nature became statistical. Max Born put statistical mechanics on a firm quantum mechanical basis in 1926, when he showed that Schrödinger's deterministic equation for the wave function predicts only probabilities for directions after an electron collision.

Boltzmann's student Franz S. Exner defended the idea of absolute chance and indeterminism as a hypothesis that could not be ruled out on the basis of observational evidence. Exner did this in his 1908 inaugural lecture at Vienna University as rector (two years after Boltzmann's death), and ten years later in a book written during World War I. But Exner's view was not the standard view. Ever since the eighteenth-century development of the calculus of probabilities, scientists and philosophers assumed that probabilities and statistical phenomena, including social statistics, were completely determined. They thought that our inability to predict individual events was due simply to our ignorance of the details.

In his 1922 inaugural address at the University of Zurich, What Is a Law of Nature?, Erwin Schrödinger said about his teacher,

"It was the experimental physicist, Franz Exner, who for the first time, in 1919, launched a very acute philosophical criticism against the taken-for-granted manner in which the absolute determinism of molecular processes was accepted by everybody. He came to the conclusion that the assertion of determinism was certainly possible, yet by no means necessary, and when more closely examined not at all very probable.

"Exner's assertion amounts to this: It is quite possible that Nature's laws are of thoroughly statistical character. The demand for an absolute law in the background of the statistical law — a demand which at the present day almost everybody considers imperative — goes beyond the reach of experience."

[Ironically, just four years later, after developing his continuous and deterministic wave theory of quantum mechanics, Schrödinger would himself "go beyond the reach of experience" searching for deterministic laws underlying the discontinuous, discrete, statistical and probabilistic indeterminism of the Bohr-Heisenberg school, to avoid the implications of absolute chance in quantum mechanics. Planck and Einstein too were repulsed by randomness and chance. "God does not play dice," was Einstein's famous remark.]

A major achievement of the Ages of Reason and Enlightenment was to banish absolute chance as unintelligible and atheistic. Newton's Laws provided a powerful example of deterministic laws governing the motions of everything. Surely Leucippus' and Democritus' original insights had been confirmed.

In 1718 Abraham De Moivre wrote a book called The Doctrine of Chances. It was very popular among gamblers. In the second edition (1738) he derived the mathematical form of the normal distribution of probabilities, but he denied the reality of chance. Because it implied events that God could not know, he labeled it atheistic.

Chance, in atheistical writings or discourse, is a sound utterly insignificant: It imports no determination to any mode of existence; nor indeed to existence itself, more than to non existence; it can neither be defined nor understood.

As early as 1784, Immanuel Kant had argued that the regularities in social events from year to year showed that they must be determined.

"Thus marriages, the consequent births and the deaths, since the free will seems to have such a great influence on them, do not seem to be subject to any law according to which one could calculate their number beforehand. Yet the annual (statistical) tables about them in the major countries show that they occur according to stable natural laws."

In the early 1800's Adolphe Quetelet and Henry Thomas Buckle argued that these regularities in social physics proved that individual acts like marriage and suicide were determined by natural law.

Franz Exner was not alone in defending chance before quantum uncertainty. In the nineteenth century in America, Charles Sanders Peirce coined the term "tychism" for his idea that absolute chance was the first step in three steps to "synechism" or continuity.

Peirce was influenced by the social statisticians, Buckle and Quetelet, by French philosophers Charles Renouvier and Alfred Fouillee, who also argued for some absolute chance, by physicists James Clerk Maxwell and Ludwig Boltzmann, but most importantly by Kant and Hegel, who saw things arranged in the triads that Peirce so loved.

Quetelet and Buckle thought they had established an absolute deterministic law behind all statistical laws. Buckle went so far as to claim it established the lack of free will.

Renouvier and Fouillee introduced chance or indeterminism simply to contrast it with determinism, and to discover some way, usually a dialectical argument like that of Hegel, to reconcile the opposites. Renouvier argues for human freedom, but nowhere explains exactly how chance might contribute to that freedom, other than negating determinism.

Maxwell may have used the normal distribution of Quetelet and Buckle's social physics as his model for the distribution of molecular velocities in a gas. Boltzmann also was impressed with the distribution of social statistics, and was initially convinced that individual particles obeyed strict and deterministic Newtonian laws of motion.

Peirce does not explain much with his Tychism, and with his view that continuity and evolutionary love is supreme, may have had doubts about the importance of chance. Peirce did not propose chance as directly or indirectly providing free will. He never mentions the ancient criticisms that we cannot accept responsibility for chance decisions. He does not really care for chance as the origin of species, preferring a more deterministic and continuous lawful development, under the guidance of evolutionary love. But Peirce does say clearly, well before Exner, that the observational evidence simply does not establish determinism.

