Boethius: On Aristotle on Interpretation 4–6 9781472551771, 9780715639191, 9781849668316

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Conventions [ ] Square brackets indicate additions to the translation to complete the sense. < > Angle brackets indicate additions to the Latin text. Citations from Aristotle are in italics. Propositions, phrases or words referred to explictly are put in inverted commas. Italics are also used for Latin words and titles of books. Bold type is occasionally employed for emphasis. The references to Aristotle’s text by chapter and page/line are added to aid the reader and do not indicate that Boethius divided his work in this way. All lemmata are those provided by Boethius himself. Divergences from the lemmata in the continuous translation and the first edition of the commentary are noted as are any divergences from the received text of Aristotle.

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Textual Emendations 231,16 320,29 396,6-7 424,21

I have restored the MS reading illa … subiecta. I have changed the MSS correction finitum ‘finite’ back to the uncorrected indefinitum ‘indefinite’. I have followed S2 in deleting the words non enim propositionis. Adding negationes with F2.

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Introduction Richard Sorabji Boethius’ second and larger commentary on Aristotle’s On Interpretation was written in Latin in the early sixth century AD in the style of Greek commentaries on Aristotle. Both commentaries were part of his project to bring to the Latin-speaking world knowledge of Plato and Aristotle. His project was for comprehensive translation of them and for adaptation of the Greek commentaries on them. The project was cruelly interrupted by his execution at the age of about 45 between 524 and 526 AD, leaving the Latin world under-informed about Greek Philosophy for 700 years, although his commentary on Aristotle’s On Interpretation remained the standard introduction throughout the Latin Middle Ages. Aristotle’s On Interpretation In the first six chapters of his On Interpretation Aristotle defines name, verb, sentence, statement, affirmation and negation. This has standardly been seen as a progression beyond the subject of his Categories, which distinguishes single terms. For On Interpretation already studies the complexity of a statement, and it can be seen as pointing forward to the treatment in his Analytics of syllogistic arguments, which combine three statements, two of them premisses and one a conclusion. But C.W.A. Whitaker has argued that what turns out to interest Aristotle from Chapter 7 onwards is contradictory or contrary pairs of statements, and that these contradictory or contrary pairs relate rather to the practice of dialectical refutation discussed in Aristotle’s other logical works, the Topics and Sophistici Elenchi.1 In Chapters 8 to 10, Aristotle examines exceptions to the rule that in contradictory or contrary pairs one statement will be false and the other true. Chapter 11 addresses some puzzles about complex assertions, Chapters 12 to 13 consider pairs of statements involving possibility and necessity, while the last chapter, 14, discusses beliefs that are contrary.

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Introduction Boethius’ use of Alexander on the role of thoughts

Boethius reveals to us how On Interpretation was understood not only by himself, but also by some of the best Greek interpreters, especially by the Aristotelian Alexander of Aphrodisias (who flourished around 205 AD) and the Neoplatonist Porphyry (232-309 AD). Alexander, so Boethius tells us (11,13-13,11), defended the authenticity of the work against Andronicus. The latter was already concerned with questions of authenticity in the first century BC and had questioned a cross-reference to Aristotle’s On the Soul. But he did so only because he failed to understand that when Aristotle said in Chapter 1 that his book was about the ‘affections’ which he had already discussed in that other work, he was not referring to passions. He was referring to thoughts, which were indeed discussed in On the Soul, as they are here (noêmata, 16a10 and 14). In fact the point made here that truth and falsity have to do with combination (sunthesis, 16a12 and 14) had been made in connexion with thoughts at On the Soul 430a27-7 (sunthesis noêmatôn). Boethius, like the Neoplatonists Dexippus and Ammonius before him, goes a little further and insists that truth and falsity are primarily created at the level of thoughts, not of spoken sounds, but only when the thoughts are combined, not while they remain simple (49,23-32). Aristotle himself had stated at 16a6 that spoken sounds are signs in the first place (prôtôn) of affections of the soul, in other words, of thoughts (noêmata, 16a10). Boethius’ use of Porphyry on written, spoken and mental names and verbs Later in the first chapter at 30,1-14, Boethius quotes Porphyry ascribing a distinction to the Aristotelian school, and making use of it to explain Aristotle’s wording. According to Porphyry, the school recognised three sentences (orationes), evidently types of sentence, one written, one spoken and one composed in the mind, or at 42,1517, one in letters, one in spoken sound and one in thoughts. Porphyry infers that the school would want the sentence in the mind to be analysable into separate components corresponding to name and verb. Thus there would be three types of name and verb, one written, one spoken and one exercised in the quiet of the mind. Porphyry does not raise the further question asked by Augustine in a theological context a little later, when Augustine says (On the Trinity 15.10.1920), ‘The word which is sounded externally is a sign of the word that shines inside, to which the name “word” is more applicable. … [This word] is a prerequisite of any language, but is prior to all the signs by which it is communicated.’ In other words, contrary to many modern views, soliloquy is causally prior to communication. Of this

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word in the mind, Augustine claims that it ‘does not belong to any language, at any rate not to any of those which are called the languages of the nations, of which our own Latin is one’. Porphyry does not tell us whether the word in the mind is Greek. But in Aristotle’s text the spoken and written names and verbs are both Greek, and he does not consider whether the thoughts (noêmata) in the soul at 16a9ff. are themselves names and verbs. Nonetheless, Porphyry’s idea that they are names and verbs is repeated by Ammonius in the period between Porphyry and Boethius and ascribed to Aristotle himself in Boethius’ report.2 The idea that thinking is a kind of inner talking goes back to Plato, but it did not at first enter into such details as those raised by Porphyry and Augustine.3 Augustine’s idea that thought is a language different from any natural language was revived in modern times by Jerry Fodor,4 developing the ideas of Noam Chomsky. Fodor was interested in a language of thought that corresponded to whole sentences of any level of complexity, not just to simple sentences consisting of names and verbs. Nonetheless, he and Porphyry and Augustine in their different ways were speaking of a language of thought and Fodor called his language ‘mentalese’. Boethius’ use of propositio for written, spoken, or mental sentences (orationes) Porphyry’s idea helps us to understand Boethius’ definition of a proposition (propositio). Boethius defines a proposition in his De differentiis topicis 1174C as a kind of sentence (oratio), one which signifies what is true or false.5 This is closest to, but not identical with, Aristotle’s definition of logos (sentence) at 16b26. We would not nowadays think of a proposition as a spoken, or as a written sentence. But Boethius thinks of it as a wide term, neutral between any of the three kinds of sentence, written, spoken, or mental. It is wide in other ways as well. Boethius continues his definition of a proposition (1174C-D) by saying that it can be a statement (enuntiatio) or assertion (prolatio), or, if brought into doubt, a question, or, if confirmed by arguments, a conclusion. It can have complexity, if, for example, it is a conditional (1175A-B). In a conditional the ‘if’-clause and the ‘then’-clause can each be called a proposition. A further complication concerns the word oratio, which is sometimes applied to something less than a sentence, a phrase which does not on its own signify what is true or false. Thus one oratio is predicated of another in the sentence ‘Socrates with Plato and the students investigates the essence of philosophy’ (1175D-1176A). Here oratio might be rendered ‘expression’. But as this is the exception and does not fit the definition of a proposition as signifying what is true or false, the rendering ‘sentence’ has been maintained in the translation below.

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Introduction Boethius’ use of Porphyry on the differentiation of individuals by unshareable characteristics

In Chapter 7 Boethius says that a proposition acquires its character in the first place from thought (intelligentia), and in the second place (136,11-12) from the things of which the thought (intellectus) consists. As an example of the second, if the sentence is singular, it gets its singularity from the subject that it gets hold of, e.g. Plato, rather than man (136,16). This gives Boethius occasion to introduce an influential idea of Porphyry’s, that individuals are distinguished from each other by each having a composite quality that is actually unshareable (incommunicabilis, 136,17-137,26; 139,4-19). We know that this idea is Porphyry’s, because he puts it in an even stronger form in his Introduction or Isagôgê 7,19-8,3. The individual is there said to be nothing but a bundle (athroisma, sundromê) of characteristics that are (severally or jointly) distinctive. Distinctive characteristics are called idiotêtes (Latin proprietates). I do not believe that Porphyry is here drawing on Aristotle or the Stoics, because he leaves out their idea that the distinctive characteristics would have to inhere in, or be otherwise dependent on, matter, which the Stoics called substance (ousia). I suspect he leaves matter out because he is speaking to beginning students who are about to read Aristotle’s Categories, which does not even mention matter and form, so Porphyry does not want to go into those complications. I believe Porphyry is drawing instead on Plato. Plato Theaetetus 209C speaks of an individual (atomon), such as Socrates, consisting of (ex hôn ei) uniquely distinctive characteristics (the word idios is used earlier at 154A, 166C), such as his distinctive snubness of nose. Snubness of nose is precisely the example used by Boethius when he discusses Porphyry in his second commentary on Porphyry’s Isagôgê (235,5-236,6, ed. Brandt, CSEL). Plato has the idea that one cannot think of Theaetetus at all without having his distinctive characteristic in mind. In Porphyry what is unique may be a bundle (athroisma, a word used at Plato Theaetetus 157B-C, or sundromê) of characteristics, rather than a single one, and for Porphyry it is unique in the strong sense that it would (ouk an, Isagôgê 7,16-24) not belong to another individual. Hence Boethius’ word, ‘unshareable’ (incommunicabilis). Plato is likely to have been the Stoics’ source of inspiration for their idea that each individual has a distinctive characteristic. Because Porphyry’s work was presented as an introduction to many of Aristotle’s ideas, the notion of the individual as a unique bundle of characteristics was taken by subsequent Neoplatonists, by Proclus ap. Olympiodorum Commentary on Alcibiades 1 Westerink 204,8-12 and possibly by ‘Philoponus’ in An. Post. 2 437,21-438,2 , as representing the Aristotelian view, despite the lack of any reference to matter, or a subject for the characteristics to inhere in.

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Does truth or falsity depend on the existence of the subject of reference in a singular statement? Aristotle had already anticipated in his Categories the subject of On Interpretation Chapters 8 to 10. In Categories Chapter 10 at 13b12ff., he had supplied an exception to the rule that in contrary pairs of statements, one of the pair must be true and the other false. If Socrates no longer exists, then neither ‘Socrates is sick’ nor ‘Socrates is well’ will be true. The subject arises again when Aristotle resumes in On Interpretation Chapter 11 the discussion of puzzles about compound sentences started in Chapter 8. But here he allows us to say that the deceased Homer is a poet (21a25-8). The existential import of singular statements had already been most brilliantly discussed by Alexander and the Stoics.6 Boethius, and before him Ammonius, overlap in the way they understand Aristotle’s treatment of ‘Homer is a poet’. ‘Is’, according to Aristotle, is predicated ‘accidentally’ of Homer because he is a poet, and not in its own right. Boethius takes Aristotle to mean that ‘is’ applies to Homer only because of his being a poet, and not because of his being Homer. Boethius (374,1427) and Ammonius (Commentary on Aristotle’s On Interpretation 212,2-4) infer that the ‘is’ would no longer be applicable, if ‘poet’ were not applicable. Presumably that is why the ‘is’ does not imply Homer’s continued existence. The interpretation is repeated at 374.9376,15, but there Boethius addresses a further remark that Aristotle adds (21a22-3) that the possibility of thinking about what is not does not imply that it is. Boethius explains that the same analysis can be repeated in relation to ‘Homer is thought about’. The ‘is’ there attaches primarily to ‘thought about’, not to Homer, and so does not imply his existence. Mario Mignucci has suggested that Aristotle did not intend to generalise beyond his particular illustrative sentences. ‘Homer is a poet’ obviously does not imply the subject’s present existence, ‘Socrates is well’ obviously does, but not through the verb ‘is’, since On Interpretation 6b19-25 tells us that that is nothing in itself, but merely signifies a combination.7 Determinism: is a singular statement predicting a future contingent event true or false? By far the most famous example of a singular statement that is perhaps neither true nor false was raised by Aristotle in Chapter 9 of On Interpretation. On one interpretation of 18b9-16, 18b33-19a6, Aristotle saw it as a threat that events such as a future sea-battle would have been irrevocable 10,000 years ago, if it was true 10,000 years ago that there would be a sea-battle on that day. The idea of inevitability or determinism is therefore a major theme in Boethius’

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commentary. But he did not interpret Aristotle’s problem of the future sea-battle in the way just suggested, and he did extend his discussion to many other aspects of determinism as well. Through Porphyry’s records he had access to the defence of indeterminism mounted around 200 AD by the Aristotelian Alexander against the deterministic arguments of Stoics and dialecticians. This led him to discuss a whole range of topics that were then at issue: Is the idea of chance merely a function of our ignorance?8 Is there room for free choice of the will?9 For unactualised possibilities?10 For the idea of things being up to us?11 Is God benevolent, if his actions are inevitable?12 How far down the scale of beings does divine Providence spread?13 How is possibility defined by Stoics and Aristotelians and by the dialecticians Diodorus Cronus and his pupil Philo?14 Do predictions by oracles imply determinism?15 On the interpretation of Aristotle just mentioned, which is not that of Boethius, Aristotle is worried by the irrevocability of past truth about the future occurrence of a sea-battle. His solution, on this interpretation, is to deny that it was either true or false 10,000 years ago that there would be a sea-battle, although the prediction might eventually start being true after a certain date. What would remain true after the sea-battle would not presumably be a future-tensed prediction. For after the battle it is not true that there will be a sea-battle on that date. What remains true would rather need to be either a past tensed proposition, or, as in modern logic, the tenseless proposition that a sea-battle coincides with such and such a date. If that represents Aristotle’s solution suitably adapted, it would, I believe, be a viable but unnecessary line of thought. For Aristotle need not have worried, if his anxiety was that past truth is irrevocable. Past truth about a future sea-battle really has to do with the future, not the past. We may compare how I can now make my most recent birthday to have been my last by plunging a dagger into my bosom. That is not really a case of my affecting the past, because to describe my most recent birthday as my last is to describe its relation to the future. It is to say that it has no successor. Similarly to make a past prediction to have been true is not really to affect the past. It is to create a relation between a past prediction and a subsequent state of affairs. That is why it is not too late now to make a past prediction to have been true or false. By conducting or not conducting a sea-battle tomorrow, I can make the prediction that I would conduct one true or false. I need not go into too much detail on alternative interpretations of Aristotle’s sea-battle by Boethius and by other ancient commentators on Chapter 9 of Aristotle’s On Interpretation. For another whole volume of the present series was devoted to the subject.16 It contained translations by David Blank and Norman Kretzmann of the commentaries of Ammonius and Boethius on this particular chapter,

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along with four essays: ‘The three deterministic arguments opposed by Ammonius’, ‘Boethius, Ammonius and their different Greek backgrounds’, both by Richard Sorabji, ‘Boethius and the truth about tomorrow’s sea-battle’ by Norman Kretzmann, and ‘Ammonius’ seabattle’ by Mario Mignucci. The present volume puts the subject in the different perspective of Aristotle’s On Interpretation as a whole. What needs to be said is that Boethius explains the idea of the irrevocability of the past. But he takes the threat of determinism to turn not on the irrevocability of past truth, but instead on the principle, which does not seem to be Aristotle’s, that mere predictability implies inevitability.17 He decisively rules out the interpretation, which he calls Stoic, that Aristotle meets the problem by denying that statements about future contingents are true or false.18 Instead he takes an interpretation which may already have been described and attacked by Alexander,19 and which had subsequently been endorsed by Ammonius. This interpretation makes use of the idea of definite truth, although that idea does not occur in Aristotle’s chapter on the sea-battle. According to this interpretation, contradictory predictions about whether there will be a sea-battle tomorrow definitely divide truth and falsity between them. Hence each of the rival predictions is either true or false. All Aristotle is saying is that neither of them taken singly is yet definitely true or false. What does ‘definitely’ mean? It would beg the question if ‘definitely’ simply meant deterministically, because the question at issue is whether determinism holds. Possibly Ammonius was guilty of understanding the word ‘definitely’ in this question-begging way, but Mignucci has suggested a different interpretation of him. Boethius does not beg the question. He focuses on the pair of propositions ‘there will be a sea-battle tomorrow’, ‘there will not be a sea-battle tomorrow’. The pair is treated differently from the members taken singly. It has one member true and one false, and that is how ‘neither true nor false’ is avoided. But the truth and falsity are not yet distributed in one direction rather than the other. Picking up Boethius’ word ‘volubilis’, we can imagine the truth and falsity already contained somewhere in the pair, ready to roll (volubilis) into their respective positions, but not yet having rolled. So far this is a metaphor, and it is not clear how to give it a coherent interpretation. Kretzmann suggests that for Boethius the future-tensed proposition, ‘there will be a sea-battle’ is either-trueor-false, but if the battle eventually happens, that will retrospectively make the proposition to have been true, even though we could not predict that outcome. The retrospection already makes this a distinctive interpretation. In addition, if we were to attempt a prediction, saying ‘there will be a sea-battle’, the speech act of predicting would have been false, as implying some necessity about the battle, even in the case where subsequent events make the proposition ‘there will be a sea-battle’ to have been true.

