The Timpson Lyceum · History of Philosophy (2024)

Aristotle's Organon: Categories & On Interpretation – Lecture 23 (History of Philosophy)

Overview

The Organon ("instrument") is Aristotle's collection of logical works — Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and Sophistical Refutations — and the first systematic logic ever produced. It builds in strict order: the Categories classify simple concepts (the words and terms from which sentences are made), On Interpretation studies propositions (whole sentences that are true or false), and the Prior Analytics studies how propositions combine into valid arguments. First the terms, then the sentences, then the inferences.

The lecture develops the Categories — the ten highest genera under which every simple concept falls, headed by substance — together with Aristotle's fourfold classification of things (by whether they are said of a subject and/or in a subject), his theory of definition by genus and differentia, and his careful disambiguation of tricky words (opposite, prior, simultaneous) and of change. It then turns to On Interpretation: the analysis of the proposition into noun (subject) and verb (predicate), the four categorical forms obtained by combining quantity (universal/particular) with quality (affirmative/negative), and the logical relations among them — the square of opposition — which sets up the syllogistic to come.

Key Concepts

• The Organon and its order — Six logical works; the course focuses on the first four. Categories → terms, On Interpretation → propositions, Prior Analytics → syllogisms, Posterior Analytics → the foundations of science.
• The ten Categories — The highest genera into which any simple concept resolves: substance (man, horse), quantity (four-foot, five-foot), quality/qualification (white, grammatical), relation (double, half, larger), place/where (in the marketplace), time/when (yesterday, last year), position (is lying, is sitting), having/state (has shoes on, has armor on), action/doing (cutting, burning), and being-affected/passion (being cut, being burned). None is true or false by itself; only their combination yields an assertion.
• Primary vs. secondary substance — Primary substance is the individual particular (this man), neither in nor said of anything; secondary substance is the species or genus (man, animal), said of a subject but not in one. Everything else depends on primary substances for its existence.
• The fourfold "in / said-of" square — Combining predicated of a subject with present in a subject yields: said-of-not-in (secondary substances, e.g. man), in-and-said-of (universals only in something, e.g. red, running), in-not-said-of (particular non-substances, e.g. this memory), and neither (primary substances). Said-of ≈ universal; in ≈ accidental (as opposed to essential).
• Genus, species, differentia — Both genus and species are relative terms. A definition states a thing's genus plus the differentia that marks off a species: man = rational (differentia) animal (genus); an even integer $n$ = an integer such that $n = 2k$ for some integer $k$. The differentia must capture the essence, not merely pick out the right extension ("featherless biped" fails — pluck a chicken).
• Categories cannot be defined — As highest genera, the ten categories are species of nothing further, so they have no definition; they are grasped by abstraction from instances. A genus must be differentiated by something outside it, so "being" cannot serve as the first genus.
• Substances admit no degrees and no contraries — No one is "more man" than another; there is no opposite of man. Yet a substance can receive contraries over time (the same person now healthy, later sick) — distinctive of substance alone.
• Univocal vs. equivocal — Univocal = same word, same definition; equivocal = same word, different definitions. Rigorous knowledge requires univocal terms; equivocation ("infinite in time" slid to "infinite in space") breeds fallacy. Derived terms (adding prefixes/suffixes) need no fresh definition.
• Six kinds of change — Not merely coming-to-be: generation and destruction (adding or removing a form from persisting matter), increase and diminution (size), alteration (quality), and change of place (locomotion). The matter persists through generation and destruction, so nothing is created from or reduced to nothing.
• Disambiguating "opposite," "prior," "simultaneous" — Opposite covers relatives/correlatives, contraries, privation/possession, and affirmation/negation (the most precise). Prior covers time, implication of existence, order, and the like. Sophists exploit sliding senses of such words; the Organon is the antidote.
• On Interpretation — noun and verb — A proposition divides into noun (the word for the subject) and verb (the sign of what is predicated, carrying time in its tense). Neither alone is true or false; only their combination — a declarative sentence — expresses a proposition.
• Quantity and quality of propositions — A universal subject needs a quantifier: the universal $\forall$ ("all") or the existential $\exists$ ("some"); an unquantified "men are mortal" is indefinite and unfit for logic. Crossed with affirmation/negation, this yields the four categorical forms.

Worked Example

The Square of Opposition (from On Interpretation). Take a subject term $S$ and predicate term $P$. Combining quantity (universal / particular) with quality (affirmative / negative) gives four categorical propositions, traditionally labeled $A, E, I, O$:

1. A — universal affirmative, "All $S$ are $P$": $\ \forall x\,(S(x) \rightarrow P(x))$.
2. E — universal negative, "No $S$ are $P$": $\ \forall x\,(S(x) \rightarrow \neg P(x))$.
3. I — particular affirmative, "Some $S$ are $P$": $\ \exists x\,(S(x) \wedge P(x))$.
4. O — particular negative, "Some $S$ are not $P$": $\ \exists x\,(S(x) \wedge \neg P(x))$.

Now derive their logical relations.

1. Contradictories (exactly one true, one false) lie on the diagonals. $A$ and $O$ deny each other, as do $E$ and $I$:

$A \leftrightarrow \neg O, \qquad E \leftrightarrow \neg I.$

Indeed $\neg\,\forall x\,(S(x)\rightarrow P(x))$ is logically equivalent to $\exists x\,(S(x)\wedge\neg P(x))$, which is exactly $O$.

1. Contraries — $A$ and $E$ (the two universals) cannot both be true, though (with a nonempty $S$) they may both be false:

$\neg(A \wedge E).$

1. Subcontraries — $I$ and $O$ (the two particulars) cannot both be false, though they may both be true:

$I \vee O.$

1. Subalternation — from a universal, its corresponding particular follows (assuming $S$ is nonempty):

$A \rightarrow I, \qquad E \rightarrow O.$

1. Check for consistency. Suppose $A$ is true. By subalternation $A \rightarrow I$, so $I$ is true; by contradiction $A \leftrightarrow \neg O$, so $O$ is false; and since $O$ is false while $E \leftrightarrow \neg I$ and $I$ is true, $E$ is false. Thus a single truth-value for $A$ fixes all four — the square is a coherent web of entailments, not a list of independent claims. $\blacksquare$

Summary

• The Organon is Aristotle's founding logic, built term-first: the Categories classify simple concepts, On Interpretation handles propositions, and the Prior Analytics handles inference.
• The ten categories — headed by substance and including quantity, quality, relation, place, time, position, having, action, and passion — are the highest genera of all simple concepts and are themselves indefinable.
• Aristotle's theory of definition (genus + essential differentia) and his insistence on univocal language equip a rigorous science and expose the sophistical equivocations he catalogs under "opposite," "prior," and "simultaneous."
• On Interpretation resolves the proposition into noun (subject) and verb (predicate), adds quantifiers to universal subjects, and yields the four categorical forms $A, E, I, O$.
• The square of opposition locks these forms into fixed relations — contradictories ($A$–$O$, $E$–$I$), contraries ($A$–$E$), subcontraries ($I$–$O$), and subalternation ($A \rightarrow I$, $E \rightarrow O$) — the launchpad for the syllogistic.