On Induction (1850-1874)

"The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space." (Charles Davies, "The Logic and Utility of Mathematics", 1850)

"However logical our induction, the end of the thread is fastened upon the assurance of faith." (Edwin H Chapin, "Characters in the Gospels: Illustrating Phases of Character at the Present Day", 1852)

"Hypotheses, treated as mere poetic fancies in one age, scouted as scientific absurdities in the next - preparatory only to their being altogether forgotten - have often, when least expected, received confirmation from indirect channels, and, at length, become finally adopted as tenets, deducible from the sober exercise of induction." (Michael Faraday, "The Subject Matter of a Course of Six Lectures on the Non-Metallic Elements", 1853)

"The principle of deduction is, that things which agree with the same thing agree with one another. The principle of induction is, that in the same circumstances and in the same substances, from the same causes the same effects will follow. The mathematical and metaphysical sciences are founded on deduction; the physical sciences rest on induction." (William Fleming, "A vocabulary of the philosophical sciences", 1857)

"The distinction of Fact and Theory is only relative. Events and phenomena, considered as particulars which may be colligated by Induction, are Facts; considered as generalities already obtained by colligation of other Facts, they are Theories." (William Whewell, "The Philosophy of the Inductive Sciences: Founded Upon Their History" Vol. 2, 1858)

"It is possible to express the laws of thermodynamics in the form of independent principles, deduced by induction from the facts of observation and experiment, without reference to any hypothesis as to the occult molecular operations with which the sensible phenomena may be conceived to be connected; and that course will be followed in the body of the present treatise. But, in giving a brief historical sketch of the progress of thermodynamics, the progress of the hypothesis of thermic molecular motions cannot be wholly separated from that of the purely inductive theory." (William J M Rankine, "A Manual of the Steam Engine and Other Prime Movers", 1859)

"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)

"Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain." (James J Sylvester, "A Plea for the Mathematician", Nature Vol. 1, 1870)

"[Mathematics] is that [subject] which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"The Mathematician deals with two properties of objects only, number and extension, and all the inductions he wants have been formed and finished ages ago. He is now occupied with nothing but deductions and verification." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"An inductive science of nature presupposes a science of induction, and a science of induction presupposes a science of man." (Noah Porter, "The Sciences of Nature Versus the Science of Man", 1871)

"It is difficult, however, for the mind which has once recognised the analogy between the phenomena of self-induction and those of the motion of material bodies, to abandon altogether the help of this analogy, or to admit that it is entirely superficial and misleading. The fundamental dynamical idea of matter, as capable by its motion of becoming the recipient of momentum and of energy, is so interwoven with our forms of thought that, when ever we catch a glimpse of it in any part of nature, we feel that a path is before us leading, sooner or later, to the complete understanding of the subject." (James C Maxwell, "A Treatise on Electricity and Magnetism" Vol. II, 1873)

"Experience gives us the materials of knowledge: induction digests those materials, and yields us general knowledge." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them on the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge, - knowledge mingled with ignorance, producing doubt." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"Mathematics is a science of Observation, dealing with reals, precisely as all other sciences deal with reals. It would be easy to show that its Method is the same: that, like other sciences, having observed or discovered properties, which it classifies, generalises, co-ordinates and subordinates, it proceeds to extend discoveries by means of Hypothesis, Induction, Experiment and Deduction." (George H Lewes, "Problems of Life and Mind: The Method of Science and its Application", 1874)

"By induction we gain no certain knowledge; but by observation, and the inverse use of deductive reasoning, we estimate the probability that an event which has occurred was preceded by conditions of specified character, or that such conditions will be followed by the event. [...] I have no objection to use the words cause and causation, provided they are never allowed to lead us to imagine that our knowledge of nature can attain to certainty. [...] We can never recur too often to the truth that our knowledge of the laws and future events of the external world are only probable." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"Our ultimate object in induction must be to obtain the complete relation between the conditions and the effect, but this relation will generally be so complex that we can only attack it in detail." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)