Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

INFINITE NAME is said to be “that which, when some negation is added, renders its signification indeterminate or infinite.” For negation attached to a term can act on it in two ways: first, in such a way that it passes into the term’s signification, destroying its determinate and positive signification and substituting in its place the negation of the thing signified, which indeed applies to all subjects capable of such a negation. Second, negation can be attached to a term without changing its signification, but by 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. In the second way it is said to negate, and it makes the proposition itself negative. Hence this effect of negating, since it concerns the copula that it negates, is exercised only within a proposition. Thus, for the infinitization of a name, the negation must not be signified by the very first imposition; rather, an added negation, by affecting the name itself, must render the name negated and its signification indeterminate—that is, signifying not what a 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. Hence it also follows that in an infinite name the signification is not changed by a new imposition, but by the impediment of negation, which by its negative signification has the power to impede the signification of another thing and, by impeding it, to remove it.

FROM THIS IT FOLLOWS that an infinite name is incomplex and connotative. That it is incomplex is expressly taught by Aristotle in the first book of the Perihermeneias, in the chapter on the Name,¹ and by St. Thomas there, lectures 4 and 5.² The reason is that an infinite name does not leave its signification in the state it was in, but changes it into its opposite, namely, into the negation of its signification. Therefore it does not retain a double signification, namely, the positive one it signifies of itself 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 there, as complexity requires. Thus we see that in the complex expression “no man” no infinitization occurs, because both significations remain intact. Therefore, when infinitization occurs, it is a sign that both significations do not remain intact; consequently, the expression does not remain complex, because it no longer has a double signification.

That it is connotative is clear from this: an infinite name cannot signify negation abstractly, for otherwise it would not be verified of anything positive. One cannot say that a stone is the negation of a man, but one says that it is a non-man. Therefore the negation of man is signified concretely, so that it can be verified of that of which it is predicated; therefore it is also signified connotatively, since formally it signifies the denied form and, on the side of what has that form, the subject of which it is concretely verified. This is what it is for something to be connotative.

GIVEN THESE POINTS, I SAY: An infinite name is excluded from the account of a name by the particle “finite.”

This conclusion is expressly stated by Aristotle in the chapter on the Name and by St. Thomas there, lectures 4 and 5. As to the FIRST PART, namely, that it is not a name, nearly everyone agrees. The reason is that infinitization removes the proper and essential function of a name, which is to be a mark of something. For it is called a name because it is a mark; therefore it must mark and designate something in order to be a mark. But an infinite name neither marks nor designates anything, because it leaves its signification indeterminate and signifies only what something is not, and not what it is.

And observe that signifying something determinate is understood in two ways: first, on the side of the thing signified, because the thing itself is determinate; second, by the mode of signifying, because that mode is determinate, that is, designative of what it signifies. 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 if it is a negation—if that very indifferent and common account is signified, this suffices for a name’s determinate signification, because we can conceive what even negation itself or any common account is, or what it is like. What is required is that something be determinate in the second way, so that it signifies what something is and not merely what it is not; for in the latter case it determines and designates nothing, and so impedes the very function of a name, which is to name, designate, or mark something. For by naming we designate and distinguish one thing from another.

THE SECOND PART, namely, that an infinite name is excluded by the particle “finite” and not by another, is opposed to some recent writers, who strike out that particle as superfluous. But the contrary is clear from St. Thomas, both in Opusculum 48, chapter on the Name,³ where he adds that particle to the definition of a name, and because in the first book of the Perihermeneias, lecture 5,⁴ treating of the infinite verb—and the same applies to the name—he says that the Philosopher first defined the verb in general and afterward, by these particles, excluded things that are imperfectly verbs. Thus a perfect and exact definition of a name and a verb requires these particles, so that what belongs to the quiddity of a name may be set down explicitly and expressly. For since the definition of a name had stated that it is a significant utterance, and a name must signify not just anyhow but by way of a mark and designation, it was necessary to add the particle “finite” in order to explain this function.

Nor was the infinite name sufficiently excluded by the particle “incomplex,” because, as we have seen, an infinite name is not complex but incomplex; otherwise, if it were complex, a proposition whose subject was infinitized would thereby be a negative proposition, because that negation would extend to the copula as well, and not only to the subject. But the copula, when negated, makes the proposition negative. This consequence is absurd and admitted by no dialectician, as is evident in conversion by contraposition, which proceeds from a negative to an affirmative proposition with infinitized terms.

OBJECTIONS ARE ANSWERED.

First you will object: Negation must enter the name it infinitizes not only materially but also significatively and by its ultimate concept; therefore it does so by a concept different from the one it infinitizes, and so the infinite name is subordinated to a double concept, which is to be complex.

The antecedent is clear, because the force of negation in infinitizing a name is founded on negation as signified, and not on the material sound of the word “non”; for if negation is not signified, it removes or negates nothing. Therefore, in the infinitization of a name, negation enters not materially but significatively and by its ultimate concept.

