Reasoning by elimination — rule out the impossible, affirm what survives — recurs as a mechanism from Stoic disjunctive syllogism through Jevons's Logic Piano to symbolic AI, and inverts in modern neural inference

One inference mechanism — eliminate the impossible, affirm what survives — recurs across more than two thousand years of the vault's inference cluster, under different names and in different substrates:

• Ancient (~230 BCE): the disjunctive syllogism. Chrysippus's three-road hunting dog rules out two paths and takes the third without checking it (claim-chrysippus-dog-disjunctive-syllogism). Modus tollendo ponens: deny all but one disjunct, affirm the remainder.
• Victorian (1869–70): mechanized elimination. Jevons's "Logic Piano" physically struck out the combinations of premises inconsistent with the inputs, leaving only the deducible conclusions (claim-jevons-logic-piano-1869-mechanical-inference-machine). The mechanism is the disjunctive move made of wood and levers.
• Symbolic AI (1970s): backward chaining. Goal-directed inference engines enumerate candidate conclusions and work backward, knocking out those the knowledge base cannot support (claim-inference-classic-ai-engines).
• Intelligence analysis (1999): falsificationist elimination. Heuer's Analysis of Competing Hypotheses instructs analysts to disprove hypotheses rather than prove them, so the survivor of disconfirmation — not the best-supported guess — is judged most likely (claim-ach-step-5-instructs-analysts-to-disprove-not-prove).

The recurrence is a structural rhyme, not a single documented transmission chain. Two of the links are only echoes: whether Jevons himself drew on the Stoic example is unverified (question-verify-jevons-cited-chrysippus-dog-elimination), and whether ACH's Step 5 owes anything to backward chaining is likewise an observed parallel, not a lineage (question-ach-backward-chaining-structural-echo).

The through-line also sets up a contrast. Classical, mechanical, and symbolic inference all eliminate the impossible; modern neural "inference" instead generates the probable — a forward pass over frozen weights that concludes nothing new and rules nothing out. The word survived and the mechanism inverted, a shift the vault already tracks through the term's own history (claim-inference-word-etymology, claim-inference-logical-types).