The one-page course in Traditional Logic

THE SQUARE OF OPPOSITION

A: universal affirmative; E: universal negative;
I: particular affirmative; O: particular negative

AÞI; EÞO; AÛ'~O'; EÛ'~I'; AÞ'~E'; '~I'ÞO
from AÞI and AÛ'~O' the rest are derivable

SYLLOGISTICS

Figures	I.	II.	III.
Major	M-P	S-M	M-S
Minor	S-M	P-M	M-P
Conclusion	S-P	S-P	S-P

NINETEEN MODES OF THREE FIGURES

i. barbara celarent darii ferio baralipton
celantes dabitis fapesmo frisesimorum
ii. cesare cambestres festino barocho iii. darapti
felapto disamis datisi bocardo ferison

Derivation rules: B, C, D, F indicate direction of reduction; prop. before S is to be converted simply (terms simply swapped, valid: e, O); prop. before P to be converted per accidens, (terms swapped, quantity changed, valid AÞI, EÞO); M indicates transposition (order of premises changed); C indicates that the mode is to be proved by reductio. Contraposition: swap terms changing finite terms to infinite terms, valid: A, O.

Example: CESARE: ~$ S-M; " P-M Þ ~$ S-P /S=man, M=plant, P=oak/

Counterexample (ampliation): No dead are alive and some men are dead; therefore, some men are not alive

Counterexample (topics): Socrates is a man; therefore, Socrates is an animal

Counterexample (equivocation): Whatever is healthy is alive; some medicine is healthy; therefore, etc.

Counterexample (quantification): A man sees every donkey; Brunellus is a donkey; therefore, etc.