# Jevons, William Stanley (1835–1882)

# JEVONS, WILLIAM STANLEY

*(1835–1882)*

The British economist and logician William Stanley Jevons was the son of Thomas Jevons, a Liverpool iron merchant, and Mary Anne Roscoe, a lady of some literary note. After early schooling at Liverpool, he attended University College School and University College, London, where he sat under Augustus De Morgan. In 1854 he left London to take up the post of assayer at the mint in Sydney, Australia, but returned five years later to complete his studies. Soon after, in 1863, he secured a junior teaching position at Owens College, Manchester. By this time he had already published various minor papers on meteorology and economics, a statistical study of commercial fluctuations, and a small work, titled *Pure Logic* (London, 1864, reprinted 1890), reflecting the influence of George Boole. His book on *The Coal Question* (London, 1865) attracted the attention of William Gladstone and was the first to make him known as an economist. In 1866 he was appointed professor of logic and political economy at Manchester, and in the following year married Harriet Taylor, daughter of the proprietor of the *Manchester Guardian*.

Jevons was a conscientious lecturer, but he neither enjoyed nor excelled at the work; and his laborious habits of study led to recurrent breakdowns of health, which had to be repaired by Continental travel, generally to Norway. In spite of this, he wrote prolifically, publishing *The Substitution of Similars* (London, 1869, reprinted 1890); *Elementary Lessons in Logic* (London, 1870), a widely used textbook introductory to J. S. Mill; and *The Principles of Science* (London, 1874; 2nd ed., 1877), his most important contribution to scientific methodology, containing, among much else, an account of his celebrated logical machine. *The Theory of Political Economy* (London, 1871; 2nd ed., 1879) was an equally important landmark in the development of mathematical economics and the theory of utility, followed soon after by a no less influential work of applied analysis and description, *Money and the Mechanism of Exchange* (London, 1875). The once-famous speculations on the relation of sunspot cycles to financial crises, posthumously published in *Investigations in Currency and Finance* (London, 1884), exhibit, more curiously, the range of his interests and the originality of his mind.

Wearying of his duties, Jevons resigned his chair at Manchester in 1876 to take up a similar but more congenial post as professor of political economy at University College, London. This he also resigned, however, in 1880. The main works of this later period were *Studies and Exercises in Deductive Logic* (London, 1880) and *The State in Relation to Labour* (London, 1882). In 1882 he accidentally drowned, probably as the result of a heart attack, while bathing off the coast of Kent. His *Letters and Journal*, edited by his wife (London, 1886), gives an interesting portrait of him. His last work, *The Principles of Economics*, appeared, unfinished, in 1905.

## Logic

Although marked by no special distinction of style, the writings of Jevons are still worth reading, both for their logical penetration and for their wealth of factual information drawn from many sources of knowledge. His logic owes something to De Morgan and a good deal more to Boole. It represents in the main an attempt to simplify Boole's system by eliminating the more complex and uninterpretable of its mathematical operations and by reducing its procedures of calculation to a mechanical routine. Jevons's own claim to independence in developing his logic as a calculus of qualities, rather than of classes or propositions, is of no great significance; and his method of treating propositions as identities and inferring from them by substitution, though simple enough in its way, is too lacking in subtlety to have become the "logic of the future" that he once hoped it would be. The most successful of his reforms of the Boolean algebra have been the removal of its inverse operations of subtraction and division and the proposal to read the disjunctive symbol ("either … or") as including the possibility "both"—a practice now universal and resisted at the time only by the conservative John Venn.

Jevons's most interesting adaptation of Boole is to be seen in his method of indirect inference—the principle underlying his "logical piano" and other mechanical aids to calculation—whereby premises are used to eliminate inconsistent combinations of terms from a matrix listing all the possibilities under which a given set of terms and their negatives can be associated. The machine itself, exhibited at the Royal Society in 1870 and described in the *Philosophical Transactions* for the same year, anticipates in its design a number of the features of modern logical computers, while its mode of operation has some fairly obvious affinities with the use of a truth table, though it can hardly be said that Jevons had much grasp of its applications in that respect.