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Whatever Boethius’ interpretation of ‘definitely true’, it was different from that of Ammonius, and this is not the only aspect of the reply to determinism on which they differed. Ammonius, though familiar with Porphyry, made most use of a later source, his teacher Proclus,20 and therefore of Iamblichus, who influenced Proclus. James Shiel has effectively replied to the earlier view of Pierre Courcelle that Boethius was particularly dependent on Ammonius.21 Boethius, Consolation of Philosophy In Boethius’ later Consolation of Philosophy, written in prison awaiting execution, he posed the related problem of future events being inevitable because of God’s foreknowledge of them. This is not so far from the question of the sea-battle, given Boethius’ interpretation that the threatened inevitability of the sea-battle turns on its predictability by humans. It is important, however, that in the Consolation of Philosophy, Book 5, Boethius turns to predictability by God. For God’s knowledge, unlike human knowledge, is infallible. If in addition God is aware for ever in advance of what we will do, that awareness will be irrevocable. The combination of infallibility and irrevocability will make it impossible for us to do anything else. One way of avoiding this deterministic conclusion would be to see God’s knowledge not as foreknowledge, but as outside of time altogether. (After all, God is the creator of time.) God’s awareness will not then be irrevocable. It is possible, but controversial, whether that timelessness is part of what Boethius means when he makes God’s knowledge eternal. Notes 1. C.W.A. Whitaker, Aristotle’s De Interpretatione: Contradiction and Dialectic, Oxford 1996. 2. Ammonius On Aristotle’s On Interpretation 23,10-15. 3. I have traced the development onwards from Plato Theaetetus 189E and Sophist 263E in Philosophy of the Commentators 200-600 AD, A Sourcebook, London 2004, vol. 3, Logic and Metaphysics, ch. 7b. 4. Jerry Fodor, The Language of Thought, New York 1975, based on the work of Noam Chomsky, and criticised by Hilary Putnam, Representation and Reality, Cambridge MA 1988. 5. Boethius, De topicis differentiis, Book 1, Patrologia Latina vol. 64, col. 1174C, translated by Eleonore Stump, with notes and essays, Ithaca NY 1978. 6. Richard Sorabji, Philosophy of the Commentators 200-600 AD, A Sourcebook, vol. 3, Logic and Metaphysics, London 2004, ch. 11a. 7. Mario Mignucci, ‘Aristotle on the existential import of propositions’, Phronesis 52, 2007, 121-38. 8. 193,26-195,2, cf. 224,3-9, Meiser. 9. 195,2-197,10.

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10. 197,10-198,3. 11. 217,17-219,9. 12. 226,13-22. 13. 231,11-232,13. 14. 234,10-236,4. 15. 224,27-225,9. 16. Ammonius: On Aristotle On Interpretation 9 with Boethius: On Aristotle On Interpretation 9, London 1998. 17. 228,3-4; 229,21-230,3. 18. 208,1-18. 19. So Robert W. Sharples, commenting on Alexander Quaestio 1.4, at p. 35n.81 of his Alexander of Aphrodisias: Quaestiones 1.1-2.15, London 1992. 20. 1,6-11; cf. 181,30-1. 21. James Shiel, ‘Boethius’ commentaries on Aristotle’, in Richard Sorabji (ed.), Aristotle Transformed, London 1990, 349-372, revised from a paper of 1958. Pierre Courcelle, Les letters grecques en Occident, Paris 1948, translated Harvard University Press 1969.

Bibliography Ackrill, J.L., Aristotle’s Categories and De Interpretatione, Oxford 1963. Blank, D and Kretzmann, N., Ammonius: On Aristotle On Interpretation 9 with Boethius: On Aristotle On Interpretation 9, London 1998. Chiesa, C., Le problème du langage intérieur chez les stoïciens’, Revue internationale de philosophie 45, 1991, 301-21. Gaskin, R., ‘Alexander’s sea battle: a discussion of Alexander of Aphrodisias De Fato 10’, Phronesis 38, 1993, 75-94. Gaskin, R., ‘The commentators’ interpretation of de Interpretatione 9’, ch. 12 in his The Sea Battle and the Master Argument: Aristotle and Diodorus Cronus on the Metaphysics of the Future, Berlin 1995. Isaac, J., Le Peri Hermeneias en Occident de Boèce à Saint-Thomas, Paris 1953. Kretzmann, N., ‘Semantics, history of’, in P. Edwards (ed.), The Encyclopaedia of Philosophy, NY and London, 1967, vol. 7, 359-406. Kretzmann, N., ‘Medieval logicians on the meaning of the propositio’, Journal of Philosophy 62, 1970, 767-87. Kretzmann, N., ‘Boethius and the truth about tomorrow’s sea battle’, in Blank and Kretzmann 1998, 24-52. Magee, J., Boethius on Signification and Mind, Leiden 1989. Mignucci, M., ‘Ammonius’ sea battle’, in Blank and Kretzmann 1998, 53-86. Mignucci, M., ‘Aristotle on the existential import of propositions’, Phronesis 52, 2007, 121-38. Nuchelmans, G., Theories of the Proposition, Ancient and Medieval Conceptions of the Bearers of Truth and Falsity, Amsterdam 1973. de Rijk, L.M., ‘On the chronology of Boethius’ works on logic’, Vivarium 2, 1964, 1-49; 125-62. de Rijk, L.M., ‘Boèce logicien et philosophe: ses positions sémantiques et sa métaphysique de l’être’, in L. Obertello, Atti congresso internazionale di studi Boeziani, Rome 1981. de Rijk, L.M., Aristotle, Semantics and Ontology, vol. 1, ch. 3, Leiden 2002. Seel, G. (ed.), Ammonius and the Sea Battle, Berlin 2001.

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Shiel, J., ‘Boethius’ commentaries on Aristotle’, in Richard Sorabji (ed.), Aristotle Transformed, London 1990, 349-72, revised from a paper of 1958. Sharples, R.W., commenting on Alexander Quaestio 1.4, at p. 35 n. 81 of his Alexander of Aphrodisias Quaestiones 1.1-2.15, London 1992. Sorabji, R., Necessity, Cause and Blame, London 1980, ch. 5. Sorabji, R., ‘The three deterministic arguments opposed by Ammonius’, in Blank and Kretzmann 1998, 3-15. Sorabji, R., ‘Boethius, Ammonius and their different Greek backgrounds’, in Blank and Kretzmann 1998, 16-23. Sorabji, R., Philosophy of the Commentators 200-600 AD, A Sourcebook, vol. 3, Logic and Metaphysics, London 2004. Sorabji, R., ‘Meaning: ancient comments on five lines of Aristotle’, in Christopher Shields (ed.), Oxford Handbook of Aristotle, forthcoming Oxford 2010. Stump, E., Boethius’s De topicis differentiis, translated with notes and essays on the text, Ithaca NY, 1978. Whitaker, C.W.A., Aristotle’s De Interpretatione: Contradiction and Dialectic, Oxford 1996.

Translator’s Note Boethius always takes great care to ensure that his reader knows exactly what part of the text of Aristotle he is commenting on. This sometimes involves him citing repeatedly the Aristotelian text. Although it was tempting to make omissions or relegate such repetitions to a footnote I have given Boethius’ text in full to keep faithful to the style of the original even where the effect is somewhat clumsy. The manuscript usually gives the lemma or portion of text which Boethius comments on. It should, however, be noted that this Latin translation of Boethius in the lemmata is not always identical with his separately published translation of the whole text of de Interpretatione. On one occasion where a lemma has been omitted from the manuscript I have reconstructed it from his commentary (22b29-36); otherwise I have left the commentary to speak for itself. The original pagination of the Meiser edition is indicated by bold figures in the body of the text. I have also included the traditional division of the Aristotelian text into chapters. This convention is irrelevant for Boethius, but I have included these chapter numbers since they are sometimes used in modern discussions of the Aristotelian text. From time to time I have also attempted to clarify the arrangement of Boethius’ comments by the inclusion of letters or numbers in the translation. It should be understood that this is not part of Boethius’ text. I have retained the traditional and not very informative translation of interpretatio as ‘interpretation’ in my rendering of the title of the work to avoid confusion. In the body of the text, however, I have ventured to translate interpretatio as ‘communication’. Although this translation, too, is not altogether satisfactory, it is possibly less odd than ‘interpretation’. ‘Communication’ should, however, not be taken in the sense of communication between two people but rather the transfer of signification from thing via thought to verbal expression. Lastly, I would like to thank the many readers who have carefully looked through my first attempts at translation of a difficult text. I have had to make many compromises in my response to their always enlightening comments. With their help I hope to have removed at

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least some of the most serious errors from the text and remain fully responsible for any that remain. Thanks also are due to much help and encouragement from Richard Sorabji and for the patience of the editors in the final stages of publication.

BOETHIUS On Aristotle On Interpretation 4-6 Translation

The second edition or larger commentary of Anicius Manlius Severinus Boethius on Aristotle’s ‘On Interpretation’ in six books BOOK 4 The obscure ordering of the presentation in this book, which bears the Latin title de interpretatione and the Greek peri hermeneias, is added to the very obscure doctrines1 and so I would not have commented on it in long volumes except to complete in the second edition as clearly as I could, without flinching at the work involved, whatever I had omitted in the first edition in terms of depth and complexity. But you must forgive my prolixity and weigh the length of my work against the obscurity of Aristotle’s book. However I have different levels to satisfy the application and attention of readers desiring to know important things in a very easy way; for after the two commentaries on this book I am composing a sort of summary2 where I will use Aristotle’s own words partly, in fact almost entirely, except that where he spoke obscurely through his terseness, I will make the sequence of argument clearer with the addition of extra words, so that between the terseness of the text and the diffuseness of the commentary we will have an intermediate format which will bring together what has been said diffusely and spread out the very closely written work. So this is for later. But now, because Aristotle showed above that in future contingent propositions truth and falsity are not divided in a fixed and definite manner and whatever the previous very broad discussion embraced, his present intention is to enumerate such categorical propositions as are composed in a simple form with a definite or indefinite name. In the first volume3 it [is] said that a name is, e.g. ‘man’, and an infinite name is, e.g. ‘not man’. Predicative (i.e. categorical) propositions are ones which consist of just two simple terms, either with a definite name, e.g. ‘man walks’, or with an indefinite name, e.g. ‘not man walks’. He now applies himself to the enumeration of those simple categorical propositions which are formed by the addition of an infinite name. But because all propositions differ either in quality or quantity (in quality that one is affirmative, the other negative, in quantity that one embraces several, the other few), how do the propositions which say ‘man walks’ and ‘not man walks’ differ from each other? In quality or in quantity? For ‘man walks’ designates a certain quality of substance, i.e. that a man walks, and pronounces that a definite thing and substance and single species is ‘walking’,

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whereas if I say ‘not man walks’ I abolish man as a definite thing and signify countless things. Therefore that proposition which says ‘man walks’ will appear to differ rather in quality, ‘not man walks’ in quantity. Or is the following likely to be truer?: that ‘man’ in ‘man walks’ as a simple name is very close to an affirmation, whereas the infinite name ‘not man’ in ‘not man walks’ seems to be like a negation. But affirmation and negation differ in quality, and these are like an affirmation and a negation, therefore they differ in quality rather than any quantity. Or is the following likely to be truer, that ‘man walks’ has the same relationship to ‘not man walks’ as does ‘Socrates walks’ to ‘some man walks’? It is necessary that ‘some man walks’ is true, if several are walking, but if several are walking, it is not necessary that Socrates is walking. For several can be walking and Socrates not be walking. But when several are walking, some man is walking. This is the case because in the proposition ‘some man is walking’ we join a particularity to the universality, i.e. man, and if any do come under that universality ‘walking man’, the proposition ‘some man is walking’ must be true. But when we say ‘Socrates is walking’, because Socrates concerns the property of a single individual, unless Socrates himself is walking, it is not true to say ‘Socrates is walking’, although all men walk. Then just as ‘some man walks’ is indefinite , so too with ‘man’ and ‘not man’. One who says ‘man walks’ says that some animal is walking and he specifies this by name and quality in saying ‘man walks’. But one who says ‘not man walks’ does not remove everything, but only man, while he declares that other animals are walkers. Therefore whether a horse, ox or lion walks, ‘not man walks’ is true; but ‘man walks’ is not true unless man himself walks. Therefore just as in the difference between ‘some man walks’ and ‘Socrates walks’ it is implied that if several men were walking, ‘some man walks’ is true but ‘Socrates walks’ is not true unless Socrates himself were walking, the same can be said of ‘man walks’ and ‘not man walks’. For several things that are not men walk, it is true to say that ‘not man walks’, but not true to say that ‘man walks’ unless man himself walks. They seem then to differ in definiteness and property rather than in any quantity as a whole or as a part or in any quality. For, as will be demonstrated later, ‘not man walks’ is more an affirmation than a negation. We have made enough introductory remarks. Let it suffice to have gone so far with our introductory remarks. Chapter 10

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19b5-18 But because an affirmation is what signifies something of something and this is a name or what has received no name, and what is affirmed must be one thing and about one thing (we have already spoken about name and what has received no

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name; for I do not mean that ‘not man’ is a name but an infinite name; for it signifies in some way one infinite thing, just as ‘not runs’ is not a verb but an infinite verb), every affirmation will be composed of a name and a verb or an infinite name and a verb. But there can be no affirmation or negation without a verb; for ‘is’, ‘will be’, ‘was’, ‘becomes’ or other things of this kind are verbs according to what we have established; for they additionally signify time. Then a first affirmation and negation are: ‘man is’, ‘man is not’; then ‘not man is’ and ‘not man is not’; again, ‘every man is’ and ‘every man is not’, ‘every not man is’, ‘every not man is not’. In the second book,4 I think, we said that every simple statement, i.e. predicative, consists of a subject and predicate and that the predicate is always a verb or its equivalent5 as though a verbal expression was put in, e.g. when we say ‘man walks’ a verb is put in, whereas when we say ‘man rational’ the verb ‘is’ is understood, so that the full thought is ‘man is rational’. So it is necessary that either a verb is always predicated or what is like a verb and its equivalent in statements. What acts as subject, we said, is either explicitly a name or what can take the place of a name. Thus our main conclusion must be that in a categorical proposition every subject is a name and every predicate a verb. But because when he was talking about name he introduced another kind of name which was not name in itself and in the simple sense but was called infinite name, that which is expressed with a negative particle, and because every proposition has a name as subject, and a categorical proposition is one which predicates or denies something of something, and that of which it predicates [something] is a name and, because infinite name is also included in ‘name’, it is necessary that a categorical proposition always have as subject either a name or what is called an infinite. Infinite name is what he now calls what has received no ‘name’. So all predicative proposition is divided into two types: either with a subject formed from an infinite name or from a simple name; from an infinite name when I say ‘not man walks’, and from a finite and simple name, e.g. ‘man walks’. And there are two kinds with a finite and simple name: either with a universal name for a subject, e.g. ‘man walks’ or with a singular name, e.g. ‘Socrates walks’. The division is then as follows: of all simple statements, which consist of two terms, there are those (1) with an infinite name as subject, and those (2) with a finite and simple name. Of those that have a simple subject some have a (2a) simple universal as subject, (2b) others a singular as subject. Now above he taught us very clearly that there are differences between propositions which posit a simple name as subject: that some are universal, some particular and others indefinite; they differ this way in quantity, and in quality in that some are

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affirmative, others negative. The same is true of propositions which are stated with an infinite name as subject; for some of these are indefinite, others definite. And of the definite some are universal, others particular. Here too are the same differences in quantity as well as quality in the case of propositions with infinite names; for we say that some are affirmative, others negative. The table below shows us which are simple affirmatives, which [simple] negatives, and which are affirmative with an infinite name and which negatives. And we have attached them all to their proper determinations and even put the indefinite for each type of proposition, but have excluded simple propositions with a singular subject. The simple indefinite propositions are: ‘man walks’, ‘man does not walk’; opposed to these those with an infinite name: ‘not man walks’, ‘not man does not walk’; the universals with a simple name as subject are: ‘every man walks’, ‘no man walks’; opposed to these the universals with an indefinite name: ‘every not man walks’, ‘no not man walks’; the particulars with a finite name as subject: ‘some man walks’, ‘some man does not walk’; and against these those with an infinite name: ‘some not man walks’, ‘some not man does not walk’. The table below shows this.

