Occam's Razor = The Law of Parsimony (1500 - 1899)

"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, as far as possible, assign the same causes." (Isaac Newton, "Philosophiæ Naturalis Principia Mathematica" ["Mathematical Principles of Natural Philosophy"], 1687) 

"Entia non sunt multiplicanda praeter necessitatem."
"Entities are not to be multiplied beyond what is necessary." (John Ponce, cca. 17th century)

"Parsimony is enough to make the master of the golden mines as poor as he that has nothing; for a man may be brought to a morsel of bread by parsimony as well as profusion." (Henry Home [Lord Kames] ," Introduction to the Art of Thinking", 1761)

"Mere parsimony is not economy. Expense, and great expense, may be an essential part in true economy." (Edmund Burke, "A Letter to a Noble Lord", 1796)

"It is, after all, a principle of logic not to multiply entities unnecessarily." (Antoine-Laurent Lavoisier, "Réflexions sur le phlogistique", 1862)

"The first obligation of Simplicity is that of using the simplest means to secure the fullest effect." (George H Lewes, "The Principles of Success in Literature", 1865)

"In no case may we interpret an action [of an animal] as the outcome of the exercise of a higher psychical faculty, if it can be interpreted as the outcome of the exercise of one which stands lower in the psychological scale." (Conwy Lloyd Morgan, "An Introduction to Comparative Psychology", 1894) [Morgan's canon, the principle of parsimony in animal research]

"The question is therefore to demonstrate all geometrical truths with the smallest possible number of assumptions." (Augustus de Morgan, "On the Study and Difficulties of Mathematics", 1898)

"Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses." (Ernst Mach)

Occam's Razor = The Law of Parsimony (1950 - 1999)

"Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor." (Willard van Orman Quine, "On What There Is" From a Logical Point of View: Nine Logico-Philosophical Essays", 1953)

"[…] the grand aim of all science […] is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms.” (Albert Einstein, 1954)

"The principle of parsimony is valid esthetically in that the artist must not go beyond what is needed for his purpose. (Rudolf Arnheim," Art and Visual Perception: A Psychology of the Creative Eye", 1954)

"Our craving for generality has [as one] source […] our preoccupation with the method of science. I mean the method the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws; and, in mathematics, of unifying the treatment of different topics by using a generalization." (Ludwig Wittgenstein, "The Blue and Brown Books", 1958)

"[…] entities must not be reduced to the point of inadequacy and, more generally, that it is in vain to try to do with fewer what requires more." (Karl Menger, "A Counterpart of Occam's Razor in Pure and Applied Mathematics Ontological Uses", Synthese Vol. 12 (4), 1960)

"Let us consider, for a moment, the world as described by the physicist. It consists of a number of fundamental particles which, if shot through their own space, appear as waves, and are thus [...] of the same laminated structure as pearls or onions, and other wave forms called electromagnetic which it is convenient, by Occam’s razor, to consider as travelling through space with a standard velocity. All these appear bound by certain natural laws which indicate the form of their relationship." (G Spencer-Brown, "Laws of Form", 1969)

"For if as scientists we seek simplicity, then obviously we try the simplest surviving theory first, and retreat from it only when it proves false. Not this course, but any other, requires explanation. If you want to go somewhere quickly, and several alternate routes are equally likely to be open, no one asks why you take the shortest. The simplest theory is to be chosen not because it is the most likely to be true but because it is scientifically the most rewarding among equally likely alternatives. We aim at simplicity and hope for truth." (Nelson Goodman, "Problems and Projects", 1972)

"As glimpsed by physicists, Nature's rules are simple, but also intricate: Different rules are subtly related to each other. The intricate relations between the rules produce interesting effects in many physical situations. [...] Nature's design is not only simple, but minimally so, in the sense that were the design any simpler, the universe would be a much duller place." (Anthony Zee, "Fearful Symmetry: The Search for Beauty in Modern Physics", 1986)

"A mechanistic model has the following advantages: 1. It contributes to our scientific understanding of the phenomenon under study. 2. It usually provides a better basis for extrapolation (at least to conditions worthy of further experimental investigation if not through the entire range of all input variables). 3. It tends to be parsimonious (i. e, frugal) in the use of parameters and to provide better estimates of the response." (George E P Box, "Empirical Model-Building and Response Surfaces", 1987)

"I seek […] to show that - other things being equal - the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth." (Richard Swinburne, "Simplicity as Evidence for Truth", 1997)

"Were it not for Occam's Razor, which always demands simplicity, I'd be tempted to believe that human beings are more influenced by distant causes than immediate ones. This would especially be true of overeducated people, who are capable of thinking past the immediate, of becoming obsessed by the remote. It's the old stuff, the conflicts we've never come to terms with, that sneaks up on us, half forgotten, insisting upon action."(Richard Russo,"Straight Man", 1997)

"It is part of the lore of science that the most parsimonious explanation of observed facts is to be preferred over convoluted and long-winded theories. Ptolemaic epicycles gave way to the Copernican system largely on this premise, and in general, scientific inquiry is governed by the oft-quoted dictum of the medieval cleric William of Occam that 'nunquam ponenda est pluralitas sine necesitate' , which may be paraphrased as 'choose the simplest explanation for the observed facts' ." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

Occam's Razor = The Law of Parsimony (2000-)

