Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Exponible propositions are “those which, because of a term signifying a sense explicable by several propositions, necessarily need to be expounded or clarified.” Since they are clarified by several propositions, they are said to be virtually hypothetical. Some are exponible because of the thing signified, as with the verbs “begins,” “ceases,” “differs,” and similar terms; for “begins” is expounded by saying, “It is now, and it was not before.” We omit these here and leave them to be explained where their subject matter is treated—for example, beginning and ceasing in Physics VI,¹ and difference in the Predicables.² Other expressions need exposition because of their very mode of signifying, and these properly belong to dialectic.

There are three species: exclusive, exceptive, and reduplicative propositions. An exclusive proposition is one modified by a term signifying exclusion, such as “only,” “alone,” and the like. It can either form a proposition about the excluded extreme, namely, when it belongs on the side of the predicate, as “Peter is only a dialectician”; or it can make the whole proposition exclusive, namely, when it belongs on the side of the subject, as “Only a human being is capable of laughter”; or it can exclude by reason of otherness, that is, signify that the predicate does not belong to other subjects, as “Only a human being is capable of laughter,” meaning that no one other than a human being is capable of laughter; or it can exclude by reason of plurality, as “The categories are only ten,” meaning that they are no more than ten.

Although an exclusive proposition can be affirmative or negative, and the negative may be negative only as to the mode, only as to the dictum, or as to both, for now it suffices to give the exposition of the affirmative. From it, one can see that the negative must be expounded in the opposite way.

An exclusive proposition is therefore expounded by two categorical propositions taken conjunctively. One affirms that the predicate belongs to the subject and is called the antecedent proposition, that is, a simple proposition that simply predicates one thing of another. The other denies that the predicate belongs to another subject and is thus a universal negative with respect to every other subject. For example, “Only a human being is capable of laughter” is expounded as “A human being is capable of laughter, and nothing other than a human being is capable of laughter.” “The categories are only ten” is expounded as “The categories are ten, and they are no more than ten.” Hence an affirmative exclusive proposition converts into a universal affirmative when the terms are transposed. Thus “Only a human being is capable of laughter” correctly entails “Everything capable of laughter is a human being.” Consequently, “only” is a sign of confusion with respect to the term it immediately affects, because in its converse that term, affected by “only,” is affected mediately by the universal affirmative sign, which is to be confused.

There are three topics of argument for exclusives. First: The consequence from an exponible proposition to its exponents, and conversely, is good. Second: From an exponible proposition expounded conjunctively, there is a good consequence to any one of its exponents. Third: From any of the exponents to the exponible proposition disjunctively, the consequence holds.

Observe carefully that although the particle “only,” when placed on the side of the subject, makes the whole proposition exclusive, and when placed on the side of the predicate makes a proposition about the excluded extreme, exclusion affects its term in such a way that it virtually bears on that term. Therefore it is not permissible to argue from a proposition about the excluded extreme to an exclusive proposition, or conversely, just as this does not follow: “Only Adam is white; therefore Adam is only white.” The first was true if Adam alone were white in the world; the second is false, because there are many other things in Adam besides whiteness. Likewise, “Only the sun shines; therefore the sun only shines”; “the predicables are only five; therefore only the predicables are five.”

The second exponible proposition is the exceptive, as when you say, “Every animal except a human being is irrational.” Note that if such an exceptive proposition is affirmative, it has three exponents taken conjunctively: its antecedent proposition, a universal affirmative in which the term from which the exception is made is predicated of the excepted part, and a negative proposition in which the predicate is denied of the excepted part. Thus the exponents of the proposition just given are: “Every animal that is nonhuman, or other than a human being, is irrational”; “Every human being is an animal”; and “No human being is irrational.” The contradictory of this proposition, however, is expounded disjunctively by the contradictories of its exponents. Some expound the particle “except” more briefly by the particle “excepting,” saying, “Every animal, excepting a human being, is irrational,” or by a conditional conjunction, saying, “Every animal that is not a human being is irrational.” But this is not to posit exponents, only equivalents within a single term, since it too needs exposition: “excepting” needs exposition just as much as “except.”

