Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

The last topic remaining to be considered in the intellect’s second operation is the other species of enunciation, the hypothetical proposition. Until now we have treated the categorical proposition and its properties. The hypothetical is closer to the intellect’s third operation, because it joins several categorical propositions. It is therefore defined as “a proposition that has two categorical propositions joined as its principal parts,” such as “If a man flies, he has wings.” Hence the copula of a hypothetical is not a verb but an adverb or some mark joining propositions, for example, “and,” “if,” and so on. In a hypothetical conjunction, one conjunct is therefore not predicated of the other, as in a categorical proposition; only a verb is the mark of things that are predicated.

A hypothetical proposition is divided into three species that are formally hypothetical, according to the three different connectives joining propositions: if, and, and or. It can also be divided into three other species that are virtually hypothetical and are properly called exponible propositions, because although they are categorical in themselves, they contain a term that must be resolved and expounded through several categorical propositions that make a hypothetical; thus they can be called hypothetical virtually. We will discuss them in the following chapter.

The species of hypothetical proposition are therefore conditional, copulative, and disjunctive. A conditional joins propositions by the particle if, as in “If a man runs, a man moves.” A rational conditional, which joins propositions by the particle therefore, is reduced to this species. For every conditional virtually includes an inference; properly, however, therefore makes an inference and discourse, not a hypothetical proposition.

A copulative joins propositions by the particle and, as in “Peter is white and Paul is black.” The particle and, when it joins terms, makes a proposition with a copulated extreme and has the force of universality if it is taken distributively rather than collectively; it confuses the term placed after it. For example, “Peter and Paul runs,” “Pepper is sold in Paris and Rome.” In these, “pepper” stands confusedly, and one may not immediately descend under it.

A disjunctive joins propositions by the particle or, as in “Peter runs or Paul speaks.” When that particle joins terms, it makes a proposition with a disjunctive extreme and has the force of particularity, as in “Peter or Paul speaks,” “A man or a horse is white.”

In these species of hypothetical proposition, only two things must be noted. First, what is required for the truth of any hypothetical proposition; second, what the topics or rules of argument are in such hypotheticals.

AS TO THE FIRST. For conditionals there is this rule: For a conditional to be true, it is not required that either part be true; the validity of the inference suffices. For it to be false, it suffices that the inference be invalid. We take “conditional” strictly to mean an inferential conditional. If the particle if is taken only to signify the concomitance of one thing with another, as in “If Peter speaks, Paul walks,” it is not properly the conditional with which we are concerned here. Since the truth of an inferential conditional requires only a valid inference, it follows that every true conditional is necessary and every false one impossible: a valid inference is always and necessarily valid, for if it can fail, it is invalid. The validity of an inference is grounded in the connection of its extremes. St. Thomas teaches this in his Opusculum on Logic, treatise on Enunciation, ch. 14.¹ You will therefore discern that cognition of things under the particle if, when it is taken with the force of an inferential conditional, belongs to necessary cognition, since such a conditional is either necessary or impossible. But if it is not taken with the force of an inferential conditional, but for the concomitance or order of one thing with another, cognition of the conditional terms is cognition of the coexistence and proportion of one thing with another, or of the position of one together with the position of the other. It must be reduced to some cause that joins or proportions one to the other and in fact grounds the truth the proposition in fact has, even if its extremes do not in fact exist.

For copulatives the rule is: For a copulative to be true, both parts must be true; for it to be false, it suffices that either part be false. Thus “A man is rational and a horse neighs” is true because both parts are true; its truth consists in the conjunction of truths. But if you say, “Peter disputes and a stone runs,” the whole is false because one part is false. The same applies to possibility and necessity as to truth: for a copulative to be possible or necessary, each part must be possible and necessary; for it to be impossible or contingent, it suffices that one part be impossible or contingent. If one part is contingent and the other impossible, the whole is impossible, as in “Peter is a stone and Paul runs.” Thus, in a defect the whole follows the weaker part, while for a good effect it requires the complete cause.

For disjunctives the rule is: For a disjunctive to be true, it suffices that either part be true, since its truth consists in separating truth, and its falsity in the opposite. The same applies to necessity and possibility: it suffices that either part be necessary or possible. For example, “A man is an animal or the sun is black” is true and necessary by reason of one part alone. For a disjunctive to be false, however, both parts must be false; the same applies to impossibility. For example: “A man neighs or a horse can laugh.”

In sum, a copulative always follows the weaker part, a disjunctive the stronger. The stronger part is said to be true, necessary, or possible; the weaker, false, contingent, or impossible. For the positing of one stronger part makes the whole disjunctive true, necessary, or possible, while the positing of one weaker part makes the whole copulative false or impossible. Finally, for a disjunctive to be contingent it suffices that one part be contingent, provided none is necessary and they are not all incompatible in falsity. For example: “Peter disputes, or a man is a stone.”

AS TO THE SECOND. In conditionals these are the topics of argument. First: From the whole conditional, with the consequent destroyed, there is a valid inference to the destruction of the antecedent. For example: “If the sun shines, it is day; therefore, if it is not day, the sun does not shine.” Second: From the whole conditional, with the antecedent posited, there is a valid inference to the consequent. For example: “If the sun shines, it is day; the sun shines; therefore it is day.” Third: From a conditional to a disjunctive consisting of its consequent and the contradictory of its antecedent, the inference is valid. For example: “If the sun shines, it is day; therefore it is either day or the sun does not shine.”

In copulatives: From an affirmative copulative to any of its parts there is a formal inference, but conversely there is no formal inference. Thus “Peter runs and disputes; therefore Peter disputes” follows well. But “Peter disputes; therefore he runs and disputes” does not hold. In negative copulatives, however, the whole does not entail a part. This does not hold: “It is not the case that some man is a horse and a man is a stone; therefore a man is a stone.” Nor is there a negative formal inference: “Peter does not dispute and Peter runs; therefore Peter does not run” does not hold. For suppose he runs and does not dispute: the antecedent is true, since it is not the case that he both disputes and runs, while the claim that he does not run is false.

In disjunctives: First, from one part of a disjunction to the whole there is a valid inference. For example, “Peter is just; therefore he is either just or rich,” since the consequent requires no more for its verification than the antecedent requires for its truth. Second: From the whole disjunction, with one part destroyed, there is a valid inference to the other part. For example, “Peter disputes or runs, and he does not dispute; therefore he runs.”

What is said of propositions with a copulated, disjunctive, or conditional extreme—for example, “Peter is white and cold,” where the predicate or subject is a copulated or disjunctive one—does not belong to the present topic. Such propositions are not formally hypothetical but virtually so. We must resolve or reduce them to the corresponding copulative, disjunctive, or conditional propositions and judge them as we do the hypothetical propositions just discussed.