Inductive reasoning

"Induction... is a process of inference; it proceeds from the known to the unknown; and any operation involving no inference, any process in which what seems the conclusion is no wider than the premises from which it is drawn, does not fall within the meaning of the term. ...A general proposition is one in which the predicate is affirmed or denied of an unlimited number of individuals; namely, all, whether few or many, existing or capable of existing, which possess the properties connoted by the subject of the proposition."

"Counter-induction is... both a fact—science could not exist without it—and a legitimate and much needed move in the game of science."

"If there really be an instance of inductive reasoning not expressible in Syllogism, why is it that some form of words conveying such reasoning has not been propounded?"

"Inductive reasoning is reasoning from particular facts to a general law, or proposition, called the conclusion. Inductive reasoning is synthetic; that is, it builds up the law (the proposition) by giving particular instances in which that law is true. It is by inductive reasoning that we have established most of our laws in the natural sciences. We have proved the proposition, Wild geese fly south in winter, by inductive reasoning, for we have noted particular instances, and from the particular facts we have reasoned to the proposition."

"The distinction between deductive and inductive reasoning is thus: In deductive reasoning the process is from the whole to the parts; in inductive reasoning, on the other hand, the process is from the parts to the whole."

"Inductive reasoning in mathematics is more closely related to deduction and the conclusions more certain than in the natural sciences, for the concepts in mathematics are not gained directly from observation (e.g., square, right angle, circle), but are made by putting together in the definition certain simple characteristics that are already known, while in the natural sciences the essential characteristics of any class of things are determined by observation and experiment, and may be changed at any time by examination of other specimens."

"The mistake frequently committed... has its origin in the vague and erroneous definition usually given of the inductive process... the method of induction... is indeed the only process of reasoning whereby it is possible to pass, at will, and in a given direction, beyond the boundaries of our knowledge."

"Although... there is not yet extant a body of Inductive Logic, scientifically constructed; the materials for its construction exist, widely scattered, but abundant: and the selection and arrangement of those materials is a task with which intellects of the highest order, possessed of the necessary acquirements, have at length consented to occupy themselves. Within a few years three writers, profoundly versed in every branch of physical science, and not unaccustomed to carry their speculations into still higher regions of knowledge, have made attempts, of unequal but all of very great merit, towards the creation of a Philosophy of Induction: Sir John Herschel, in his [A Preliminary] Discourse on the Study of Natural Philosophy; Mr. Whewell, in his History and Philosophy of the Inductive Sciences; and, greatest of all, M. Auguste Comte, in his Cours de Philosophic Positive, a work which only requires to be better known, to place its author in the very highest class of European thinkers. That the present writer does not consider any of these philosophers, or even all of them together, to have entirely accomplished this important work, is implied in his attempting to contribute something further towards its achievement..."

"Induction may be defined the operation of discovering and proving general propositions."

"The examples of plausible reasoning collected in this book... may throw light upon a much agitated philosophical problem: the problem of induction. The crucial question is: Are there rules for induction? ...the question should be... treated... in closer touch with the practice of scientists. ...older writers, such as Euler and Laplace, clearly perceived... that the role of inductive evidence in mathematical investigation is similar to its role in physical research. ...so the door opens to investigating induction inductively."

"The first and second editions of the "System of Logic" contained a passage which purported to controvert the views of Archbishop Whately respecting Inductive Syllogism. In the third edition the most controversial portions of this passage are omitted, and additions are made, which materially modify the result. But it is still implied, that "Archbishop Whatelys must be held to be the correct account" of no more than "the immediate major-premise in every inductive argument;" and it is still maintained, that "if we throw the whole course of any inductive argument into a series of syllogisms, we shall arrive, by more or fewer steps, at an ultimate syllogism, which will have for its major-premiss the principle, or axiom, of the uniformity of the course of nature;" which principle or axiom is regarded by Mr. Mill as known to us only by "induction."

"My intention is not to replace one set of general rules by another such set: my intention is, rather, to convince the reader that all methodologies, even the most obvious ones, have their limits. The best way to show this is to demonstrate the limits and even the irrationality of some rules which she, or he, is likely to regard as basic. In the case of induction (including induction by falsification) this means demonstrating how well the counterinductive procedure can be supported by argument."