THE ANSWER IS that in an infinite name, as in other 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 one is derived from the signification of another, just as, in the etymology of names, one name usually originates from the signification or significations of others; yet this does not suffice for complexity, as is clear in itself. But as regards the composition of an infinite name, the word “non” and the name attached to it are related materially; nevertheless, that infinitization by which the name’s positive signification is impeded proceeds from the signification of the negative word, as it were derivatively and efficiently, not compositionally. For infinitization is not just any negation, but a negation that changes and impedes the name’s signification; and the signification that results from this impediment and infinitization applies to both words as to a single term of composite form. Hence, by infinitizing the name, the word “non” accidentally destroys its own signification.

Second you will object: An infinite name is truly a term, since it does not lose its signification but changes it; and similarly, it is an extreme of a proposition, as is clear in “A stone is a non-man.” Therefore it has the account of a name.

The consequence is proved, because nothing more is required for the account of a name; and St. Thomas says in the first book of the Perihermeneias, lecture 1,⁵ 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: if some verb truly copulated the extremes in a proposition, it would truly be a verb; therefore, if some name truly is an extreme capable of being copulated, it truly is a name. For just as a verb is that which copulates, so a name is that which can be copulated; in this respect a verb and a name are correlative.

THE ANSWER IS that the consequence is denied. To the proof, it is said that, for something to have the account of a name, it suffices to be an extreme of a proposition when it has this in its own right and, as it were, intrinsically, but not when it does so accidentally, because it takes on something like the status and property of a name. For many things can be placed in a proposition as extremes, not because they are names, but because they are held in the force of a name, as St. Thomas teaches in the first book of the Perihermeneias, lecture 5,⁶ and in Opusculum 48, chapter on the Verb;⁷ for example, “To run is to move.” Indeed, adverbs too can be so taken, as in “Yesterday is not today” and “Quickly is not slowly.” For through the accommodation of the intellect they acquire a certain use as a name, not through the proper character of their signification; and when so taken in the force of a name, they can form an utterance or proposition accidentally, not in their own right.

To the confirmation it is said that if a verb copulates in its own right and by the proper character of its signification, it truly is a verb; but if it does so through accommodation or extrinsic derivation, it is not a verb in its own right. Thus the cases of a verb are excluded from the verb, although they copulate in a proposition, because they are derived from and fall away from the verb that they copulate. Or, second, it is said that a verb has no exercise other than signifying by copulating when it is inside a proposition; hence, if it has this, it is a verb. But a name has not only the function of being capable of copulation and union, but also of being a marker and designator, as it were a mark of a thing, without which it does not have the true function of a name. Therefore, although it is capable of being copulated in a proposition where it is taken in the force of a name, it is not thereby a name, because it is not a mark.

Finally, it is argued: An infinite name signifies something certain and determinate on the side of its formal signification, although it signifies indeterminately on the side of its material signification and what it connotes. Therefore it is simply a name; for each thing is to be judged by the character of its formal signification, which is primary, and not by what it connotes.

The antecedent seems certain, 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; and yet “blind” truly and properly is a name. Indeed, in this use, transcendent or supertranscendent names such as “intelligible” and “imaginable” also signify something indeterminate, because they are said both of what is and what is not, of real beings and beings of reason; and yet they truly are names. Therefore, and so on.

It is confirmed: these transcendent or supertranscendent names can be infinitized by adding a negation, and yet they remain true names; therefore so do other names. The minor is proved by the name “non-being”: when so infinitized, it either signifies something or nothing. If nothing, then it does not signify, and so it will not be a name or a term, but will have been stripped of its signification. But if it signifies something, then it signifies being, and thus “non-being” would signify being, which is contradictory.

THE ANSWER IS that infinitization in a name consists in its being indeterminate by its mode of signifying, not on the side of the thing signified; and this mode belongs on the side of the formal signification, because it signifies the negation of the form itself, not by saying what the negation itself is, but what the form is not. Something is judged to be a name not only by the thing signified, but also by the mode in which it is signified, just as a verb signifies in one way and a name in another, although they concern the same thing, as “I run” and “running” do. Thus, because an infinite name does not signify in a determinate mode, as if marking and designating, it is not a name. The opposite is true of “blind” and similar names, which signify the negation of a form itself, and not what the form is not. Transcendent names signify something determinate on the side of the mode of signifying, although on the side of the thing signified it is indeterminate and most common; for they signify what that most common concept is, not what it is not.

To the confirmation, the minor is denied, and to the proof it is said that those infinitized names signify the negation of being not in a determinate mode—that is, by saying what the negation of being is—but in an indeterminate mode, namely, by saying what is not being. And to the objection that this negation of being is a being and signifies something, namely, something of reason, it is answered that insofar as it is signified by that infinitized name, it signifies precisely the negation of being in that indeterminate mode, although through reflexive cognition that negation can be cognized in the manner of a being. This, however, belongs to another name, which signifies that reflex concept of non-being in the manner of a being, not to the infinitized name.