[Loyola Book Comp., run.tex: 0 AQR–Vol. W–rev. 0, 17 Jun 2009 ] [The Aquinas Review–Vol. W–rev. 0: 1 17 Jun 2009, 9:15 a.m.] . Anthony P. Andres The Place of Conversion in Aristotelian Logic Anthony P. Andres From at least the time of John of St. Thomas, scholas- tic philosophers have usually learned logic from scholas- tic handbooks. If there were no significant differences be- tween the handbook tradition and Aristotle’s Organon, that would not be a problem. But since there are many differ- ences, especially in the order and manner of teaching, the careful Thomist must ask himself whether the changes proposed by handbooks are a development of the Aris- totelian tradition in logic. By reflecting on the place of propositional conversion in Aristotelian logic, this essay takes a step toward a negative answer to that question. The handbooks, following John of St. Thomas, teach conversion in the second part of logic, but the Organon teaches it in the third. This essay argues that Aristotle teaches conversion in the right place and that in this re- spect the handbooks corrupt the tradition. The first part of this essay will examine the implicit argument for the modern placement of conversion; the second part will ar- gue in favor of its placement within the Organon; and the third will answer a serious objection against Aristotle. Argument for the Handbook Tradition Anthony Andres is a graduate of Thomas Aquinas College. He is now Associate Professor of Philosophy at Christendom College. 1 [Loyola Book Comp., tony: 2 AQR–Vol. W–rev. 0, 17 Jun 2009 ] [The Aquinas Review–Vol. W–rev. 0: 3 17 Jun 2009, 9:15 a.m.] . The Place of Conversion in Aristotelian Logic Anthony P. Andres Before we take up our main business, we should briefly but from certain passages in John of St. Thomas we can review the order of Aristotelian logic. The scholastic lo- reconstruct a plausible argument for it. gicians divide and order the parts of logic according to In his Cursus Philosophicus John writes, ‘‘We take the the division and order of three operations of the human proposition and the enunciation as the same thing, since intellect. Therefore they teach that the first part of logic such a use obtains even among the wise, just as hap- aids the intellect in understanding indivisibles, the second pens in common disputations.’’⁴ That is, although ‘enun- in composing and dividing them, and the third in reason- ciation’ and ‘proposition’ are two different words, John ing discursively. On this basis they divide the treatises of believes that they mean the same thing, as the usage of the Organon into three: the Categories belongs to the first both the common run of scholars and of the wise attests. part of logic,On Interpretation to the second, and the rest, Three chapters later he begins to teach about conversion beginning with the Prior Analytics, belongs to the third.¹ itself: ‘‘The properties which follow the whole proposi- Aristotle gives the rules for the conversion of proposi- tion are three: opposition, conversion, and equivalence.’’⁵ tions in the second and third chapters of the Prior Ana- Since, however, he has already said that the proposition lytics.² For example, he states that the universal negative and enunciation are the same, we can conclude with John proposition is converted universally, so that if it is true that conversion is also a property of the enunciation. that ‘No A is B,’ it is also true that ‘No B is A.’ Simi- We can now argue that conversion belongs in the sec- larly, the particular affirmative proposition is convertible, ond part of logic. In the proemium to his commentary so that ‘Some A is B’ implies that ‘Some B is A.’ Notice on Aristotle’s On Interpretation, St. Thomas notes that the that in each case what is the subject of the first proposi- enunciation is the subject of the second part of logic.⁶ And tion becomes the predicate of the second, and what is the since every science discusses the properties of its subject, predicate likewise becomes the subject. From such exam- the second part of logic should discuss the properties of ples, St. Albert draws the following definition of conver- the enunciation. John of St. Thomas, however, teaches sion: ‘‘Conversion in terms is a transposition of terms, so that conversion is a property of the enunciation. There- that the subject becomes the predicate, and the predicate fore treatises on logic should teach conversion in the sec- the subject.’’