Necessity is the idea that everything that has ever happened and ever will happen is necessary, and can not be otherwise. Necessity is often opposed to chance and contingency. In a necessary world there is no chance. Everything that happens is necessitated.
The great atomist Leucippus stated the first dogma of determinism, an absolute necessity.
"Nothing occurs at random, but everything for a reason and by necessity."
But we must distinguish between this claim of physical necessity and the simpler logical necessity of formal systems. Aristotle's logic defended the logical necessity that only one of two contradictory statements can be true, and the other false. Diodorus Cronus developed the Master Argument to show that only one answer to a question about a future event can be true. Either Yes or No. This led to the Megarian idea of actualism, that there is no future contingency and only one possible future.
Diodorus' paradox was the result of the principle of bivalence or the law of the excluded middle. Only one of two logically contradictory statements can be necessarily true. Aristotle solved the paradox by saying that the truth of statements about the future is contingent on the actual future, as follows,
"A sea battle must either take place tomorrow or not,The major founder of Stoicism, Chrysippus, took the edge off strict necessity. Like Democritus, Aristotle, and Epicurus before him, Chrysippus wanted to strengthen the argument for moral responsibility, in particular defending it from Aristotle's and Epicurus's indeterminate chance causes. Whereas the past is unchangeable, Chrysippus argued that some future events that are possible do not occur by necessity from past external factors alone, but might depend on us. We have a choice to assent or not to assent to an action. Later, Leibniz distinguished two forms of necessity, necessary necessity and contingent necessity. This basically distinguished logical necessity from physical (or empirical) necessity. In the eighteenth century debates about freedom and necessity (free will versus determinism), many thinkers distinguished a moral necessity from physical necessity. Moral necessity describes the will being (self) determined by an agent's reasons and motives. Extreme libertarians insisted on a will that was not determined by reasons, fearing that this implies pre-determinism, which it does not. In two-stage models of free will, indeterminism in the generation of alternative possibilities for action breaks the causal chain of determinism.
Chance is regarded as inconsistent with logical determinism and with any limits on causal, physical or mechanical determinism.
Despite abundant evidence to the contrary, 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 would make the state of the world totally independent of any earlier states, which is nonsense, but it shows how anxious they are about chance.
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 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 the result of chance alone.
We call this "soft" causality. Events are caused by prior (uncaused) events, but not determined by events earlier in the causal chain, which has been broken by the uncaused cause.
Necessity is critical for the question of free will. 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 required from strict necessity 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. And Hume himself strongly, if inconsistently, believed in necessity while denying causality. He said "'tis impossible to admit any medium betwixt chance and necessity."
Even in a world with chance, macroscopic objects are determined to an extraordinary degree. This is the basis for physical necessity. 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. Our actions are determined by our thoughts. But our thoughts themselves are free. This means that our actions were not pre-determined from before we began thinking.
We call this kind of determinism (determined but not pre-determined) "adequate determinism." Physical determinism is adequate enough for us to predict eclipses for the next thousand years or more with extraordinary precision.
The presence of quantum uncertainty leads some philosophers to call the world indetermined. But indeterminism is misleading, with strong negative connotations, 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 for all practical purposes carried on deterministically in a physical brain where quantum events do not interfere with normal operations, unless the agent deliberately seeks to be original and creative.
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 which are the source of novel ideas.
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.
[Necessity must be limited to its proper use in logic, and disambiguated from its close relatives causality, determinism, certainty, and predictability.]