![]() 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). 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 resulting principle is very different, however, depending on which interpretation is given (see Payne's summary of Schopenhauer's Fourfold Root). ∀ P ∃ Q ( Q → P ) Ī 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. For every proposition P, if P is true, then there is a sufficient explanation for why P is true.For every event E, if E occurs, then there is a sufficient explanation for why E occurs.For every entity X, if X exists, then there is a sufficient explanation for why X exists.The principle has a variety of expressions, all of which are perhaps best summarized by the following: 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. Some philosophers have associated the principle of sufficient reason with ex nihilo nihil fit ( nothing comes from nothing). Notably, the post-Kantian philosopher Arthur Schopenhauer elaborated the principle, and used it as the foundation of his system. ![]() The principle can be seen in both Thomas Aquinas and William of Ockham. A clearer connection is with the cosmological argument for the existence of God. 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. 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. Leibniz formulated it, but was not an originator. The modern formulation of the principle is usually ascribed to early Enlightenment philosopher Gottfried Leibniz. 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. ![]() The principle of sufficient reason states that everything must have a reason or a cause.
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