## Induction

The logical machine gave its answers only by displaying the combinations compatible with the information fed to it, leaving to the operator the task of finding a compendious formula to express them. The difficulties of this "inverse process" resist mechanical solution and are comparable, in Jevons's view, to those of induction, which he represents accordingly as the inverse operation of deduction—the problem, that is, of deciphering from a given set of phenomena the hidden laws they obey. The treatment of this problem in *The Principles of Science* is in line with the work of William Whewell and De Morgan and in somewhat embittered opposition to the views of Francis Bacon and Mill. Jevons, in short, is an apostle of the hypothetico-deductive method in science, although, unlike Whewell at least, he does not believe it to be a demonstrative procedure or capable of extending knowledge beyond the range of present or past observation. We are necessarily ignorant of the long-term behavior of the universe at large, and when to this ignorance are added the inevitable deficiencies of observation and measurement, it is evident that inductive conclusions can never be more than probable.

## Probability

Jevons was led by the above considerations to give detailed attention to the theories of measurement, approximation, and error and also to bring the whole conception of inductive inference into closer association with the theory of probabilities than was usual with the writers who preceded him. Probability he holds, with De Morgan, to be essentially subjective, though it is a measure of appropriate, rather than of mere actual, belief. It determines "rational expectation, by measuring the comparative amounts of knowledge and ignorance," as represented by the evidence available. That evidence, as nature presents it in the inductive situation, consists of sets of phenomena in combination. Having previously ascertained them (and presumably selected them, somehow, for relevance), we proceed, by more or less intuitive methods (of which Jevons gives no satisfactory account), to erect a hypothesis to explain them. From this in turn we deduce the direct probability of various sets of possible consequences. We then compare these supposed consequences with the known facts in order to determine the probability of their having occurred under the hypothesis in question. This process being repeated for every conceivable hypothesis, we are thereby in a position to assign a probability to each of them by use of the inversion theorem derived, via De Morgan, from Pierre Simon de Laplace. There is no guarantee that by this method the right answers will be forthcoming; but it justifies the adoption of the most probable hypothesis as a matter of practical policy, and that is the best we can expect.

The mathematical theory of inverse probability is, unfortunately, not equal to the weight that Jevons here put upon it, and his conclusions are accordingly unsound. There is no means of knowing that the a priori probabilities of the rival hypotheses are equal, as the theory requires; and there is still less warrant for its extension, by the "rule of succession," to the prediction of new instances or for the employment, where ignorance is total, of the "principle of indifference" to confer a probability of ½ on a proposition merely because knowledge of its truth or falsity is the same (namely, nil) in either case. The fallacies that Jevons committed under this head have since become notorious; the measurement of ignorance is less simple—and nature less like a ballot box—than he was apt to suppose. Errors of conception apart, however, his general view of scientific method has in recent years met with increasing support and is probably his most enduring legacy to the history of thought.

** See also ** Bacon, Francis; Boole, George; De Morgan, Augustus; Induction; Logic, History of; Logic Machines; Mill, John Stuart; Probability and Chance; Venn, John; Whewell, William.

## Bibliography

Jevons had no commentators. For a discussion of his logic, see references in the bibliography to the Logic, History of, entry. There is an early criticism of his theory of induction in Thomas Fowler, *Elements of Inductive Logic*, 3rd ed. (London: Clarendon Press, 1876), and scattered remarks of value occur in such general treatises as J. M. Keynes, *A Treatise of Probability* (London, 1921); William Kneale, *Probability and Induction* (Oxford: Clarendon Press, 1949); and G. H. von Wright, *The Logical Problem of Induction*, 2nd ed. (Oxford, 1949), and *A Treatise on Induction and Probability* (London: Routledge and Paul, 1951). See also the brief sketch in J. A. Passmore, *A Hundred Years of Philosophy* (London: Duckworth, 1957), pp. 132–136.

*P. L. Heath (1967)*

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