It remained for William James, Peirce's close friend, to assert that chance can provide random unpredictable alternatives from which the will can choose or determine one alternative. James was the first thinker to enunciate clearly a two-stage decision process, with chance in a present time of random alternatives, leading to a choice which selects one alternative and transforms an equivocal ambiguous future into an unalterable determined past. There are undetermined alternatives followed by adequately determined choices.

"The stronghold of the determinist argument is the antipathy to the idea of chance...This notion of alternative possibility, this admission that any one of several things may come to pass is, after all, only a roundabout name for chance...

What is meant by saying that my choice of which way to walk home after the lecture is ambiguous and matter of chance?...It means that both Divinity Avenue and Oxford Street are called but only one, and that one either one, shall be chosen." (James, The Dilemma of Determinism, in The Will to Believe, 1897, p.155)

Chance is critically important for the question of free will because strict necessity implies just one possible future. Absolute chance means that the future is fundamentally unpredictable at the levels where chance is dominant. Chance allows alternative futures and the question becomes how the one actual present is realized from these potential alternative futures.

The amount of chance and the departure from strict causality required for free will is very slight compared to the miraculous ideas often associated with the "causa sui" (self-caused cause) of the ancients. For medieval philosophers, only God could produce a causa sui, a miracle. Modern quantal randomness, unless amplified to the macroscopic world, is often insignificant, not a miracle at all.

Despite David Hume's critical attack on causality, many philosophers embrace causality strongly, including Hume himself in his other writings, where he dogmatically asserts "'tis impossible to admit of any medium betwixt chance and an absolute necessity." Since Chrysippus twenty-two centuries ago, philosophers still connect causality to the very possibility of logic and reason.

Bertrand Russell said "The law of causation, according to which later events can theoretically be predicted by means of earlier events, has often been held to be a priori, a necessity of thought, a category without which science would not be possible." (Russell, External World p.179) Although he felt some claims for causality might be excessive, Russell was unwilling to give up strict determinism, saying "Where determinism fails, science fails."(Determinism and Physics, p.18)

Henri Poincaré said "Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose. For him, in fact, the word chance would have no meaning, or rather there would be no such thing as chance."

We know that even in a world with microscopic chance, macroscopic objects are determined to an extraordinary degree. Newton's laws of motion are deterministic enough to send men to the moon and back. In our Cogito model, the Macro Mind is macroscopic enough to ignore quantum uncertainty for the purpose of the reasoning will. The neural system is robust enough to insure that mental decisions are reliably transmitted to our limbs.

We call this kind of determinism "adequate determinism." Despite quantum uncertainty, the world is adequately determined to send men to the moon. Quantum uncertainty leads some philosophers to fear an undetermined world of chance, one where Chrysippus' imagined collapse into chaos would occur and reason itself would fail us. But the modest indeterminism required for free will is no chaotic irrational threat, since most physical and mental events are overwhelmingly "adequately determined."

There is no problem imagining that the three traditional mental faculties of reason - perception, conception, and comprehension - are all carried on with "adequate determinism" in a physical brain where quantum events and thermal noise do not interfere with normal operations.

There is also no problem imagining a role for chance in the brain in the form of quantum level noise (as well as pre-quantal thermal noise). Noise can introduce random errors into stored memories. Noise could create random associations of ideas during memory recall. Many scientists have speculated that this randomness may be driven by microscopic fluctuations that are amplified to the macroscopic level. This would not happen in some specific location in the brain. It is most likely a general property of all neurons.

We distinguish seven increasingly sophisticated ideas about the role of chance and indeterminism in the question of free will. Many libertarians have accepted the first two. Determinist and compatibilist critics of free will make the third their central attack on chance, claiming that it denies moral responsibility. But very few thinkers appear to have considered all seven essential requirements for chance to contribute to libertarian free will.

1. Chance exists in the universe. Quantum mechanics is correct. Indeterminism is true, etc.

2. Chance is important for free will because it breaks the causal chain of determinism.

3. But chance cannot directly cause our actions. We cannot be responsible for random actions.

4. Chance can only generate random (unpredictable) alternative possibilities for action or thought. The choice or selection of one action must be adequately determined, so that we can take responsibility. And once we choose, the connection between mind/brain and motor control must be adequately determined to see that "our will be done."

5. Chance, in the form of noise, both quantum and thermal noise, must always be present. The naive model of a single random microscopic event, amplified to affect the macroscopic brain, never made sense. Under what ad hoc circumstances, at what time, at what place in the brain, would it occur to affect a decision?

6. Chance must be overcome or suppressed by the adequately determined will when it decides to act, de-liberating the prior free options that "one could have done."

7. To the extent that chance is not completely suppressed by the will, the resulting choice can be considered to have an element of randomness. The agent can still take responsibility for allowing the choice to be partially or completely random, the equivalent of flipping a mental coin.