Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Having explained the properties of a proposition with respect to its extremes and the parts of which it is composed, we must now consider those that are properties of the whole and not of its parts, and therefore usually belong to one proposition in comparison with another. There are three: opposition, equipollence, and conversion. Since these three properties belong to a proposition only in relation to another—because one proposition is opposed to another, equipollence is also the equivalence of two propositions, and conversion is the changing of one into another—they must be exercised between propositions that are not disparate but consist of the same terms. For example, “Peter runs” and “Paul does not dispute” are not opposed to one another, nor is one converted into or equipollent to the other.

Opposition in general can therefore be defined as “the affirmation and negation of the same thing of the same thing.” This definition does not include subalternation, which is not properly an opposition except in a relative sense, namely, between a higher and a lower. The remaining oppositions are exercised through affirmation and negation.

Three conditions are therefore required for opposition between propositions. First, on the part of the extremes, they must be propositions consisting of the same parts or extremes, so that nothing is posited in one and not in the other that could vary the subject or predicate of the proposition. Second, the same interpretation of terms must be preserved, that is, the same kind of supposition, the same ampliation, restriction, and appellation. The kind of supposition must be the same: for example, if in one proposition a term supposes simply or personally, so too in the other, though not necessarily the same species of personal supposition, since this changes in some oppositions, for example, from universal to particular, as will be said in the next chapter. Ampliation, appellation, and restriction must be preserved, because these pertain as it were to the identity of the matter and extremes. Third, on the part of the copula there must be an opposed quality, namely, one proposition is affirmed and the other denied.

The opposition just described is divided into three species: contradictory, contrary, and subcontrary.

CONTRADICTORY opposition, if defined according to its formal account, is that which is incompatible with respect to truth and falsity, so that two contradictories can never be simultaneously true or false; if one is true, the other is false. On the side of what is related as it were materially, contradictory propositions are a universal and a particular, one of which is affirmed and the other denied; or two propositions with a singular subject, one affirmed and the other denied. An example of the first is “Every man is white” and “Some man is not white”; of the second, “Peter runs” and “Peter does not run.”

CONTRARY opposition, if defined according to its formal account, is that which is incompatible with respect to truth but not with respect to falsity, so that two contraries can never be simultaneously true, though they can be simultaneously false. On the side of the material account, contrary propositions are a universal affirmative and a universal negative of the same thing of the same thing, as “No man is white” and “Every man is white.” Both can be false simultaneously, but contraries can never be simultaneously true. We do not mean, however, that they are always false simultaneously, only that they can be, namely, in contingent matter.

SUBCONTRARY opposition, according to its formal account, is that which is incompatible with respect to falsity but not with respect to truth, so that the propositions can be simultaneously true but never simultaneously false. According to the material account, subcontrary propositions are a particular affirmative and a particular negative of the same thing of the same thing, as “Some man runs” and “Some man does not run.”

Note that when opposition is exercised according to the quantity of the subject of a proposition, and the propositions have the incompatibility formally required for that kind of opposition, they are said to be opposed by rule and by mode. When they have the incompatibility required for that opposition but not the quantity, they are said to be opposed by rule but not by mode. Thus, formal incompatibility is called opposition by rule, while opposition on the side of the quantity of the subject is called by the mode of enunciation. For example, “Every man disputes” and “No man disputes” are contrary by mode and by rule. But “Some man disputes” (restricting “some” to males only) and “Every man does not dispute” (not restricting “every” to males only) are contrary by rule but not by mode. In that case both are false and cannot be true if a woman were to dispute and no male were to dispute.