sufficient reason, principle of

Principle that there must be a sufficient reason – causal or otherwise – for why whatever exists or occurs does so, and does so in the place, time and manner that it does.

The principle goes back to at least the early 5th century BC – being used by Parmenides (see Eleaticism) in his Fragment 8, lines 9-10 – but it is most famously associated with Gottfried Wilhelm Leibniz (1646-1716), who used it to exclude all arbitrariness, and to account for ‘truths of fact’ (while the law of contradiction accounted for ‘truths of reason’).

He also derived the identity of indiscernibles from it.

Also see: principle of perfection, causal principle

Source:
H G Alexander, ed., The Leibniz-Clark Correspondence (1956)

The principle of sufficient reason states that everything must have a reason or a cause. The modern^[1] formulation of the principle is usually attributed to early Enlightenment philosopher Gottfried Leibniz,^[2] although the idea was conceived of and utilized by various philosophers who preceded him, including Anaximander,^[3] Parmenides, Archimedes,^[4] Plato and Aristotle,^[5] Cicero,^[5] Avicenna,^[6] Thomas Aquinas, and Spinoza.^[7] Notably, the post-Kantian philosopher Arthur Schopenhauer elaborated the principle, and used it as the foundation of his system. Some philosophers have associated the principle of sufficient reason with “ex nihilo nihil fit“.^[8][9] William Hamilton identified the laws of inference modus ponens with the “law of Sufficient Reason, or of Reason and Consequent” and modus tollens with its contrapositive expression.

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.

A sufficient explanation may be understood either in terms of reasons or causes, for like many philosophers of the period, Leibniz did not carefully distinguish between the two. The resulting principle is very different, however, depending on which interpretation is given (see Payne’s summary of Schopenhauer’s Fourfold Root).

It is an open question whether the principle of sufficient reason can be applied to axioms within a logic construction like a mathematical or a physical theory, because axioms are propositions accepted as having no justification possible within the system.^{[citation needed]} The principle declares that all propositions considered to be true within a system^[clarify] should be deducible from the set axioms at the base of the construction.^{[citation needed]} However, Gödel has shown that for every sufficiently expressive deductive system a proposition exists that can neither be proved nor disproved (see Gödel’s incompleteness theorems).

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.”^[11] The sufficient reason for a necessary truth is that its negation is a contradiction.^[4]

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.^[12]

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.

In consequence of this, the case also of Buridan’s ass between two meadows, impelled equally towards both of them, is a fiction that cannot occur in the universe….For the universe cannot be halved by a plane drawn through the middle of the ass, which is cut vertically through its length, so that all is equal and alike on both sides…..Neither the parts of the universe nor the viscera of the animal are alike nor are they evenly placed on both sides of this vertical plane. There will therefore always be many things in the ass and outside the ass, although they be not apparent to us, which will determine him to go on one side rather than the other. And although man is free, and the ass is not, nevertheless for the same reason it must be true that in man likewise the case of a perfect equipoise between two courses is impossible. (Theodicy, pg. 150)

Leibniz also used the principle of sufficient reason to refute the idea of absolute space:

I say then, that if space is an absolute being, there would be something for which it would be impossible there should be a sufficient reason. Which is against my axiom. And I prove it thus. Space is something absolutely uniform; and without the things placed in it, one point in space does not absolutely differ in any respect whatsoever from another point of space. Now from hence it follows, (supposing space to be something in itself, beside the order of bodies among themselves,) that ’tis impossible that there should be a reason why God, preserving the same situation of bodies among themselves, should have placed them in space after one particular manner, and not otherwise; why everything was not placed the quite contrary way, for instance, by changing East into West.