Chance is often defined as the opposite of Necessity.
Chance is regarded as inconsitent with causal determinism and with limits on physical or mechanical determinism.
Despite abundant evidence, many philosophers deny that chance exists. If a single event is determined by chance, then indeterminism would be true, they say, and undermine the very possibility of certain knowledge. Some go to the extreme of saying that chance makes the state of the world totally independent of any earlier states, which is nonsense, but it shows how anxious they are about chance.
The core idea of indeterminism is closely related to the idea of causality. Indeterminism for some is simply an event without a cause. But we can have an adequate causality without strict determinism, which implies complete predictability of events and only one possible future.
An example of an event that is not strictly caused is one that depends on chance, like the flip of a coin. If the outcome is only probable, not certain, then the event can be said to have been caused by the coin flip, but the head or tails result was not predictable. So this causality, which recognizes prior events as causes, is undetermined and athe result of chance alone.
Chance is also closely related to the ideas of uncertainty and indeterminacy. Uncertainty 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.
Chance is important for the question of free will because strict necessity implies just one possible future. Chance means that the future is unpredictable. Chance allows alternative futures and the question becomes how the one actual present is realized from these potential alternatives.
The departure from strict causality is very slight compared to the miraculous ideas associated with the "causa sui" (self-caused cause) of the ancients.
Despite David Hume's critical attack on the necessity of causes, many philosophers embrace causality strongly. Some even connect it to the very possibility of logic and reason.
Even in a world with 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. Our Cogito model of the Macro Mind is large 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 determinism, limited as it is in extremely small structures, "adequate determinism." The world is adequately determined to send men to the moon. The presence of quantum uncertainty leads philosophers to call the world "indetermined." But indeterminism is seriously misleading when most 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 deterministically in a physical brain where quantum events 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. Noise can introduce random errors into stored memories. Noise could create random associations of ideas during memory recall. This randomness may be driven by microscopic fluctuations that are amplified to the macroscopic level.
Our Macro Mind needs the Micro Mind for the free action items and thoughts in an Agenda of alternative possibilities to be de-liberated by the will. Chance in the Micro Mind is the "free" in free will and the source of human creativity. The adequately determined Macro Mind is the "will" in free will that de-liberates, choosing actions for which we can be morally responsible.
For Teachers
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Chapter 3.7 - The Ergod Chapter 4.2 - The History of Free Will
Part Three - Value Part Five - Problems