Principle of sufficient reason
The principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by Arthur Schopenhauer and Sir William Hamilton, 9th Baronet.
History[edit]
The modern[1] formulation of the principle is usually ascribed to early Enlightenment philosopher Gottfried Leibniz. Leibniz formulated it, but was not an originator.[2] 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] 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 Thomas Aquinas and William of Ockham.[2]
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 (Nothing comes from nothing).[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.[10]
The principle has a variety of expressions, all of which are perhaps best summarized by the following:
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.
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 (i.e., that they ensue necessarily if we assume the system's axioms to be true). 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).
Different Views[edit]
Leibniz's view[edit]
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,
As a law of thought[edit]
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 19th centuries. It was influential in the thinking of Leo Tolstoy, amongst others, in the elevated form that history could not be accepted as random.
A sufficient reason is sometimes described as the coincidence of every single thing that is needed for the occurrence of an effect (i.e. of the so-called necessary conditions).[23] Such view could perhaps be also applied to indeterministic systems, as long as randomness is in a way incorporated in the preconditions.