The Doctrine of the Indefinite Terms in the
Manuel A. Correia
The labour of translation of and comment on the ancient interpreters of Aristotle, which in our days have been edited by Professor R. Sorabji,(1) has put modern readers in contact with new dimensions of Aristotle's thought. In these ancient commentaries, many of the traditional and well-known doctrines of Aristotle find not only theoretical basis, but also a number of obscure and condensed texts reach an important and valuable elucidation and explanation.
The subject-matter that I would like to discuss today is a sample of how these commentators can still contribute to understand Aristotle. I would like to warn, however, that the theme of the indefinite terms is especially illustrative of what I indicate, for the modern comments on this topic have been made without a profounder consideration of the ancient teaching. In my opinion, however, a more reliable and complete explanation about this difficult subject is to be found in the analysis of the ancient view.
The commentaries of Boethius(2) and Ammonius son of Hermeias(3) contain in a slightly different manner the ancient doctrine of indefinite names and verbs. They explain some questions whose answers are not evident in Aristotle's Peri Hermeneias (= PeriH.):(4) namely, (i) why does Aristotle introduce indefinite names and verbs after defining name and verb? I.e. Why does Aristotle consider adequate to define expressions like 'not-man', 'does not recover', etc., once he has defined 'man' and 'recovers' as name and verb respectively? Even more, (ii) why does Aristotle in Chapter 10 of PeriH. leave indefinite verbs aside and introduces only indefinite names in simple (= categorical) propositions?
As far as I know, modern commentators have considered (i) and (ii) as 'open questions' in Aristotle.(5) Some of them have even suggested the idea that Aristotle has simply failed in attempting to give a consistent account of indefinite terms in language.(6) However, I would like to show that all this has a precise answer in Boethius' and Ammonius' commentaries.
Neither in PeriH. nor in another context, Aristotle explains directly why he considers convenient to introduce the notions of indefinite name and verb and define them, but in the ancient view he gives an indirect answer to this question when in Chapter 10 he introduces the indefinites as terms able to be subject or predicate of a simple proposition: Aristotle would suggest that the indefinite term, whether name or verb, is predicable in spite of its indeterminate and unknown signification. Actually, for Ammonius and Boethius, Aristotle considers as a well-formed proposition one in which the subject or the predicate, or both, are indefinite, and they explain that Aristotle in the beginning of Chapter 10 (19b. 8-9) gives us a clue to understand why: because what the indefinite name and verb signify is in a way one thing, but this thing is indefinite.
A first reason of why Aristotle introduces indefinite names and verbs in PeriH. lies in the fact that both indefinites are predicable. However, there is also another reason. Boethius develops an ancient doctrine stating that Aristotle in PeriH. gives strict and non-strict definitions of name, verb and phrase (lógos). Aristotle would give non-strict definitions to see all that can be called in a non-specific sense 'name', 'verb' and 'phrase', but once he gives this analytical procedure, he would intend to see the specific and strict definitions. Accordingly, Aristotle in PeriH. would not give the specific definitions of name, verb and phrase, but he would indicate us how to form them, since he says that the indefinites and the cases or inflections of the name and verb are not name or verb. So, one would remain able to get the corresponding strict definitions by excluding the inflections and the indefinites. Boethius demonstrates this by giving after analyzing the indefinites and the cases of the name and verb the strict or integerrima definitions of name and verb, and a similar situation is also verified to the case of the phrase. Let us take the case of the name: after Boethius treats the nature of the indefinite name and the inflections of the name, he asks for the pertinence of all this discussion:(10)
And he answers:
After that, Boethius gives us the strict definition of name:(11)
The ancient doctrine according to which Aristotle in PeriH. does not give absolutely specified definitions, but he would display all the elements to form them, is entirely absent in modern commentaries of PeriH. These synthetic and analytical movements led to some modern authors(12) to the wrong idea that the post-Ammonian commentators intended to exclude the indefinites and inflections from the definitions of name and verb. But actually what pre- and post-Ammonian commentators show is this ancient doctrine. Ammonius himself gives evidence of being aware of this ancient teaching,(13) for he ascribes it to Herminus, one of the presumed teachers of Alexander of Aphrodisias. Ammonius, however, presumably by following Proclus, does not follow entirely this doctrine and prefers to advance the interpretation that Aristotle in PeriH. gives many senses of name and verb, and in one of these senses the indefinites and inflections are also legitimately included as 'name' and 'verb'.(14)
There is still a third reason to explain why Aristotle considers adequate to define the nature of the indefinite name and indefinite verb. It is suggested by Boethius' commentary that Aristotle needs these two notions to constitute his theory of negation. When Aristotle in PeriH. is concerned with the simple non-modal proposition, he would consider convenient, to deny it correctly, to attach the negative particle to the verb of the proposition.(15) According to Boethius, this practice is the only not-ambiguous one. At least, it does not lead us to confusion, as the Stoic theory of negation, which claims, says Boethius, that the negative particle must be attached to the name (e.g. 'non homo ambulat' would be the negation of 'homo ambulat').(16) Boethius does not discuss further the Stoic mechanism, and apparently he is not entirely informed about it.(17) However, he is clear enough to suggest that Aristotle's theory is not ambiguous: it produces not only one and only one negation for affirmation, but also it defines all the cases that are not negation of a given proposition.
