A recent digest featured an intriguing note: AI assistants have made writing code cheaper—and there are now more programmers in the industry. The effect was called the Jevons paradox, after the 19th-century economist who showed in his 1865 book on coal that any increase in the efficiency of using a resource does not save it, but increases consumption. Coal-fired steam engines burned coal ever more efficiently—and England burned more of it than ever before.
Today, William Stanley Jevons is remembered mostly for this formula. Yet Jevons himself, when he was not counting coal or proving that machines devour raw materials, managed something far stranger: he built a mechanical piano that solved syllogisms. Not calculated, but actually solved—drew logical conclusions from given premises, clicking its levers behind a wooden panel. It was one of the first machines in history built not for calculation, but for thought.
It stood there, worked, and was exhibited during its inventor’s lifetime—and almost nobody remembers it. What people do remember are the questions it revolved around: can a machine reason, and if it can, what does that say about us? Not long ago, there was a story here about Babbage’s Analytical Engine, which was never assembled in metal. With Jevons’s machine, it was the opposite: the metal existed, the thing worked, and the idea died young.
William Stanley Jevons was born in 1835 in Liverpool, the son of an iron merchant, and in 1854, at nineteen, sailed for Sydney—to assay the gold from the mines of New South Wales. Five years in a colony that had only just struck it rich: work at the intersection of geology, chemistry, and economics; his own camera; views of Sydney and the goldfields photographed before the light faded; diaries and letters home.
Later, he said he had acquired nearly all his major ideas there—in a young city where he had income, free time, and none of Europe’s intellectual routine. He also carried Whately’s logic around Sydney and never read it; Jevons only seriously took up logic after returning to England, where he became friends with his former mathematics teacher Augustus De Morgan, and through him encountered the newly emerged symbolic logic of George Boole.
Boole turned syllogisms into equations. Jevons felt Boole’s mathematical veneer was unnecessary: logic came first, mathematics was its derivative. In 1863 he published Pure Logic (some sources give the publication date as 1864—the disagreement is minor, but stubborn)—a book that sold four copies in six months—and in 1869 formulated the principle he considered the great discovery of his life: the substitution of similars. “What is true of a thing is true of its like,” as it goes in brief. Paradoxical for a man whose name was immortalized in economics: practically everything we remember Jevons for today—coal, marginal utility, the mathematization of economic theory—came later, and separately.
But logic went its own way. In 1874, The Principles of Science appeared, in which Jevons gathered everything he believed about the scientific method. The book’s frontispiece is an engraving of a wooden cabinet with a keyboard. Jevons presented the machine as “a palpable demonstration of the universality and power” of his method.
He died in 1882, aged forty-six, drowning while swimming off the coast of Sussex. The piano outlived him.
This story began with a slate board. To find all logically possible combinations of four attributes, you have to run through sixteen combinations—“iron is a metal and an element,” “iron is a metal and not an element,” and so on—compare them against the premises, and cross out the incompatible ones. From 1863 onward, Jevons kept such a set of combinations written in chalk, then turned it into a “logical abacus”: little boards bearing combinations that moved along a rack, with the surplus shifted aside by a lever.
The method rested on an old idea of the Stoic Chrysippus about a dog at a fork in the road. Chasing a hare, the dog comes to three paths, sniffs the first, sniffs the second—and, having established that the prey went down neither, runs along the third without sniffing it. That is, it acts as though it reasons: “the hare went either there, or there, or there; not there and not there—therefore there.” The whole logic of Jevons’s machine is mechanical sniffing at forks in the road.
In 1869, he commissioned a device from a Salford clockmaker that turned this operation into a game. The craftsman’s first machine was unsuccessful; in letters, Jevons complained that he had to visit the workshop almost every day, “to see whether all I had planned was properly done,—each operation having to be performed separately.” The second machine worked, and its description sticks out of the correspondence like an absurd quotation: “in appearance it somewhat resembles a large accordion or small pianoforte, and has 21 keys, exactly like the white keys of a pianoforte.”
