The principle of sufficient reason (PSR) is often formulated as the claim that every contingent fact has a sufficient reason. It is sometimes interpreted as the stronger claim, that everything has a cause, for example within a deterministic system of universal causation. Necessary truths are generally regarded as not requiring a cause, since causation presupposes contingency, though they may still be said to have a sufficient reason or explanation in virtue of their necessity. Confusion may arise when using the words "reason" and "cause" interchangeably. A sufficient reason is sometimes described as the coincidence of every single thing that is needed for the occurrence of an effect. The principle is relevant to Munchausen's trilemma, as it seems to suppose an infinite regress, rather than a foundational brute fact. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz. Arthur Schopenhauer wrote On the Fourfold Root of the Principle of Sufficient Reason.
History The modern formulation of the principle is usually ascribed to the early Enlightenment philosopher Gottfried Leibniz, who formulated it, but was not its originator. The idea was conceived of and utilized by various philosophers who preceded him, including Anaximander, Parmenides, Archimedes, Plato, Aristotle, Cicero, Avicenna, Thomas Aquinas, and Baruch Spinoza. One often pointed to is in Anselm of Canterbury: his phrase quia Deus nihil sine ratione facit (because God does nothing without reason) and the formulation of the ontological argument for the existence of God. A clearer connection is with the cosmological argument for the existence of God. The principle can be seen in both Aquinas and William of Ockham. The post-Kantian philosopher Arthur Schopenhauer elaborated the principle, and used it as the foundation of his system, seeing it as the fourth "law of thought". William Hamilton also did so, and identified the rule of inference modus ponens with the "Law of Sufficient Reason, or of Reason and Consequent" and modus tollens with its contrapositive expression. The principle was influential in the thinking of Leo Tolstoy, amongst others, in the elevated form that history could not be accepted as random. In contemporary analytic philosophy, Peter Van Inwagen has questioned the principle of sufficient reason using the "big conjunctive contingent fact." Alexander Pruss defends the principle. In the realm of epistemology, Lewis White Beck also emphasized the importance of assigning equal metaphysical importance to both the principle of sufficient reason and the principle of parsimony in the formulation of explanations within both the "social" and "physical" sciences. Simply stated,
"In the logic of science there is a principle as important as that of parsimony: it is that of sufficient reason. The former directs us to look for simplest causes, the later cautions us not to simplify so far that the explanation is inadequate to the facts to be explained.... Parsimony is not itself a simple criterion of a good methodology; we cannot simply count the factors of explanation and say that the theory containing the smallest number is the best. The ideal of parsimony cannot be expressed without the proviso that the conditions for which it is a norm shall themselves be adequate."
Formulation The principle has a variety of expressions, all of which are perhaps best summarized by the following:
For every entity X, if X exists, then there is a sufficient explanation for why X exists. For every event E, if E occurs, then there is a sufficient explanation for why E occurs. For every proposition P, if P is true, then there is a sufficient explanation for why P is true.
∀ P ( P → ∃ Q ( Q → P ) ) {\displaystyle \forall P(P\rightarrow \exists Q(Q\rightarrow P))}
Different views
Leibniz's view Leibniz identified two kinds of truth, necessary and contingent truths. And he claimed that all truths are based upon two principles: (1) non-contradiction, and (2) sufficient reason. In the Monadology, he says,
Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us (paragraphs 31 and 32). Necessary truths can be derived from the law of identity (and the principle of non-contradiction): "Necessary truths are those that can be demonstrated through an analysis of terms, so that in the end they become identities, just as in Algebra an equation expressing an identity ultimately results from the substitution of values [for variables]. That is, necessary truths depend upon the principle of contradiction." The sufficient reason for a necessary truth is that its negation is a contradiction. Leibniz admitted contingent truths, that is, facts in the world that are not necessarily true, but that are nonetheless true. Even these contingent truths, according to Leibniz, can only exist on the basis of sufficient reasons. Since the sufficient reasons for contingent truths are largely unknown to humans, Leibniz made appeal to infinitary sufficient reasons, to which God uniquely has access:
In contingent truths, even though the predicate is in the subject, this can never be demonstrated, nor can a proposition ever be reduced to an equality or to an identity, but the resolution proceeds to infinity, God alone seeing, not the end of the resolution, of course, which does not exist, but the connection of the terms or the containment of the predicate in the subject, since he sees whatever is in the series. Without this qualification, the principle can be seen as a description of a certain notion of closed system, in which there is no 'outside' to provide unexplained events with causes. It is also in tension with the paradox of Buridan's ass, because although the facts supposed in the paradox would present a counterexample to the claim that all contingent truths are determined by sufficient reasons, the key premise of the paradox must be rejected when one considers Leibniz's typical infinitary conception of the world.
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