Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Here we explain the particle “finite,” by which we said that infinite names are excluded from the account of a name. An infinite name is “one which, when some negation is added, makes its signification indeterminate.” This is to be infinitized.

In this connection, note that a negation attached to a term can act upon it in two ways: either by passing into its signification, destroying it and substituting in its place the negation of the thing signified, which indeed applies to all subjects capable of such a negation; or by leaving its signification unchanged and removing composition or copulation, since its force attaches to the verb as it copulates the extremes. When it acts in the first way, it is said to infinitize, that is, to render the name itself indeterminate; when it acts in the second way, it is said to negate, and it makes the proposition negative. Hence this effect of negating is exercised only within a proposition, since it concerns the copula.

Hence, for a name to be infinitized, the negation must not be signified in its own right and by the very first imposition; rather, by affecting the name, it must render its signification indeterminate, that is, signifying not what the thing is but what it is not. Thus the names “no one” and “nothing” are not infinite, because they signify negation itself in its own right and directly under a determinate concept, rather than making some positive signification indeterminate by an added negation.

Second, it must be observed that an infinite name is incomplex and connotative.

The first is established by Aristotle and St. Thomas, who expressly assert it in the first book of the Perihermeneias, in the chapter on the Name.¹ It also follows from the reasoning: an infinite name does not leave its signification in the state it had, but changes it into its opposite, namely, into the negation of what it signifies. Therefore it does not retain a double signification, the positive one it had before and the added negation—for if it retained both, it would not change the former. Therefore it is not complex, since there is no double signification in it. Hence there is no infinitization in the complex expression “no man,” because both significations remain intact. The signification must therefore be wholly changed, from a double one into a single one, and consequently be incomplex.

That it is connotative is clear, because an infinite name signifies negation not abstractly but concretely; therefore it signifies connotatively, since formally it signifies the denied form, and on the side of the subject that has it, of which it is concretely predicated. This is what it is for something to be connotative. — The antecedent is proved as follows: an infinite name is verified of something positive, but it cannot be verified if it signifies negation abstractly; therefore it must signify negation concretely and as something inhering. The minor is proved because one cannot say of a stone, for example, “A stone is the negation of a man,” but one can say, “A stone is a non-man.” Therefore, to be predicated, it must be signified concretely and connotatively.

LET THIS, THEN, BE THE CONCLUSION: An infinite name is not a name, and is rightly excluded from the account of a name by the particle “finite.”

So say Aristotle and St. Thomas here.²

The FIRST PART, that it is not a name, is commonly admitted by all. It is proved as follows: infinitization removes the proper and essential function of a name; therefore an infinitized name is not a name.

The antecedent is proved: the proper function and account of a name is to be a mark and designator of a thing, as we said above. A name is so called from marking, because by each thing’s name we mark, distinguish, and designate it. But an infinite name neither marks, designates, nor names anything; therefore it is not a name. The minor is clear, because as soon as a name is infinitized, it renders its signification indeterminate and signifies only what something is not, not what it is, as can be seen in “non-man” and the like.

The SECOND PART of the conclusion, namely, that it is excluded by the particle “finite” and not by another, is disputed by some recent writers, who strike that particle out as superfluous. Yet it is explicit in St. Thomas, both in Opusculum 48, chapter on the Name,³ and in the first book of the Perihermeneias, lecture 5,⁴ where, treating of the infinite verb (and the same applies to the name), he says that the Philosopher first defined the verb in general and then, by these particles, excluded those things that are imperfectly verbs. Therefore a perfect and exact definition of the name and the verb requires these particles; without them—or, to speak to the point, without the particle “finite”—the proper function and mode of signification of a name are not explained: namely, signifying by way of a mark, or marking what the thing is. For this is what naming is.

Nor is the infinite name excluded by the particle “of which no part, etc.,” because, as we said, an infinite name has no parts but is incomplex. For if it were complex, a proposition with an infinitized subject would be negative, because that negation would also extend to the copula and not only to the subject, since there it would have its partial signification, which formally and significatively composes the proposition and, contrary to its nature, would destroy everything it encountered after itself. But the consequence is absurd, as is evident in conversion by contraposition, which proceeds from a negative proposition to an affirmative one with infinitized terms. Therefore, and so on.

OBJECTIONS ARE ANSWERED.

First you will object: An infinite name is truly a term; therefore it is truly a name.

The antecedent is proved: it is an extreme and a part of a proposition, as is clear in “A stone is a non-man”; therefore it is a term. The consequent is proved from St. Thomas, first book of the Perihermeneias, lecture 1,⁵ who says that every proposition must consist at least of a name and a verb, since these are its principal parts. Therefore, if a genuine proposition is formed from a verb and an infinite name, the infinite name truly is a name.

It is confirmed: a verb that serves as the copula in a proposition truly is a verb; therefore a name that is an extreme copulated or capable of being copulated truly is a name. For just as it belongs to the account of a verb to be a copula, so it belongs to the account of a name to be an extreme capable of being copulated.

The argument is answered: The antecedent is granted and the consequent denied. For to be a term, it suffices to be a part in some way; but to be a name, it must be a part by way of a mark, or of marking what the thing is. An infinite name does not have this.

To the proof from St. Thomas, it is answered by explaining the proposition “Every proposition must consist of a name, etc.”: that something acquires the status or property of a name intrinsically and in its own right, or by accommodation and accidentally, is granted; that it is intrinsically and strictly a name is denied. For many things are placed in a proposition as extremes—not because they are names, but because they are put in place of a name or are taken in the force of a name—as St. Thomas says in the present lecture 5 and in Opusculum 48, chapter on the Verb. Thus one might say, “To run is to move,” “yesterday is not today,” or “quickly is not slowly.”⁶ These expressions acquire a certain use as a name through the accommodation of the intellect, not through the proper character of their signification, but only accidentally; and thus they form a proposition. The same is said of an infinitized name.