The topics of argument for exceptives are these. First: From an exceptive proposition to all its exponents, and conversely, the consequence is formal. Second: From an exceptive proposition expounded conjunctively to any one of its exponents, the consequence is formal, as in any conjunctive proposition from the whole to a part. Third: In exceptives expounded disjunctively and contradictorily with respect to conjunctive propositions, the consequence from any exponent to the whole holds by the rule for disjunctives.

The third exponible proposition is the reduplicative, formed by the term “insofar as.” They are called reduplicatives because they seem to duplicate the subject or predicate, as in “Peter, insofar as he is a human being, is capable of laughter.” The same holds for these terms: “in so far as,” “in virtue of which,” “according to what,” “as such,” and so on.

These reduplicating terms are used in two ways: first specifically, and second reduplicatively. Specifically, they reduplicate or apply a formal and specific concept to the subject. Reduplicatively, they apply the account of a cause by reason of which something is such, and thus make the proposition causal. An example of the first is “Colored, insofar as colored, is the object of sight”: “insofar as” is taken specifically because it reduplicates only the formal account. But if I say, “A human being, insofar as white, disperses sight,” it signifies the cause by reason of which the human being disperses sight.

A reduplicative proposition is expounded by four exponents when “insofar as” is taken reduplicatively and not merely specifically: the antecedent proposition; an affirmative proposition in which the reduplicated term is affirmed of the subject of the exponible proposition; another affirmative proposition in which the predicate is affirmed of the reduplicated term; and a causal proposition, which explains the account connecting the predicate and subject. Thus, if you say, “Every human being, insofar as rational, is capable of laughter,” it is expounded as follows: “Every human being is capable of laughter”; “Every human being is rational”; “Everything rational is capable of laughter”; and “Because it is rational, it is capable of laughter.” This is the account of the ancients.

But in truth only the fourth proposition is a legitimate and sufficient exponent, namely, the causal one; at most, the third can be added, since it is implicitly contained in the causal proposition. For it suffices to say, “Because something is rational, it is capable of laughter; therefore, insofar as it is rational, it is capable of laughter.” The first and second exponents are not necessary, and sometimes even become false when the reduplicative proposition is true by means of some restriction or limitation, and not absolutely. For example, if you say, “Christ, insofar as he is a human being, is a creature,” or “Every animal, insofar as rational, is capable of laughter,” the first and second exponents are false: “Christ is a creature”; “Every animal is capable of laughter”; “Every animal is rational.” Those propositions are false when stated absolutely. It therefore suffices to posit the causal proposition as the exponent. Since that causal proposition requires the third exponent in order to be true, the third can be added. If it is true that because something is rational it is capable of laughter, it is also true that everything rational is capable of laughter; once the causal proposition is true, it is true in every case.

And observe that sometimes the terms “insofar as” and “according to which” are taken not so much specifically or reduplicatively as diminutively and restrictively, because something belongs to the subject only in a qualified way and by reason of a part, not absolutely. For example: “An Ethiopian is white according to his teeth,” or “insofar as he has teeth”; “Christ, insofar as he is a human being, is a creature, but he is not absolutely a creature.” In that case use St. Thomas’s rule in Summa theologiae III, q. 16, a. 8: when something can belong indifferently to a whole or a part, if it belongs only to the part, it does not denominate the whole absolutely, but only in a qualified way and through the phrase “insofar as.” Whiteness, for example, can belong to a whole body or to a part; if it belongs only to a part, such as the teeth, it is not predicated absolutely of the whole. But when something can belong only to a part, and on account of that part to the whole, it is predicated absolutely of the whole even if it belongs only to the part. Thus a human being is said absolutely to be curly-haired, even though curliness is only in the hair. Since being a creature, because of its transcendence, is naturally capable of belonging to the supposit and the nature, it is not predicated absolutely of Christ without explaining that it belongs to him by reason of his human nature.

Observe, second, that a reduplicative proposition sometimes does not reduplicate a cause but a condition or concomitance. For example, “Fire burns insofar as it is applied”; “An assent, insofar as it is obscure, is of faith.” Here it does not reduplicate a cause but a condition or mode. “A human being acts insofar as he exists”: “exists” signifies the concomitant condition required. Such reduplicative propositions are then not expounded by a causal proposition, but by a conditional one, in which the predicate of the reduplicative proposition is put on the side of the subject. For example: “If a human being acts, he exists”; “if an assent is of faith, it is obscure”; “if fire burns, it is applied,” and so on.