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So when devising these divisions and forming a proposition about propositional types with two terms, he assembled all the propositions from the point of view of their subject name and subdivided only those beginning with an infinite name. His main division then is this: some propositions have a finite name, and others have an infinite name. If he had wanted to make a comprehensive list of every different proposition he ought to have taken infinite verbs as well as names. But since he knew that an infinite name kept intact his model proposition, so that if it was said in an affirmative proposition it would keep the statement affirmative, e.g. ‘not man walks’, and if it was said in a negative proposition, negative e.g. ‘not man does not walk’, and that when infinite verbs are included in the proposition they effect the negation and not an affirmation, he said nothing about them, because infinite verbs are relevant only to one quality of proposition, namely the negative. For from an infinite verb a nega-

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tive always comes about. Thus he put all this together with the words but because an affirmation is what signifies, i.e. predicates, something of some subject; this means that every proposition consists of subject and predicate. But the subject is a name or what has received no name. What has received no name is that which when proposed undermines a name, e.g. ‘not man’. For the name ‘man’ differs from an infinite name by the privation seen in ‘not man’ and for this reason he also called it what has received no name. And he indicated what kind of proposition he ought to be dealing with when he said that what is affirmed must be one thing and about one thing, i.e. that a proposition ought to consist of two terms. Aristotle also recalls that he had said above6 what that which has received no name is, that he does not call the phrase not man a name, but while not calling it simply a name, with the addition of this ‘infinite’ he calls it an ‘infinite name’, because it signifies a single, but infinite thing; for ‘not man’ is one in that it abolishes the signification of what we call ‘man’ and, while it takes away one signification in its own right, there are many things still left for the mind to understand. He also recalls that he had earlier7 called ‘he does not run’ an infinite verb and not a verb simply. Then because an affirmation is something of something, and the subject has to be either a name or what has received no name, i.e. an infinite name, two kinds of proposition become apparent. For ‘every affirmation’ is ‘composed of a name and a verb or an infinite name and a verb’, and negation too in the same way. For you will never find an affirmation without a corresponding negation. But if there are two kinds of affirmation, there will also be two kinds of negation. He recalls here too what he had said above.8 For although a predicative, i.e. categorical, affirmation and negation is formed from a name and verb, or from what is not a name but an infinite name and verb (for it is not possible for there to be an affirmation or a negation without a verb or what signifies the same as a verb whether as understood or in some other form), he also sets out the verbs which in almost every proposition either occur as actual verbs or have the same function. For ‘is’, ‘will be’, ‘was’, ‘becomes’ or any other things of this kind which additionally signify time are verbs, as we can learn from what has previously been laid down and granted, when verbs were defined as what additionally signifies time.9 So if these additionally signify time they are indubitably verbs. But there can be no proposition without these or their equivalent. So it has been rightly said that a predicative proposition cannot be formed without verbs. But someone might seem right to bring forward as an objection the question why, when he has already said that there is no way in which statements can be formed without verbs, does he now repeat the same thing as though he had said nothing about this before. But it need not appear superfluous; for since an infinite name is a finite name with a negative particle, it might

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perhaps be thought that when we say ‘not man’ it is a negation. But if this is a negation, ‘man’ is an affirmation. To prevent anyone slipping into this error, it was appropriate for him to repeat and say that there cannot be a statement without a verb; which is the equivalent of saying that no one should think that an infinite name is a negation or a name an affirmation, for an affirmation and negation cannot in any way be formed without a verb. Here he also recognised that an infinite verb signifies both a negation and an infinite verb. For ‘does not walk’ is both an infinite verb and a negation, but if it is said simply on its own without any other additions it is an infinite verb; but if it is expressed with a name or with an infinite name, it is no longer understood as an infinite verb, but as a negation; so that the negative particle ‘not’ when joined with ‘does walk’ forms the infinite verb ‘does not walk’, but in the proposition ‘man does not walk’ it signifies that man does not walk. And so he says that in propositions either names or infinite names can act as subjects, but that there can be no other predicatives than verbs. For whether someone is joining one thing to another in an affirmation, the predicate is without a doubt a verb, or if in a negation, it is not an infinite verb but simply a verb which with the addition of the particle ‘not’ changes the entire quality of the proposition from affirmative to negative. Therefore he was right not to create a special class of propositions out of infinite verbs. For infinite verbs are infinite only then when they are on their own. But if they are joined with an infinite name or a name, they are no longer infinite but finite verbs, but are understood with the negative in the proposition as a whole. Then if negations, as the Stoics would have it, are to be placed with names so that ‘not man walks’ is a negation, when we say ‘not man’ it could be ambiguous whether it is an infinite name or a finite name joined to a negation. But since Aristotle thought that negatives should be joined to verbs, it is rather infinite verbs that are of ambiguous meaning, i.e. whether they are to be taken as infinite or are finite with a negation. And so the distinction is made between an infinite verb taken with a name which becomes a negation and a negative proposition, e.g. ‘man does not walk’, and said by itself in which case it is an infinite verb, e.g. ‘does not walk’. And so he admitted only one distinction in propositions, that of names and infinite names, but not that of infinite verbs, because he was talking about combinations, i.e. about names or infinite names and verbs. In this combination, what is on its own called an infinite verb is a negation. For it must not be the case that every proposition consists of either a verb or an infinite verb in the way it must have a definite or an infinite name. For there are no infinite verbs in propositions, but, as we have said, whenever such a thing is put there, the verb is finite, but the addition of a negation deprives and does away with the proposition as a whole. And an infinite verb joined to names must

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form a negation, whereas an infinite name joined to verbs need not form a negation. For ‘not man walks’ is an affirmation and not a negation. Therefore, because a negation ought to signify something of something and an indefinite name is something, whenever we say ‘not man walks’ we predicate walking, which is something, of ‘not man’, i.e. of something. But if we say ‘does not walk’ we do not so much predicate something of something as from something; for to say ‘man does not walk’ is to remove walking from man, not to predicate it of man. Therefore it is a negation rather than an affirmation. For if it were an affirmation, i.e. if the verb were infinite, it would predicate something of something. But in fact it removes something from something; therefore it is not an infinite verb, but rather a negation, so long as it is taken in the proposition as a whole. In fact he himself gives the number of propositions as we have also described them above where we gave the indefinite propositions first and then their contraries. But if anyone either looks back or pays attention here he will, with care, recognise the difference between our arrangement and Aristotle’s. For we proposed both contraries and subcontraries, whereas Aristotle proposed only those that contradicted each other when opposed and placed against each other. But Aristotle said that the same proposed differences between propositions are found not only in the present, but also in the other times too which are external; he calls the times besides the present, i.e. past and future, ‘external times’.10 19b19-31 But when ‘is’ is predicated as a joined third thing, oppositions are expressed in two ways. I mean, for example, ‘man is just’; I mean that ‘is’ is joined as a third thing, name or verb, in the affirmation. Therefore there will be four propositions, two of which will be related in sequence to affirmation and negation as the privations are, but two which will not be like this at all. I mean that ‘is’ will be joined to ‘just’ or ‘not-just’, and also the negation. Therefore there will be four. We understand what is meant from the following list. ‘Man is just’; its negation ‘man is not just’; ‘man is not-just’; its negation ‘man is not not-just’; for ‘is’ and ‘is not’ are here joined to ‘just’ and ‘not-just’. These then are arranged in this way as has been said in the ‘Analytics.’11 Another reading12 is handed down as follows: I mean that ‘is’ will be joined to ‘man’ or ‘not man’, and also the negation for ‘is’ and ‘is not’ are here joined to ‘man’ and ‘not-man’. These then are arranged in this way as has been said in the ‘Analytics.’ What is meant is very unclear and is explained carelessly by many people whose views I will record with an appropriate critique. After he has explained propositions which consist of two terms and have as

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subject either a name or, using his own expression, what has received no name, i.e. an infinite name, he now moves over to those in which ‘is’ is predicated as a joined third thing, two things being predicated of one subject; e.g. in ‘man is just’, ‘man’ is the subject, and ‘just’ and ‘is’ are both predicated. So here there are two predicates and one subject. And perhaps someone might ask why he expressed it in this way: but when ‘is’ is predicated as a joined third thing. For it is not predicated as a third thing, but as a second; for there are two things that are predicated and one subject. But it was not meant as though ‘is’ in the proposition ‘man is just’ is a third predicate, but that it is joined as a third thing and is predicated. Therefore ‘third thing’ refers to ‘joined’. Even though in the proposition ‘man is just’ ‘is’ is joined as a third thing, it is not predicated as a third thing, but as a second. And so as counted third it is joined, but as counted second it is a predicate. This is what he is saying: when ‘is’ is predicated as a joined third thing, not that it is predicated as a third thing, but that it is predicated as being joined as a third thing, i.e. in the third place. So he now considers the propositions in which ‘is’, the joined third thing, is a second predicate. And just as in the case of propositions in which only ‘is’ is predicated and was not predicated as joined, he considered how the number of ways in which the subject could be understood determined the different kinds of proposition (for the subject is either a name or an infinite name), so now he speaks about the predicate and deals with the different kinds of predicate. For in propositions in which ‘is’ is predicated as a joined third thing when sometimes a name is taken as predicate or at other times an infinite name, this makes for differences in the propositions. I mean that what is predicated in the proposition which says ‘man is just’ is ‘just’. For this is predicated of man, whereas ‘is’ is not predicated, but is predicated as a joined third thing, i.e. in the second place and joined with ‘just’, but is predicated as third in the proposition as a whole, not as a kind of particular part of the whole proposition but rather as a demonstration of quality. For ‘is’ does not constitute the proposition as a whole, but demonstrates what the proposition’s quality is, i.e. that it is affirmative. And so he did not simply say is predicated as a third thing but is predicated as a joined third thing. For it is not put in and just predicated as a third thing, but as a joined third thing, it is predicated in second place and in a way accidentally. It can be understood in the following way. Aristotle said that ‘is’ is predicated as a joined third thing in these propositions, because it can sometimes be predicated in itself, e.g. if someone says ‘Socrates the philosopher is’ so that this proposition has the meaning ‘Socrates the philosopher lives’; for ‘is’ stands for ‘lives’. If someone speaks in this way, there are two subjects and ‘is’ is only predicated and it is not joined as well. For because ‘Socrates (the) philosopher’ are both subjects, only ‘is’ is predicated. But if someone were to say ‘Socrates

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is a philosopher’, meaning by the statement not that Socrates is a philosopher and lives, but that he philosophises and is a philosopher, then we have one subject and two predicates. For Socrates is the subject, ‘philosopher’ and ‘is’ are the predicates. And of these ‘philosopher’ is predicated primarily, whereas ‘is’ is itself also predicated and joined with ‘philosopher’, but it is not predicated simply but joined. There are other propositions of the following kind: ‘Socrates will read in the Lyceum’; and these are composed of three terms. But he does not deal at all with this kind, however, but only with those in which ‘is’ is predicated as a joined third thing, e.g. ‘man is just’. But these have two opposites. And so it is right to have two opposites in the four propositions. This comes about as follows: when ‘is’ is predicated as a joined third thing what is primarily predicated is a name or an infinite name. And these propositions must be predicated either in the affirmative or negatively. And so the affirmation of a simple name and the negation of a simple name are one opposition and two propositions. But it is not the subject but the predicate which is taken to be finite or infinite, so that in ‘man is just’ ‘just’ is predicated. But this will be either a name or an infinite name. Therefore two affirmations arise from this: ‘man is just’, ‘man is not-just’; . And this is the case in indefinite propositions. But it will be demonstrated later13 that it is also the case in propositions which have a universal or particular determination. But now the diagram below shows their number and opposition.

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In the above diagram I have called simple propositions those in which a name is predicated, e.g. ‘man is just’, ‘man is not just’, ‘with an infinite’ those in which an infinite name is predicated primarily, e.g. ‘man is not-just’, ‘man is not not-just’. Whether ‘is’ is said first or later is all the same and this is not affected by the fact that Aristotle said ‘is’ first whereas we have put it at the end. It is all the same.14 And so we get two oppositions and four propositions. These four propositions have been reduced to the smaller number from six. For if we had simple propositions with two terms as well, there would be the following: ‘man is’, ‘man is not’, ‘just (man) is’, ‘just (man) is not, ‘not-just (man) is’, ‘not-just (man) is not’ and there would be these six propositions. It could also be added here that there could arise propositions concerning an infinite name as subject, e.g. ‘not-man is’, ‘not-man is not’. But he speaks about these later. And for now those six simple propositions have been taken up in the four because when

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simple things are joined together they then make a smaller total. For the actual combining reduces the number so that if there are ten things and the individuals are joined to each other to make pairs, the total combination comes to five. So too here there were six simple propositions, as I showed above, but these have been joined together and reduced by combining them. For the four propositions ‘man is’, ‘man is not’, ‘just-(man) is’, ‘just-(man) is not’, have been reduced by combining to two; for when ‘man’ is joined with ‘just’ they have made two propositions; ‘man is just’, ‘man is not just][. Again when an infinite is predicated of the very same man, the other two propositions arise rationally from an infinite predicate: ‘man is not-just’, ‘man is not not-just’. These make two oppositions and four propositions. So then from the six propositions, i.e. ‘man is’, ‘man is not’, ‘just (man) is’, ‘just (man) is not’, ‘not-just (man) is’, ‘not-just (man) is not’ (since there are six propositions, there will be three oppositions), ‘man’ subject to ‘just’ and to ‘not-just’ made only four and a double opposition. Those who have said that the propositions arising from those in which ‘is’ is predicated as joined are more numerous than from those consisting of two terms, have clearly not understood the way in which a larger number of propositions always reduces to a more restricted and smaller number when combined. And so when he says that in propositions in which ‘is’ is predicated as a joined third thing, ‘third thing’ does not refer to predication but rather to order, as he himself says I mean, for example, ‘man is just’; I mean that ‘is’ is joined as a third thing, name or verb, in the affirmation. He does not say that it is predicated as a third thing, but joined as a third thing – in order, not in predication – so that it is joined as a third thing, but so as to be predicated as joined, i.e. not predicated simply. For there is no further term in the proposition. And so if someone wants to resolve the proposition into its terms, he does not resolve it into ‘is’, but into ‘man’ and ‘just’. And there will be two terms: the subject ‘man’ and the predicate ‘just’, while ‘is’ which is predicated as joined and as a joined third, is to be understood more correctly as a quality of the proposition, as I have said, rather than as a term. And it is for this reason that he says name or verb; for he said that ‘is’ is added as a third name to show us that the first two are, of course, ‘man’ and ‘just’, and he said ‘verb or name’ because verbs are also names. This he first said with the words verbs uttered by themselves are names.15 Then after he had said what he wanted to demonstrate with the words ‘is’ is predicated as a joined third thing, that it refers to order and not to predication, he later explained how many propositions there were when he said Therefore there will be four propositions. But he said that accident, which I will explain carefully a little later,16 is common to these four. This is what has happened. Since there are four propositions, which he is going to posit later, ‘two’ of them will

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be consequently related to affirmation and negation as their privations, but two will not be like this at all. But I will explain a little later this accident in the propositions. Now let us look at how he himself says the four propositions arise. He says I mean that ‘is’ will be joined to ‘just’ or ‘not just’; for there will be a twofold proposition, if ‘is’ is joined to ‘just’ or ‘not just’ as follows: ‘man is just’, ‘man is not just’. Therefore, he says, if ‘is’ is put affirmatively first with ‘just’ and then with ‘not-just’, it makes twin affirmative propositions. Similarly too if ‘is’ is combined with a negative, i.e. not, it will also make the twin negations, ‘man is not just’, ‘man is not not-just’. And this is what he means by I mean that ‘is’ will be joined to ‘just’ or ‘not-just’. For if it is joined to ‘just’, it makes the affirmation ‘man is just’; if it is joined to ‘not just’ it makes the affirmation ‘man is not-just’, and also the negation which when joined with ‘is’ makes ‘is not’. Then the negation when joined to ‘just’ and ‘not-just’ will form two negations in opposition to the propositions we have mentioned. For if it is added to ‘just’, it makes the following negation ‘man is not just’; if to ‘not-just’, ‘man is not not-just’. Why does this happen? Because ‘is’ and ‘is not’ are joined to ‘just’ and ‘not-just’, ‘is’ with ‘just’ and ‘not-just’ making two propositions, ‘is not’ with ‘just’ and ‘notjust’ another two. From these four there are two oppositions as he says above: but when ‘is’ is predicated as a joined third thing, oppositions are expressed in two ways. This then is the general sense. But there is another reading of this passage as follows: I mean that ‘is’ will be joined to ‘man’ or ‘not man’, and also the negation. Therefore there will be four. We understand what is meant from the following list. ‘Man is just’; its negation ‘man is not just’; ‘man is not-just’; its negation ‘man is not not-just’.

