"Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it." (Eudoxus, cca. 4th century BC)
"Every stage of science has its train of practical applications and systematic inferences, arising both from the demands of convenience and curiosity, and from the pleasure which, as we have already said, ingenious and active-minded men feel in exercising the process of deduction."
"There is in every step of an arithmetical or algebraical calculation a real induction, a real inference from facts to facts, and what disguises the induction is simply its comprehensive nature, and the consequent extreme generality of its language." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)
"A mere inference or theory must give way to a truth revealed; but a scientific truth must be maintained, however contradictory it may appear to the most cherished doctrines of religion." (David Brewster, "More Worlds Than One: The Creed of the Philosopher and the Hope of the Christian", 1856)
"Truths are known to us in two ways: some are known directly, and of themselves; some through the medium of other truths. The former are the subject of Intuition, or Consciousness; the latter, of Inference; the latter of Inference. The truths known by Intuition are the original premises, from which all others are inferred." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1858)
"And first, it is necessary to distinguish from true inductions, certain operations which are often improperly called by that name. A true induction is a process of inference - it proceeds from the known to the unknown; and whenever any operation contains no inference, it is not really an induction. And yet most of the examples given in the common works on logic, as examples of induction, are of this character." (George R Drysdale, "Logic and Utility: The tests of truth and falsehood, and of right and wrong", 1866)
"It must be the ground of all reasoning and inference that what is true of one thing will be true of its equivalent, and that under carefully ascertained conditions Nature repeats herself." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)
"Economic science is but the working of common sense aided by appliances of organized analysis and general reasoning, which facilitate the task of collecting, arranging, and drawing inferences from particular facts. Though its scope is always limited, though its work without the aid of common sense is vain, yet it enables common sense to go further in difficult problems than would otherwise be possible." (Alfred Marshall, "Principles of Economics", 1890)
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