x + x = x, and reduced reasoning to a mechanical method of elimination over a "logical alphabet" of every possible combination of terms. Then he did the thing no one had done: he built a machine to run it. The Logic Piano (1866) — a wooden device with a keyboard — takes in premises and, by knocking out every combination they forbid, displays the valid conclusions on its face. It is the first machine that ever solved a problem in formal logic: a Boolean computer, seventy years before the electronic one.A real machine, a real cleanup. The Logic Piano genuinely mechanised Boolean inference (it survives in Oxford's museum), and Jevons's tidying of Boole's algebra — inclusive OR, idempotency, the method of elimination — is sound and standard.
Toy-scale, by design. The piano handles a handful of terms — it's a proof-of-concept that logic can be machined, not a general computer. The deep step (Boole's algebra IS switching circuits) waited for [[claude-shannon]].
Better known as an economist. Jevons co-founded the marginal revolution in economics (marginal utility) and named the "Jevons paradox." The Logic Piano is a brilliant footnote to a career mostly spent elsewhere.
Here is Jevons's method, working. The "logical alphabet" is every possible combination of the terms A, B, C — eight little worlds, one per key. A premise doesn't add information so much as forbid worlds: "All A are B" kills every world where something is A-but-not-B. Switch premises on and watch the contradictory keys go dark; whatever combinations survive are the consistent universe, and the valid conclusion is simply read off what's left.
"I have given much attention to lessening both the manual and mental labour of [reasoning], and I have succeeded in reducing the labour to little more than that of turning keys." — W. S. Jevons
Jevons made "or" inclusive (A or B includes both), kept the idempotent law x + x = x, and recast inference as elimination over the "logical alphabet" — dropping Boole's uninterpretable arithmetic. The form of Boolean logic we teach is closer to his.
A keyboard-driven wooden machine that performs that elimination physically. Press the keys for your premises; the inconsistent combinations are hidden; the conclusion stands revealed. The first working logic machine.
The Logic Piano sits in a precise spot in this lineage: after [[ramon-llull]]'s combinatorial wheel (which generated combinations) and [[charles-babbage]]'s calculating engines (which crunched numbers), but before [[claude-shannon]]'s switching circuits — it is the first device to decide a question of logic. It doesn't reason about quantity; it reasons about truth and consistency, by brute elimination. In doing so Jevons proved, in oak and ivory, the thesis the whole rest of computing would confirm: that inference is a mechanical operation, and the head is not its only possible home. ⚑ Press a key, forbid a world — the gate, in its first wooden draft.
Gate kept on. The achievement is real and first: the Logic Piano (1866) is the earliest machine to solve problems of formal logic, it physically works, and one survives in the Oxford Museum of the History of Science; Jevons's cleanup of Boole's algebra — inclusive disjunction, idempotency, the elimination method over the "logical alphabet" — is sound and shaped how Boolean logic is taught. Two honest qualifications. First, scope: the piano is a demonstrator — it handles only a few terms and a fixed routine, proving that logic can be mechanised rather than serving as a general computer; the profound identification of Boolean algebra with switching circuits — the thing that made the universal logic machine possible — is [[claude-shannon]]'s, seventy years later. Second, the man: Jevons is remembered first as an economist, a co-founder of the marginal-utility revolution and author of the "Jevons paradox" (efficiency gains can raise total consumption) — logic was a sideline of a restless polymath who drowned, swimming, at 46. But what a sideline: he took [[george-boole]]'s algebra of thought and built the first object that could think a little of it on its own. ⚑ [[augustus-de-morgan]] ← · next → John Venn (the picture of logic).