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

THE SYLLOGISM

Two truths, locked in a frame, force a third. Aristotle wrote the first formal logic — and it is runnable: every one of the 256 possible forms is decidable by four rules, and exactly 15 hold for Boole, 24 for Aristotle. Down the center, data flows: the terms go in, the engine decides, the verdict comes out. The blue team builds and defends it; the red team tries to break it.

source Aristotle, The Organon (Prior Analytics), E. M. Cooke tr. — archive.org/details/organoncooke01arisuoft. Rendered, not quoted.

◧ blue team · builds & defends
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THE MODEL — the four rules

Validity is not memorized; it falls out of distribution:

R1 the middle term M must be distributed in at least one premise. R2 a term distributed in the conclusion must be distributed in its premise (no "illicit" leap). R3 two negative premises prove nothing. R4 a negative premise forces a negative conclusion, and vice-versa.

For the current form, live distribution of each term:

termin premisein concl.
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THE LINEAGE — 24 vs 15 AVAN

Aristotle counts 24 valid; Boole counts 15. The nine that differ are the weakened moods — Barbari, Darapti, Felapton… — a particular conclusion from two universal premises.

Valid only if the subject class is not empty — Aristotle's silent existential import. Boole drops it, and that one deletion — a class may be empty — is the door to the algebra of 0 and 1. Each sphere is the next one's premise.

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THE WITNESS live

The blue team's live check: re-run the engine over all 256 forms and confirm the counts against the known truth. If red tampers, this badge is where it shows.

▼ the machine ▼
4

DATA IN — the terms in ↓

A categorical syllogism has three terms: S (minor), P (major), M (middle — the hinge that vanishes from the answer). Each statement is one of four kinds:

typesayssubjectpredicate
AAll S are Pdistributed
ENo S are Pdistributeddistributed
ISome S are P
OSome S are not Pdistributed

Where M sits gives the figure (1–4). "Distributed" = the statement speaks of every member. That is the whole game — and it is what you feed the panel below.

▼   feed the terms into the engine   ▼
0

▣ THE PANEL — the engine LIT

Modern: a universal claim does not assume its subject exists. 15 forms hold.

Change any control — the verdict is computed from the four rules on the spot, never looked up.

▼   the engine emits a verdict   ▼
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DATA OUT — the result out ↓

What the machine produces, proven: every one of the 256 forms decided by the four rules — exactly 15 valid for Boole, 24 for Aristotle, each valid mood named (Barbara → Fresison). The current form's verdict is above; the totals are the output.

The blue team's witness (left) confirms these numbers live; the red team (right) tries to make them wrong.

red team · attacks & breaks ◨
1

THE ADVERSARY

WALL The categorical syllogism is a fragment. It cannot express relations or multiple generality — "every boy loves some girl" is outside it entirely. Modern predicate logic (Frege, 1879) subsumes all 256 forms as a trivial special case and goes vastly further.

9 of Aristotle's 24 also lean on a metaphysical assumption (non-empty classes) a modern logician rejects — so "valid" is already a choice, which is why the panel lets you pick the reading. The syllogism is not the logic; it is the first proof that reasoning has a computable shape.

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THE GRAVEYARD

"There are 19 valid syllogisms." Cut. 19 is the strict set; the honest counts are 15 (modern) and 24 (Aristotelian) — both computed in the machine.

"Aristotle proved all four figures." Cut. He treated figures 1–3; the 4th is Theophrastus/Galen. The engine includes it, labelled — not pretended to be his.

"The mnemonics are decoration." Kept, corrected. The vowels of Barbara/Celarent/Darii are the mood (A-A-A, E-A-E, A-I-I) — a working code.

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THE TAMPER — break it

The red team's move: delete one of the four rules and try to slip a false form past. The blue team's witness (window 7) is watching.

Delete the middle-distribution rule and false forms pass — the witness recomputes, disagrees with the known counts, and turns red. Nothing is faked; the attack is real and it is caught.