23 November 2019

Occam's Razor = The Law of Parsimony (-1499)

"We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." (Aristotle, “Posterior Analytics”, cca. 400 BC)

"We may assume the superiority ceteris paribus [all things being equal] of the demonstration which derives from fewer postulates or hypotheses - in short from fewer premisses; for [...] given that all these are equally well known, where they are fewer knowledge will be more speedily acquired, and that is a desideratum. The argument implied in our contention that demonstration from fewer assumptions is superior may be set out in universal form [...]" (Aristotle, “Posterior Analytics”, cca. 400 BC)

"O immortal gods! Men do not realize how great a revenue parsimony can be!"  (Marcus Tullius Cicero, "Paradoxa Stoicorum", [Paradox VI] 46 BC) 
 
"Always take the short cut; and that is the rational one. Therefore say and do everything according to soundest reason." (Marcus Aurelius, "Meditations". cca. 121–180 AD)

"We consider it a good principle to explain the phenomena by the simplest hypothesis possible." (Ptolemy)

"That is better and more valuable which requires fewer, other circumstances being equal. [...] For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal." (Robert Grosseteste,” Commentarius in Posteriorum Analyticorum Libros”, cca. 1217–1220)

"It is superfluous to suppose that what can be accounted for by a few principles has been produced by many." (Thomas Aquinas, “Summa Theologica”, cca. 1266-1273)

"All that is superfluous displeases God and nature. All that displeases God and nature is evil." (Dante Alighieri, "De Monarchia", cca. 1312-1313)

“Numquam ponenda est pluralitas sine necessitate.”
“Plurality is never to be posited without necessity.” (William of Occam, “Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi”, 1495)

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