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Logic

study of correct reasoning

Logic (from the Greek λογική, logikē) refers to both the study of modes of reasoning (which are valid, and which are fallacious) and the use of valid reasoning.

Like a medicine, though not a panacea for every ill, it has the health of the mind for its aim, but requires the determination of a powerful will to imbibe its nauseating yet wholesome influence: it is no wonder therefore that puny intellects, like weak stomachs, abhor and reject it. ~ Porphyry

In the latter sense, logic is used in most intellectual activities, including philosophy and science, but in the first sense, is primarily studied in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take. In mathematics, it is the study of valid inferences within some formal language.

CONTENT: A-D , E-H , I-L , M-P , Q-T , U-Z , See also , External links

Quotes

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Quotes are rearranged alphabetical per author

A-D

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  • "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.
  • All men are mortal. Socrates was mortal. Therefore, all men are Socrates.
    • Woody Allen in his movie Love and Death cited in: Philip Nicholas Johnson-Laird (2006) How We Reason. p. 142
  • "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. ..."
  • 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:
'Major Premise': Sixty men can do a piece of work sixty times as quickly as one man.
'Minor Premise': One man can dig a posthole in sixty seconds; therefore --
'Conclusion': Sixty men can dig a posthole in one second.

This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.
  • Ambrose Bierce, The Cynic's Dictionary (1906); republished as The Devil's Dictionary (1911).
  • No, no, you're not thinking; you're just being logical.
    • Attributed to Niels Bohr in: William Glen (1994) The Mass-Extinction Debates: How Science Works in a Crisis. p. 62
  • If the world were a logical place, men would ride side saddle.
  • 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.
  • "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."
  • You can only find truth with logic if you have already found truth without it.
  • 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.
  • 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.
  • The morbid logician seeks to make everything lucid, and succeeds in making everything mysterious.
  • 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.
  • Pierce wrote as a logician and James as a humanist.
    • John Dewey, distinguishing the styles and focus of Peirce and William James, in The Development of American Pragmatism" in Studies in the History of Ideas (1925), Vol. II, p. 361
  • 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.
    • Joseph Dietzgen, Letters on Logic: Especially Democratic-Proletarian Logic (1906), Letter 2
  • 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.
    • Joseph Dietzgen, Letters on Logic: Especially Democratic-Proletarian Logic (1906), Letter 3
  • 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.
    • John M. Dolan (1994), Inference and Imagination
  • 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.
  • The first question we should face is: What is the aim of a physical theory? To this question diverse answers have been made, but all of them may be reduced to two main principles:
    "A physical theory," certain logicians have replied, "has for its object the explanation of a group of laws experimentally established."
    "A physical theory," other thinkers have said, "is an abstract system whose aim is to summarize and classify logically a group of experimental laws without claiming to explain these laws...
    Now these two questions — Does there exist a material reality distinct from sensible appearances? and What is the nature of reality? — do not have their source in experimental method, which is acquainted only with sensible appearances and can discover nothing beyond them. The resolution of these questions transcends the methods used by physics; it is the object of metaphysics.
    Therefore, if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics...
    Now, to make physical theories depend on metaphysics is surely not the way to let them enjoy the privilege of universal consent.
    • Pierre Duhem, translated by Philip P. Wiener (1991). The aim and structure of physical theory. Princeton University Press. p. 10. ISBN 069102524X. 

E-H

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  • Logic is usually understood nowadays as a study of certain formal systems, though in former times there were philosophers who held that the subject matter of logic was the formal rules of human thought.
  • The want of logic annoys. Too much logic bores. Life eludes logic, and everything that logic alone constructs remains artificial and forced.
    • André Gide (1956) The journals, 1889-1949. Vol 2. p. 20
  • To find themselves utterly alone at night where company is desirable and expected makes some people fearful; but a case more trying by far to the nerves is to discover some mysterious companionship when intuition, sensation, memory, analogy, testimony, probability, induction — every kind of evidence in the logician's list — have united to persuade consciousness that it is quite in isolation.
  • Logic is a feeble reed, friend. "Logic" proved that airplanes can't fly and that H-bombs won't work and that stones don't fall out of the sky. Logic is a way of saying that anything which didn't happen yesterday won't happen tomorrow.
  • To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.
    • Thomas Hobbes (1588–1679) On the proposition that the volume generated by revolving the region under 1/x from 1 to infinity has finite volume. Quoted in Mathematical Maxims and Minims by N. Rose (1988).
  • Logic is one thing and commonsense another.
 