Here ‘is not’ is joined to ‘man’. This confused the commentators and they hesitated as to what could be meant when after saying I mean that ‘is’ will be joined to ‘man’ or ‘not man’, in the example and list he put ‘is’ not with ‘man’ or ‘not-man’ but with ‘just’ and ‘not-just’ when he said We understand what is meant from the following list. ‘Man is just’; its negation ‘man is not just’; ‘man is not-just’; its negation ‘man is not not-just’

and after he had put ‘is’ and ‘is not’ with ‘just’ and ‘not-just’ which he has just said he was not going to do, but had proposed to join ‘is’ to ‘man’ and ‘not-man’, he then goes on: for ‘is’ is here added to ‘man’ after proposing that ‘is’ and ‘is not’ are added to ‘just’ and ‘not just’. For this reason Alexander too thinks that the fault lies with the reading and not with the philosopher who spoke correctly and that the reading must be emended. But he ought not to have been con-

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fused when Aristotle introduced ‘just’ and ‘not-just’ in place of ‘man’ and ‘not-man’. For these are examples rather than the only propositions possible. For saying that ‘is’ is added to ‘man’ and ‘not-man’ he understood it as the equivalent of man being predicated, e.g. ‘Socrates is a man’ or ‘Socrates is not-man’. So wanting to take any predicate at all, whether simple or infinite, he introduced ‘just’ and ‘not-just’, being indifferent as to whether ‘man’ and ‘not-man’ or ‘just’ and ‘not-just’ were predicated, provided that the predicate be in one case taken as a name and in the other as an infinite name. Alexander should not have been confused and this mode of writing with which the philosopher wanted to make us think did not confuse others such as Porphyry and Herminus who say that these are examples of a finite and infinite predicate where any predicate ought to be equally acceptable; just as it would equally well serve his purpose if after saying that ‘is’ and ‘is not’ are added to ‘man’ and ‘not-man’, he had then introduced ‘white’ and ‘not-white’; for this is to express the predicate, whether finite or infinite, with any name you choose. And because he said ‘is’ is added to ‘man’ and ‘not-man’ and then introduced ‘just’ and ‘not-just’ and put man as the subject, we are not to suppose that he had wanted to speak about subjects, ‘man’ and ‘not-man’, and then by mistake introduced the predicates ‘just’ and ‘not-just’, but rather that he understood ‘man’ and ‘not-man’ as predicated of something else, e.g. (we gave these examples above) ‘Socrates is a man’, ‘Socrates is not-man’. So here ‘man’ and ‘not-man’ are predicates. Again there is no difference between ‘man is just’ and ‘man is not-just’; for in the same way in one proposition a simple [name] is taken as predicate, in the other an indefinite, just as we have the same situation if I say that snow is white and snow is not-white. Then we should not criticise the text because after proposing to add ‘is’ to ‘man’ and ‘not-man’ it then brings in ‘just’ and ‘not-just’. There is no difference whether just and not-just or man and not-man act as predicates, provided that the predicate is taken to be sometimes finite and sometimes infinite when something is predicated as a joined third thing. And so the philosopher who is highly knowledgeable in all matters wanted to exercise our intelligence and acumen, not to confuse us with faulty composition. But when he adds in summary the words we have already cited: for ‘is’ and ‘is not’ are here added to ‘man’ and ‘not-man’, he means that in the proposition ‘man is just’ which he had just posited, ‘just’ is predicated of ‘man’, while ‘is’ in being added to ‘just’ is added also to ‘man’; and in the proposition ‘man is not just’, that ‘just’ is predicated of ‘man’ and ‘is not’ is added to ‘just’, so ‘is not’ will also be added to ‘man’. For this is what he means by for ‘is’ and ‘is not’ are here added to ‘man’ and ‘not-man’. For if ‘just’ is predicated of man and ‘is’ and ‘is not’ is added to ‘just’, it will also be added to man, as we said. Alexander thinks that this reading ought to be emended and should be put as we first

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cited it ‘for “is” and “is not” are here added to “just” and “not-just” ’. But whether we accept one reading or the other the whole sequence of ideas is clearly set out. For neither need be altered. One offers more challenge, the other is easier to understand, while both lead to the same meaning.17 It remains then to explain carefully the sentence:

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Therefore there will be four propositions, two of which will be related in sequence to affirmation and negation as the privations are, but two which will not be like this at all.

for the passage has a very concise brevity and is rendered difficult by its excess of both obscurity and sophistication. And we have already run through and explained this passage in the first edition of this work and accorded it the same very short treatment we gave other subjects there. But now we ourselves are going to reveal what truth there is in its meaning and what lies hidden in its concise format, as far as we are able and let the reader pay attention as best he can. If he then perhaps finds them a little more obscure, he can blame the difficulty of the material, but if they appear clearer than he thought, he ought to credit his intelligence. But first I will try to explain as best I can what Herminus thought about this passage. He said that propositions with an infinite name can be expressed in three ways: (1) they have an infinite subject, e.g. ‘not-man is just’; (2) an infinite predicate, e.g. ‘man is not-just’; (3) both an infinite predicate and an infinite subject, e.g. ‘not-man is not-just’. Of these, he says, those which have an infinite name as predicate term are similar to those which declare some privation. Propositions which say ‘unjust man’ declare a privation. Therefore, he says, propositions with an infinite predicate like ‘man is not-just’ agree with those like ‘man is unjust’. For, he says, for a man to be unjust is the same as for a man to be not-just. But those which have either an infinite subject, e.g. ‘not-man is just’, or both infinite, e.g. ‘not-man is not-just’ do not agree with the privative proposition ‘man is unjust’. For there is no similarity between the propositions ‘not-man is just’ and ‘man is unjust’, nor between ‘not-man is not-just’ and ‘man is unjust’. For those that have an infinite name as predicate agree with privative propositions, but the propositions which have either an infinite subject or both subject and predicate infinite are very different from privative propositions. This is what Herminus says. His introduction here of propositions with both [terms] infinite or with an infinite subject is very much at variance with the full meaning and sense of [Aristotle’s] thought. And his explanation has made nothing clear about what Aristotle means by in sequence or how the two relate in sequence as the privations are and which ones do not. And the meaning is just as obscure after Herminus’ explanation as before.

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Our opinion, following Porphyry and in agreement with that most learned man, is as follows. There are four propositions, two of which have finite names and two have indefinite names as predicates. Those with finite names are as follows: the affirmation ‘man is just’, the negation ‘man is not just’; those with infinite names as predicates: the affirmation ‘man is not-just’, the negation ‘man is not not-just’. But in the rest of our discussion we will call propositions which have infinite names as predicates infinite propositions so that the affirmation ‘man is not-just’ and the negation ‘man is not not-just’ are infinite without any further discussion, so that, as we were about to say, a proposition with an infinite name as predicate we will name infinite, but the two which have no infinite name either as subject or predicate we call simple. Then the simple propositions are ‘man is just’, ‘man is not just’. I call privative propositions those which have a privation. Privative propositions are of the kind ‘man is unjust’ for this will deprive the subject of justice, and again ‘man is not unjust’; this will in turn deprive the subject of injustice. So since there are two simple propositions, one affirmative, the other negative, and since there are two privative, here too one affirmative, the other negative, and there are also the other infinite affirmative and negative propositions, I maintain that the infinites will relate to simple propositions, in the same way as privative propositions, affirmation and negation, relate to simple affirmations and negations, i.e. according to sequence. What I mean is something like this. First put down the two simple propositions, i.e. the affirmation ‘man is just’, and its negative ‘man is not just’. Under these arrange the privative: under the simple affirmative, the negative privative and under the simple negative, the affirmative privative, so that under ‘man is just’ is placed ‘man is not unjust’, and under ‘man is not just’ is placed ‘man is unjust’. Again under the privatives arrange the infinites: under the affirmation an affirmation, under the negation a negation. Under the privative affirmation ‘man is unjust’ put the infinite affirmation ‘man is not-just’; under the privative negation ‘man is not unjust’ put the infinite negation ‘man is not not-just’. The following diagram shows this.

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What I mean is clear from the diagram, that the infinite propositions, affirmative and negative, ‘man is not-just’ and ‘man is not not-just’ will relate to the simple propositions ‘man is just’ and ‘man is not just’

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in the same way that the privative propositions, i.e. affirmative and negative, ‘man is unjust’, ‘man is not unjust’, relate to the simple propositions, ‘man is just’, ‘man is not just’, that is, in sequence. Let us see what the sequence of simple and privative propositions is, so that we can learn whether infinite propositions relate to the simple propositions in the same way as privatives to the same simple propositions. So simple propositions have been arranged in the first line, the simple affirmation ‘man is just’ and the simple negation ‘man is not just’. Under these, i.e. under simple affirmation, are two negations, one privative ‘man is not unjust’ and the other infinite ‘man is not not-just’. Under the simple negation ‘man is not just’ are two affirmations, one privative ‘man is unjust’ and the other infinite ‘man is not-just’. You can also see on the diagram that the affirmations and the negations relate to each other diagonally. For the simple affirmation ‘man is just’ is diagonally opposite both affirmations, i.e. infinite and privative, ‘man is not-just’ and ‘man is unjust’. Again the simple negation ‘man is not just’ is diagonally related to the two negations, infinite and privative. And a privative negation does follow a simple affirmation in truth. For if it is true to say that man is just, it is true to say that man is not unjust. For man who is just is not unjust. And we can posit that as a continuous and combined proposition: if man is just, man is not unjust. Therefore privative negation follows simple affirmation, so that if a simple affirmation is true, the privative negation will also be true and the truth of a privative negation follows the truth of a simple affirmation. But it is not the case in reverse. For a simple affirmation does not follow a privative negation. For if it is true to say that man is not unjust, it is not at all true to say that man is just. For it can be said truly of a horse that a horse is not an unjust man (for it isn’t a man at all and so isn’t an unjust man), but it cannot be said of a horse that a horse is a just man. So then because it is not true of horse that it is a just man, the truth of a simple affirmation does not follow the truth of a privative negation. And so a continuous and combined proposition cannot be formed starting from the privative negation; for ‘if man is not unjust, man is just’ is not a true proposition. For with regard to the horse, as we have said, it is true that it is not an unjust man, but not true that it is a just man. Therefore a simple affirmation does not follow a privative negation. It has been proved then that a privative negation follows a simple affirmation, but that a simple affirmation does not follow a privative negation. Let us see, too, what the sequence is on the opposite side. For on the other side a simple negation follows a privative affirmation, but a privative affirmation does not follow a simple negation. For if it is true to say that man is unjust, it is true to say that man is not just. For whoever is unjust, is not just. And the simple negation ‘man is not just’ follows the truth of the privative affirmation ‘man is unjust’. But this is not convert-

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ible. For a privative affirmation does not follow a simple negation. For if it is true to say that man is not just, it is not at all true that man is unjust. For it is true to say about a horse that it is not a just man (for what isn’t a man at all, isn’t a just man), but it cannot be said truly about the same horse that it is an unjust man. For what is not a man cannot be an unjust man. Therefore the truth of a privative affirmation does not follow the truth of a simple negation, whereas the truth of a simple negation follows of necessity the truth of a privative affirmation. And so it has been proved in both cases that a privative negation follows a simple affirmation, but a simple affirmation does not follow a privative negation; and again that a simple negation follows a privative affirmation, but a privative affirmation does not follow a simple negation. So with this established let us deal with indefinite and privative propositions. For privative and infinite affirmations agree with their affirmations, and the negations agree with their negations as follows. The privative affirmation ‘man is unjust’ agrees with the infinite affirmation ‘man is not-just’. For they both, the privative affirmation and the infinite affirmation, signify the same thing; and although in some speech they differ in the way they are expressed, they never differ in signification, except only insofar as whom the privative proposition posits as being unjust, the other posits as being not-just. And again the privative negation ‘man is not unjust’ agrees and is in harmony with the infinite negation ‘man is not not-just’. These too are the same because they agree with each other. Now the privative negation ‘man is not unjust’ follows the simple affirmation ‘man is just’; therefore the infinite negation follows the very same simple affirmation, i.e. ‘man is not not-just’ follows ‘man is just’; for if the privative and infinite negations agree, the infinite negation also follows what the privative negation follows; but the privative negation ‘man is not unjust’ follows the simple affirmation ‘man is just’; therefore the infinite negation ‘man is not not-just’ follows the same simple affirmation ‘man is just’. Again the same happens on the other side. Because the simple negation ‘man is not just’ followed the privative affirmation ‘man is unjust’, the simple negation ‘man is not just’ also follows the infinite affirmation ‘man is not-just’. For if a privative and infinite affirmation agree, what follows the privative also follows the infinite affirmation. But the simple negation ‘man is not just’ follows the privative affirmation ‘man is unjust’; but the privative and infinite affirmation signify the same thing and agree with each other; therefore the simple negation ‘man is not just’ follows the infinite affirmation ‘man is not-just’. But the converse does not occur. For we have now demonstrated that an infinite negation follows a simple affirmation and a simple negation follows the truth of an infinite affirmation; but the reverse is not the case, that a finite affirmation follows an infinite negation and an infinite affirmation follows a

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simple negation. For if the privative negation ‘man is not unjust’ and the infinite negation ‘man is not not-just’ signify the same thing, because the simple affirmation ‘man is just’ does not follow the privative negation ‘man is not unjust’ as we proved above, that same simple affirmation ‘man is just’ does not follow the infinite negation ‘man is not not-just’. Again on the other side if the privative affirmation ‘man is unjust’ signifies the same as the infinite affirmation ‘man is not-just’, but the privative affirmation ‘man is unjust’ did not follow the simple negation ‘man is not just’, then neither does the infinite affirmation ‘man is not-just’ follow the simple negation ‘man is not just’. But although the necessity and rationale of the sequences proves this, nevertheless let us also communicate with examples what we have demonstrated with reason. For I mean that the infinite negation ‘man is not not-just’ follows the simple affirmation ‘man is just’, just as the privative negation ‘man is not unjust’ follows the same simple affirmation ‘man is just’. For if it is true to say that man is just, it is also true to say of him that man is not not-just (for whoever is just is not not-just), just as it was true to say that the same man who is just is not unjust. Therefore the infinite negation follows the simple affirmation, just as the privative negation also followed the same simple affirmation. But this is not convertible. For it is not immediately true that whatever man is not not-just ( = whoever is not a not just man) is also just. For a horse is not a not-just man (for it is not a man at all; and what is not at all a man, could not be a not-just man), but about the horse of which it is true to say that it is not a not-just man, it is not true to say that it is a just man, just as it would have been true to apply to the same horse the privative negation which posits ‘man is not unjust’ ( = it/he is not an unjust man); for it could also have been said of the horse. But it was established as not true that the simple affirmation ‘man is just’ follows this privative negation. Therefore the simple affirmation ‘man is just’ does not follow the infinite negation ‘man is not not-just’, just as the simple affirmation ‘man is just’ followed not even the privative negation ‘man is not unjust’ which agrees with the infinite negation. Then it must be said in conclusion that an infinite negation follows a simple affirmation, just as a privative negation follows a simple affirmation, but a simple affirmation does not follow an infinite negation, just as it did not follow a privative negation. Again on the other side the same happens in reverse. For a simple negation follows an infinite affirmation, just as the same simple negation also followed the privative affirmation. For whatever man is not-just, is also of necessity not just, just as also whatever man is unjust, is of necessity not just. But if it is true to say that he is not a just man, it is not at all necessary that he is a not-just man; for a horse is not a just man (for what is not at all a man cannot be a just

