Principle of sufficient reason
The principle of sufficient reason is one of four laws of logic which states that nothing is without a causation. It is a powerful and controversial philosophical principle stipulating that everything must have a reason or cause. The formulation of the principle is usually attributed to Gottfried Leibniz, although the idea was conceived and utilized in various philosophers that preceded him, including Anaximander, Parmenides, Archimedes, Thomas Aquinas, Anaximander of Miletus, and Spinoza. Some philosophers have associated the principle of sufficient reason with "ex nihilo nihil fit". This principle bears many similarities with the Buddhist concept of Dependent Origination.
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.
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 . The principle declares that all propositions considered to be true within a system should be deducible from the set axioms at the base of the construction (with some theoretical exceptions: see Gödel's theorem).
Leibniz identified two kinds of truth, necessary and contingent truths. He believed necessary mathematical truths to be derived from the law of identity (and the principle of 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." Leibniz states that the sufficient reason for necessary truths is that their negation is a contradiction.
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. Leibniz denied that the paradox of Buridan's ass could ever occur, saying:
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)
As a Law of Thought
The principle was one of the four recognised laws of thought, that held a place in European pedagogy of logic and reasoning (and, to some extent, philosophy in general) in the 18th and nineteenth century. It was influential in the thinking of Leo Tolstoy, amongst others, in the elevated form that history could not be accepted as random.
Schopenhauer's Four Forms
According to Schopenhauer's On the Fourfold Root of the Principle of Sufficient Reason, there are four distinct forms of the principle.
First Form: The Principle of Sufficient Reason of Becoming (principium rationis sufficientis fiendi); appears as the law of causality in the understanding.
Second Form: The Principle of Sufficient Reason of Knowing (principium rationis sufficientis cognoscendi); asserts that if a judgment is to express a piece of knowledge, it must have a sufficient ground or reason, in which case it receives the predicate true.
Third Form: The Principle of Sufficient Reason of Being (principium rationis sufficientis essendi); the law whereby the parts of space and time determine one another as regards those relations. Example in arithmetic: Each number presupposes the preceding numbers as grounds or reasons of its being; "I can reach ten only by going through all the preceding numbers; and only by virtue of this insight into the ground of being, do I know that where there are ten, so are there eight, six, four."
“Now just as the subjective correlative to the first class of representations is the understanding, that to the second the faculty of reason, and that to the third pure sensibility, so is the subjective correlative to this fourth class found to be the inner sense, or generally self-consciousness.”
Fourth Form: The Principle of Sufficient Reason of Acting (principium rationis sufficientis agendi); briefly known as the law of motivation. “Any judgment that does not follow its previously existing ground or reason” or any state that cannot be explained away as falling under the three previous headings “must be produced by an act of will which has a motive.” As his proposition in 43 states, “Motivation is causality seen from within.”
- Deterministic system (philosophy)
- Law of thought
- Gödel's incompleteness theorems
- Nothing comes from nothing
- Principle of insufficient reason
- Dependent Origination
- There are numerous anticipations. One often pointed to is in Anselm of Canterbury: his phrase quia Deus nihil sine ratione facit 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 Thomas Aquinas and William of Ockham. Leibniz formulated it, but was not an originator. See chapter on Leibniz and Spinoza in A. O. Lovejoy, The Great Chain of Being.
- "Principle of Sufficient Reason".
- Freeman, Charles (1999). The Greek Achievement: The Foundation of the Western World. Allen Lane. p. 152. ISBN 0-7139-9224-7.
- Della Rocca, Michael (2008). Spinoza. New York: Routledge. pp. 8–9. ISBN 0415283302..
- Alexander R. Pruss (2007) "Ex Nihilo Nihil Fit: Augments new and old for the Principle of Sufficient Reason" in Explication Topic in Contemporary Philosophy Ch. 14
- Muhit, Abdul. "Leibniz on Necessary and Contingent Truths". Retrieved 22 April 2014.
- "Principle of Sufficient Reason".
- Ariew, Roger, and Daniel Garber, eds and trans, ed. (1989). G. W. Leibniz: Philosophical Essays. Indianapolis: Hackett Publishing Company.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, S 20, trans. E. Payne, (Open Court Publishing Company, 1997), 4.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, S 29, trans. E. Payne, (Open Court Publishing Company, 1997), 5.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, S 36, trans. E. Payne, (Open Court Publishing Company, 1997), 6.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, S 38, trans. E. Payne, (Open Court Publishing Company, 1997), 7.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, page 212, S 42, trans. E. Payne, (Open Court Publishing Company, 1997), 8.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, S 43, trans. E. Payne, (Open Court Publishing Company, 1997), 9.
- Arthur Schopenhauer, On The Fourfold Root of the Principle of Sufficient Reason, S 43, trans. E. Payne, (Open Court Publishing Company, 1997), 10.
- Principle of Sufficient Reason entry by Yitzhak Melamed, Martin Lin in the Stanford Encyclopedia of Philosophy
- The Principle of Sufficient Reason: A Reassessment by Alexander R. Pruss