I have expos'd myself to the enmity of all metaphysicians, logicians, mathematicians, and even theologians; and can I wonder at the insults I must suffer?
- David Hume (1739-40)
  • I have expos'd myself to the enmity of all metaphysicians, logicians, mathematicians, and even theologians; and can I wonder at the insults I must suffer?
    • David Hume (1739-40) A Treatise of Human Nature. Part 4 Of the sceptical and other systems of philosophy, Sect. 7 Conclusion of this book

I-L

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  • Logician: A cat has four paws.
    Old Gentleman: My dog had four paws.
    Logician: Then it's a cat.
    Old Gentleman: So my dog is a cat?
    Logician: And the contrary is also true.
  • Logic hasn't wholly dispelled the society of witches and prophets and sorcerers and soothsayers.
  • Logic is neither a science nor an art, but a dodge.
    • Benjamin Jowett in: Evelyn Abbott, Lewis Campbell (1897) The Life and Letters of Benjamin Jowett, M.A., Master of Balliol College, Oxford. Vol 1. p. 131
  • Logic is concerned with arguments, good and bad. With the docile and the reasonable, arguments are sometimes useful in settling disputes. With the reasonable, this utility attaches only to good arguments. It is the logician's business to serve the reasonable. Therefore, in the realm of arguments, it is the logician who distinguishes good from bad.
  • The book, as it stands, seems to me to be one of the most frightful muddles I have ever read, with scarcely a sound proposition in it beginning with page 45, and yet it remains a book of some interest, which is likely to leave its mark on the mind of the reader. It is an extraordinary example of how, starting with a mistake, a remorseless logician can end up in bedlam.
    • John Maynard Keynes, in Collected Works, vol. XII on Hayek's Prices and Production (1931); Hayek provided historical background up to page 45, after that came his theoretical model.
  • Metaphysics may be, after all, only the art of being sure of something that is not so, and logic only the art of going wrong with confidence.
  • "There is one basis of science," says Descartes, "one test and rule of truth, namely, that whatever is clearly and distinctly conceived is true." A profound psychological mistake. It is true only of formal logic, wherein the mind never quits the sphere of its first assumptions to pass out into the sphere of real existences; no sooner does the mind pass from the internal order to the external order, than the necessity of verifying the strict correspondence between the two becomes absolute. The Ideal Test must be supplemented by the Real Test, to suit the new conditions of the problem.
  • Anyone who has heard (Jacques Derrida) lecture in French knows that he is more performance artist than logician. His flamboyant style--using free association, rhymes and near-rhymes, puns, and maddening digressions--is not just a vain pose (though it is surely that). It reflects what he calls a self-conscious "acommunicative strategy" for combating logocentrism.
    • Mark Lilla, Review of Derrida's Moscou Aller-Retour in The New York Review of Books, June, 1998

M-P

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  • The contemporary mathematical and symbolic logic is certainly very different from its classical predecessor, but they share the radical opposition to dialectical logic. In terms of this opposition, the old and the new formal logic express the same mode of thought. it is purged from that “negative” which loomed so large at the origins of logic and of philosophic thought—the experience of the denying, deceptive, falsifying power of the established reality. And with the elimination of this experience, the conceptual effort to sustain the tension between “is” and “ought”, and to subvert the established universe of discourse in the name of its own truth is likewise eliminated from all thought which is to be objective, exact, and scientific. For the scientific subversion of the immediate experience which establishes the truth of science as against that of immediate experience does not develop the concepts which carry in themselves the protest and the refusal. The new scientific truth which they oppose to the accepted one does not contain in itself the judgment that condemns the established reality. ... In contrast, dialectical thought is and remains unscientific to the extent to which it is such judgment.
  • This fallacy [appeal to authority] is not in itself an error; it is impossible to learn much in today's world without letting somebody else crunch the numbers and offer us explanations. And teachers are sources of necessary information. But how we choose our "authorities" and place a value on such information, is just another skill rarely taught in our education systems. It's little wonder that to most folk, sound bites and talking heads are enough to count as experts. […] Teaching is reinforcing the appeal to authority, where anybody who seems more intelligent than you must ultimately be right. […] We educators must simply role-model critical thinking. […] Educators themselves have to be prepared to show that “evidence” and “answers” are two separate things by firmly believing that, themselves.
    • Mike McRae, Australian teacher and guest columnist, "Educating Future Critical Thinkers", Swift: Online Newsletter of the JREF, 31 March 2006
  • The pedant and the priest have always been the most expert of logicians—and the most diligent disseminators of nonsense and worse.
    • H. L. Mencken "Clinical Notes" in The American Mercury (January 1924), p. 75; also in Prejudices, Fourth Series (1924)
  • Logic, like whiskey, loses its beneficial effect when taken in too large quantities.
    • Edward John Moreton Drax Plunkett, Lord Dunsany (1878–1957), "Weeds & Moss", My Ireland
  • Logic is a systematic method of coming to the wrong conclusion with confidence.
  • Able logicians have a trick of being unutterably wrong when they come to write about life: the instinctive, intuitive sense of human values often fails them quite. Logic is more likely to make a man a fool than the lack of logic is.
  • It might ... have been supposed that logicians and psychologists would have devoted special attention to meaning, since it is so vital for all the issues with which they are concerned. But that this is not the case will be evident[1] to anyone who studies the Symposium in Mind (October 1920 and following numbers) on "The Meaning of 'Meaning.'"
  • Logicians tell us that a system of ideas containing a contradiction can be used to deduce any statement whatsoever, no matter how absurd.
    • Steven Pinker (2007) "Introduction" in: John Brockman, ed. What is Your Dangerous Idea? p. xxix
  • Logic and mathematics seem to be the only domains where self-evidence manages to rise above triviality; and this it does, in those domains, by a linking of self-evidence on to self-evidence in the chain reaction known as proof.
 