According to Boethius (so too Ammonius), Aristotle in PeriH. realizes the existence of two types of simple propositions: namely, (i) those in which the predicate is a verb: e.g. 'a man walks' ('homo ambulat'), and (ii) those in which 'is' is predicated additionally as a third element, e.g. 'a man is just' ('homo iustus est'). Now, according to Boethius, Aristotle would define not only the specific negation of these two types of propositions, but also all the possible expressions that could reasonably be a negation of the proposition in question. To illustrate this, let us take all the possible cases of (i) in any positions of its terms:(18)
According to Boethius, the proposition
(i) a man walks is denied by
(i) a man does not walk, i.e. by the indefinite verb does not walk.
Accordingly, the expression
(i.1) a not-man walks is not the negation of (i).
But what is it? It is an affirmation with indefinite name as subject.
Similarly, in (ii), i.e. a man is just: if Aristotle considers convenient to attach the negative particle to the verb of the simple proposition, then (ii) a man is not just is the negation of (ii), and the following two, in any order of their terms, are not negations of (ii):
(ii.1) a not-man is just
(ii.2) a man is not-just
Again, Aristotle will be able to determine what (ii.1) and (ii.2) are, because of the notions of indefinite name and verb. In the first case, there is an affirmation with indefinite name as subject. In the second case, there is an affirmation with indefinite predicate, or 'transposed' as Theophrastus , the associate of Aristotle, called it.(19)
To follow with our proposed questions, it suits now to discuss why an indefinite term, since it can be considered as a valid term, is not included in the simple propositions that Aristotle presents in Chapter 10 of PeriH.. In other words: if the indefinite verb can be legitimately considered as a term, why, unlike the indefinite name, does the indefinite verb fail to retain presence in Aristotle's further analysis of PeriH.
Again, while this question is presented in some modern commentaries on PeriH. as a difficulty,(20) the ancient commentators have a consistent and rather simple explanation. According to Ammonius and Boethius, an indefinite verb can be predicated, but there are no indefinite verbs in simple propositions.(21) The answer is not an ad hoc solution. It is rather the result of an interpretation of Aristotle's concise formulae in PeriH. As is said above, Aristotle here would distinguish two and only two types of simple propositions, namely, (i) the one in which the predicate is a verb, like in 'a man walks', 'Socrates runs', etc., and (ii) the other in which 'is' is predicated additionally as a third thing, like in 'a man is just', 'Socrates is wise', etc., (19b. 19-20). Now, since these two types would contain all the possible species of simple propositions, they say that there are no indefinite verbs in simple propositions because in (i) the indefinite verb states the negation, and (ii) that which is predicated is always a name or an indefinite name, but never a verb. Indeed, in (i), the indefinite verb, i.e. 'does not walk' states, as they say, the corresponding negation, namely, 'a man does not walk', which is the negation of a definite action and not an affirmation of an indefinite predicate. As to (ii), what is principally predicated is a name or an indefinite name, i.e. 'just' or 'not-just', but never an indefinite verb.
The coherence and validity of the ancient position depends in a great length not only on these grammatical analyses, but also on the exhibition of all the species of simple propositions, and that explains why the ancient interpreters emphasized in their commentaries an arithmetical calculus of the number of all the simple propositions. The arithmetical calculus of the totality of the species of simple propositions is not an absurd count or an idle arithmetical expedient, as it has been qualified by modern commentators,(22) but the direct consequence of the fact that Aristotle, as the ancient commentators thought it, intended to get the totality of the species of simple propositions. In the list provided already by Syrianus, the master of Proclus, which is adopted by Boethius,(23) it becomes clear that no simple proposition can be constituted by indefinite verbs.
Accordingly, in Ammonius' and Boethius' view, expressions like 'does not recover' lose legitimately presence in propositions due to the very syntactical structure of the simple proposition and the nature of the indefinite verb. Neither in the first type of proposition nor in the second one an indefinite verb occurs as such in propositions. Boethius' and Ammonius' teaching stems from Alexander of Aphrodisias:(24) an indefinite verb, i.e. an expression like 'does not recover', is an indefinite verb only when it is in isolation, but when it composes a proposition it states a negation.
Our discussion above shows how different are in some cases ancient from modern exegeses of PeriH. In our case, the ancient commentators seem to have something still to say. One can even get some further differences by analyzing the enormous material that Boethius and Ammonius commentaries devote to the logic of the propositions with indefinite names, something which Aristotle treated in what is our Chapter 10 of PeriH..