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man), but no one can say of the same one that the horse is a not-just man (for what is not a man cannot be a not-just man), just as when we said ‘man is not just’, the privative affirmation ‘man is unjust’ did not follow. For a horse is not a just man, but no one can say about the same horse that it is an unjust man. Again then we must say in conclusion that a simple negation follows an infinite affirmation, just as it followed a privative negation, but not conversely. For an infinite affirmation does not follow a simple negation, just as a privative negation did not follow a simple negation. So then there are four propositions, two simple and two infinite. The two simple propositions are ‘man is just’ and ‘man is not just’; the two infinite are ‘man is not-just’ and ‘man is not not-just’. Of these four two, the infinite negation and the simple negation, follow the two others, the infinite negation follows the simple affirmation, ‘man is not not-just’ follows ‘man is just’, and the simple negation follows the infinite affirmation, ‘man is not just’ follows ‘man is not-just’. The other two, the simple affirmation and the infinite affirmation, do not follow the infinite negation and the simple negation. This also happens in privative propositions so that a privative affirmation does not follow a simple negation, though the simple negation follows it, and again a privative negation does follow a simple affirmation, though a simple affirmation does not follow a privative negation. Hence it was right to say that of these four, the two simple and the two infinite propositions, two of them follow the two others and have a certain relationship of sequence to the others; thus infinite negation and simple negation follow simple affirmation and infinite affirmation. Privatives are similar; for a privative negation too followed a simple affirmation and a simple negation followed a privative affirmation. Thus two have a relationship of sequence, i.e. an infinite negation and a simple negation have a relationship of sequence to a simple and to an infinite affirmation, like privatives too (for privatives too behave similarly as I have often demonstrated above), but two which will not be like this at all have no relationship of sequence; for a simple affirmative does not follow an infinite negation nor an infinite affirmation a simple negation, just as was the case too with privatives. For in privatives the simple affirmation did not follow the privative negation nor the privative affirmative the simple negation. The meaning of the passage is then: ‘there will be four’, i.e. propositions, from which he had said a double opposition is formed. The four are the two simple propositions, the affirmative ‘man is just’ and the negative ‘man is not just’, and the two infinites, the affirmative ‘man is not-just’ and the negative ‘man is not notjust’. Two of these, he says, meaning the infinite negative and the simple negative, will relate to affirmation and negation in sequence, i.e. the two negations follow the two other affirmations, simple and infinite, just as the privations followed them. ‘But two which will not

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be like this at all’, i.e. the simple affirmation and the infinite affirmation, these two affirmations will not relate in sequence to the two negations, infinite and simple, which they did not follow, just as the privative affirmations too did not follow these negations. The phrase to affirmation and negation is not to be understood as though there were one affirmation or one negation, but that in the four propositions, in which two will be affirmations and two negations (the affirmations are: simple ‘man is just’; infinite ‘man is not-just’; the negations: simple ‘man is not just’; infinite ‘man is not not-just’), because the two negations followed the two affirmations, the simple ‘man is just’, the infinite ‘man is not-just’ (the simple negation ‘man is not just’ followed the infinite affirmation ‘man is not-just’ and again the infinite negation ‘man is not not-just’ followed the simple affirmation), because then, as we have said, the two negations, simple and infinite, followed the two affirmations, simple and infinite, and this also was the case in privations, this is why it was said that two of these four propositions relate in sequence to affirmation and negation, just as the privations also relate. He said ‘to affirmation and negation’ because the two negations follow the two affirmations, ‘but two which will not be like this at all’, i.e. because the two affirmations do not follow the two negations. For the simple affirmation did not follow the infinite negation nor the infinite affirmation the simple negation, just as they did not do so in the privatives, as has often been demonstrated above. But no one should think that we mean a negative and affirmative proposition from the same genus. For we did not say that a simple negation follows simple affirmation. For this is impossible. For a simple affirmation and a simple negation never agree with each other; nor do an infinite negation and an infinite affirmation. For it is impossible for the negation ‘man is not just’ to agree with the affirmation ‘man is just’ or for the affirmation ‘man is not-just’ to agree with the negation ‘man is not not-just’. * * *18 For the privative negation ‘man is not unjust’ follows the simple affirmation ‘man is just’, but the simple affirmation ‘man is just’ does not follow, they say, the infinite negation ‘man is not not-just’. Therefore the simple affirmation ‘man is just’ does not follow the infinite negation ‘man is not not-just’ in the same way as the privative negation ‘man is not unjust’ does follow the simple affirmation ‘man is just’. We must make the reply that they do not properly understand this sequence and that there is no incongruity in this kind of sequence. For how can they know that the finite affirmative ‘man is just’ does not follow the infinite negative ‘man is not not-just’? For they ought not to think that this is anything surprising. For the simple affirmation ‘man is just’ does not follow the infinite negation ‘man is not not-just’, because it did not follow the privation before; for the simple affirmative ‘man is just’ did not

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follow the privative negation ‘man is not unjust’; and that is the reason why it does not follow an infinite negation either. For an infinite and a privative, as we have often said above, agree with each other. Therefore there is no incongruity. For if a simple affirmation did follow a privative negation, it would also follow the corresponding infinite negation. But now since a simple affirmation does not follow a privative negation, neither does it follow an infinite negation either. But those who assumed that a privative negation follows a simple affirmation and said that there was disagreement in that sequence because a simple affirmation does not follow an infinite negation, ought not to have assumed incongruity, but rather that if an infinite negation did not follow a simple affirmation in the same way as a privative negation a simple affirmation, there then would be a discrepancy in the sequence. But now there is no discrepancy at all. And on this side the propositions do not in any way disagree or are discordant. Let us now look at the other side where they say that there is a discrepancy between what follows for simple propositions from infinites and privatives, so that we can see whether there is any discrepancy there too. For they say that the simple negative ‘man is not just’ is in agreement and harmony with the privative affirmation ‘man is unjust’, and just as the simple negation follows the privative affirmation, so the infinite affirmation ‘man is not-just’, they say, does not follow the simple negation ‘man is not just’. For this does not follow that. Again we give them the reply that the infinite affirmation ‘man is not-just’ does not follow the simple negation ‘man is not just’ precisely because the privative affirmation ‘man is unjust’ does not follow the simple negation ‘man is not just’. But if the privative affirmation did follow the simple negation, without doubt the indefinite affirmation would also follow the same simple affirmation. But now since the privative affirmation does not follow the simple negation, neither does the infinite affirmation follow the simple negation. For the privative affirmation and the infinite affirmation agree with each other. But those who wanted to show a lack of agreement in the implications of the infinite and privative with respect to the simple proposition, with the argument that when a simple negation follows a privative affirmation an indefinite affirmation does not follow the simple negation in the same way, ought not to have concluded that there was a discrepancy. But if, just as the privative affirmative ‘man is unjust’ , the infinite affirmation ‘man is not-just’ followed the simple negation ‘man is not just’, then they really would have had to say that there was some lack of agreement in the implications of the infinite and privative with respect to the simple proposition. But now since an infinite affirmation does not follow a simple negation in exactly the same way in which a privative affirmation does not follow a simple

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negation, it is clear that there is no difference between these – in fact they are alike in all respects –, and that the objectors have not said anything right with the idea they want to add. In fact they involve the already obscure meaning in even greater obscurities. But we should really understand it in such a way that we take the sentence two of which will be related in sequence to affirmation and negation as the privations are, but two which will not be like this at all as if he had said: of the four propositions, two simple, two infinite, the two negations (simple and infinite) follow the two affirmations (simple and infinite), just as the privations too (for in the privations the privative negation followed the simple affirmation, the simple negation the privative affirmation), which leaves two, i.e. the simple affirmation and the infinite affirmation which have no relationship of sequence to the negations (simple and infinite), just as with the privations too (for the privative affirmation did not follow the simple negation nor the simple affirmation the privative negation). So we say as follows: ‘therefore there will be four propositions’, two simple, two infinite, ‘of which’, i.e. the two simple and the two infinites, ‘two’, i.e. the simple and infinite negations, relate to the simple and infinite affirmations in sequence as the privations are, but two which will not be like this at all, i.e. the simple and infinite affirmations in relation to the two negations (simple and infinite); saying ‘will be related in sequence to affirmation and negation’, i.e. that the negations follow the affirmations; as the privations are, i.e. just as was maintained with the privations too; but two means that the simple and infinite affirmations will not relate in sequence to the two negations, the simple and the infinite, just as the privations too did not relate in sequence. For the privative affirmation did not follow the simple negation nor the simple affirmation the privative negation. There is another simpler interpretation which Alexander recorded after the many other interpretations which he had considered. Since, he says, there are four propositions, two of which are infinite and two simple, the two infinite propositions have the same relationship to the privatives in affirmation and negation, whereas the two simple propositions do not have the same relationship to their corresponding privative propositions. He means as follows: the infinite affirmation agrees with the privative affirmation; for the infinite affirmation ‘man is not-just’ agrees with the privative affirmation ‘man is unjust’; and the infinite negation ‘man is not not-just’ agrees with the privative negation ‘man is not unjust’; and these two, the infinite affirmation and the infinite negation relate to affirmation and negation as the privations are, i.e. they affirm or deny the same things as the privations affirm or deny. But two which will not be like this at all means that the two simple propositions do not relate at all to affirmation and negation as the privations do. For the simple affirmation has no bearing on the privative affirmation. For the

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proposition ‘man is just’ does not agree with the proposition ‘man is unjust’. Nor again does the simple negation agree with the privative negation. For the simple negation ‘man is not just’ disagrees entirely with the privative negation ‘man is not unjust’. Therefore since there are four, simple affirmation and simple negation, infinite affirmation and infinite negation, two of these, infinite affirmation and indefinite negation, affirm or deny something in the same way as the privations (this is what is meant by saying that they relate to affirmation and negation as the privations are), but two which will not be like this at all. For the two simple propositions do not affirm and deny in the same way as the two privatives. For the simple affirmation is at variance with the privative affirmation and again the simple negation entirely disagrees and is at variance with the privative negation. But this interpretation of Alexander is, as we have said, given as a simpler explanation after many others. It is not, however, to be rejected, but our previous interpretation seems to be truer, as Aristotle himself bears witness. For just afterwards he says ‘these then are arranged in this way as has been said in the ‘Analytics’. For at the end of the first book of the Prior Analytics (in Greek Analutika) he arranged the sequence of privative and infinite propositions in relation to simple propositions in the way in which I have recorded it in my interpretation above. And Porphyry says that some of his contemporaries interpreted this book, and because by singling out individual interpretations from Herminus, Aspasius or Alexander they found many contradictions and inconsistencies in those poorly presented interpretations, thought that this book of Aristotle could not be interpreted in a worthy manner, and that many men of this period bypassed the entire contents of this book because they considered its darkness incapable of explanation. And we passed over this passage very briefly in the first edition, but, what we there set out briefly for the sake of simplicity of comprehension, here we have interpreted the entire thrust and extent of the meaning at great length. Then since I think we have supplied a worthy interpretation above, let us look at the text and meaning of the next section. 19b32-6 There is a similar relationship also if an affirmation is about a universal name, e.g. ‘every man is just’, ‘not every man is just’; ‘every man is not-just’, ‘not every man is not-just’. But it does not happen that the diagonals are true in the same way; it does, however, happen sometimes. After some preliminary remarks about indefinite propositions he now says of propositions which are determined by the addition of universality or particularity that they too relate in a similar way to those opposed simple and infinite propositions which are said without any determination. Some have understood the words there is a

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similar relationship also if an affirmation is about a universal name referring his word similar to the number of opposites and propositions. For just as in the indefinite and undelimited propositions there are two pairs of opposites, one of simple negation and simple affirmation, the other of infinite affirmation and infinite negation, i.e. four propositions in all as has been said above, so too in propositions with a universal or particular determination four propositions and two pairs of opposites are produced. For one pair of opposites consists of a simple universal affirmation and a simple particular negation, e.g. ‘every man is just’, ‘not every man is just’. This is one pair of opposites. The other consists of an infinite universal affirmation and an infinite particular negation, e.g. ‘every man is not-just’, ‘not every man is not-just’. Therefore here too, since there are two opposites, there will without doubt be four propositions, exactly as in the case of those he had mentioned above which were lacking in determination. But others who have looked deeply into Aristotle’s thought say that determined propositions relate similarly not only with respect to the number of opposites and propositions, but also with respect to their sequence. For the sequential relationship of negations to affirmations in simple and infinite propositions expressed without a determination is exactly the same as in those expressed with a determination. But because not everything is similar in every respect, he added the remark but it is not the case that the diagonals are true in the same way; it is, however, sometimes the case. The complete meaning of the passage is as follows. He says the propositions which are expressed as infinite in accordance with their determination relate to simple propositions and simple propositions to infinites, just as indefinite propositions were said without any determination. But they have a certain dissimilarity in that the diagonal propositions which are said with determination are not true in the same way as either infinite or simple propositions expressed without any determination. Let us therefore first see whether there is the same sequence between determinate propositions as there is between indefinite ones, and afterwards see what difference there may be in the diagonals. Therefore let there be set out not only simple or indefinite propositions, but also privative ones. Let them be set out firstly in this way: the simple affirmation and the simple negation; and these are both indefinite, i.e. without the addition of universality or particularity. Beneath these put the privative negation under the simple affirmation and the privative affirmative under the simple negation; these are also indefinite. Then under them put the infinite affirmation under the privative affirmation and the simple negation, and put the infinite negation under the privative negation and the simple affirmation; and these too are indefinite and indeterminate without any universality or particularity. Then beneath these put those

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propositions which we call determined through either a quantity of universality or particularity: first of all the simple universal affirmation, and opposite this the simple particular negation. Then beneath the simple universal affirmation put the privative particular negation; under the simple particular negation put the privative universal affirmation. And now put the infinite particular negation under the privative particular negation and the simple universal affirmation and put the infinite universal affirmation under the privative universal affirmation and the simple particular negation.