How it played: the user entered premises on the keyboard—“all A are B,” “everything that is A and B is either C or D”—and pressed the copula key, equality. Inside, levers and cords compared the premises with every possible combination of attributes, while the period at the end of the phrase removed from the front panel all combinations refuted by those premises. What remained on the panel was the answer: all the possibilities your premises had not disproved. The “finis” key reset everything completely.
Jevons reported to the Royal Society with engineering sobriety: “Simply by reading the premises upon the keys, the machine makes their comparison, and returns any answer which is logically deducible from them. Thus the process of logical inference is reduced to a purely mechanical form.”
The limitation was obvious: the machine could handle no more than four terms. Jevons dreamed of sixteen, but such a machine would have taken up an entire office wall. Engineering honesty: 2⁴ = 16 rows to check, 2¹⁶ = 65 536 rows—not a cabinet anymore, but furniture.
In 1870, the machine was shown to the Royal Society. Wikipedia recounts the details of the demonstration with the irritating note “citation needed”—the direct quotation from the proceedings reaches readers mostly through retellings, and this is one of those stories where the source of the firsthand testimony has nearly vanished. Still, the chronology—“1869: built, 1870: shown”—holds firm across the sources.
Contemporaries had mixed feelings about the piano. Some saw it as a precursor to computing technology; others thought the task too toy-like to speak seriously of machine reasoning.
A computer historian at the Computer History Museum notes a subtle historical irony: Jevons’s machine is connected to modern computers precisely by what they were not—calculators. Before them, the word “computer” meant a clerical worker, usually a woman, who manually calculated enormous tables for major scientific projects. Babbage and Lovelace belonged to that calculating lineage.
Jevons, by contrast, saw a broader possibility in Babbage’s work: if equations could be solved mechanically (Babbage), and syllogisms translated into equations (Boole), then reasoning itself could be entrusted to a mechanism. A machine that took on judgments rather than arithmetic was, in its own way, bolder.
What happened to the apparatus afterward: it survives to this day. The original machine now stands in Oxford’s Museum of the History of Science, and in 2004–2006 it was displayed in Sydney’s Powerhouse Museum—at an exhibition devoted to Jevons’s life and work. The circle closed with almost cinematic neatness: the man who arrived in Sydney as a nineteen-year-old assayer in 1854 returned there with his piano exactly a century and a half later. In the neighboring display case, the Powerhouse kept a fragment of Babbage’s Difference Engine—two specimens of computing prehistory placed side by side.
Jevons’s incursion into logic would have remained a British curiosity if, across the ocean, there had not been a man who decided the piano could be improved. In the 1881–1882 academic year, Princeton logic instructor Allan Marquand built his own logical machine. Its case was made from red cedar from Princeton’s oldest estate; its dimensions were about 30×20×15 centimeters; inside were rods, levers, gut strings, coil springs, and—a brilliant touch—an electric annunciator of the kind used in hotels: little tabs opened in sequence and displayed the remaining permissible combinations.
Marquand’s machine was more compact and more sophisticated than Jevons’s, portable, with input and output controlled by separate switches. It still exists—kept at Princeton’s Firestone Library. Marquand published a description in 1886 under the title “A New Logical Machine.”
Marquand’s personal trajectory is more curious than his machine. The son of Henry Gurdon Marquand—a millionaire and art collector, the second president of the Metropolitan Museum of Art—he passed through theological seminary, received a PhD from Johns Hopkins in 1880 under Charles Sanders Peirce (his dissertation concerned the logic of the ancient philosopher Philodemus), and returned to Princeton to teach logic.
Then something happened that today would be called institutional vandalism. Princeton president James McCosh, having acquainted himself with the mathematical bent of Marquand’s course, declared it “unorthodox and un-Calvinistic.” In 1883, Marquand was apparently transferred gently: he was offered the first chair of art history in America. He accepted, founded the department of art and archaeology, and directed the university museum until his retirement in 1922. The man who built a machine for logical inference spent the rest of his career explaining the Italian Renaissance to students: at 19th-century Princeton, algebraic logic was deemed more dangerous than painting.
