Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

We are not speaking of a verb when it is taken with the force of a noun, as when I say, “To run is not to rest”; then it can be made infinite, like other nouns. Rather, we speak of a verb when it exercises the role of copula. The difficulty is this: can negation be attached so subtly to a verb within a proposition that it makes the verb’s signification infinite without affecting the exercise of connecting, which is proper to a verb within a proposition? For if negation affects the verb as copula, the proposition will be negative and the verb negated, not made infinite. When negation makes a term infinite, it consumes all its force within the term to which it is attached, without passing to another term, as when I say, “A non-man is non-rational,” where the first negation does not pass beyond its term; otherwise it would negate the verb and the proposition would not be affirmative. If, then, negation affects the verb both with respect to signification and with respect to copula, it makes the verb negated, not infinite. The doubt thus consists in seeing whether negation can affect the verb’s signification without affecting the copulation or exercise of uniting.

THE CONCLUSION IS: A verb cannot be made infinite within a proposition; when negation is added, it is negated. Outside a proposition, however, it can be made infinite.

St. Thomas says this expressly in On Interpretation II, lect. 1,¹ saying: “A negation affecting a verb within a proposition removes the verb from something and thus makes the enunciation negative. This does not happen on the side of the noun; for an enunciation becomes negative only by denying the composition conveyed in the verb. Therefore an infinite verb placed in an enunciation becomes a negative verb.” What could be clearer?

THE FIRST PART IS PROVED BY REASON: A verb within a proposition has the role of copula and exercises the function of uniting; therefore negation affecting a verb within a proposition negates it and does not make it infinite.

The consequent is proved: Negation affecting a union destroys it and makes the proposition negative. A proposition’s being negative is nothing other than the extremes being removed from one another and their union, which the verb exercises, being dissolved and destroyed by the addition of negation. Therefore, precisely because negation affects a verb within the proposition in which it exercises the function of uniting, it negates the verb and does not make it infinite.

You may say that negation affects the verb’s signification, not its function of uniting or its role as copula, and thus makes it infinite, not negative. Against this: Either negation affects the verb only with respect to its signification and not its function of uniting, or it affects the verb with respect to both. If the second, the verb is negated and the whole proposition becomes negative, because the function of uniting is destroyed and the extremes are removed. The first cannot occur, because negation affecting the verb’s signification cannot leave the union affirmed; it must also attack and destroy that union. This is proved as follows: Give me an infinite verb. Does not that infinitization turn the verb’s signified meaning into its denied and removed opposite? For this is what it is to be made infinite. Therefore, by force of such infinitization, the copula cannot be preserved as affirmative. The consequence is clear, because negation must be signified as removing and indetermining a positive form. Therefore, however it is applied to a verb, it signifies by removing. St. Thomas’s reasoning thus stands firm: because in a proposition “negation removes the verb from something, it makes the enunciation negative,” and in this way a verb cannot be made infinite.

To say that negation will make the verb infinite with respect to signification and negate it with respect to its role as copula is contradictory. The same negation would then be taken negatively and infinitively, which is plainly incompatible, since as infinitive it forms one simple and incomplex concept with the term made infinite, while as negative it must have a distinct and complex concept with the thing negated, as was said above. One negation cannot at once belong to a complex and an incomplex concept with respect to the same thing.

THE SECOND PART OF THE CONCLUSION, that a verb can be made infinite outside a proposition, is clear from what was said, since outside a proposition it is not taken with the force of connecting. The holy Doctor also teaches this in On Interpretation I, lect. 5, § “It excludes certain things.”²

OBJECTIONS ARE RESOLVED.

First it is objected: An infinite verb still signifies with tense within a proposition; therefore it signifies by uniting.

The antecedent belongs to Aristotle, in the chapter on the Verb.³ It is proved because such a verb is inflected through past and future tenses.

The consequent is proved: A verb has the character of union because it signifies with tense; therefore wherever it signifies with tense, it signifies by uniting. The antecedent is clear, because the only part of the definition of a verb that explains its being a union is “to signify with tense.” Since this means signifying in the mode of action, flow, or motion, and action or motion rests, as it were, on two termini, “from which” and “toward which,” a verb signifying in this way is indicated as resting on two extremes and being their copula.

This is confirmed: “Peter has not-to-run; therefore Peter does not run” is a valid inference. Therefore not-run in the consequent is made infinite. The consequent is proved: If it is not made infinite but is negated, the inference is invalid, because it argues from an undistributed to a distributed term. Consider the case in which Peter runs and disputes: the antecedent, “He has not-to-run,” that is, to dispute, is then true, but the consequent, “Therefore he does not run,” is false if not is taken negatively, since its contradictory, “Peter runs,” is true. Therefore not in the consequent must be taken infinitively.

THE REPLY to the argument is to distinguish the antecedent: If the verb signifies with tense by removing and eliminating the form it makes denied and indeterminate, I concede it; if it posits some determinate form, I deny it. Therefore, that it signifies by uniting must also be distinguished: if it unites positively, I deny it; if removively, I concede it. In this way it makes a negative proposition, because an affirmative proposition requires it to unite determinately and apply something. It cannot instead remove and eliminate the verb’s signification, since in this way it would also remove it from the subject if applied to it, which is to negate, not to make infinite. This is how Aristotle is explained when he said, “An infinite verb consignifies tense and is always of something,” that is, as the holy Doctor explains there,⁴ “it is a mark of things that are predicated.” Its signifying tense and being a mark does not mean applying and uniting, but indetermining and removing; within a proposition, this occurs only by negating.

To the confirmation we reply that the inference is invalid and nothing against us follows from it. If “not-to-run” in the antecedent is taken negatively, the inference is valid, but proves nothing because the verb is not made infinite.

Second it is objected: Aristotle makes this inference in Posterior Analytics I, lect. 23, as cited by St. Thomas:⁵ “The non-twinkling stars are near us; the planets do not twinkle; therefore they are near us.” But the minor premise cannot be negative; therefore it must contain an infinite verb. The minor premise is proved: If it contained a negated verb, it would be a negative minor premise and consequently would yield a negative conclusion, not an affirmative one.

THE REPLY is that Aristotle did not form that syllogism in this way, but as St. Thomas says there: “Let the syllogism be formed thus: Every non-twinkling thing is near; the planets are non-twinkling; therefore they are near.” In both premises, “not twinkling” is taken infinitively. Even if Aristotle had said, “The planets do not twinkle,” it should be understood equivalently: they are stars that do not twinkle, or they are non-twinkling.

Finally, it is argued: An oblique verb has the role of a verb even within a proposition; therefore an infinite verb does too.

THE REPLY is that the two cases differ, as St. Thomas says in On Interpretation II, lect. 1,⁶ because an oblique verb can unite the extremes in a proposition at least in the past and future. It departs from a verb only with respect to signification of present time, not with respect to indetermination of action or the role of copula. For a verb in any tense other than the present indicative does not signify an action insofar as it is in the process of coming to be, but insofar as it is to be done in the future or has already been done in the past. Hence such verbs are said to depart from the proper account of a verb, which consists in signifying action or motion insofar as it is in the process of coming to be. An infinite verb, however, through infinitization loses or has impeded its positive and determinate copulation, which is grounded in the signification of determinate action, as was said. An infinite verb can enter a proposition in the force of a noun, as predicate or subject, but not by connecting positively. When it is taken with the force of a noun, it does not change its signification by ceasing to signify with tense; rather, it changes its acceptance, since it is taken as predicate or subject, which is also required of a verb that is not made infinite, as when I say, “To run is to move.”