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It is clear what the diagonals are in the diagram of propositions which we have drawn above. They are affirmations to affirmations and negations to negations. And in the indefinite propositions the diagonal affirmations are as follows: the simple affirmation ‘man is just’ is diagonally opposite the privative affirmation ‘man is unjust’ and the infinite affirmation which proposes ‘man is not-just’. Then the simple negation that ‘man is not just’ is diagonally opposite the privative negation which says ‘man is not unjust’ and the infinite negation that ‘man is not not-just’. Likewise, if anyone looks at the defined propositions, he will without any doubt find the same. For the simple universal affirmation that ‘every man is just’ is diagonally opposite the privative universal affirmation which states ‘every man is unjust’ and the infinite universal affirmation, which proposes ‘every man is not-just’. Likewise, the simple particular negation that ‘not every man is just’ is diagonally opposite the privative particular negation which says ‘not every man is unjust’ and the infinite particular negation which proposes ‘not every man is not-just’. Therefore affirmations are diagonal to affirmations and negations to negations both in the list of indefinite and defined propositions. We have, therefore, to consider their sequence. For it was said before that a privative and infinite negation would follow a simple indefinite affirmation, but that a simple affirmation would not follow them. Again, a simple negation follows an infinite affirmation and a

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privative affirmation, but these do not follow a simple negation. Again if someone looks back at the list of defined propositions, he will discover the same. For a privative particular negation and an infinite particular negation follow a simple universal affirmation; for if the simple universal affirmation which says ‘every man is just’ is true, the privative particular negation which says ‘not every man is unjust’ is also true. This is so because the proposition which says ‘not every man is unjust’ can mean the same as a simple proposition and is similar to the simple particular affirmation which proposes ‘some man is just’. For if not every man is unjust, some man is just. But the simple particular affirmation follows the simple universal affirmation. For when the universal affirmation which says ‘every man is just’ is true, the particular affirmation which proposes ‘some man is just’ is also true. But the privative particular negation which proposes ‘not every man is unjust’ agrees with the proposition which proposes ‘some man is just’. Therefore the privative particular negation will also agree with the simple universal affirmation. Therefore that privative particular negation ‘not every man is unjust’ follows that simple universal affirmation ‘every man is just’. But the infinite particular negation ‘not every man is not-just’ agrees with the privative particular negation ‘not every man is unjust’. For if it is true that not every man is unjust, it is also true that not every man is not-just. For to be unjust and to be not-just are the same. But the privative particular negation follows the simple universal affirmation; therefore, the infinite particular negation follows the simple universal affirmation and agrees with it, if the universal affirmation is already true. Therefore the privative particular negation ‘not every man is unjust’ and the indefinite particular negation ‘not every man is not-just’ without a doubt follow the simple universal affirmation ‘every man is just’. And so here too the negations follow the affirmation. But this is not convertible. For, since, as has been said, the privative particular negation ‘not every man is unjust’ agrees with the simple particular affirmation ‘some man is just’, but the universal affirmation does not follow this particular affirmation (for if it is true that some man is just, it is not necessarily and automatically true that every man is just), therefore the simple universal affirmation ‘every man is just’ does not follow the simple particular affirmation ‘some man is just’ (for if the particular is true the universal can be false), but the simple particular affirmation agrees with the privative particular negation; therefore the simple universal affirmation does not follow the privative particular negation. Therefore the simple universal affirmation ‘every man is just’ does not follow the proposition ‘not every man is unjust’. But the privative particular negation agrees with the infinite particular negation; therefore the simple universal affirmation does not follow the infinite particular negation. So that simple universal affirmation ‘every man

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is just’ does not follow the infinite particular negation ‘not every man is not-just’. Thus two particular negations, infinite and privative follow the simple universal affirmation, just as it was in indefinite propositions. For the two indefinite negations, infinite and privative, followed a simple indefinite affirmation, but not conversely. For a simple universal affirmation does not follow particular infinite and privative negations, just as a simple indefinite affirmation too did not follow privative and infinite negation. Thus in this one list the defined propositions are similar to the indefinites; for the negations are true whenever the affirmations are true, but the truth of the affirmations does not follow true negations, nor does it agree with them. Let us now inspect the other side to see how the simple particular negation follows the universal affirmations, both privative and infinite. For the simple particular negation ‘not every man is just’ follows the privative universal affirmation ‘every man is unjust’; for the proposition ‘every man is unjust’ agrees with the simple universal negation ‘no man is just’; for if every man is unjust, no man is just. But the simple particular negation follows this. i.e. the simple universal negation; for if it is true that no man is just, it is true that not every man is just. But a simple universal negation agrees with a privative universal affirmation; therefore the simple particular negation ‘not every man is just’ follows the privative universal affirmation ‘every man is unjust’. But this agrees with the infinite universal affirmation; for ‘every man is unjust’ and ‘every man is not-just’ signify the same thing. Therefore the simple particular negation ‘not every man is just’ also follows the infinite universal affirmation ‘every man is not-just’. Here too the simple particular negation follows the universal affirmations, both privative and infinite, but they are not convertible. For since the universal negation ‘no man is just’ does not follow the simple particular negation ‘not every man is just’ (for if it is true that not every man is just, it is not true that no man is just) while the simple universal negation agrees with and signifies the same thing as the privative universal affirmation, the privative universal affirmation ‘every man is unjust’ does not, therefore, follow the simple particular negation ‘not every man is just’, just as the universal negation did not follow the same particular negation. But the privative universal affirmation agrees with the infinite universal affirmation. Therefore the infinite universal affirmation ‘every man is not-just’ does not follow the particular negation ‘not every man is just’. Therefore here too the simple particular negation follows the two universal affirmations, privative and infinite, just as also the indefinite negation followed the two indefinite affirmations, privative and infinite, but the two universal affirmations, privative and infinite, do not follow the simple particular negation, just as also the two indefinite affirma-

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tions, privative and infinite, did not follow the indefinite simple negation. Thus defined propositions are similar to indefinite ones with regard to sequence. But the diagonals do not correspond in the same way. For it happens that the diagonals of indefinite propositions are true at the same time. For if it is true that ‘man is just’, which is a simple indefinite affirmation, is true, there is nothing to prevent the proposition ‘man is unjust’ and again ‘man is not-just’, which are indefinite affirmations, privative and infinite, from also being true. Again, it happens that diagonal negations are also true, so that if the proposition ‘man is not just’ is true, there is nothing to stop ‘man is unjust’ and ‘man is not-just’ from also being true. Therefore in indefinite propositions nothing stops the diagonals from agreeing with each other in point of truth, but only in those terms which are things which inhere as neither natural nor impossible, as we explained in book two.19 For if someone says ‘man is rational’, its diagonals cannot be true, i.e. ‘man is irrational’ and ‘man is not-rational’. For rationality inheres naturally in man. The same too has to be said about things which are impossible. But if the [terms] are such as to be neither impossibly nor naturally inherent (e.g. in ‘man is just’, it is necessary that justice is neither natural nor impossible in man), it is clear that the diagonals always agree with each other in point of truth. And it is right to say the same thing about the diagonal negations as well. Thus it happens that in those terms which are neither natural nor impossible those negations which are diagonal to negations and the affirmations which are diagonal to affirmations are always true at the same time. And this is the case with those propositions which are indefinite. But in those propositions which are defined and participate in universality and particularity it does not happen in the same way. For whatever the terms are, whether possible, natural, or impossible, the affirmations cannot agree in point of truth with the corresponding diagonal affirmations, but the negations which are diagonal to negations will be able to agree in point of truth, though only when the terms are neither natural nor impossible. We must first show how, whatever the terms, affirmations which are diagonal to affirmations cannot agree with each other. For ‘every man is just’ and its diagonal, ‘every man is unjust’, cannot be true at the same time. For ‘every man is unjust’ does not differ at all from ‘no man is just’. But ‘every man is just’ and ‘no man is just’, since they are contraries, cannot both be true at the same time. But ‘no man is just’ agrees and is consonant with ‘every man is unjust’. Therefore ‘every man is just’ and ‘every man is unjust’ cannot be true at the same time. But the same proposition which proposes ‘every man is unjust’ agrees, as we have often said, with ‘every man is not-just’. In this case, therefore, this proposition cannot agree in point of truth with the proposition ‘every

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man is just’. Thus the simple universal affirmation ‘every man is just’ in no way agrees at the same time with its diagonal universal affirmations, privative and infinite, ‘every man is unjust’ and ‘every man is not-just’, just as in the case of indefinite propositions the affirmations could not agree in point of truth with the affirmations diagonal to them nor the negations with the negations [diagonal to them]. In the case of defined propositions, however, the diagonal affirmations cannot be true at the same time. It was thus right to say that the sequence of defined and indefinite propositions is similar in all other cases. For the negations agree in point of truth with the affirmations, but the affirmations do not entirely agree with the negations; this similarity in sequence is in both, i.e. in defined and indefinite propositions. But there is the difference that it does not happen that the diagonals are true in the same way. It does happen that in indefinite propositions the affirmations which are diagonal to affirmations and the negations which are diagonal to negations are true at the same time. But with propositions which are defined it sometimes happens that the affirmations which are diagonal to affirmations are not at all true. And this will be clear if someone proposes examples both where the terms are natural and impossible, and also where they are possible, not natural and not impossible. For in all cases he will find that defined affirmations cannot be true at the same time as the defined affirmations diagonal to them. His addition it does, however, happen sometimes means that although defined affirmations cannot be true at the same time as the affirmations diagonal to them whatever their terms, it can nevertheless happen that negations which are diagonal to negations are found to be true and that this is similar to indefinite diagonal propositions. For just as there indefinite negations diagonal to negations could be true at the same time where the [terms] were neither natural nor impossible, so too here, that is in the diagram of defined propositions, it happens that defined negations diagonal to defined negations are true at the same time where they are neither impossible nor natural. For the simple particular negation ‘not every man is just’ can be true at the same time as the proposition ‘not every man is unjust.’ For it can happen that some people are just and that some are not just; and in this case both propositions are true, both ‘not every man is just’ because some are unjust and ‘not every man is unjust’ because some will be able to be just. But the latter proposition agrees with the infinite particular negation ‘not every man is not-just’. For to say ‘not every man is unjust’ is the same as saying that ‘not every man is not-just’. For which reasons these diagonal propositions too can be true at the same time. For if some are just, some unjust, it is true to say that ‘not every man is just’ because some are unjust; in turn it is true to say that ‘not every man is not-just’ because some are just. Therefore defined negations can be true at the same time as the

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negations diagonal to them and this is similar to indefinite propositions where negations agree in point of truth with the negations diagonal to them, just as affirmations agree with the affirmations diagonal to them. The complete meaning of the passage is as follows: he says There is a similar relationship, i.e. the sequence of propositions will be similar to what it was in indefinite propositions also if an affirmation is about a universal name, i.e. if defined affirmations and negations are posited, as he showed with examples, saying that the simple particular negation ‘not every man is just’ is opposed to the simple universal affirmation ‘every man is just’. And next he opposed the infinite universal affirmation ‘every man is not-just’ to ‘not every man is not-just’. These propositions, he says, have a similar relationship to indefinite propositions with respect to sequence. And he has shown above how they relate to each other as regards sequence.20 But it does not happen that the diagonals are true in the same way; for in indefinite propositions the affirmations could be true at the same time as the affirmations diagonal to them, but in defined propositions they cannot be true at the same time; it does, however, happen sometimes that in defined propositions the diagonals are true in a similar way as in indefinite propositions; for defined negations agree at the same time in point of truth with the negations diagonal to them, as was found to be the case with those indefinite propositions which we described above. This then is the complete meaning. But Herminus explains this in another way. Four propositions, he says, will make two oppositions in a similar way if there were two simple and two infinite propositions, yet with the addition of a determination. And he shows this as follows. He first proposes the simple universal proposition ‘every man is just’, and opposite this the simple particular negation ‘not every man is just’; beneath the simple universal affirmation he puts the infinite universal affirmation ‘every man is not-just’, and opposite this, beneath the simple particular negation, the infinite particular negation ‘not every man is not-just’. every man is just every man is not-just

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not every man is just not every man is not-just

In this arrangement, he says, two oppositions arise. For the proposition ‘not every man is just’ is ranged against ‘every man is just’. This is because a simple universal affirmation and a simple particular negation are opposed to each other as contraries. This is one opposition. Then the infinite universal affirmation ‘every man is not-just’ is ranged against the same simple affirmation ‘every man is just’, and this too as a contrary; for ‘every man is not-just’ signifies the same thing and agrees with the proposition ‘no man is just’. But ‘no man is

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just’ is ranged against, as a contrary, the proposition ‘every man is just’. Therefore ‘every man is not-just’ will also be the contrary of ‘every man is just’. Therefore there will be this second opposition too. Thus there are two oppositions, just as there also are with indefinite propositions. Although they were opposed in another way, there were still two oppositions. But in their diagonals it does not happen that they are true in a similar way, as he says himself. For the former, since they were indefinite, happened to have diagonals that were true at the same time all with each other. But if someone returns to our descriptions of indefinite proposition,21 he will understand this thoroughly. Here, however, with defined propositions, it is not the same. He demonstrates this as follows: ‘Every man is just’ does not agree with its contradictory ‘not every man is just’. Again ‘every man is not-just’ does not agree in turn with ‘not every man is not-just’. For the latter agreed with its contrary. Therefore when the simple universal affirmation ‘every man is just’ is true, the proposition ‘every man is not-just’ is without doubt false. But if the latter is false, its contradictory will be true. Thus the negation ‘not every man is not-just’ is true. Therefore these two diagonal propositions, ‘every man is just’ and ‘not every man is not-just’ are at different times found to be true. Thus it happens sometimes that they are true, but not, he says, entirely. For if you begin from an infinite particular negation, it is not the same, i.e. the same truth does not come to light. This can be proven as follows: if it is true that not every man is not-just, ‘every man is not-just’ is false; for they are opposed as contradictories. But if the latter proposition ‘every man is not-just’ is false, ‘every man is just’ must not be entirely true for the reason that these two propositions are opposed as contradictories. And we demonstrated above,22 however, contrary propositions can be false at the same time. Therefore if ‘every man is not-just’ is false, it is not necessary for the proposition ‘every man is just’ to be true. But if this is not necessary, it can come about that both are false. Thus it sometimes happens that when the proposition ‘not every man is not-just’ is true, the proposition ‘every man is just’ is false. Therefore the diagonal propositions do not agree with each other in point of truth in a similar manner. And with this incorrect explanation Herminus confuses the list. If someone examines carefully what Herminus says and what we said above, he will recognise that there is a great difference in interpretation, and judging the interpretation mentioned previously to be better he will, if he gives any credence to us, rightly agree with it. 19b36-20a3 These then are two pairs of opposites, but there are others if an addition is made to ‘not-man’ as a kind of subject, e.g. ‘not-man is just’, ‘not-man is not just’, ‘not-man is not-just’,

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‘not-man is not not-just’. But there will not be more oppositions than these. And these will be on their own and separate from the previous ones in that they use ‘not-man’ as a name. He had already said above23 that every subject consists either of a simple and definite name or, on the other hand, of an infinite name; and he showed that they had two pairs of opposites and four propositions, two having a simple name as subject and two an infinite name. After these when ‘is’ is predicated as a joined third thing, there too, he said, a pair of oppositions is generated, when, that is to say, the subject is predicated as a 24 or an infinite name. And he demonstrated how they were related to each other in a sequence, the privative to the corresponding simple propositions with which propositions with an infinite name were compared. Moreover this whole variety of propositions is produced in such a way that when ‘is’ is predicated as a joined third thing either both subject and predicate are definite or the subject is definite, while the predicate is infinite (he mentioned these when he demonstrated their sequence) or they have an infinite subject but a definite predicate or both an infinite subject and predicate. Examples of propositions with both a definite subject and predicate are ‘man is just’, ‘man is not just’; with a definite subject and an infinite predicate, ‘man is not-just’, ‘man is not not-just’. Their sequence has been shown above. There are, however, others which have an infinite subject and employ an infinite name as a sort of name, e.g. ‘not-man is just’, ‘not-man is not just’; for these propositions use the subject, i.e. ‘not-man’, as a name, and ‘just’ as predicate. This is what he means when he says but there are others if something is added to ‘not-man’ as subject. For if someone puts ‘not-man’ as subject and predicates of this either a definite name, e.g. ‘just’, or an infinite, e.g. ‘not-just’, he will again form two pairs of opposites with either procedure. These are the four propositions: not-man is just not-man is not-just

not-man is not just not-man is not not-just

In all four propositions, then, ‘not-man’ acts as subject of the two pairs of opposites, but in the first pair of opposites a definite name, ‘just’, is predicated, But those propositions, he says, which have an infinite predicate but a definite subject or in which the predicate and subject are definite, are related to each other in some sequence, whereas those which we spoke of afterwards, i.e. those which had an infinite subject but a predicate that was either definite or infinite, have no sequential relationship to those propositions which consist of either a definite or infinite predicate and a definite subject. This is what he means when he says and these will be on their own and separate from the former,

