Belief in Causality is deeply held by many philosophers and scientists. Many say it is the basis for all thought and knowledge of the external world. Causal closure is the idea that everything that happens in the world is caused by physical objects in the world. The core idea of causality is closely related to the idea of determinism. But we can have causality without determinism. And we will see that the departure from strict causality needed to negate determinism is very slight compared to the miraculous ideas associated with the "causa sui" (self-caused cause) of the ancients, which some found unintelligible.
Despite David Hume's critical attack on the necessity of causes, which should have made us all skeptics about the logical necessity for causality, many philosophers embrace it strongly. Some even identify causality with 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)
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 otherwise 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 itself was not predictable. So this causality, which recognizes prior events as causes, is undetermined and the result of chance alone.
We call this "soft" causality. Events are caused by prior (uncaused) events, but not completely determined by prior events in the causal chain back to a primal first cause. That Aristotelian chain has been broken by the uncaused cause. Uncaused events start new causal chains.
Determinism is critical for the question of free will. Strict determinism 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.
Even in a world that contains quantum uncertainty, 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 randomness 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. The random 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.
Causality must be disambiguated from its close relatives certainty, determinism, necessity, and predictability.
"We must admit that the mind of each one of our greatest geniuses — Aristotle, Kant or Leonardo, Goethe or Beethoven, Dante or Shakespeare — even at the moment of its highest flights of thought or in the most profound inner workings of the soul, was subject to the causal fiat and was a instrument in the hands of an almighty law which governs the world." Max Planck, Where Is Science Going, p.156. [In Existentialism, the will condemns all the unchosen alternatives to nothingness as it grants being to the one chosen.]