Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

THE SENSE OF THE DIFFICULTY does not concern a verb when it is taken with the force of a noun; then it is clear that it can be made infinite even within a proposition, like other nouns, as when I say, “To run is not to rest.” Rather, the question concerns the verb itself when it exercises the role of copula. Nor is there a difficulty about negation itself when it is attached to the verb in such a way that it applies not only to the being signified but also to the very role of copula. For then it is clear that the negation is taken negatively and not infinitively: it makes the proposition negative precisely because it applies to the union, since it is impossible to deny the copula without the extremes remaining removed and disjoined. How, once the union has been denied, can the extremes remain united? Precisely because negation passes to disjoining and removing the extremes, the proposition becomes negative and negation is not taken infinitively. For an infinitizing negation consumes all its force within the term to which it is attached, without passing to another term. This is clear in propositions with an infinite subject, as when I say, “A non-man is non-rational,” where the first negation does not pass beyond its term; otherwise it would deny the verb and the proposition would not be affirmative.

The whole difficulty therefore consists in this point: can negation be attached so subtly to a verb inside a proposition that it makes the verb’s signification infinite without affecting or denying the copula?

ON THIS DIFFICULTY, some recent authors hold the affirmative side. St. Thomas clearly holds the opposite in On Interpretation II, lect. 1,¹ where he says: “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.”

THIS REASON can be explained further as follows: Precisely because negation is added to a verb exercising the role of copula within a proposition, it cannot fail to affect the union itself and to pass to the extremes that are united. But that is to be taken not infinitively but negatively. Therefore.

The major premise is clear. If negation attached to a verb makes it infinite with respect to its signification but does not touch it as copula, either it makes the signification infinite while denying the copula, or it makes the verb infinite in signification without denying the copula, leaving the copula affirmed. The first is impossible, because one negation cannot at once be taken negatively with respect to the copula and infinitively with respect to the signification. To make a term infinite, it forms one simple, incomplex concept with the term made infinite; to negate, it must have a distinct, complex concept with the thing negated, as was shown in the preceding question.² But one negation cannot at once belong to a complex and an incomplex concept with respect to the same thing. The second is also impossible, because once the signification of the verb is made infinite, the resulting union cannot be positive and affirmative: an infinite verb does not convey an affirmed mode of action, but one denied and removed. The action signified by the verb is changed by the infinitizing negation into its denied opposite; therefore an affirmative copula cannot follow from a denied vital action. Although negation can be signified and united positively, as in verbs signifying negation, infinitizing negation does not permit this. It does not signify negation by reason of itself and as a form applicable to another, but as removing and indetermining a positive form. Therefore, if it is applied to something, it signifies by removing from it, not by applying negation, because it signifies by removing it. St. Thomas’s reasoning therefore holds: because in a proposition negation removes one thing from another, the verb cannot be made infinite. Outside a proposition, however, since the verb is not taken with the force of connecting, it can be made infinite. St. Thomas also teaches this in On Interpretation I, lect. 5, § “It excludes certain things.”³

OBJECTIONS ARE RESOLVED.

First you will object: Infinite verbs signify with tense even within a proposition; therefore they signify by uniting.

The consequent is clear because the union of the verb is grounded in its very mode of signifying with tense. The antecedent is asserted by the Philosopher in the chapter on the Verb⁴ and is proved because infinite verbs are declined in past and future tenses. Just as “does not run” is made infinite in the present, so are “did not avail” and “will not avail” in the past and future.

This is confirmed because the following inference is valid: “Peter has not-to-run (taken infinitively); therefore Peter does not run.” But if in this inference the term is taken negatively and not infinitively, the inference is invalid, since we argue 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, because its contradictory is true, namely, “Peter runs.” Therefore not must be taken infinitively in the consequent, and thus the verb is made infinite in the proposition.

THE REPLY is to distinguish the antecedent of the principal argument: If it 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. To the consequence we say that it does not unite positively but removively, which makes the proposition negative. For an affirmative proposition requires that it unite determinately, or apply something; it cannot remove and eliminate the signification of the verb, since in that way it will also remove it from the subject, if applied to it, which is to negate, not to make infinite. When the Philosopher said in the chapter on the Verb that an infinite verb consignifies tense and is always of something, that is, as St. Thomas explains there,⁵ that it is a mark of things predicated, the meaning is not that it signifies tense or is a mark of predicated things by applying and uniting positively and determinately, but by indetermining and removing. This can be done through all its inflections outside a proposition, but within a proposition only by negating.

To the confirmation we reply that the inference is invalid, as the argument shows, and so proves nothing against us. 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 you will object: In Posterior Analytics I,⁶ lect. 23 in St. Thomas,⁷ the Philosopher makes this inference: “Non-twinkling stars are near us; but the planets do not twinkle; therefore they are near us.” But the minor premise cannot contain a negated verb; therefore it contains an infinite verb.

The minor premise is clear: if the verb were taken negatively, the premise would be negative and consequently would yield a negative conclusion, not an affirmative one.

THE REPLY is that the Philosopher does not formulate that syllogism in this way, but as St. Thomas explains there: “Let the syllogism be formed as follows: Every non-twinkling thing is near; the planets are non-twinkling; therefore they are near.” In both premises “not twinkling” is taken infinitively. Thus when the argument says, “The planets do not twinkle,” it is understood equivalently: they are stars that do not twinkle, or they are non-twinkling.

Finally, it is argued: An oblique verb, even with the force of a verb, and an infinite noun are found within a proposition; therefore an infinite verb is too.

The consequence is proved both from parity of reasoning and because an infinite verb composes a proposition: it truly is a term, and not in the mode of a noun, because it signifies with tense; therefore it is in the mode of a verb.

THE REPLY is that there is a great difference between an oblique and an infinite verb, as St. Thomas says in On Interpretation II, lect. 1,⁸ because an oblique verb departs from a verb only with respect to signification of present time, which is simply time, but not with respect to indetermination of action, as an infinite verb does. Thus an oblique verb can serve as a copula at least in the past and future, but an infinite verb cannot. For although infinitization is directly applied to the verb’s signification, it consequently prevents a positive and determinate copulation, which is grounded in the signification of a determinate action, as was said. An infinite noun, however, enters a proposition as predicate or subject; for that reason an infinite verb too can enter and compose a proposition with the force of a noun, but not by connecting positively or negatively. It is understood to have the force of a noun not because it changes its signification by no longer signifying with tense, but because it changes its acceptance, being taken as predicate or subject. This also occurs with a verb that is not infinite, as when we say, “To run is to move.”