Jevons' 1874 book The Principles of Science: a Treatise on logic and Scientific Method criticized the Baconian method of induction as the source of new scientific ideas, instead claiming that random hypotheses are the source of novel creative new ideas.

In his 1880 Atlantic Monthly, essay, William James credits Jevons with the idea that new ideas come to us randomly.

To Professor Jevons is due the great credit of having emphatically pointed out how the genius of discovery depends altogether on the number of these random notions and guesses which visit the investigator's mind. To be fertile in hypotheses is the first requisite, and to be willing to throw them away the moment experience contradicts them is the next. The Baconian method of collating tables of instance may be a useful aid at certain times. But one might as well expect a chemist's note-book to write down the name of the body analyzed, or a weather table to sum itself up into a prediction of probabilities of its own accord, as to hope that the mere fact of mental confrontation with a certain series of facts will be sufficient to make any brain conceive their law. The conceiving of the law is a spontaneous variation in the strictest sense of the term. It flashes out of one brain, and no other, because the instability of that brain is such as to tip and upset itself in just that particular direction. But the important thing to notice is that the good flashes and the bad flashes, the triumphant hypotheses and the absurd conceits, are on an exact equality in respect of their origin. Aristotle's absurd Physics and his immortal Logic flow from one source: the forces that produce the one produce the other.

("Great Men, Great Thoughts, and the Environment," Atlantic Monthly, vol. 46, October, 1880 pp.456-7)

Almost the greatest difficulty in this subject consists in acquiring a precise notion of the matter treated. What is it that we number, and measure, and calculate in the theory of probabilities? Is it belief, or opinion, or doubt, or knowledge, or chance, or necessity, or want of art?

Does probability exist in the things which are probable, or in the mind which regards them as such? The etymology of the name lends us no assistance: for, curiously enough, probable is ultimately the same word as provable, a good instance of one word becoming differentiated to two opposite meanings.

Chance cannot be the subject of the theory, because there is really no such thing as chance, regarded as producing and governing events. This name signifies falling, and the notion is continually used as a simile to express uncertainty, because we can seldom predict how a die, or a coin, or a leaf will fall, or when a bullet will hit the mark. But every one knows, on a little reflection, that it is in our knowledge the deficiency lies, not in the certainty of nature's laws. There is no doubt in lightning as to the point it shall strike; in the greatest storm there is nothing capricious; not a grain of sand lies upon the beach, but infinite knowledge would account for its lying there; and the course of every falling leaf is guided by the same principles of mechanics as rule the motions of the heavenly bodies.

Chance then exists not in nature, and cannot co-exist with knowledge; it is merely an expression for our ignorance of the causes in action, and our consequent inability to predict the result, or to bring it about infallibly. In nature the happening of a physical event has been pre-determined from the first fashioning of the universe. Probability belongs wholly to the mind; this indeed is proved by the fact that different minds may regard the very same event at the same time with totally different degrees of probability.

(The Principles of Science, Vol. I, Chapter X, Theory of Probability, pp.224-225)

Nevertheless, Jevons is unequivocal that scientists have a freedom to hypothesize. In a section entitled Freedom of Theorizing,, which reminds us of the Free Will Axiom, he declares

It would be a complete error to suppose that the great discoverer is one who seizes at once unerringly upon the truth, or has any special method of divining it. In all probability the errors of the great mind far exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must almost of necessity be many times as numerous as those which prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record may remain of more than the hundredth part. There is nothing intrinsically absurd except that which proves contrary to logic and experience. The truest theories involve suppositions which are most inconceivable, and no limit can really be placed to the freedom of framing hypotheses.

In the preface to The Principles of Science, Jevons deprecates Baconian induction in favor of a combination of hypotheses and deduction, with experimental testing the main criterion for accepting the ideas as new knowlege.

In following out my design of detecting the general methods of inductive investigation, I have found that the more elaborate and interesting processes of quantitative induction have their necessary foundation in the simpler science of Formal Logic. The earlier, and probably by far the least attractive part of this work, consists, therefore, in a statement of the so-called Fundamental Laws of Thought, and of the all-important Principle of Substitution, of which, as I think, all reasoning is a development. The whole procedure of inductive inquiry, in its most complex cases, is foreshadowed in the combinational view of Logic, which arises directly from these fundamental principles. Incidentally I have described the mechanical arrangements by which the use of the important form called the Logical Abecedarium, and the whole working of the combinational system of Formal Logic, may be rendered evident to the eye, and easy to the mind and hand.

The study both of Formal Logic and of the Theory of Probabilities, has led me to adopt the opinion that there is no such thing as a distinct method of induction as contrasted with deduction, but that induction is simply an inverse employment of deduction. Within the last century, a reaction has been setting in against the purely empirical procedure of Francis Bacon, and physicists have learnt to advocate the use of hypotheses. I take the extreme view of holding that Francis Bacon, although he correctly insisted upon constant reference to experience, had no correct notions as to the logical method by which, from particular facts, we educe laws of nature. I endeavour to show that hypothetical anticipation of nature is an essential part of inductive inquiry, and that it is the Newtonian method of deductive reasoning combined with elaborate experimental verification, which has led to all great triumphs of scientific research.

In attempting to give an explanation of this view of Scientific Method, I have first to show that the sciences of number and quantity repose upon and spring from the simpler and more general science of Logic. The Theory of Probability, which enables us to estimate and calculate quantities of knowledge, is then described, and especial attention is drawn to the Inverse Method of Probabilities, which involves, as I conceive, the true principle of inductive procedure. No inductive conclusions are more than probable, and I adopt the opinion that the theory of probability is an essential part of logical method, so that the logical value of every inductive result must be determined consciously or unconsciously, according to the principles of the inverse method of probability.

(The Principles of Science, pp.vi,vii)

Haying once deliberately chosen, the philosopher may rightly entertain his theory with the strongest love and fidelity. He will neglect no objection; for he may chance at any time to meet a fatal one; but he will bear in mind tbe inconsiderable powers of the human mind compared the tasks it has to undertake. He will see that no theory can at first be reconciled with all possible objections simply because there may be many interfering causes, or the very consequences of the theory may have a complexity which prolonged investigation by successive generations of men may not exhaust. If then, a theory exhibit a number of very striking coincidences with fact, it must not be thrown aside until at least one conclusive discordance is proved, regard being had to possible error in establishing that discordance. In science and philosophy something must be risked. He who quails at the least will never establish a new truth.

(The Principles of Science, pp.233-34)

Charles Sanders Peirce was greatly influenced by Jevons, visiting him on one of his U.S.-Coast-Survey-sponsored trips to Europe around the time (mis-1870's) Jevons published Principles of Science. Peirce called hypothesis formation "abduction," in his logical triad abduction-induction-deduction.