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i.e. those that retain an infinite subject in the list of propositions have no sequential relationship to the propositions mentioned earlier which consist of a definite subject. Then after having listed both those consisting of two definite [terms], i.e. both subject and predicate, and those with a definite subject but an infinite predicate, he added also those which had an infinite subject and a definite predicate, as well as those which were seen to consist of both a subject and a predicate that were infinite. Thus having listed them, he said but there will not be more oppositions than these. For every pair of opposites, as we have already said above,25 consists either of two definite [terms], e.g. ‘man is just’, ‘man is not just’, or a definite subject and an infinite predicate, e.g. ‘man is not-just’, ‘man is not not-just’, or an infinite subject and a definite predicate, e.g. ‘not-man is just’, ‘not-man is not just’, or both an infinite subject and predicate, e.g. ‘not-man is not-just’, ‘not-man is not not-just’. It is absolutely impossible for a fifth pair of opposites to be found. Let this then be what is said on the topic of propositions with ‘is’ predicated as a joined third thing. 20a3-15 In cases where ‘is’ is not appropriate, e.g. ‘to run’ or ‘to walk’, when the verbs are posited in this way, the same effect is achieved as if ‘is’ were added, e.g. ‘every man runs’, ‘every man does not run’; ‘every not-man runs’, ‘every not-man does not run’. For one must not say ‘not every man’, but must add the negation ‘not’ to ‘man’. For ‘every’ does not signify a universal but that it is taken universally. This is clear from ‘man runs’, ‘man does not run’, ‘not-man runs’, ‘not-man does not run’; for these differ from the previous ones in that they are not taken universally. Thus ‘every’ or ‘no’ signify nothing in addition other than that a proposition affirms or denies something of a name taken universally. Thus the rest ought to be added unchanged. There are certain propositions in which ‘is’ is predicated as a joined third thing and is understood by its own sound and utterance and there are others where the predicate verb is such as not to be predicated as a joined third thing but still has and contains within it the verb ‘is’. If this kind of predicate, where the predicate, which, when previously expressed by the verb alone, was predicated as a second thing, is resolved into a participle and a verb, ‘is’ will be predicated in the third place and the proposition becomes like one that also has the verb ‘is’ actually uttered in it. For if someone says ‘every man runs’, in this proposition the first element is the subject, the second the predicate; for ‘man’ is made subject and ‘runs’ is predicated. We cannot be of the opinion that there are three terms in this proposition, for the reason that ‘every’ is not a term but the determination of the subject term; for when it says ‘every man runs’

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it signifies that a universal thing, i.e. ‘man’, is taken universally as the subject of ‘running’. For no man is excepted when the determination is present that every [man] runs. Thus when we say ‘every’ it is not put in the position of a term, but rather is the determination of the term which is the subject. Therefore in the proposition ‘every man runs’ there are two terms, ‘man’ and ‘runs’. Therefore in the same proposition, although the verb ‘is’ is not predicated in utterance, it is, nevertheless, contained in the signification of the verb ‘runs’. For if someone resolves the proposition ‘every man runs’ into a participle and verb, he will make ‘every man is running’, and the participle plus verb signifies the same as the verb signifies, which embraces both. For when I say ‘every man runs’, I proclaim that the action is there for every man; but if I in turn say the same thing in the form ‘every man is running’, it proposes that the same action is again present to man. Thus the verb ‘runs’ has the same signification as ‘is running’. And in the proposition ‘every man runs’, although ‘is’ is not uttered, it is, nevertheless, predicated potentially as a third thing. And this is discerned if the entire proposition is resolved into a participle and verb. For which reason an affirmation cannot be produced from an infinite verb in the same way as it comes from an infinite name as subject, but the force of a negation is soon recognised in the former. For we cannot say that an affirmation is produced when we propose ‘every man does not run’ in the same way in which we make an affirmation when we say ‘every not-man runs’, where we treat ‘notman’ as an infinite subject. For the former proposition is now a negation. Thus wherever there is ‘does not run’, ‘does not work’, ‘does not walk’, or ‘does not read’, in all of these there is a negation, wherever an indefinite verb is predicated. However, although an affirmation can never be produced from an infinite verb, but it is always a negation which is produced from this kind of predicate, someone will be in doubt whether if this same proposition, too, is resolved into a participle and verb, an affirmation could arise from an indefinite participle. In the proposition ‘every man runs’ one who proposes it thus, ‘every man does not run’, cannot make an affirmation, but without doubt only a negation; but if the same proposition, too, is resolved into a participle and verb, so that one says ‘every man is running’, and if the infinite ‘not-running’ is produced, and ‘every man is not-running’ is said, the question is whether this is an affirmation or definitely a negation having the equivalent force of saying ‘every man is not running’. But there were some who inferred this both from many other sources and also from a syllogism in Plato, and the definition which they drew from it they acknowledged on the authority of the most learned men. For a syllogism cannot in fact be produced from two negative propositions. In one of his dialogues26 Plato argues a syllogism of this kind: the senses, he says, do not have contact with the definition of a sub-

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stance; what does not have contact with the principle of a substance, does not have contact with the idea of truth itself; therefore the senses do not have contact with the idea of truth. It appears that he has made a syllogism from all negatives, which is impossible, and so they say that he put the infinite verb ‘does not have contact’ in place of the infinite participle ‘not-having-contact’. For in many other instances it is often possible to find an infinite verb put in the place of an infinite name. Thus some people maintained that a verb always makes a negation if it is proposed as an infinite, but that participles or names, if they are infinite, can make an affirmation. And so whenever an infinite verb and two negations are proposed by great men in a syllogism, it is defended on the grounds that an infinite verb is said to have been put in place of a participle and that the participle is predicated in the proposition in place of a name. And this is what Alexander of Aphrodisias and many others think. For they say that an affirmation cannot be produced from an infinite verb since just as the verb ‘is’, when it is an infinite verb, will immediately bring about an entire negation, so too verbs which contain in themselves the verb ‘is’ will not make an infinite affirmation, but rather a negation. For if someone says ‘man is not running’, no one would say this is an affirmation. But if someone says ‘man does not run’, this proposition too is not an affirmation since ‘run’ contained within it the verb ‘is’, and just as the negative particle when joined to the verb ‘is’ does not make an affirmation, but rather a negation, so too when the negation is joined to the verb which contains ‘is’ within itself, it brings about a full negation. Aristotle, however, does not seem to make this distinction,27 but to think that it is similar whether one puts in ‘is’ with a participle or the verb which encloses and embraces the verb ‘is’ within itself without the participle. For this is what he says: in cases where ‘is’ is not appropriate, e.g. ‘to run’ or ‘to walk’, when the verbs are posited in this way the same effect is achieved as if ‘is’ were added. And he gives as an example ‘every man runs’. For in the proposition ‘every man runs’ it is not appropriate to put in the verb ‘is’; in the same way, if one says ‘every man walks’ here, too, it is not appropriate to put in the verb ‘is’; but these are such as they would be if ‘is’ were added. This he showed with an example; for just as ‘every man is running’ is an affirmation showing the presence of running, so, too, the affirmation ‘every man runs’ has the same force and signification. He next lists the affirmations with simple subjects where it is not appropriate to say ‘is’ when he says ‘every man runs’ (currit omnis homo), putting the determination ‘every’ (omnis) in the middle between the predicate ‘runs’ (currit) and the subject ‘man’ (homo). Opposite this he ranges the simple negation ‘every man does not run’. In addition he forms an affirmation from an infinite name, ‘every not-man runs’, to which he opposes a negation with an infinite name as subject, ‘every not-man does not run’. And he proposed these to

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show that the same thing happens in propositions where it is not appropriate to predicate ‘is’ as in those where ‘is’ is predicated as a joined third thing. But when he said ‘every not-man does not run’ as a negation with an infinite name as subject, someone could have said that the proposition ‘every not-man does not run’ does not form the correct negation of the affirmation ‘every not-man runs’, but that the opposites ought rather to have been ‘every not-man runs’ and ‘not every man does not run’. And it is for this very reason that he demonstrates that the negation should be formed in the way he set it out; for he says for one must not say ‘not every man’, but must add the negation ‘not’ to ‘man’. The meaning of this is that whenever we form the negation of the affirmation ‘every not-man runs’, the negative particle ‘not’ must not be attached to ‘every’ but rather to the subject, i.e. the name ‘man’. For when we say ‘every not-man runs’, the negation must be formed as ‘every not-man does not run’. For we must not say ‘not every man does not run’, and the negative particle ‘not’ is not to be attached to ‘every’, but rather to ‘man’. The reason for this is that the determination ‘every’ is not classed as a term, but rather with its own force, that is, as a determination. For ‘every’ does not in itself signify something universal, but ‘man’ signifies the universal, while ‘every’ is a determination, since one predicates what is universal, i.e. ‘man’, universally. Thus the determination ‘every’ does not signify something universal, but rather that a universal name is predicated universally. And so whenever a negation of such propositions is produced, the negation ought to refer to the subject name and not to the determination. But in case anyone is in doubt, let him say that opposites should be produced here as elsewhere. For in propositions which have a finite subject, when we say ‘every man runs’, if the contradictory negation is ranged against this, the negative particle must be placed against the determination, so that ‘not every man runs’ is ranged against ‘every man runs’. But with propositions which are produced with an infinite name as subject, whether in affirmation or negation, the negation must not be separated from the subject name. This is very easily understood if the determinations are removed for a moment and the consideration turned to indefinite propositions with an infinite name as subject. Take the indefinite affirmation ‘not-man runs’. Ranged against this will be the negation ‘not-man does not run’. Then if these propositions have been made in universal terms (for ‘man’ is a universal term), but do not have the determination added, [indicating] that they are predicated universally, i.e. ‘every’, and the negative particle in both affirmation and negation is kept with the subject (for it was always of necessity infinite), even when something which determines is added the negation is attached not to the determination but rather to the subject name. One must take care that whatever was infinite in an affirmation, remains infinite in the negation. For just as in indefinite propo-

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sitions an indefinite28 and simple term ought to be preserved in the affirmation and the negation, so that we say ‘man runs, man does not run’, so too in a pair of opposites formed with an infinite name as subject one has to ensure that what is the subject in the affirmation is also kept as subject in the same form in the negation. But if this happens in indefinite propositions, why should the same thing not also seem to have to happen in defined propositions? For defined propositions differ from indefinite propositions in only one respect, that while indefinite propositions predicate universals without a universal determination, determined and defined propositions predicate that same universal with the additional signification that it is predicated universally. Therefore ‘every’ and ‘no’ have no other signification than that what is stated as a universal is predicated universally. Thus all the same things that were posited in an indefinite affirmation and negation, must also be kept the same in the same determined propositions. For ‘every’ and ‘no’ are not terms, but determinations of a universal term. Then after Aristotle’s treatment of these issues, let us also bring in Syrianus’ (we have already referred to his having the surname Philoxenus)29 very relevant and useful compilation of all the propositions weighed up in the discussions of this book. And we must first see how many of the categorical propositions are indefinite. For there will be as many universals and particular propositions and propositions involving singulars as there are indefinite propositions. And first let us look at the affirmations as follows: there are four kinds of proposition; for propositions are either undefined, universal, particular, involving singulars and individuals. Then if we investigate how many indefinite affirmations there are, if I multiply these by four, I will get the number of affirmations. If I double this, I will in this way also get the number of negations. For ‘is’ is predicated either on its own or certainly as a third thing joined with another. And if ‘is’ is predicated on its own, it must be predicated of a simple finite name or of an infinite. From these arise two affirmations: ‘man is’, ‘not-man is’. But whenever ‘is’ is predicated as a joined third thing, there will be four affirmations: (1) when the subject alone is infinite, ‘not-man is just’, (2) when the predicate alone is infinite, ‘man is not-just’, (3) when both are finite, ‘man is just’, (4) when both are infinite, ‘notman is not-just’. But more propositions than these cannot be found, as Aristotle himself says.30 Since there are six affirmations, two in which ‘is’ is predicated, four where it is added, if I multiply them by four, the result will be twenty-four. If I multiply them again by two, my total will increase somewhat to forty-eight. That then will be the number of whatever affirmations and negations have ‘is’ either as predicate or predicated as a joined third thing. Then since there are three other qualities of propositions – necessary, contingent and signifying that something is merely inherent – and all the former

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propositions are expressed according to these three attributes, if we multiply our forty-eight propositions by three, i.e. the attributes of the propositions, the total number of predicative propositions dealt with in this book will rise to one hundred and forty-four. I have at this point added below a list of the forty-eight propositions with their negations, excluding the tripling of the attributes. If I multiply them by the attributes, – necessary, contingent, signifying something –, the result will be one hundred and forty-four.

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So we have also arranged by name the propositions which Syrianus computed with calculations, since credence will more easily be given to the count if examples are given and also, at the same time, since a person badly instructed in these propositions used to dispute in the most perverse way, putting affirmations in place of negations and negations in place of affirmations and mixed up the whole list. Therefore, so that his discourse does not lead anyone astray from the truth of right reason, I have made this arrangement to help the memory to be more retentive. 20a16-20 Since the contrary negation of ‘every animal is just’ is that which signifies that ‘no animal is just’, it is clear that these will never be true at the same time or of the same thing, but that

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Translation their opposites sometimes will, e.g. ‘not every animal is just’ ‘some animal is just’.

This too has been carefully proved above, that contraries sometimes divide the true and false between them, namely when they are proposed in relation to either natural things or impossibilities, but that sometimes they can be found to be false at the same time, when they predicate things that are neither natural nor impossible. And it has been said that contraries are whatever propositions make a universal declaration either affirmatively or negatively. Thus he now says that propositions which are contraries cannot be true at the same time. And he said this with a certain determination of the things; for he says since the contrary negation of ‘every animal is just’, meaning the affirmation, is that which signifies that ‘no animal is just’, meaning the negation, it is clear, he says, that these, since they are contraries which cannot be true at the same time, will never be true at the same time or of the same thing. But never be true at the same time means that nothing prevents the possibility of a universal affirmation and negation being proposed truly at different times. Thus if someone says ‘every man is just, if it were said of the golden age, the proposition would be very true. But if someone, on the other hand, says ‘no man is just’ and says this of the iron-age, the proposition will be true. Therefore it happens that both the universal affirmation and negation, which are clearly contraries, are true but not at the same time. For one is in the golden age, if that happens to be the case, the other in the iron-age. But these times are different and not simultaneous. Therefore he was right to say in addition that it is clear that these will never be true at the same time. The addition or of the same thing applies to another determination of the same thing. For a universal affirmation and negation can be true at the same time and together, but only if they are not predicated of the same thing, e.g. if someone says that ‘every animal is rational’, the affirmation is true if it is predicated of men; but if someone says that ‘no animal is rational’, if he says this of horses, the universal negation when made in opposition to the universal affirmation will be true at one and the same time, but not of the same thing; for the affirmation was made about men, the negation about horses. Therefore he was right to say that contraries can never be true at the same time or of the same thing, i.e. at one and the same time or about one subject. But since in these a particular negation was opposed to a universal affirmation and a particular affirmation to a universal negation, and we said31 these are called subcontraries because they permit different things, so to speak, from contraries, it is clear that just as contraries cannot be true at the same time but sometimes do divide between themselves truth and falsity, in the same way subcontraries also sometimes divide true and false between them, when the contraries

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too have made this division; they can, however, be found to be simultaneously true when the universals and contraries are simultaneously false, but it can on no account of the matter happen that they are simultaneously false. Thus no one will ever find contraries to be true at the same time and of the same subject; but it is possible for subcontraries to be found to be true in relation to each other when opposed to universals and contraries. So in the example which he himself gave, ‘not every animal is just’ is true, and again ‘some animal is just’ is also true. Therefore contraries cannot be true at the same time, but nothing prevents subcontraries from being found to be true at the same time.

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20a20-3 These propositions follow from each other: ‘every man is not-just’ follows ‘no man is just’,32 and its opposite ‘not every man is not-just’ follows from ‘some man is just’; for there must be someone [who is just].

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He has said enough above about the sequence of simple and indefinite propositions, but now his intention is not to show what particular affirmation or negation follows what universal affirmation or negation, which he has already shown above, but what universal negation follows a universal affirmation or what particular negation agrees with a particular affirmation. He posits these four propositions, saying that a simple universal affirmation and an infinite universal affirmation follow from each other and agree with each other, and it is the same with their opposites, i.e. a simple particular negation and an infinite particular negation follow from each other both in truth and in falsity and do not in any way disagree with each other. Set out these four propositions: first the infinite universal affirmation ‘every man is not-just’; underneath and agreeing with it the simple universal negation ‘no man is just’; now on the other side, ranged against the infinite affirmation, put the simple particular affirmation ‘some man is just’; beneath this the infinite particular negation ‘not every man is not-just’.