Because of some strange reason, very few of this ancient doctrine has been used in modern interpretations of PeriH.. In many aspects, then, the ancient exegesis of PeriH. is still in a unexplored status. Therefore, some aspects of the ancient paideia are still waiting for illuminating our modern world.
NOTES(1) Richard Sorabji is Professor of Ancient Philosophy in King's College London and the General Editor of the project 'The Ancient Commentators on Aristotle. The plan intends to cope the 15000 pages of the ancient Greek commentators of Aristotle between 200 and 600 AD.
(2) Anicii Manlii Severini Boetii Commentarii in Librum Aristotelis Peri Hermêneias. Prima et secunda editio. C. Meiser (Ed.), Leipzig 1877-1880. (= in Int.).(3) Ammonii in Aristotelis De Interpretatione Commentarius. A. Busse (Ed.), in Commentaria in Aristotelem Graeca (= CAG), vol. iv, 4.6, Berlin 1895. (4) Aristotelis Categoriae et Liber de Interpretatione, L. Minio-Paluello (Ed.), Oxford 1949. (5) cf. Ackrill, J.L. Aristotle's Categories and De Interpretatione, Oxford 1963, pp. 120-1. Also Montanari, E. La Sezione Linguistica del Peri Hermeneias di Aristoteles, vols. i and ii, Firenze 1988. (6) cf. Ackrill (1963), pp. 120-121. (7) Boethius in Int. 18-25, p. 127. quod autem dixit non homo enim nomen quidem non dico, sed infinitum nomen, huiusmodi est: nomen, inquit, omnia quidem definita significat, non homo, vero quamvis unum quodlibet eorum designare possit, quae homines non sunt, tamen quid designet infinitum est et dubium. nam cum multa sint quae homines non sunt et unum quodlibet eorum significare possit, quid significet ignoratur (...). (8) Amm. in Int. p. 42, 2-8. (9) Ammonius refers to his comments on 19b. 9: "for what it [the indefinite name] signifies is in a way one thing, but indefinite." (10) Boethius in Int. 12-14, p. 55. sed quorsum istuc? ut definitio scilicet nominis integerrima conpleretur. (11) Boethius in Int. 14-20, p. 55. etenim iam nunc definitio nominis hoc modo est: nomen est vox significativa, secundum placitum sine tempore, cuius nulla pars significativa est separata, definitum aliquid significans, cum est aut non est iuncta faciens enuntiationem. Also in Int. 2 (= second edition commentary) 22-28, p. 65. The expressions 'definitum aliquid significans' and 'cum est aut non est iuncta faciens enuntiationem' exclude indefinites and inflections respectively. (12) cf. Montanari (1988), vols i and ii, pp. 152-3 and pp. 161-2. (13) cf. Amm. in Int. p. 52, 25-27. (14) Amm. in Int. p. 52, 32-p. 53, 30; p. 45, 15 ff. (15) Boethius in Int. 2, 2-5, p. 262. (16) Ibid., 26-2, pp. 261-2. (17) It is amply accepted today that the Stoics applied the negative particle to the whole proposition and not to the name, as Boethius points out here. Cf. B. Mates, Stoic Logic, Berkeley/Los Angeles, 1961, p. 31. (18) These cases correspond to the 6 permutations of order of 3 things (1*2*3=6), namely, homo, ambulat and non.
1. homo ambulat non 4. ambulat non homo
The expressions 1. and 2. are not considered by Boethius commentary (but they are not relevant either, for they are ellyptical expressions unable to be considered as well-formed propositions); 4. and 5. are affirmations with indefinite name as subject. While, 3. and 6. are correct negations of homo ambulat and ambulat homo respectively.(19) Cf. Ammonius in Int. p. 161, 5-11, and 24-32. Also, Alexander of Aphrodisias in An. Pr. p. 396, 34-p. 397, 4. (20) Montanari (1988), vol. ii, p. 155. (21) cf. Boethius in Int. 2, 6-9, p. 261. id enim quod dicimus non ambulat et infinitum verbum et negatio, sed per se quidem si dicatur simplex sine aliquibus aliis adiectionibus infinitum verbum est; sin vero cum noine aut cum infinito nomine proferatur, non iam verbum infinitum, sed negatio accipitur (...). ("For that which we say 'does not walk' is both an indefinite verb and a negation; in fact it is an indefinite verb if it is said purely and without any other addition; however, if it is expressed together with a name or an indefinite name, it is not longer an indefinite verb, but it is taken as negation."). Cf. also Amm. in Int. p. 157. 9-24. (22) cf. Chadwick, H., Boethius. The Consolation of Music, Logic, Theology and Philosophy, Oxford 1981, p. 154. And Zimmermann, F., Al-Farabi's Commentary and Short Treatise on Aristotle's de Interpretatione, Oxford 1991, p, lxxxix. (23) cf. Boethius in Int. 2, 20-24, pp. 321-324. (24) cf. references in n. 21.