mathematics

"From a drop of water, a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other."

"These, briefly, are the key elements of the stereotype: logic cripples and constrains; it forces one into narrow and mechanical modes of thought that cut one off from a vast range of superior thoughts, feelings and perceptions; logic is an enemy of wit and humor (Mr. Spock's face was always an impassive mask); logic makes us dull and pedantic (Mr. Spock always spoke in a monotone); logic presupposes a simple-minded, black-and-white, yes-no conception of the world. ... Logic misses the point of half the things we ordinarily say and cannot match the insight of the humblest person's common sense."

"“It’s logical,” Sario said. “Lots of people don’t like coping with logic when it dictates hard decisions. That’s a problem with people, not logic.”"

"Adherents of formal logic may be compared to a maker of porcelain dishes who would contend that he was simply paying attention to the form of his dishes, pots, and vases, but that he did not have anything to do with the raw material."

""I refuse to prove that I exist," says God, "for proof denies faith, and without faith, I am nothing." "Oh," says man, "but the Babel fish is a dead give-away, isn't it? It proves You exist, and so therefore You don't." "Oh, I hadn't thought of that," says God, who promptly vanishes in a puff of logic. "Ah, that was easy," says man, and for an encore goes on to prove that black is white, and gets killed on the next zebra crossing. Most leading theologians claim that this argument is a load of dingo's kidneys."

"It is with logic as it is with other sciences. They draw wisdom from the mysterious source of plain experience. Agriculture, e. g., aims to teach the farmer how to cultivate the soil; but fields were tilled long before any agricultural college had begun its lectures. In the same way human beings think without ever having heard of logic. But by practice they improve their innate faculty of thought, they make progress, they gradually learn to make better use of it. Finally, just as the farmer arrives at the science of agriculture, so the thinker arrives at logic, acquires a clear consciousness of his faculty of thought and a professional dexterity in applying it."

"Pierce wrote as a logician and James as a humanist."

"We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathematical sect puts out the logical eye, the logical sect puts out the mathematical eye; each believing that it can see better with one eye than with two."

"The morbid logician seeks to make everything lucid, and succeeds in making everything mysterious."

"The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait."

"Utility and necessity of logic - It would be a mistake to imagine that, above and beyond what is called the Natural Logic of sound common sense, the study of the Science of Logic is absolutely necessary for right reasoning. Men reasoned rightly before Aristotle ever formulated a canon of logic. It was, in fact, by an analysis of such reasonings that he discovered those canons: they could never have been discovered otherwise. Here as elsewhere the art came before the science; theory followed practice. A man may reason rightly without knowing a single rule of the syllogism; or, conversely, he may know all the details of logic and be an indifferent guide to truth just as a first-rate geometrician may be a failure as an engineer. But still, just as his knowledge of geometry will enable the geometrician to detect the defects in a piece of engineering, so too will an explicit knowledge of the canons of reasoning enable us to discover more readily where the fallacy of a misleading argument lies. Without professing to guard us infallibly from error, logic familiarizes us with the rules and canons to which right reasoning processes must conform, and with the hidden fallacies and pitfalls to which such processes are commonly exposed."

"You can only find truth with logic if you have already found truth without it."

"Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."

"Logic is a large drawer, containing some useful instruments, and many more that are superfluous. A wise man will look into it for two purposes, to avail himself of those instruments that are really useful, and to admire the ingenuity with which those that are not so, are assorted and arranged."

"If the world were a logical place, men would ride side saddle."

"No, no, you're not thinking; you're just being logical."

"R. A. Fisher, J. Neyman, R. von Mises, W. Feller, and L. J. Savage denied vehemently that probability theory is an extension of logic, and accused Laplace and Jeffreys of committing metaphysical nonsense for thinking that it is."

"LOGIC, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion -- thus:"

"In the logic of science there is a principle as important as that of parsimony: it is that of sufficient reason. The former directs us to look for simplest causes, the later cautions us not to simplify so far that the explanation is inadequate to the facts to be explained....Parsimony is not itself a simple criterion of a good methodology; we cannot simply count the factors of explanation and say that the theory containing the smallest number is the best. The ideal of parsimony cannot be expressed without the proviso that the conditions for which it is a norm shall themselves be adequate."

