Moral necessity describes the will being (self) determined by an agent's reasons and motives.

In the eighteenth-century debates about freedom and necessity (free will versus determinism), many thinkers distinguished a moral necessity from physical necessity and logical necessity. Extreme libertarians insisted on a will that was not determined by reasons or motives, 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.

Not all the eighteenth century debates, by thinkers such as Samuel Clarke, William King, Anthony Collins, David Hume, and Thomas Reid, clearly distinguished logical, physical, and moral necessity.

Logical necessity is a property of formal systems, predicate and propositional logic, and mathematics, for example. It is logically necessary that only one of two contradictory statements can be true, and the other false. This is the principle of bivalence or the law of the excluded middle.

Physical 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. We usually describe this as physical determinism.

Anthony Collins prefaced his 1717 essay, A Philosophical Inquiry Concerning Human Liberty, with this declaration,

When I affirm Necessity, I contend only for what is called Moral Necessity, meaning thereby, that man, who is an intelligent and sensible being, is determined by his reason and his senses; and I deny man to be subject to such necessity as is in clocks, watches, and such other beings, which for want of sensation and intelligence, are subject to an absolute, physical, or mechanical necessity. And here also I have the concurrence of almost all the greatest asserters of Liberty, who either expressly maintain moral necessity, or the thing signified by those words.

(A Philosophical Inquiry Concerning Human Liberty, p. xx. Google Scholar)

Samuel Clarke was the greatest defender of Newtonian physics and of natural religion based on Newtonian determinism for the physical universe. But Clarke thought the human mind, like the mind of God, was not physically determined. The immaterial mind has "libertarian free will." He claimed correctly that when the will was necessitated by motives, the "moral necessity" was not in fact, necessity at all (either physical or logical), except that once something is actually done, it is impossible that it not has been done.

As to the...necessity of the will's being determined by the last judgment of the understanding, this is only a necessity upon supposition, that is to say, a necessity that a man should will a thing, when it is supposed that he does will it; just as if one should affirm that everything which is, is therefore necessary to be, because when it is it cannot but be. It is exactly the same kind of argument as that by which the true church is proved to be infallible, because truth cannot err, and they who are in the right cannot possibly, while they are so, be in the wrong. Thus, whatever a man at any time freely wills or does, it is evident (even upon supposition of the most perfect liberty) that he cannot at that time but will or do it, because it is impossible anything should be willed and not willed, whether it be freely or necessarily, or that it should be done and not done at the same time. The necessity of the will's being determined by the last judgment of the understanding is, I say, only a necessity upon supposition, a necessity that a man should will a thing, when it is supposed that he does will it. For the last judgment of the understanding is nothing else but a man's final determining, after more or less consideration, either to choose or not to choose a thing; that is, it is the very same with the act of volition. Or else, if the act of volition he distinguished from the last judgment of the understanding, then the act of volition, or rather the beginning of action consequent upon the last judgment of the understanding, is not determined or caused by that last judgment as by the physical efficient, but only as the moral motive. For the true, proper, immediate, physical efficient cause of faction is the power of self-motion in men, which exerts itself freely in consequence of the last judgment of the understanding. But the last judgment of the understanding is not itself a physical efficient, but merely a moral motive upon which the physical efficient or motive power begins to act.

The necessity, therefore, by which the power of acting follows the judgment of the understanding is only a moral necessity, that is, no necessity at all in the sense wherein the opposers of liberty understand necessity. For moral necessity is evidently consistent with the most perfect natural liberty.

(A Demonstration of the Being and Attributes of God, Section X, p. 73. Google Scholar)

Logical philosophers argued that necessity implies actualism, that there is only one possible future, thus only one possible willed action. This is based on an ancient paradox developed by Diodorus Cronus, which claimed that only one of two contradictory statements about the future can be true and the other false. Only one answer to a question about a future event can be true. Either Yes or No. Actualism makes Clarke's "last judgment of the understanding" pre-determined by past events.

"A sea battle must either take place tomorrow or not,
but it is not necessary that it should take place tomorrow,
neither is it necessary that it should not take place,
yet it is necessary that it either should or should not
take place to-morrow."
(De Interpretatione IX, 19 a 30)

And Clarke's morally necessitated will has the same contingent status. The priniciple of bivalence and the excluded middle apply to timeless (tenseless) logical propositions, but not to tensed potential empirical facts, before they become actual.

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.