“Both induction and deduction, reasoning from the particular and the general, and back again from the universal to the specific, form the essence to scientific thinking.”

— Hans Christian von Baeyer

Source: Information, The New Language of Science (2003), Chapter 16, Unpacking Information, The computer in the service of physics, p. 138

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Hans Christian von Baeyer 25

American physicist 1938

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“In a certain sense all knowledge is inductive. We can only learn the laws and relations of things in nature by observing those things. But the knowledge gained from the senses is knowledge only of particular facts, and we require some process of reasoning by which we may collect out of the facts the laws obeyed by them. Experience gives us the materials of knowledge: induction digests those materials, and yields us general knowledge. When we possess such knowledge, in the form of general propositions and natural laws, we can usefully apply the reverse process of deduction to ascertain the exact information required at any moment. In its ultimate foundation, then, all knowledge is inductive—in the sense that it is derived by a certain inductive reasoning from the facts of experience.”

William Stanley Jevons (1835–1882) English economist and logician

Source: The Principles of Science: A Treatise on Logic and Scientific Method (1874) Vol. 1, p. 14

“The psycho-physiological hypothesis is both inductively and deductively the sine qua non of the science of psychology.”

Boris Sidis (1867–1923) American psychiatrist

Source: The Foundations of Normal and Abnormal Psychology (1914), p. 86

“Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i. e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle …”

Carl B. Boyer (1906–1976) American mathematician

Source: The Rainbow: From Myth to Mathematics (1959), p. 88

“[T]he human reason discovers new relations between things not by deduction, but by that unpredictable blend of speculation and insight… induction, which—like other forms of imagination—cannot be formalized.”

Jacob Bronowski (1908–1974) Polish-born British mathematician

"The Reach of Imagination" (1967)

“Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? …If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.”

Henri Poincaré book Science and Hypothesis

Source: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Context: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6

“Whatever lies beyond the limits of experience, and claims another origin than that of induction and deduction from established data, is illegitimate.”

George Henry Lewes (1817–1878) British philosopher

Vol. 1, p. 17
The Foundations of a Creed (1874-5)

“It is actually impossible in theory to determine exactly what the hidden mechanism is without opening the box, since there are always many different mechanisms with identical behavior. Quite apart from this, analysis is more difficult than invention in the sense in which, generally, induction takes more time to perform than deduction: in induction one has to search for the way, whereas in deduction one follows a straightforward path.”

Valentino Braitenberg (1926–2011) Italian-Austrian neuroscientist

Source: Vehicles: Experiments in Synthetic Psychology (1984), p. 20 as cited in: Yll Haxhimusa (2006) The Structurally Optimal Dual Graph Pyramid and Its Application in Image Partitioning. p. 149

“As regards the sequence in the movement of man's knowledge, there is always a gradual growth from the knowledge of individual and particular things to the knowledge of things in general. Only after man knows the particular essence of many different things can he proceed to generalization and know the common essence of things.”

Mao Zedong book On Contradiction

On Contradiction (1937)
Original: (zh-CN) 就人类认识运动的秩序说来，总是由认识个别的和特殊的事物，逐步地扩大到认识一般的事物。人们总是首先认识了许多不同事物的特殊的本质，然后才有可能更进一步地进行概括工作，认识诸种事物的共同的本质。

“I shall endeavor to show that induction is really the inverse process of deduction.”

William Stanley Jevons (1835–1882) English economist and logician

Source: The Principles of Science: A Treatise on Logic and Scientific Method (1874) Vol. 1, p. 14

“For an induction, despite its formal generality, is always in its own value a particular judgment, always comes short of full universality; whereas, to establish the apriority of an element, we must show it to be strictly universal, or, in other words, necessary.”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), Later German Philosophy, p.176

“Both induction and deduction, reasoning from the particular and the general, and back again from the universal to the specific, form the essence to scientific thinking.”

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Hans Christian von Baeyer 25

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