Marquand’s machine had a second author who had not yet laid hands on it. Charles Sanders Peirce—one of the century’s greatest logicians, who taught logic at Johns Hopkins from 1879 to 1884. In 1880, he showed that all of Boolean algebra could be expressed through a single binary operation—“and-not,” or its dual counterpart.
Marquand’s mechanical machine was received with disappointment, and Peirce set about reviving it. In an 1886 letter, he proposed electricity to his student—and that proposal is considered the first step toward electrical logical machines. The chronology diverges among sources here: some call 1886 the year of the first electrical logical machine, others the year of the letter, while Marquand published a detailed drawing in 1887, inventing his own graphic notation for it in the process, “Marquand diagrams.”
After 1886, Marquand wrote no more about logical machines—but Peirce published an article, “Logical Machines,” in the American Journal of Psychology in 1887 and discussed the subject for almost another twenty years, until 1906. Marquand’s archive preserves a diagram of an electromagnetic machine from around 1890: sixteen electromagnetic elements, each with five coils, an armature with an air gap, and a spring holding the armature in its de-energized position. The work cycle looks astonishingly familiar: the operator resets the machine with a switch, enters the first premise using program keys, activates it, the machine stores the state, the second premise is entered—and the armature indicators reveal which combinations still agree with both.
In effect, it is sequential rule loading and register reading. Historians wonder whether Peirce devised the entire electromagnetic design himself: by then, his student had moved on from the subject.
There were other varieties of the same obsession. John Venn, author of the diagrams familiar to every schoolchild, sketched a design in his 1894 Symbolic Logic for a logical machine handling four types of premises after the model of Jevons’s—and it remains unclear whether anyone ever built it. By the mid-1890s, the wave had passed: the machines of Jevons, Marquand, and Venn remained cabinet curiosities, while logic moved into algebraic calculi, where the 20th century would raise it. Wikipedia calls mechanical logical machines an early branch from which 20th-century proof assistants—programs that verify proofs—and an entire field of mathematical knowledge management grew. The tree died, the root took hold.
Here comes the unexpected turn: these machines solved the Entscheidungsproblem—the “decision problem,” formulated by David Hilbert and Wilhelm Ackermann in 1928. The problem sounds almost word for word like Jevons’s report to the Royal Society: given a formal statement, an algorithm must answer “yes” or “no”—is it universally valid, is it derivable from the rules of logic? Yet the idea is two and a half centuries older: after building a mechanical calculating device, Gottfried Leibniz dreamed of a machine that would manipulate symbols and pass judgment on truth. The Victorians simply assembled Leibniz’s dream from wood and cords for the first time—within the limits of four terms.
In 1936, Alonzo Church and Alan Turing independently proved that no general solution to the Entscheidungsproblem exists in principle. Turing proved it by presenting an abstract machine that has borne his name ever since. So history answered “no” to the question “can a machine solve any logical problem”—but only seventy years later, and only in a precise formulation Jevons never had.
And the question “can a machine reason?” still hangs in the air, while the wording of the dispute has changed remarkably little since the 1870s. The Computer History Museum puts it bluntly: arguments about whether a machine can reason have always really been about something else—what it means for a human being to reason at all. Victorians objected that crossing out rows on a wooden panel was too primitive a game to be called thought. Today’s arguments over whether statistically predicted text continuation counts as understanding sound in the same register; only the term has changed.
The Jevons paradox spread as a law of the market: burn more efficiently—and you will burn more. His piano tested the same logic on the mind. The machine made inference cheaper within the bounds of four terms—and there were no more philosophers; what increased was the confidence that inference could be entrusted to mechanism, while calculating work disappeared into machines so thoroughly that it ceased to be visible at all.
The question Jevons asked turned out not to be about a piano. It was about what we are prepared to count as mind—and how much work we are willing to give away in exchange for freedom from exhaustive checking. The machine stands under glass in Oxford; the fork in the road where Chrysippus’s dog sniffs the paths has not gone anywhere—only now, others know how to sniff it.