An example of the former is saying, Man is an animal; an example of the latter is, Man is a monosyllable. In a formal suppositio, the name is sometimes of the first intention, or of personal supposition, that is, in a normal act of understanding (acceptio): as in the phrase, Man is an animal. Otherwise it is of the second intention, or of simple suppositio for the idea or the term, that is, when a term of art (aliquid artificiale) is used of the same thing, for example, Man is a species.14
The divisions of terms into universal and singular, abstract and concrete, are evident from the divisions of ideas.
A transcendent term is one which belongs to every real thing, such as being, thing, one, something. A supertranscendent term is one which also belongs to fictions, such as imaginable, possible. All other terms are non-transcendental.
Every term where “not” is absent is finite; where the particle “not” is present, it is infinite, as in not-man, not-learned. “Not” is said to be infinitans. Finite and infinite [terms] together comprehend every being disjunctively: every being is either learned or not-learned, and so on; they exaust the whole range of being.
A univocal term is “predicable of several things individually according to the same idea,” as animal [is predicable] of man and of beast.
An equivocal term is “predicable of several things individually according to different ideas,” like Gallus. “Where there is some underlying reason for it or affinity of meaning,” a term is said to be analogous or deliberately equivocal, as [when] healthy [is predicated] of animal and of food, or Alexander of a man and of a picture. When there is no reason, it is said to be equivocal by chance, like Gallus or (in English) canon.15
CHAPTER 9
Compatible terms may be predicated of one and the same thing at the same time, like strong and pious; they are often disparate.
Conflicting or opposed terms [are those] which “cannot be predicated of each other, nor of the same thing, in the same respect, and at the same time.” This opposition of terms is noncomplex; the opposition of propositions, on the other hand, is said to be complex.16
There are four species of noncomplex opposition: contrary, contradictory, relatively opposed, and privatively opposed. Disparates do not conflict ( pugnant), for they are “terms denoting ideas in which there is very little or nothing in common, beyond the vague idea of being or of mode,” as in brave and tall or sweet and white.
Contraries are “true opposed qualities,” such as pain and pleasure.
Contradictories are “a word and its negation,” such as learned and not-learned or man and not-man.
Relatively opposed are relative terms, such as father and son.
Privatively opposed are “a quality and its absence in a subject which has the capacity for it,” as in sighted and blind in the case of an animal.
Negatively opposed are “a quality and its absence in any kind of subject,” as in sighted and nonsighted, which are also contradictories.
On the Noetic Judgment and the Proposition
CHAPTER 1
A judgment is “an action of the mind by which it gives a verdict on two ideas in comparison with each other.” That is, a verdict is given that either the ideas represent the same object, or a certain relation or connection exists between their objects.1
A noetic judgment is “when a verdict is given about ideas which are being directly compared with each other.”
A dianoetic judgment is “a verdict of the mind about two ideas, by means of comparison of both with a third.”2
A proposition 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