Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Two things are certain here. First, any proposition, when negation is placed at its beginning, becomes the contradictory of that proposition, because that negation denies the whole that the other proposition affirms. Second, if propositions have a singular term on the subject side, nothing more is required for them to be contradictories than that one deny what the other affirms, while supposition, restriction, ampliation, and appellation remain unchanged. For example: “Peter speaks”; “Peter does not speak.”

If they have a common term, three conditions are required for contradictory opposition. First, the term must not be universally distributed in both propositions or have particular supposition in both, but must be universal in one and particular in the other. Second, the term that is universal in one proposition must become particular in the other, and conversely the particular term must become universal. Third, a term standing universally in relation to a term standing confusedly must change to determinate particularity; and a term standing universally in relation to a term standing determinately must change to confused particularity. An example is “Every man is white” and “Some man is not white.” Here “man” is universal in the first and particular in the second, determinately. “White” in the second stands universally in relation to “man” taken determinately, while in the first it stands confusedly.

In contrary opposition, which concerns only common terms, if the contrariety is by mode, the same universality must remain in both propositions; if a term is held particularly, it must be changed to universal. For example: “Every man is white”; “No man is white.” But in propositions contrary not by mode but by rule, nothing more is required than a defect of truth in them: they cannot be true together, but can be false together. See an example of contraries by rule alone below, at the end of this chapter, and above, at the end of the preceding chapter.

In subcontrary opposition, which also concerns common terms, the reverse order from contraries is required: first, if there is any universality in one subcontrary proposition, it must change to particularity in the other, if the subcontrariety is by mode. In subcontrary opposition by rule alone, nothing more is required than a defect of falsity: the propositions cannot be false together, though they can be true together, regardless of whether the propositions are universal or particular.

Note that universality and particularity can be found in propositions in two ways: in one way, by reason of a sign that marks particularity or universality, such as “every,” “no,” “some,” and so on; in another way, by reason of a mode affecting a modal proposition, such as “impossibly,” “necessarily,” or “possibly.” The same applies to “and” taken copulatively and “or” disjunctively when they function on the side of a term: the former is universality and the latter particularity. Therefore, when we say that universality must change to particularity and conversely, this applies to universality of signs and of modes, unless universality becomes part of an extreme and does not perform the function of distributing or particularizing. In that case it need not change. For example, if you say, “That which is every man is an animal,” “every” is part of the extreme and should not change.

There are also signs that have universality and particularity partly, and are called incomplete universals and incomplete particulars. An example is “every” taken for each genus, but not for each individual of that genus. Thus “Every animal was in Noah’s ark” is true of every species of animal, but not of every individual. “Both” likewise produces incomplete universality, as does “contingently,” since it is resolved by “and” taken copulatively and by “possibly,” which is a mode of particularity. If you say, “A man runs contingently,” it is resolved as: “A man can possibly run and can possibly not run.” Therefore, if these incomplete modes are affirmed in both opposed propositions or denied in both, then, even if the copula itself is denied in one proposition and affirmed in the other, the propositions do not share any law of opposition. For example, “Every man contingently runs” and “Some man contingently does not run,” with “contingently” affirmed in both, are not contradictories and do not share the law of opposition; indeed, they are equivalent with respect to the mode, because in both cases “contingently” includes universality and particularity. If, however, two exponible propositions virtually include contrary exponents, they have contrary opposition. Thus “Only man is an animal” and “Only man is not an animal” are contraries, because among their exponents are “Every animal is man” and “Every animal is not man.”

There are two rules for recognizing contrary and subcontrary propositions, both by mode and by rule. First: Given two propositions of opposite quality concerning the same extremes, if the affirmative entails the contradictory of the negative, and is not entailed by it, the propositions are contraries. Second: If, for two propositions of opposite quality concerning the same extremes, the affirmative is entailed by the contradictory of the negative, but not conversely, they are subcontraries. Therefore one must always attend, as if to a principle and rule, to the contradictory of the negative (which is always affirmative) and see whether it is entailed by an affirmative proposition or entails it; from this we judge whether the proposition is contrary or subcontrary.

The reason for the first rule is this: once the contradictory of the negative proposition is posited, if it is entailed by the affirmative, the affirmative cannot be true without the contradictory of the negative also being true, since it follows from it; in a good inference, if the antecedent is true, so is the consequent. If the contradictory of the negative is true, the negative itself cannot be true but must be false, since it is its contradictory. Consequently, those two propositions, the affirmative and the negative, conflict in truth. They do not, however, conflict in falsity but can be false together, because the affirmative does not follow from the contradictory of the negative. Thus the contradictory of the negative can be true and the affirmative false, since where there is no good inference the antecedent can be true and the consequent false. In the same case the negative is also false, since its contradictory is true; therefore the negative and the affirmative can both be false. This can be practiced in the propositions “Every man runs” and “No man runs.” The contradictory of the negative is “Some man runs,” which follows from the affirmative, but does not entail it.

The reason for the second rule is the reverse. Given an affirmative and a negative proposition concerning the same extremes, if the contradictory of the negative entails the affirmative, they can never be false together. For if the contradictory of the negative is true and entails the affirmative, the affirmative is already true. If it is said that the affirmative is false, even though it is entailed by the contradictory of the negative, that contradictory must be false, since in a good inference, if the consequent inferred is false, the antecedent is false too. But then the negative is true, since its contradictory is false; thus the propositions can never both be false. They can, however, be true together, because the affirmative does not entail the contradictory of the negative. The affirmative can therefore be true while the contradictory of the negative is false, by the rule of a bad inference, in which the antecedent can be true and the consequent false. Since the contradictory of the negative is false, the negative, its contradictory, is true; therefore both can be true. An example is “A man is white” and “Some man is not white,” given that the contradictory of the negative is “Every man is white.”

It follows that if the contradictory of the negative neither entails the affirmative nor is entailed by it, the propositions share no law of opposition. For example: “A man is every white thing”; “A man is not white.” These are contraries: “Peter runs”; “No man runs.” The affirmative entails “Therefore some man runs,” which is the contradictory of “No man runs,” but “No man runs” does not entail it. Both propositions are false in the case where Peter is dead and John is running. They are contraries by rule, but not by mode of enunciation.