On the Mechanical Performance of Logical Inference, §§ 1–8 Mechanical Assistance in Mental Operations: Jevons on the Logic Machine William Stanley Jevons (1835–1882) read 20 January 1870 Cold Library · Open Stacks · S-007208 · https://coldlibrary.com/s/007208 Rights: Published in 1870; Jevons died in 1882. Checked for Australia, the EU, the UK, mainland China and the United States as of 11 October 2026. Guidance, not legal advice. Source: Internet Archive, philtrans01714956 (Phil. Trans. R. Soc. 160, 1870), https://archive.org/details/philtrans01714956 (retrieved 2026-10-11) Generated 2026-10-14 from https://coldlibrary.com/en/open-stacks/jevons-mechanical-assistance-in-mental-operations ---- 1. It is an interesting subject for reflection that from the earliest times mechanical assistance has been required in mental operations. The word calculation at once reminds us of the employment of pebbles for marking units, and it is asserted that the word ἀριθμός is also derived from the like notion of a pebble or material sign. Even in the time of Aristotle the wide extension of the decimal system of numeration had been remarked and referred to the use of the fingers in reckoning; and there can be no doubt that the form of the most available arithmetical instrument, the human hand, has reacted upon the mind and moulded our numerical system into a form which we should not otherwise have selected as the best. 2. From early times, too, distinct mechanical instruments were devised to facilitate computation. The Greeks and Romans habitually employed the abacus or arithmetical board, consisting, in its most convenient form, of an oblong frame with a series of cross wires, each bearing ten sliding beads. The abacus thus supplied, as it were, an unlimited series of fingers, which furnished marks for successive higher units and allowed of the representation of any number. The Russians employ the abacus at the present day under the name of the shtshob, and the Chinese have from time immemorial made use of an almost exactly similar instrument called the schwanpan. 3. The introduction into Europe of the Arabic system of numeration caused the abacus to be generally superseded by a far more convenient system of written signs; but mathematicians are well aware that their science, however much it may advance, always requires a corresponding development of material symbols for relieving the memory and guiding the thoughts. Almost every step accomplished in the progress of the arts and sciences has produced some mechanical device for facilitating calculation or representing its result. I may mention astronomical clocks, mechanical globes, planetariums, slide rules, &c. The ingenious rods known as Napier's Bones, from the name of their inventor, or the Promptuarium Multiplicationis of the same celebrated mathematician, are curious examples of the tendency to the use of material instruments. 4. As early as the 17th century we find that machinery was made to perform actual arithmetical calculation. The arithmetical machine of Pascal was constructed in the years 1642-45, and was an invention worthy of that great genius. Into the peculiarities of the machines subsequently proposed or constructed by the Marquis of Worcester, Sir Samuel Morland, Leibnitz, Gersten, Scheutz, Donkin, and others we need not inquire; but it is worthy of notice that M. Thomas, of Colmar, has recently manufactured an arithmetical machine so perfect in construction and so moderate in cost, that it is frequently employed with profit in mercantile, engineering, and other calculations. 5. It was reserved for the profound genius of Mr. Babbage to make the greatest advance in mechanical calculation, by embodying in a machine the principles of the calculus of differences. Automatic machinery thus became capable of computing the most complicated mathematical tables; and in his subsequent design for an Analytical Engine Mr. Babbage has shown that material machinery is capable, in theory at least, of rivalling the labours of the most practised mathematicians in all branches of their science. Mind thus seems able to impress some of its highest attributes upon matter, and to create its own rival in the wheels and levers of an insensible machine. 6. It is highly remarkable that when we turn to the kindred science of logic we meet with no real mechanical aids or devices. Logical works abound, it is true, with metaphorical expressions implying a consciousness that our reasoning powers require such assistance, even in the most abstract operations of thought. In or before the 15th century the logical works of the greatest logician came to be commonly known as the Organon or Instrument, and, for several centuries, logic itself was defined as Ars instrumentalis dirigens mentem nostram in cognitionem omnium intelligibilium. When Francis Bacon exposed the futility of the ancient deductive logic, he still held that the mind is helpless without some mechanical rule, and in the second aphorism of his 'New Instrument' he thus strikingly asserts the need:— > Nec manus nuda, nec Intellectus sibi permissus, multum valet; Instrumentis et auxiliis res perficitur; quibus opus est, non minus ad intellectum, quam ad manum. Atque ut instrumenta manus motum aut cient, aut regunt; ita et Instrumenta mentis, Intellectui aut suggerunt aut cavent. 7. In all such expressions, however, the word Instrument is used metaphorically to denote an invariable formula or rule of words, or system of procedure. Even when Raymond Lully put forth his futile scheme of a mechanical syllogistic, the mechanical apparatus consisted of nothing but written diagrams. It is rarely indeed that any invention is made without some anticipation being sooner or later discovered; but up to the present time I am totally unaware of even a single previous attempt to devise or construct a machine which should perform the operations of logical inference; and it is only I believe in the satirical writings of Swift that an allusion to an actual reasoning machine is to be found. 8. The only reason which I can assign for this complete inability of logicians to devise a real logical instrument, is the great imperfection of the doctrines which they entertained. Until the present century logic has remained substantially as it was moulded by Aristotle 2200 years ago. Had the science of quantity thus remained stationary since the days of Pythagoras or Euclid, it is certain that we should not have heard of the arithmetical machine of Pascal, or the difference-engine of Babbage. And I venture to look upon the logical machine which I am about to describe as equally a result and indication of a profound reform and extension of logical science accomplished within the present century by a series of English writers, of whom I may specially name Jeremy Bentham, George Bentham, Professor De Morgan, Archbishop Thomson, Sir W. Hamilton, and the late distinguished Fellow of the Royal Society, Dr. Boole. The result of their exertions has been to effect a breach in the supremacy of the Aristotelian logic, and to furnish us, as I shall hope to show by visible proof, with a system of logical deduction almost infinitely more general and powerful than anything to be found in the old writers. The ancient syllogism was incapable of mechanical performance because of its extreme incompleteness and crudeness, and it is only when we found our system upon the fundamental laws of thought themselves that we arrive at a system of deduction which can be embodied in a machine acting by simple and uniform movements.