Classification of the Proposition

The most general classification of propositions presents them as simple and compound. A simple proposition has one subject and one predicate. A compound proposition is a combination of two or more simple propositions.

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a) Simple Propositions

A simple proposition has but one subject and one predicate.

In quality, simple propositions are either affirmative or negative. In quantity, they are universal, particular, singular, or indefinite.

For practical purposes, singular propositions are always treated as universal (their subject has the Extension of only one and must be taken in full Extension, which is precisely the definition of a universal proposition). Indefinite propositions (using the subject in indeterminate Extension, e.g., “Men like sports”) are always reducible by context to either universal or particular.

Therefore, propositions are distinguished in quantity as universal and particular only.

Combining the classifications, there are four kinds of simple proposition, each designated by a vowel letter:

Symbol	Name	Quantity	Quality	Example
A	—	Universal	Affirmative	”All men are mortal”; “John is wise”
E	—	Universal	Negative	”No man is wise”; “No tyrants are just”
I	—	Particular	Affirmative	”Some man is wise”; “Men like sports”
O	—	Particular	Negative	”Some man is not wise”; “Some sports are not laudable”

(The vowels A, I come from affirmo*; E, O from* nego*.)*

The student must master these letter-symbols thoroughly; they are supposed as known throughout all that follows.

Two Principles of Distribution

First Principle: In an Affirmative Proposition the Predicate is undistributed.

In affirmative propositions the predicate is not taken in full Extension. “Every stone is a body” — the predicate body is not taken in full Extension (which would mean no other sort of body exists but a stone). It is taken in partial Extension: stones belong to the class bodies, though other bodies also exist.

A term used in full Extension is said to be distributed; in partial Extension, undistributed.

Two exceptions: (1) When the predicate is a singular term (individual, Extension of one; if used at all, used in full Extension). “That man is Al Smith.” (2) When the predicate is an essential definition (necessarily coextensive with the subject). “Man is a rational animal.”

Second Principle: In a Negative Proposition the Predicate is Distributed.

In a negative proposition the predicate is taken in full Extension. “An animal is not a stone” — the entire class stone is denied to the class animal.

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b) Compound Propositions

Compound propositions are combinations of simple propositions. There are five classes:

1. Modal Propositions

A modal proposition not only expresses the agreement or disagreement of subject and predicate but also indicates the manner (mode) of that agreement or disagreement. The simple agreement/disagreement is the dictum; the manner is the mode. In “God is necessarily just,” the dictum is “God is just” and the mode is “necessarily.”

Four types, according as the mode expresses necessity, contingency, possibility, or impossibility:

• Necessary: “A circle has to be round”; “A sentient being must be alive”; “God is necessarily just.”
• Contingent: “John is, it happens, ill”; “A rider chanced to come his way.”
• Possible: “The earth may possibly collide with another planet”; “Such accidents can happen.”
• Impossible: “God cannot be cruel”; “A circle cannot be square.”

All modals are always compound, never simple — the dictum and mode each constitute a simple proposition.

Note: Necessary modals are always A-propositions (the predicate must apply universally to the subject). Impossible modals are always E-propositions.

2. Compound Categorical Propositions

A categorical proposition expresses an unconditional judgment. Compound categoricals divide into those obviously compound and those not obviously compound.

I. Obviously Compound:

• Copulative: more than one subject, predicate, or both, joined by conjunctions. “Peter and James were Apostles.” Truth depends on the truth of the component simple propositions.
• Adversative: express opposed judgments, shown by particles like but, however, nevertheless. “Samson was strong; nevertheless he fell.” Truth depends on both the component propositions being true AND on a genuine opposition existing between them.
• Relative: partial propositions connected by correlative particles (when—then, so—as, where—there). “Where two or three are gathered in my name, there am I in the midst of them.” Truth depends on the truth of the component propositions and on the existence of a true relation between them.
• Causal: propositions united by causal particles (because, since, for). “Man is free because he is rational.” Truth depends on the component propositions and on the truth of what is assigned as cause.

II. Not Obviously Compound (Exponible Propositions):

These need to be drawn out of obscurity and shown to be compound; the simple propositions into which they resolve are called their exponents.

• Exclusive: attached to subject or predicate are exclusive particles (only, alone). “God only knows.” Exponents: “God knows” and “Others do not know.”
• Exceptive: express a limited predication, using particles (except, but, save). “All save John had gone.” Exponents: “John had not gone” and “All others had gone.”
• Comparative: declare a predicate is enunciated of one subject equally with, or more or less than, another. “Good name is better than great riches”; “John and Jim are equally enthusiastic.”
• Reduplicative: view a subject from different angles using words like inasmuch as, in as far as. “The physician, inasmuch as he is a physician, treats human ailments; inasmuch as he is a man, he thinks and wills.” If the reduplicative particle is equivalent to because, reduce to the causal type. If it indicates a changed point of view (specificative), reduce to the copulative type.

3. Hypothetical Propositions

A hypothetical proposition is conditioned: it makes no absolute predication but expresses a dependency between two or more propositions. Three types:

I. Connective (Conditional): always has a member introduced by if (the antecedent or condition) and a consequent. “If a fast day falls upon Sunday, the fast is not observed.” The consequent depends on the antecedent such that if the antecedent is true, the consequent must be true. Truth depends solely on the genuine relation of dependence between antecedent and consequent.

II. Conjunctive: enunciate the impossibility of two things occurring simultaneously. “Socrates is not at once a philosopher and an ignoramus.” Truth depends on a genuine exclusive opposition between the component parts. Reducible to two conditional propositions: “If Socrates is a philosopher, he is not an ignoramus” and “If Socrates is an ignoramus, he is not a philosopher.”

III. Disjunctive: enumerate exhaustive possibilities no two of which can be simultaneously true, nor can all be simultaneously false — one must be true and the rest false. “It is either day or night.” Two requirements: (1) the enumeration of possibilities must be complete; (2) there must be exclusive opposition between the enumerated possibilities.

4. Complex Propositions

A complex proposition has a complex term as subject. It may be reduced to two exponents, one containing the principal member of the complex term, the other containing the incidental member. “The fear of God is the beginning of wisdom.”

5. Multiple Propositions

A multiple proposition formally expresses more than one predication. A compound proposition may contain many simple propositions as exponents and yet not be multiple (e.g., “Peter, James, and John beheld the Transfiguration” — many subjects, one predication). But “John runs and jumps” is both compound and multiple: one subject, two distinct predications.

Axiom: A multiple proposition is always compound, but a compound proposition is not necessarily multiple.

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Summary of the Article

Propositions are classified:

I. By Quantity and Quality: A (universal affirmative), E (universal negative), I (particular affirmative), O (particular negative).

II. By Structure:

Simple
Compound:
  a) Modal         — necessary · contingent · possible · impossible
  b) Categorical   — obviously compounded (copulative, adversative, relative, causal)
                   — not obviously compounded / exponible (exclusive, exceptive,
                     comparative, reduplicative)
  c) Hypothetical  — connective · conjunctive · disjunctive
  d) Complex
  e) Multiple