Part II, Chapter 3: Of what is meant by a Proposition, and of Four Kinds of Propositions
After having conceived things through ideas, we compare these ideas together; and, finding that some agree together, and that others do not agree, we unite or separate them, which is called affirming or denying, and generally, judging.
This judgment is called also a proposition, and must have, as will be easily seen, two terms; the one, that of which we affirm or deny something, called the subject; and the other, that which we affirm or deny, called the attribute, or predicate.
It is not sufficient to conceive these two terms,—the mind must also unite or separate them; and this action of our mind is denoted, as we have already said, in discourse, by the verb is, either alone, when we affirm, or with the negative particle, when we deny. Thus, when I say, God is just; God is the subject of that proposition, just is the attribute; and the word is marks the operation of my mind in affirming, that is to say, in connecting together these two ideas, God and just, as agreeing with each other. And if I say, God is not unjust; is, being joined with the particle not signifies the contrary action to that of affirming, to wit, that of denying, by which I regard these two ideas as repugnant to each other, since there is something contained in the idea of unjust which is contrary to what is contained in the idea of God.
But though every proposition contains necessarily these three things, yet, as we have said in the preceding chapter, it may have only two words, or even one alone. For men, wishing to abbreviate their speech, have made a multitude of words which express in themselves an affirmation—express, that is to say, what is signified by the substantive verb, and a certain attribute which is affirmed, besides.
Such are all verbs except the substantive verb: as Deus existit, i.e. is existing; God loves men, i.e. God is loving men. And the substantive verb, when it is alone, ceases to be purely substantive: as when I say, I think, therefore I am, because there is then joined to it the most general of attributes, which is being; for I am, means I am a being, I am something.
There are also certain other cases in which the subject and the affirmation are contained in a single word, as in the first and second persons of the verb, especially in Latin, as when I say, Sum Christianus. For the subject of the proposition is ego, which is contained in sum. Whence appears, that in that language a single word makes a proposition in the first and second persons of verbs, which, in their nature, already contain the affirmation with the attribute; thus, veni, vidi, vici, are three propositions.
We see from this that every proposition is affirmative or negative, and that this is denoted by the verb which is affirmed or denied.
But there is another difference of propositions which arises from their subject, which is that of being universal or particular, or singular. For terms, as we have already said in the First Part, are either singular, or common or universal.
And universal terms may be taken either according to the whole extension, by joining them to universal signs, expressed or understood: as omnis, all, &c., for affirmation; nullus, none, for negation; as all men, no man.
Or according to an indeterminate part of their extension which is, when there is joined to them aliquis, some, &c., as some man, some men; or other words, according to the custom of languages.
Whence arises a remarkable difference of proposi tions; for when the subject of a proposition is a common term, which is taken in all its extension, propositions are called universal, whether affirmative, as, Every impious man is a fool,—or negative, as. No vicious man is happy.
And when the common term is taken according to an indeterminate part only of its extension, since it is then restricted by the indeterminate word some, the proposi tion is called particular; whether it affirms, as, Some wicked men are cowards—or whether it denies, as, Some poor men are not unhappy.
And if the subject of a proposition be singular as when I say, Louis XIII. took Rochelle, it is called singular. But though this singular proposition may be different from the universal, in that its subject is not common, it ought nevertheless to be referred to it, rather than to the particular; for this very reason, that it is singular, since it is necessarily taken in all its extension, which constitutes the essence of a universal proposition, and which distinguishes it from the particular. For it matters little, so far as the universality of a proposition is concerned, whether its subject be great or small, provided that, whatever it may be, the whole is taken entire. And hence it is that singular propositions take the place of universals in reasoning. Thus we may reduce all propositions to four sorts, which, in order to assist the memory, have been denoted by these four vowels—A, E, I, O:
A. Universal affirmative: as, Every vicious man is a slave.
E. Universal negative: as, No vicious man is happy.
I. Particular affirmative: as, Some vicious men are rich.
O. Particular negative: as, Some vicious men are not rich.
The following two verses have been made for the better remembering of these:
Asserit A, negat E, verum generaliter ambo; Asserit I, negat O, sed particulariter ambo.
It is customary to call the universality or particularity of propositions their quantity. By quality is meant the affirmation or negation, which depends on the verb; and this is regarded as the form of a proposition.
Thus A and E agree in quantity, and differ according to quality; and so also I and O.
But A and I agree according to quality, and differ according to quantity; and in the same way, E and O.
Propositions are divided, again, according to their matter into true and false. And it is clear that there are none which are not either true or false, since every proposition denoting the judgment which we form of things is true when that judgment is conformed to truth, and false when it is not so conformed.
But since we are often in want of light to recognise true and false, besides those propositions which appear to us certainly true, and those which appear certainly false, there are others which appear to us true, but whose truth is not so evident as to free us from all apprehension that they may be false, or which appear to us false, but of whose falsity we are not certainly sure. These are the propositions which we call probable, of which the first are more probable and the last less probable. We shall say something in the Fourth Part of what enables us to judge with certainty whether a proposition is true.