Principle of sufficient reason

The principle of sufficient reason states that everything must have a reason or a cause. The modern formulation of the principle is usually attributed to Gottfried Leibniz, although the idea was conceived of and utilized by various philosophers who preceded him, including Anaximander,Parmenides, Archimedes,Plato and Aristotle,Cicero,Avicenna,Thomas Aquinas, and Spinoza. Some philosophers have associated the principle of sufficient reason with "ex nihilo nihil fit".,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.

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.

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).

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