³ Thus Aristotle puts the transposition of the ond part, as indeed the handbooks do. parts of the proposition into the third part of logic. The writers of the handbooks might have used such As noted above, the handbook tradition moves the an argument to claim that they have developed the Aris- teaching of conversion out of the third part of logic and totelian tradition in logic. Their claim, however, rests on into the second, which Aristotle expounds in On Interpre- the contention that the conversion is a property of the tation. The handbooks do not explicitly justify this change, ⁴ John of St. Thomas, Cursus Philosophicus Thomisticus (Taurini: Ma- rietti, 1820), p. 23. John does acknowledge that St. Thomas draws a dis- ¹ Cf. St. Thomas Aquinas, I Peri Herm., proem., n. 2. tinction between the enunciation and the proposition, but he ignores it in ² Aristotle, On Interpretation, 25a1. his own treatment. ³ St. Albert the Great, I Prior Anal., tract. 1, c. 8 (all translations are ⁵ Ibid., p. 28. my own). ⁶ Cf. St. Thomas Aquinas, I Peri Herm., proem., n. 2. 2 3 [Loyola Book Comp., tony: 4 AQR–Vol. W–rev. 0, 17 Jun 2009 ] [The Aquinas Review–Vol. W–rev. 0: 5 17 Jun 2009, 9:15 a.m.] . The Place of Conversion in Aristotelian Logic Anthony P. Andres enunciation, a fact they assume was overlooked by Aris- that which can be measured by time can be considered as totle. But he did not overlook the fact; by his principles, such; and since what is first and chiefly measured by time as explained by St. Thomas, the enunciation cannot be is motion, in which action and suffering consist, then the converted. Before we can understand why, however, we verb, which signifies action and suffering, signifies with ⁹ need to understand the parts of the enunciation. time. St. Thomas is here establishing a connection between ‘sig- The Noun and Verb nifying with time’ and ‘signifying action and being acted In the second chapter of the Categories, while identify- upon.’ The verb signifies ‘with time’ because it in some ing its subject, Aristotle makes a distinction between two way signifies what is measured by time, motion. But it kinds of ‘‘things said.’’⁷ The first kind includes things signifies motion because it signifies action and suffering, said ‘‘with intertwining,’’ the complex expressions, exam- which are constituted by motion. Thus the verb signifies ples of it being ‘‘man runs’’ and ‘‘man wins.’’ The sec- with time because it signifies an action or a suffering. ond includes things said ‘‘without intertwining,’’ simple Of course, not only verbs proper, but also participles, expressions, examples being ‘‘man,’’ ‘‘runs,’’ and ‘‘wins.’’ infinitives, and even some nouns signify actions and suf- Since the Categories helps us to understand indivisibles, it ferings. In order to distinguish the verb proper from these, is concerned with the second kind of ‘‘things said,’’ not St. Thomas draws a second distinction. He says that the the first. And thus Aristotle goes on in the Categories to verb not only signifies action and suffering, it ‘‘signifies divide simple ‘‘things said’’ according to what they signify. action through the mode of action, the nature of which is At the beginning of On Interpretation, however, he dis- that it inheres.’’¹⁰ The noun, however, ‘‘signifies something tinguishes two kinds of simple ‘‘things said,’’ not accord- as existing by itself.’’¹¹ That is, the verb differs from the ing to what they signify, but according to how they sig- noun and similar expressions because the former signifies nify. He calls them the noun and the verb.⁸ The noun and something as inhering in another, while the latter signifies verb are both simple expressions signifying something by it as existing by itself. convention, but the former signifies something without A consequence of the aforesaid distinction is that the implying any time, while the latter necessarily signifies noun may signify the subject in a complex expression, that something according to some time. For example, ‘man’ is ‘‘in which something inheres,’’¹² but the verb is always the a noun and ‘runs’ is a verb, the former not implying any predicate, or, as Aristotle puts it, ‘‘is always a sign of those time, the latter implying the present. things which are said of another.’’¹³ As we shall see, this This initial distinction between the noun and verb, how- function of being ‘‘said of another’’ makes the discussion ever, is rooted in a deeper one. St. Thomas notes: Time itself, insofar as it is a certain thing, can be signified ⁹ St. Thomas, I Peri Herm., lect. 4, n. 42. by a noun like any other thing. In another way, however, ¹⁰ Ibid., lect. 5, n. 59. ¹¹ Ibid., n. 56. ⁷ Aristotle, Categories, 1a16. ¹² Ibid., n. 59. ⁸ Aristotle, On Interpretation, 16a20 and 16b6. ¹³ Aristotle, On Interpretation, 16b7. 4 5 [Loyola Book Comp., tony: 6 AQR–Vol. W–rev. 0, 17 Jun 2009 ] [The Aquinas Review–Vol. W–rev. 0: 7 17 Jun 2009, 9:15 a.m.] . The Place of Conversion in Aristotelian Logic Anthony P. Andres of the verb relevant to On Interpretation, the treatise about the whole, but it is not an enunciation since it is not true the enunciation.