To the confirmation it is answered: the antecedent is granted and the consequent denied. The difference is that for something to be a verb, nothing more is required than that it signify by copulating, or by way of a copula; for this is the proper function and office of a verb, so that if it has this, it truly is a verb. A name, however, does not merely have to be an extreme capable of being copulated; it must also be so by way of a mark, or of marking. An infinite name does not have this, and therefore is not a name.

Second argument: An infinite name signifies something certain and determinate on the side of its formal signification, although it signifies indeterminately on the material side and as regards what it connotes; therefore it truly is a name.

The consequent is clear, because each thing, in order to be or be called this or that, must be judged according to its formal character, which is primary and specificative in it, and not according to its material or connoted character. The antecedent is proved because “non-man,” for example, signifies a determinate negation, namely, of man and not of horse, just as “blind” signifies the negation of sight and not of hearing. Therefore, just as “blind” truly and properly is a name, so too are “non-man” and the other infinite names.

It is confirmed: “intelligible” and “imaginable” signify something indeterminate, just as “non-man” does. For they are said both of what is and of what is not, both of real beings and of beings of reason, and yet they truly are names. Therefore, the fact that an infinite name signifies something indeterminate should not exclude it from the account of a name.

A second confirmation: transcendent or supertranscendent names can be infinitized by adding a negation, just like other names; and yet when so infinitized they truly remain names. It is proved as follows: “non-being,” for example, when so infinitized, either signifies something or nothing. If it signifies nothing, then it does not signify, and so it is neither a term nor a name, but falls away from its signification through the added negation. If it signifies something, then it signifies being; and thus “non-being” would signify being, which is contradictory.

The argument is answered: The antecedent is distinguished: that an infinite name signifies something certain and determinate on the side of the thing signified is granted; that it does so by its mode of signifying is denied, and the consequent is denied. For to be a name, it is neither sufficient nor necessary to signify a certain and determinate thing; rather, it must signify in a certain, determinate, designative, certifying mode, by way of a mark.

To the proof: “Non-man signifies a determinate negation” is distinguished: on the side of the thing signified, granted; by a determinate mode, as if marking and designating, denied. In this connection, note that signifying something determinate can be understood in two ways: either on the side of the thing signified, that is, signifying a determinate thing; or according to the mode of signifying, that is, in a mode that designates what the thing signified is. For something to be a name, it is not required that it signify something determinate in the first way. However indifferent and common something may be—even negation itself, or “intelligible,” “imaginable,” or “being”—if it is signified in a designative and marking mode, that is, one that says what the thing is or how it is, it will be a true name. But if it signifies a determinate thing in an indeterminate mode, one that does not designate or mark what it is, but rather what it is not, it will not be a name, because it lacks the function and office of a name, which is to name or designate; for by naming we distinguish and designate one thing from another. Nor is something judged to be a name solely by the thing signified, but also by the mode, which belongs to the formal signification and distinguishes a verb from a name: a verb signifies in one way, a name in another, although they signify the same thing, as “I run” and “running” do.

Hence the answer to the proofs and confirmations is clear. Although “blind” signifies the negation of sight, it signifies as if marking and designating what something is, not what a form is not, as “non-man,” “intelligible,” and “imaginable” do: these signify the most indeterminate things, but in a determinate mode. — To the final proof, the minor is denied. To the proof that “non-being” either signifies something or nothing, it is said to signify the negation of being, not in a determinate and designative mode that says what the negation of being is, but by saying what is not. Therefore, “non-being signifies something” is distinguished: insofar as it is signified by the infinitized name “non-being,” it is denied, for in that respect it signifies precisely the negation of being in an indeterminate mode. Insofar as, through reflexive cognition, that negation of being can be cognized in the manner of a being and become a being of reason, it is granted; for then it will signify a being, or something of reason, not by the name “non-being,” but by another name signifying that reflex concept of non-being in the manner of a being, for example, “a negation of reason” or “a being of reason.”

Finally, it is argued: An infinite name has parts that signify separately; therefore it remains excluded from the account of a name by the particle “of which no part, etc.,” and is not excluded by “finite.”

The antecedent is proved: “non-man” consists of “non” and “man”; but “non” composes the infinite name not materially, but significatively and according to its ultimate concept. Therefore the name is subordinated to a concept different from the one it infinitizes, and consequently to a double concept, and it is complex. The minor is proved: the infinitization of the expression “non-man” does not come from the material sound of the word “non,” but from its most formal signification; for if “non” does not signify, it removes or negates nothing. Therefore it infinitizes by signifying and not merely by composing materially.

The answer is, as was said above about “republic,” “proconsul,” and so forth, that in an infinite name, as in names of composite form, there is both the derivation of one name from another and composition. If we attend to derivation, it is certain that the signification of “non-man” was derived from the signification of “non.” If we attend to composition, “non” and “man” are related materially in the expression “non-man”; nevertheless, the infinitization that impedes the name’s positive signification originates and proceeds from the signification of “non” and “man” derivatively and efficiently, not compositionally and formally. Therefore a new imposition and signification is given, according to which the infinite name is subordinated to a single concept and signifies the negation of man concretely, since the lack of names leaves us without simple words to signify it. Thus, in infinitization, “non” is not a negation of just any kind, but a negation that changes and impedes the name’s signification.