"Aristotle is noted for his writings on logic, physics, biology, psychology, metaphysics, ethics, politics, and literature. These works are marked by sober tone, subtle analysis, and empirical accuracy. In logic, he produced the first textbooks ever written. They deal with some of the problems which Plato had suggested but not considered in detail."

"You can prove anything you want by coldly logical reason—if you pick the proper postulates. We have ours and Cutie [robot QT-1] has his." "Then let’s get at those postulates in a hurry. The storm’s due tomorrow." Powell sighed wearily. "That’s where everything falls down. Postulates are based on assumptions and adhered to by faith. Nothing in the Universe can shake them. ..."

"[ Fuzzy logic is ] a logic whose distinguishing features are (i) fuzzy truth-values expressed in linguistic terms, e.g., true, very true, more or less true, or somewhat true, false, nor very true and not very false, etc2.; (2) imprecise truth tables; and (3) rules of inference whose validity is relative to a context rather than exact."

"Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing."

"Memory, then, is a necessary part of the logical faculty. ... The proposition A = A must have a psychological relation to time, otherwise it would be At1 = At2."

"Logic is a law which must be obeyed, and man realizes himself only in so far as he is logical. He finds himself in cognition."

"As to the most prudent logicians might venture to deduce from a skein of wool the probable existence of a sheep; so you, from the raw stuff of perception, may venture to deduce a universe which transcends the reproductive powers of your loom."

"Logic tends to reduce everything to identities and genera, to each representation having no more than one single and self-same content in whatever place, time, or relation it may occur to us. And there is nothing that remains the same for two successive moments of its existence. My idea of God is different each time that I conceive it. Identity, which is death, is the goal of the intellect."

"The moment we stop assuming that the ideas of any milieu form static 'propositional systems', and recognize that they constitute historically developing 'conceptual populations', we are free to abandon also the philosophers' traditional assumption that rationality is a sub-species of logicality. ...In non-intellectual contexts... we judge the rationality of a man's conduct, not by how he habitually behaves, but rather how far he modifies his behaviour in new and unfamiliar situations, and it is arguable that the rationality of intellectual performances should be judged, correspondingly, by considering, not the internal consistency of a man's habitual concepts and beliefs, but rather the manner in which he modifies this intellectual position in the face of new and unforeseen experiences."

"Poetry — No definition of poetry is adequate unless it be poetry itself. The most accurate analysis by the rarest wisdom is yet insufficient, and the poet will instantly prove it false by setting aside its requisitions. It is indeed all that we do not know. The poet does not need to see how meadows are something else than earth, grass, and water, but how they are thus much. He does not need discover that potato blows are as beautiful as violets, as the farmer thinks, but only how good potato blows are. The poem is drawn out from under the feet of the poet, his whole weight has rested on this ground. It has a logic more severe than the logician's. You might as well think to go in pursuit of the rainbow, and embrace it on the next hill, as to embrace the whole of poetry even in thought."

"It takes extraordinary wisdom and self-control to accept that many things have a logic we do not understand that is smarter than our own."

"An idea starts to be interesting when you get scared of taking it to its logical conclusion."

"Logic is in the eye of the logician."

"Logic is the beginning of wisdom, not the end."

"Conceptual graphs are system of logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. The purpose of the system is to express meaning in a form that is logically precise, humanly readable, and computationally tractable."

"[My aim is] to design logic as a calculating discipline, especially to give access to the exact handling of relative concepts, and, from then on, by emancipation from the routine claims of natural language, to withdraw any fertile soil from "cliché" in the field of philosophy as well. This should prepare the ground for a scientific universal language that, widely differing from linguistic efforts like Volapük [a universal language like Esperanto, very popular in Germany at the time], looks more like a sign language than like a sound language."

"When emotion brings us ghosts from the past, only logic can root us in the present."

"A crisis in doctrine occurred when they discovered that the square root of two was irrational. That is: the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were. "Irrational" originally meant only that. That you can't express a number as a ratio. But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of "irrational"."