"A smaller model with fewer covariates has two advantages: it might give better predictions than a big model and it is more parsimonious (simpler). Generally, as you add more variables to a regression, the bias of the predictions decreases and the variance increases. Too few covariates yields high bias; this called underfitting. Too many covariates yields high variance; this called overfitting. Good predictions result from achieving a good balance between bias and variance. […] fiding a good model involves trading of fit and complexity." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Mathematics is not about abstract entities alone but is about relation of abstract entities with real entities. […] Adequacy relations between abstract and real entities provide space or opportunity where mathematical and logical thought operates parsimoniously." (Navjyoti Singh, "Classical Indian Mathematical Thought", 2005)

"The model theory postulates that mental models are parsimonious. They represent what is possible, but not what is impossible, according to assertions. This principle of parsimony minimizes the load on working memory, and so it applies unless something exceptional occurs to overrule it." (Philip N Johnson-Laird, Mental Models, Sentential Reasoning, and Illusory Inferences, [in "Mental Models and the Mind"], 2006)

"Two systems concepts lie at the disposal of the architect to reflect the beauty of harmony: parsimony and variety. The law of parsimony states that given several explanations of a specific phenomenon, the simplest is probably the best. […] On the other hand, the law of requisite variety states that for a system to survive in its environment the variety of choice that the system is able to make must equal or exceed the variety of influences that the environment can impose on the system." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"What advantages do diagrams have over verbal descriptions in promoting system understanding? First, by providing a diagram, massive amounts of information can be presented more efficiently. A diagram can strip down informational complexity to its core - in this sense, it can result in a parsimonious, minimalist description of a system. Second, a diagram can help us see patterns in information and data that may appear disordered otherwise. For example, a diagram can help us see mechanisms of cause and effect or can illustrate sequence and flow in a complex system. Third, a diagram can result in a less ambiguous description than a verbal description because it forces one to come up with a more structured description." (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)

"In my view, the argument from parsimony is really no argument at all - it typically functions only to shut down more interesting discussion. If history is any guide, it's never a good idea to assume that a scientific problem is cornered." (David Eagleman, "Incognito: The Secret Lives of the Brain", 2011)

"Scientists often talk of parsimony (as in 'the simplest explanation is probably correct', also known as Occam’s razor), but we should not get seduced by the apparent elegance of argument from parsimony; this line of reasoning has failed in the past at least as many times as it has succeeded. For example, it is more parsimonious to assume that the sun goes around the Earth, that atoms at the smallest scale operate in accordance with the same rules that objects at larger scales follow, and that we perceive what is really out there. All of these positions were long defended by argument from parsimony, and they were all wrong. In my view, the argument from parsimony is really no argument at all - it typically functions only to shut down more interesting discussion. If history is any guide, it’s never a good idea to assume that a scientific problem is cornered." (David Eagleman, "Incognito: The Secret Lives of the Brain", 2011)

"What can be done with fewer [assumptions] is done in vain with more." (Alan Baker, "Simplicity", The Stanford Encyclopedia of Philosophy, 2012)

Occam's Razor = The Law of Parsimony (1900-1949)

"Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well." (Charles S Peirce, "Pragmatism and Pragmaticism", [lecture] 1903)

"Nothing perhaps has so retarded the reception of the higher conclusions of Geology among men in general, as ... [the] instinctive parsimony of the human mind in matters where time is concerned. (Charles Lapworth, Proceedings of the Geological Society of London, 1903)

"The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience. This process, however, has no logical foundation but only a psychological one. It is clear that there are no grounds for believing that the  simplest course of events will really happen." (Ludwig Wittgenstein, "Tractatus Logico-Philosophicus", 1922)

"Whenever possible, substitute constructions out of known entities for inferences to unknown entities." (Bertrand Russell, 1924)

"In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world 'simplest'. It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = K(d2x/dy2) much less simple than 'it oozes', of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plainman, namely, the rate of change of a rate of change." (John B S Haldane, "Possible Worlds", 1927)

"In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict facts of the same kind. The  catch in this criterion lies in the world 'simplest'." (John B S Haldane, "Possible Worlds and Other Essays", 1928)

“It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience." (Albert Einstein, "On the Method of Theoretical Physics", [The Herbert Spencer Lecture, delivered at Oxford] 1933)

"In the conception of a machine or the product of a machine there is a point where one may leave off for parsimonious reasons, without having reached aesthetic perfection; at this point perhaps every mechanical factor is accounted for, and the sense of incompleteness is due to the failure to recognize the claims of the human agent. Aesthetics carries with it the implications of alternatives between a number of mechanical solutions of equal validity; and unless this awareness is present at every stage of the process [...] it is not likely to come out with any success in the final stage of design." (Lewis Mumford," The Esthetic Assimilation of the Machine", Technics and Civilization, 1934)

"When two hypotheses are possible, we provisionally choose that which our minds adjudge to be simpler, on the supposition that this is the more likely to lead in the direction of truth. It includes as a special case the principle of Occam's razo - entia non multiplicana praeter necessitatem." (James Jeans,"Physics and Philosophy", 1942)

"When two hypotheses are possible, we provisionally choose that which our minds adjudge to the simpler on the supposition that this Is the more likely to lead in the direction of the truth." (James H Jeans, "Physics and Philosophy" 3rd Ed., 1943)

"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended its area of applicability." (Albert Einstein, "Autobiographical Notes", 1949)

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)