is “a statement which expresses a noetic judgment.” There are three parts to it: subject, predicate, and copula.
The subject is “that about which something is affirmed or denied.” The predicate is “that which is affirmed or denied.” The copula is the logical verb (verbum), is or is-not.
N.B. Subjects and predicates are distinguished not by their position but by the sequence of speech. These three parts are always present, either explicitly or suppressed and implied: for example, curro [“I-run”] = ego sum currens [“I am running”].
CHAPTER 2
In respect of their internal form or quality, propositions, like judgments, are either affimative or negative.3
In respect of their content, propositions are either true or false. Every [proposition] is either true or false; no [proposition] is both true and false; and there are no [propositions] which change from true to false, if we look at the judgment itself and not at the words. Those which seem to be both true and false are double or denote two judgments. Those which seem to change are likewise double; this is obvious from the nature of the word, which is “a word which implies time.” Hence, when the same words are uttered at different times, they sometimes give rise to quite different propositions.
Logical truth is “the agreement (convenientia) of the signs with the things signified.” Moral truth is “the agreement of the signs with the sense of the mind”; it belongs to the ethical forum.
With regard to quantity, propositions are universal, particular, singular, or indefinite.
1. A universal proposition is “when the subject is a universal term in its whole extension,” or is distributed.
2. A particular proposition is one “whose common subject is restricted to a part of its extension,” or is not distributed.
The marks of distribution or universality are all, no, each, etc. Notes of particularity are someone, a certain, not every, etc.
3. A singular proposition is one “whose subject is singular or individual,” i.e., [a subject] which, not having a divisible extension, is understood of the whole; the same rules apply to singulars as to universals.
4. An indefinite proposition is “when a common subject is not modified by any mark of quantity.” In the sense of the speaker, however, it is always either universal or particular. For example, men are animals is universal; men are learned is particular; it depends whether the content is necessary or contingent.
We need only look at two of these kinds, namely universal and particular, because the others come under the same rules.
From the different combinations of quality and quantity, four classes of propositions arise, which are indicated by well-known symbols.
A asserts, E denies, and both generally.
I asserts, O denies, but both particularly.4
In respect of substance, propositions are either categorical or hypothetical. A categorical [proposition] “indicates something absolutely.” A hypothetical proposition “indicates something subject to a condition.”
The [following] divisions show the responses to the most frequent questions about propositions.
What [proposition]? Categorical or hypothetical. What sort of [proposition]? Negative or affirmative. What quantity of [proposition]? Universal, particular, indefinite, singular.
CHAPTER 3
Axioms about the quantity of terms:
1. “In every affirmative proposition the predicate is taken particularly,” and it is not also required that it be true.
2. “In a negative proposition the predicate is taken universally” or is distributed, for a negation is understood to be false if any part of the predicate may be truly affirmed of the subject.
3. The quantity of subjects is understood from the signs prefixed [to them]. Hence in A, the subject is universal, and the predicate is particular. In E, both are universal. In I, both are particular. In O, the subject is particular, and the predicate is universal.
Only those propositions are said to be universal in which the subject is distributed, and a predicate is affirmed or denied of the individual things which are covered by the common word. This is not the case when the predicate is [made up] of several [things] collectively: thus, All men are mortal is universal, but not the following: All men form one state; all the apostles were twelve.
Propositions about kinds of individuals are in a certain sense universal; e.g., Every animal was in Noah’s ark, or, the Gospel has been preached to men of all nations.
Here it is said that certain individuals of each kind were in the ark or have heard the Gospel, but these things are not predicated separately of every individual or of each individual in the kinds.
CHAPTER 4
These are the axioms about universals:
1. “Whatever is affirmed of a distributed subject (that is, [of a subject] universally taken) may be affirmed of all the inferiors which are contained in its extension.”
2. “Whatever is denied of a distributed subject can equally be denied of all its inferiors.” These two in combination are the dictum de omni et nullo; on this depend both subalternation and the force of the syllogism, which we shall discuss later.5
CHAPTER 5
Some propositions are simple, others complex; simple [propositions] “denote one single judgment”; complex [propositions] “denote more than one judgment.”
Among complex propositions, the modal propositions are preeminent [which are] “when something is both predicated and the mode of its connection with the subject is made clear.” There are four modes: the necessary, the impossible, the possible, and the contingent.6 But generally modal [propositions] are simple [propositions], or signify a single judgment of a speaker. For they are ambiguous. Sometimes they merely affirm or deny the statement itself more emphatically, as in saying, “God most certainly exists” or “Certainly no man is immortal.” Sometimes the proposition itself, which is called the statement, is the subject, and the mode is predicated of it, as in saying, “the Divine existence is necessary,” or “God is, is a necessary proposition”; and similarly with the other modals.
In the same way it is shown that the four kinds [of modal propositions], which might appear from their names to be complex, are simple, namely: (1) conditional [propositions]; (2) disjunctive [propositions]; (3) negative copulative [propositions]; and (4) relative [propositions].
In a conditional or hypothetical [proposition] there are two parts, the antecedent and the consequent: for example, if God exists, the world is governed by providence. Neither of these is asserted; it is merely asserted that they are connected. Hence this [proposition] also is equally true: If there were no God, there would be no providence.
In disjunctive [propositions] the whole subject is said to be included in two connected predicates; for example, it is either day or night means the same as all time is included in daytime and nighttime.7
In negative copulative [propositions] it is denied
