Claim. Categorical judgments reduce to four basic forms — universal affirmative (A), universal negative (E), particular affirmative (I), and particular negative (O) — each requiring proper distribution of subject and predicate to avoid fallacy.
Elaboration. A judgment is an affirmation or denial of a relation among concepts, expressed as ‘S—P’ (subject-copula-predicate). Following Kant, formal logic recognizes twelve judgment forms across four headings (quantity, quality, relation, modality), but the categorical judgment is the most basic (3. Judgment).
Combining quantity (universal/particular) with quality (affirmative/negative) yields the four basic forms, coded from the Latin affirmo and nego:
- A — Universal Affirmative: Every S is P
- E — Universal Negative: No S is P
- I — Particular Affirmative: Some S is P
- O — Particular Negative: Some S is not P
A term is distributed when the judgment applies to its entire extension, undistributed when only to part. The distribution pattern differs by form: in A (‘Every man is an animal’) subject is distributed, predicate is not; in E (‘Every bird is a non-mammal’) both are distributed; in I (‘Some flowers are red’) neither is; in O (‘Some birds are non-carnivorous’) subject undistributed, predicate distributed.
Violating distribution rules produces fallacy. Lee’s example: from ‘Every hermit is a lover of mountains’ one cannot conclude ‘Every lover of mountains is a hermit’ — this commits undue distribution, treating an undistributed predicate as if it were distributed.
Lee presents this machinery sympathetically; Unification logic will not contest it. His later evaluation says formal logic ‘is in agreement with Unification logic just as is’ regarding forms and laws — the critique is that formal logic stops short of content, purpose, and the give-and-receive grounding of these forms. The detailed exposition here serves the later argument that even classical syllogism is itself an instance of contrast-type give-and-take action.
See also. concept-intension-extension-categories, inference-deduction-induction-analogy, formal-logic-four-laws-of-thought