◀ WORLD II · THE FOLDTHE OCHO · blue builds │ the machine │ red breaks

THE LOGIC PIANO

In 1869 William Stanley Jevons built the first machine that reasoned. Press a premise like a piano key and the machine mechanically removes every combination of terms that premise forbids; whatever combinations survive are the conclusion. Down the center, data flows: the premises go in, the machine eliminates, the surviving worlds come out. The blue team builds and defends it; the red team tries to break it.

source W. S. Jevons, The Principles of Science (1874), Bk I — "The Logical Abacus / The Logical Machine"; mechanism first given in The Substitution of Similars (1869). archive.org/details/principlesofscie01jevouoft (AMBER: work confirmed on archive.org, exact page not quoted). Rendered, not quoted.

◧ blue team · builds & defends
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THE MODEL — elimination

Three terms A, B, C give 8 possible worlds — the machine's "logical alphabet", from 000 to 111. Every world starts standing.

A premise is a filter. "A → B" forbids any world where A holds but B does not (a ≤ b); "A" forbids every world where A is false. Pressing the key strikes out exactly the worlds it contradicts — no search, no lookup, just removal.

Live distribution of each variable across the surviving worlds:

vartrue infalse inreads
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THE LINEAGE — Boole, made mechanical AVAN

Boole turned logic into an algebra of 0 and 1. Jevons's leap was that this algebra could be worked by a machine: substitution of similars becomes striking rows off a board.

The prior sphere is the algebra — its 0/1 classes are this machine's premise filters. The next is the logic gate: Shannon (1937) showed the same true/false algebra is a switching circuit. The Logic Piano is the hinge — each sphere is the next one's premise.

7

THE WITNESS live

The blue team's live check: for a battery of premise sets, re-run the machine's elimination and compare it, world for world, against an independent brute-force oracle. If red tampers, this badge is where it shows.

▼ the machine ▼
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DATA IN — the premises in ↓

The inputs are premises over three terms. Each is a claim the world must obey; press it to feed it in:

keysaysforbids worlds where
A → Bevery A is a BA=1, B=0
B → Cevery B is a CB=1, C=0
A → Cevery A is a CA=1, C=0
AA is trueA=0
¬BB is falseB=1
CC is trueC=0

Feed A→B and B→C together and the machine, having removed everything else, will have already removed every world violating A→C. That transitive step — nobody typed it — is the inference.

▼   press the keys into the machine   ▼
0

▣ THE PANEL — the machine LIT

ABCstatus
Surviving worlds = the models of your premises. A variable that is true in every survivor is proved.

Toggle any key — each row is struck live by pressing the premise filters in turn, never looked up.

▼   the machine emits the survivors   ▼
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DATA OUT — the survivors out ↓

What the machine produces, proven: the surviving worlds are exactly the models of the conjoined premises — and any variable constant across them is the conclusion. For A→B, B→C, A the machine leaves a single world, 111, so C is forced true. The result above is computed live; the totals are the output.

The blue team's witness (left) confirms this matches brute force live; the red team (right) tries to make a bad world survive.

red team · attacks & breaks ◨
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THE ADVERSARY

WALL The Logic Piano does not reason — it enumerates. It writes out every possible world and crosses off the losers. That is exponential: n terms means 2ⁿ rows. Jevons's real machine stalled at 4 terms (16 combinations); ours shows 3. It is a decision procedure by exhaustion, not a proof engine.

And it is class/propositional logic only — no relations, no quantifiers. "Every boy loves some girl" cannot even be stated. The machine proves that inference has a mechanical shape; it does not prove that shape is efficient or complete.

2

THE GRAVEYARD

"The Logic Piano was the first computer." Cut. It is not programmable or general-purpose. It was the first machine to solve logic problems mechanically — a real first, but not a computer.

"Jevons invented Boolean algebra." Cut. Boole did (1847/1854). Jevons simplified it (the substitution of similars) and mechanized it — credited as builder, not author.

"It reasoned over any number of terms." Kept, corrected. The mechanism generalises, but the physical piano handled 4 terms / 16 rows. The engine here models the method at 3.

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THE TAMPER — break it

The red team's move: make the machine skip one elimination — drop the last premise's filter — so a world it should have struck stays standing. The blue team's witness (window 7) is watching.

Skip the last premise and inconsistent worlds survive — the witness recomputes, disagrees with brute force, and turns red. Nothing is faked; the attack is real and it is caught.