Existential graph by C.S. Peirce.
  • Three conceptions are perpetually turning up at every point in every theory of logic, and in the most rounded systems they occur in connection with one another. They are conceptions so very broad and consequently indefinite that they are hard to seize and may be easily overlooked. I call them the conceptions of First, Second, Third. First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and second are brought into relation.
  • Logical analysis applied to mental phenomenon shows that there is but one law of mind, namely that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas.
  • A certain maxim of Logic which I have called Pragmatism has recommended itself to me for diverse reasons and on sundry considerations.
    • Charles Sanders Peirce (1903) Pragmatism and Pragmaticism. Lecture I : Pragmatism : The Normative Sciences, CP 5.14
  • It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
    • Henri Poincaré, Science and Method (1908) Part II. Ch. 2 : Mathematical Definitions and Education, p. 129
  • The utility of a science which enables men to take cognizance of the travellers on the mind's highway, and excludes those disorderly interlopers, verbal fallacies, needs but small attestation. Its searching penetration by definition alone, before which even mathematical precision fails, would especially commend it to those whom the abstruseness of the study does not terrify, and who recognise the valuable results which must attend discipline of mind. Like a medicine, though not a panacea for every ill, it has the health of the mind for its aim, but requires the determination of a powerful will to imbibe its nauseating yet wholesome influence: it is no wonder therefore that puny intellects, like weak stomachs, abhor and reject it.

Q-T

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  • Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one. They differ as boy and man: logic is the youth of mathematics and mathematics is the manhood of logic. This view is resented by logicians who, having spent their time in the study of classical texts, are incapable of following a piece of symbolic reasoning, and by mathematicians who have learnt a technique without troubling to inquire into its meaning or justification. Both types are now fortunately growing rarer. So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premises which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
  • The question of "unreality," which confronts us at this point, is a very important one. Misled by grammar, the great majority of those logicians who have dealt with this question have dealt with it on mistaken lines. They have regarded grammatical form as a surer guide in analysis than, in fact, it is. And they have not known what differences in grammatical form are important.
    • Bertrand Russell (1919) Introduction to Mathematical Philosophy. Ch. 7: Rational, Real and Complex Numbers.
  • All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestial life but only to an imagined celestial existence... logic takes us nearer to heaven than other studies.
    • Bertrand Russell (1923) as cited in Gaines (1976) "Foundations of fuzzy reasoning" in: International Journal of Man-Machine Studies 8(6), p. 623
  • The apparent world goes through developments which are the same as those the logician goes through if he starts from Pure Being and travels on to the Absolute Idea. [...] Why the world should go through this logical evolution is not clear; one is tempted to suppose that the Absolute Idea did not quite understand itself at first, and made mistakes when it tried to embody itself in events. But this, of course, was not what Hegel would have said.
  • 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".
    • Carl Sagan (1990 Update) Cosmos: A Personal Voyage.
  • [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.
    • Ernst Schröder, cited in: V. Peckhaus, "19th Century Logic between Philosophy and Mathematics," Bulletin of Symbolic Logic, 5 (1999), 433-450.
  • 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.
    • John F. Sowa (1993) Conceptual graphs for knowledge representation. p. 3-51.
  • Logic is in the eye of the logician.
    • Gloria Steinem (1984) cited in: Robert Byrne (2002) The 2,548 Best Things Anybody Ever Said
  • An idea starts to be interesting when you get scared of taking it to its logical conclusion.
    • Nassim Nicholas Taleb, The Bed of Procrustes: Philosophical and Practical Aphorisms (2010) Preludes, p.3.
  • 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.
    • Nassim Nicholas Taleb, The Bed of Procrustes: Philosophical and Practical Aphorisms (2010) Epistemology and Subtractive Knowledge, p. 78.
  • 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.
  • The moment we stop assuming that the ideas of any millieu 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.
    • Stephen Toulmin, Human Understanding (1972) Vol. 1 The Collective Use and Evolution of Concepts.

U-Z

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  • 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.
  • 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.
    • Evelyn Underhill (1914) Practical Mysticism. Chapter II, The World Of Reality, p. 38
  • 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.
  • 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.
  • 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.
  • [ 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.
    • Lotfi A. Zadeh (1975) "Fuzzy logic and approximate reasoning". Synthese 30: p. 407

See also

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