Logic piano

Jevons' work in logic went on pari passu with his work in political economy. In 1864 he published a small volume, entitled Pure Logic; or, the Logic of Quality apart from Quantity, which was based on Boole's system of logic, but freed from what he considered the false mathematical dress of that system. In the years immediately following he devoted considerable attention to the construction of a logical machine, exhibited before the Royal Society in 1870, by means of which the conclusion derivable from any given set of premisses could be mechanically obtained. In 1866 what he regarded as the great and universal principle of all reasoning dawned upon him; and in 1869 he published a sketch of this fundamental doctrine under the title of The Substitution of Similars. He expressed the principle in its simplest form as follows: "Whatever is true of a thing is true of its like," and he worked out in detail its various applications including the "Logic Piano", a mechanical computer he designed and had built in 1869.

In the following year appeared the Elementary Lessons on Logic, which soon became the most widely read elementary textbook on logic in the English language. In the meantime he was engaged upon a much more important logical treatise, which appeared in 1874 under the title of The Principles of Science. In this work Jevons embodied the substance of his earlier works on pure logic and the substitution of similars; he also enunciated and developed the view that induction is simply an inverse employment of deduction; he treated in a luminous manner the general theory of probability, and the relation between probability and induction; and his knowledge of the various natural sciences enabled him throughout to relieve the abstract character of logical doctrine by concrete scientific illustrations, often worked out in great detail. An example is his discussion of the use of one-way functions in cryptography, including remarks on the integer factorization problem that foreshadowed its use in public key cryptography. Jevons' general theory of induction was a revival of the theory laid down by Whewell and criticized by John Stuart Mill; but it was put in a new form, and was free from some of the non-essential adjuncts which rendered Whewell's exposition open to attack. The work as a whole was one of the most notable contributions to logical doctrine that appeared in the UK in the 19th century. His Studies in Deductive Logic, consisting mainly of exercises and problems for the use of students, was published in 1880. In 1877 and the following years Jevons contributed to the Contemporary Review some articles on Mill, which he had intended to supplement by further articles, and eventually publish in a volume as a criticism of Mill's philosophy. These articles and one other were republished after Jevons' death, together with his earlier logical treatises, in a volume, entitled Pure Logic, and other Minor Works. The criticisms on Mill contain much that is ingenious and much that is forcible, but on the whole they cannot be regarded as taking rank with Jevons's other work. His strength lay in his power as an original thinker rather than as a critic; and he will be remembered by his constructive work as logician, economist and statistician.

On Jevons as logician, see Grattan-Guinness (2000).

Number Theory

Jevons had written in his Principles of Science, p. 123, "Can the reader say what two numbers multiplied together will produce the number 8616460799 ? I think it unlikely that anyone but myself will ever know." This became known as Jevons' Number and was factored by Derrick Norman Lehmer in 1903[9] and later on a pocket calculator by Solomon W. Golomb.

(source:wikipedia)