Claim. Inference draws conclusions from premises; when two or more premises are used (indirect inference) it takes three principal forms — syllogism (deduction), induction, and analogy.
Elaboration. Sang Hun Lee summarizes formal logic’s account of inference (4. Inference).
Syllogism (deduction) draws a particular conclusion from universal premises. The categorical syllogism has major premise (containing major term P and middle term M), minor premise (minor term S and middle term M), and conclusion (S–P). Classic example: ‘Every man is mortal; every hero is a man; therefore every hero is mortal.’ The extension hierarchy is P > M > S.
Induction generalizes from observed particulars to a universal claim: ‘Horses, dogs, chickens, and cows are mortal; they are animals; therefore all animals are mortal.’ Strictly, this is fallacious — the conclusion treats ‘animal’ as distributed when the premises only sampled a part of its extension. Yet induction works in natural science because of two auxiliary assumptions: the principle of uniformity in nature (phenomena have the same form everywhere) and the law of causality (same cause → same effect).
Analogy infers an unobserved trait in B from observed common traits with A. Earth and Mars share traits (a)–(d): both are planets, have air, similar temperatures, four seasons and water; therefore Mars may have living beings as Earth does. Three requisites for analogical accuracy: many similarities, essential rather than accidental similarities, no incompatible qualities.
Lee notes analogy’s wide use in early science and in family, group, school, business, and creative life. The introduction is brisk — Lee says his intent is only to lay out the main points before moving to Unification logic. Notably, all three inference modes will later be re-described as forms of contrast-type give-and-take action between premises and between concepts, grounding formal inference in the more fundamental law.
See also. judgment-aeio-and-distributed-terms, concept-intension-extension-categories, formal-logic-four-laws-of-thought