“Since reasoning, or inference, the principal subject of logic, is an operation which usually takes place by means of words, and in complicated cases can take place in no other way: those who have not a thorough insight into both the signification and purpose of words, will be under chances, amounting almost to certainty, of reasoning or inferring incorrectly.”

— John Stuart Mill , book A System of Logic

Source: A System of Logic (1843), p. 11: Cited in Gaines (1976) "Foundations of fuzzy reasoning" in: International Journal of Man-Machine Studies 8(6), p. 623

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John Stuart Mill 179

British philosopher and political economist 1806–1873

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“The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.”

George Pólya (1887–1985) Hungarian mathematician

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“We should infer in the case of a beautiful dwelling-place that it was built for its owners and not for mice; we ought, therefore, in the same way to regard the universe as the dwelling-place of the gods.”

Chrysippus (-281–-208 BC) ancient Greek philosopher

As quoted in De Natura Deorum by Cicero, iii. 10.

“Since most subjects studied in school consist largely of theories… language education must include not only the serious study of what truth and falsehood mean in the context of a subject, but also what is meant by a fact, an inference, an assumption, a judgment, a generalization… In this way students will be learning both the language of a subject and the methods of inquiry in that subject, since inquiry consists of nothing else but the generation of questions, the invention of definitions and metaphors, the separation of facts from inferences, the forming of generalizations…”

Neil Postman (1931–2003) American writer and academic

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“A presumption of any fact is, properly, an inferring of that fact from other facts that are known; it is an act of reasoning; and much of human knowledge on all subjects is derived from this source.”

Charles Abbott, 1st Baron Tenterden (1762–1832) British barrister and judge, Lord Chief Justice of the King's Bench

King v. Burdett (1820), 1 St. Tr. (N. S.) 140.

“You can have the other words — chance, luck, coincidence, serendipity. I'll take grace.”

Mary Oliver (1935–2019) American writer

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Context: You can have the other words — chance, luck, coincidence, serendipity. I'll take grace. I don't know what it is exactly, but I'll take it.

“Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws.”

Alfred Tarski (1901–1983) Polish-American logician

Introduction to Logic: and to the Methodology of Deductive Sciences. (1941/2013) Tr. Olaf Helmer, pp. 108-110.

“To those who inquire as to the purpose of mathematics, the usual answer will be that it facilitates the making of machines, the travelling from place to place, and the victory over foreign nations, whether in war or commerce. … The reasoning faculty itself is generally conceived, by those who urge its cultivation, as merely a means for the avoidance of pitfalls and a help in the discovery of rules for the guidance of practical life.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

1900s, "The Study of Mathematics" (November 1907)

“There is nothing in any object, consider'd in itself, which can afford us a reason for drawing a conclusion beyond it; […] even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience.”

David Hume book A Treatise of Human Nature

Part 3, Section 12
A Treatise of Human Nature (1739-40), Book 1: Of the understanding

“There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly.”

Alfred Tarski (1901–1983) Polish-American logician

Introduction to Logic: and to the Methodology of Deductive Sciences. (1941/2013) Tr. Olaf Helmer, p. 109.

“A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:
:"The probability of an event is the reason we have to believe that it has taken place, or that it will take place."
:"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible" (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 243-4; As cited in: "George Boole (1815–64)" in: Oxford Dictionary of Scientific Quotations, Edited by W. F. Bynum and Roy Porter, January 2006

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John Stuart Mill 179

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