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Then when they have been arranged in this way, if the infinite universal affirmation ‘every man is not-just’ is true, the simple universal negation ‘no man is just’ is also true. This is better understood in examples closer to the truth. Suppose that it is true that every man is a non-quadruped; then it is also true that no man is a quadruped. But if one of these is false, the other will also be false. For if it is false that every man is not-just, insofar as it is actually false, then the simple negation ‘no man is just’ has also made a completely

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false predication. Therefore an infinite universal affirmation and a simple universal negation agree with each other, so that when one is true, the other is necessarily true; and the falsity of one follows from the falsity of the other as well. The same also happens on the other side [of the list]. For if it is true that some man is just, it is also true that not every man is not-just; for there is someone [who is just]. For ‘not every’ is the equivalent of saying ‘someone is not’. This will be seen more clearly in another example too. If someone says that not every man is just, this is the same as saying that someone is not just. Thus ‘not every’ signifies ‘someone [is] not’. If, therefore, someone proposes that ‘some man is not not-just’, he confirms that the man he says is not not-just is just. So the man of whom it is said that he is not not-just will be just. Hence it happens that ‘not every man is not-just’ agrees with ‘a certain man is not not-just’. But this agrees with ‘a certain man is just’. Therefore this proposition agrees too with the proposition ‘not every man is not-just’. But since this perhaps seems to some extent rather obscure, their mutual implications should be taken in this way. Suppose that an infinite universal affirmation and a simple universal negation agree with each other, so that the truth or falsity of the one follows from the truth and falsity of the other. If the infinite universal affirmation ‘every man is not-just’ is false, the infinite particular negation ‘not every man is not-just’ which is opposed to this will be true. But when the infinite universal affirmation is false, the simple universal negation ‘no man is just’ is also false. But if this is false, the particular affirmation ‘some man is just’, which is opposed to this as a contradiction, is necessarily true. Therefore when an infinite universal affirmation is false, the infinite particular negation is true; and when the simple universal negation is false, the simple particular affirmation is true. But the infinite universal affirmation and the simple universal negation are simultaneously false and agree with each other in their falsity. Therefore the simple particular affirmation and the infinite particular negation will be simultaneously true. Again if the infinite universal affirmation is true, the infinite particular negation will be false; for it is opposed to it as a contradiction. If, on the other hand, the simple universal negation is true, the simple particular affirmation is false. But the infinite universal affirmation and the simple universal negation are simultaneously true. Therefore the simple particular affirmation and the infinite particular negation will be simultaneously false. Thus these propositions too, i.e. the simple particular affirmation and the infinite particular negation, agree with each other in truth and falsity, and each follows the truth and falsehood of the other. Thus both the universal affirmation and the universal negation, one simple, the other infinite, follow each other and agree with each other; and the particulars, i.e. the simple affirmation and the infinite negation

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opposed to the universals, also agree with each other. So the list is correct in making the infinite particular negation agree with the simple particular affirmation, just as the simple universal negation agrees with the infinite universal affirmation. 20a23-30 And it is clear that in singular propositions too if, when questioned, it is true to deny something, then it is also true also to affirm something, e.g. do you think that Socrates is wise? No. Then Socrates is not-wise. In universals, however, a similar [affirmation] is not true, but the negation is true, e.g. do you think that every man is wise? No. Then every man is not-wise. This is false, but ‘then not every man is wise’ is true. This is the opposite, the former is the contrary. While discussing the implications of propositions and how they agree with each other, he has left that topic for a short while and has proposed to show what things happen in an answer about singulars, if the negative particle has been attached to their predicate, and then what things take place in universal propositions when the negative particle has been attached to the predicate. For one ought not to form the statements in the same way. For what happens in each type of predication is not the same. And this is clear from the following considerations. If someone, when asked a question about an individual, makes a denial, the questioner can make with an infinite name as predicate by attaching the negation which the respondent previously denied, and this predication he will make truly. But it will be evident that the same truth cannot come about with universals if an affirmation is made from them. For if someone asks another person ‘do you think Socrates is wise?’, if he replies ‘no’, the questioner comes to the right conclusion, saying ‘then Socrates is not-wise’. Let us make this clear with another more obvious example and question someone in this way: ‘is Socrates a Roman?’ Suppose he replies ‘no’; we can correctly conclude ‘then Socrates is not-Roman’, making from the negation in his reply and the name predicated in our proposition an affirmation with an infinite name: ‘Socrates is not-wise’ or ‘Socrates is not-Roman’. For it was shown above that these affirmations have an infinite name. So if someone asks the same sort of question about universal subjects, saying ‘is every man wise?’, we will certainly reply ‘no’. He then states his conclusion in the same manner. For he says ‘then every man is not-wise’. Therefore no man is wise; for it has been demonstrated that ‘every man is not-wise’ agrees with ‘no man is wise’. It will appear then that a false conclusion has in some way been inferred from a true answer. To this we say [however] that we gave a negative reply not so that the negative should be attached to the predicate, but to the determination. For we did not want to take away wisdom from

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every man when we replied ‘no’ to the question whether every man is wise, but we wanted rather to remove wisdom from ‘every’, i.e. the determination, meaning that one person has wisdom and another does not have it, so that when we said ‘no’ it was the equivalent of our saying ‘not every’. Therefore if our negation is attached to the name, i.e. wise, it forms the universal affirmation ‘every man is not-wise’, which agrees with the universal negation ‘no man is wise’. But this is the contrary of the question. For the question was ‘is every man wise?’ This contains a universal affirmation, whose contrary is a universal negation, with which in turn the infinite universal affirmation agrees. Thus the conclusion ‘every man is not-wise’ is the contrary of the simple universal affirmation located in the question ‘is every man wise?’ But if the conclusion says ‘not every man is wise’, it is both true and is the opposite of the question. For if the answer ‘no’ was given to the question ‘is every man wise?’ and the negative was attached to ‘every’, the particular negation ‘not every man is wise’ is produced and this is the opposite of the universal affirmation proposed in the question. This is what he means by this is the opposite, the former is the contrary. The meaning, word for word, should be taken as follows: And it is clear, he says, that in singular propositions, e.g. Socrates and anything individual, if, when questioned, it is true to deny something, i.e. if when someone is asked a question he gives a true denial, e.g. when someone is asked whether Socrates is a Roman, and he denies it, it is true also to affirm [the denial], so that the questioner forms an infinite affirmation from the negation and the predicated name. And an example of this is do you think that Socrates is wise? The reply is No. The conclusion is then Socrates is not-wise. But it is not a similar situation with universals, as he now demonstrates when he says in universals, however, a similar [affirmation] is not true, i.e. an infinite affirmation formed from the predicated name and the respondent’s negation is not true. But it is rather the negation which is true, not the affirmation. An example of this: the question is do you think that every man is wise? The answer is No. The false conclusion is then every man is not-wise. This is false, and is similar to what we predicated above of a singular subject, whereas it should rather be ‘then not every man is wise’, so that the respondent’s negation is attached to ‘every’ and a particular negation is produced; for this is true. This is the opposite; for when the universal affirmation ‘every man is wise’ has been put as a question, ‘not every man is wise’ is produced as a conclusion from the negative particle, and they are opposites. For the former is a universal affirmation, the latter a particular negation. The former is the contrary; for if the negative ‘not’ is attached to the predicate, an infinite universal affirmation is produced, which agrees with the finite universal negation. But this is in opposition to the finite universal affirmation which is contained

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in the question. Therefore the infinite universal affirmation will also be a contrary. We must, however, enquire what is the reason why in singular propositions an affirmation with an infinite name or a finite negation agree with each other, whereas in universals a universal affirmation with an infinite name does not agree with a finite particular negation. For if someone says ‘Socrates is not-wise’ and ‘Socrates is not wise’, it is the same thing and these two agree with each other; if, however, someone says ‘every man is not-wise’ and again ‘not every man is wise’, these two do not agree with each other. But the explanation is that in singular subjects there are not two opposites but only one, i.e. what makes a negation, whereas in universals predicated universally there are two opposites, one contrary, the other contradictory. Therefore if there is an affirmation of the kind ‘Socrates is wise’, there is only one opposite to this, ‘Socrates is not wise’. If, therefore, someone says ‘Socrates is not-wise’, this will have no meaning other than ‘Socrates is not wise’. For we have said that there is only one opposite in singular propositions. Therefore whatever others there are they will concur in the same signification. In universal propositions predicated universally, however, it is not the same. For if there is a universal affirmation ‘every man is wise’, there stands against it both ‘no man is wise’ and also ‘not every man is wise’. The former is a contrary, the latter a contradictory. These two opposites cannot then agree with each other. For the universal negation takes away everything, the finite particular negation takes away part. But the universal negation agrees with the universal affirmation that has an infinite name. Therefore this too will be different from the definite particular negation. Then since there are two opposites in universals, one in singulars, it is correct that the same truth and falsity does not occur, though there is a similarity of predication. 20a31-40 Those negations, however, which are opposite because they have infinite names and verbs, e.g. ‘not-man’, ‘not-just’ will appear to be, in a manner of speaking, negations without a name or a verb. But they are not. For a negation must always be either true or false. But one who has said ‘not-man’ was, if nothing is added, no more true or false concerning ‘man’, but even less so. ‘Every not-man is just’ does not signify the same as any of the above nor does its opposite ‘every not-man is not just’. But ‘every not-man [is] not-just’ signifies the same as ‘no not-man [is] just’. We know that propositions can be produced from infinite names. So in analysing these Aristotle next takes an infinite name as an expression and debates concerning it, 33 if it is set against a finite

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name, this appears to be a kind of opposition that makes a statement. For if someone takes ‘not-man’ and ranges ‘man’ against it, it will perhaps seem to some extent to form an opposite. For since every negative particle when added to a verb that which it contains as a proposition it makes a negation, if ‘not’ is predicated as another mode of proposition, as must be demonstrated later, the addition of the negative particle seems to make a kind of negation, so that if the particle ‘not’ is attached to ‘man’, it will make ‘not-man’. This is what he means when he says those negations, however, which are opposite because they have infinite names or verbs, e.g. ‘not-man’, ‘not-just’ appear to be, in a manner of speaking, negations without a name or a verb. For if someone says ‘does not run’, this produces a negation without a name. But if someone says ‘not-man’, this too is a negation, without a verb. These expressions because of their infinite name and verb are opposed to the definite verb or name, ‘runs’ and ‘man’. Thus these will seem to be negations because of their infinite name or verb, which are predicated, but they are not. For the greatest proof shows that they are not negations: every negation is either true or false, but when we say ‘not-man’ or ‘does not run’, although the simple and finites ‘man’ and ‘runs’ also signify nothing true or false, their infinites in fact indicate something much less true or false. It is not because the simple expressions signify something true or false that we say that the infinite expressions indicate truth or falsity less than the simple ones, but because the simple name or verb proposes something definite even though they designate nothing true or false, so that there is something finite and a single species in ‘man’. But when someone says ‘not-man’, he does away with the species that is present, but by proposing nothing gives us to understand an infinite number of other species. Thus although finite verbs or names cannot in themselves be true or false, except when they are combined with others, yet infinite names or verbs are much less capable of truth or falsity. They do not even posit the very thing which they signify, but they cancel it, and do not by themselves establish in their meaning any other thing. In sum, finite expressions are nearer to the understanding of truth or falsity. Thus an expression consisting of an infinite name is less true or false than one consisting of some simple and finite word. 20a36-40 ‘Every not-man is just’ does not signify the same as any of the above nor does its opposite, ‘every not-man is not just’. But ‘every not-man [is] not-just’ signifies the same as ‘no not-man [is] just’. After having spoken at sufficient length about propositions which have an infinite predicate and having shown their oppositions and demonstrated their implications and in the midst of this having

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briefly noted concerning infinite names that they are not negations, he now returns to propositions which have an infinite subject, but whose predicate is finite or infinite. And he first of all teaches us whether the propositions with an infinite subject are the same and signify the same thing and whether they have some sequential arrangement, as those which have an infinite predicate or those which have both [terms] finite. For he says that the two propositions, ‘every not-man is just’, ‘every not-man is not just’, do not signify the same thing as any of those that have either both [terms] finite or an infinite predicate. Let us arrange in order those propositions which have both [terms] finite or an infinite predicate. First of all put in place the simple universal affirmation; under this, the universal negation with an infinite predicate and which agrees with the simple affirmation above it. On the other side, put the simple universal negation and under this the universal affirmation with an infinite predicate; it is agreed that these agree with each other, but the universal affirmation with infinite predicate takes precedence. every man is just no man is not-just

no man is just every man is not-just

Once affirmations and negations which have a simple subject but an infinite or simple predicate have been arranged in this way, Aristotle now says that propositions which have an infinite subject do not signify the same things as any of those we have set out above. For ‘every not-man is just’ does not agree with ‘every man is just’ nor with ‘every man is not-just’ nor with ‘no man is just’ or ‘no man is not-just’. For these all have ‘man’ as subject, whereas it has ‘not-man’. Nor therefore will the negation of this, i.e. the particular negation of a universal affirmation with an infinite subject, be able to agree with any of the propositions which have a finite subject. For ‘every notman is not just’ agrees neither with ‘every man is just’ nor with ‘every man is not-just’ nor with ‘no man is just’ or ‘no man is not-just’. But he is not saying that propositions with an infinite subject are different from those which have either a finite or an infinite predicate, but a finite subject. For predications can be different, but sometimes still have the same signification. For instance, although ‘every man is unjust’ is different from ‘no man is just’, they still sometimes signify the same thing, if the privative affirmation has preceded; for it has been said that negations without doubt follow from preceding affirmations. Therefore he is not saying that propositions with an infinite name as subject and a finite or infinite predicate are different but whose subject is finite, but that they entirely neither agree with each other nor signify the same thing, i.e. they are dissimilar in the entire quality of the

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proposition. And this is what he said about propositions which have a finite subject and an infinite predicate. He now comes to the implications of propositions which consist of an infinite name as subject. And just as before he showed us the implications of propositions with both [terms] as finites or with an infinite predicate, so too conversely he points out the implications of propositions which consist of both [terms] as infinite names or have an infinite name as subject. These are his words: but ‘every not-man [is] not-just’ signifies the same as ‘no not-man [is] just’. He points out only these two propositions, namely the affirmative universal with both [terms] infinite, ‘every not-man [is] not-just’, [which] agrees with the universal negation with only the subject infinite, ‘no notman [is] just’. In these propositions the particle ‘is’ is understood, so that the complete proposition is ‘every not-man is not-just’ and again ‘no not-man is just’. For just as in propositions where the subject was finite but the predicate infinite or finite, the simple universal negation consisting of both [terms] finite, ‘no man is just’, followed the affirmation formed from a finite subject and an infinite predicate, ‘every man is not-just’, so too the same thing occurs in propositions where the subject alone has been changed. For just as in the former case the universal negation with both [terms] finite followed the universal affirmation formed from a finite subject and an infinite predicate, so too in the latter case a universal affirmation with both [terms] infinite is followed by a negation which is itself also universal formed from an infinite subject. And he included only the sequence of these two propositions, but made no effort to run through the rest, as he thought they were easy to understand. But we add them here so that nothing might appear to have been ignored. The sequence is as follows: every not-man is not-just no not-man is just every not-man is just no not-man is not-just

some not-man is just not every not-man is not-just some not-man is not-just not every not-man is just

If one looks carefully at these two comparative lists, they will show a sequence and agreement which is very suited to the two [of them]. BOOK 5

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I have now covered most of the work and although what follows presents numerous problems I will tackle it with greater confidence and spirit. Small details ought not to deter us from our undertaking to explain and publish the doctrine of the whole treatise. And so I have continued on exactly from where we left off.

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20b1-12 When names or verbs are transposed they signify the same thing, e.g. ‘man is white’, ‘white is man’. For if this is not the case, there will be many negations of the same thing. But it has been shown that there is only one of each; for the negation of ‘man is white’ is ‘man is not white’ and the negation of ‘white is man’, if it is not the same as ‘man is white’, will be either ‘white is not not-man’ or ‘white is not man’. But one of these is the negation of ‘white is not-man’, the other of ‘man is white’. Thus there will be two negations for one affirmation. Then it is clear that if the name or verb is transposed the same affirmation or negation is produced. He now informs us that if verbs or names are transposed and one is predicated first, the other after it, there is no doubt that they keep the same signification. For if someone says ‘man is white’ (est homo albus) or ‘white is man’ (est albus homo)34 or changes the order of predication in any other way, the same signification will doubtless remain. And this may be seen in oratory and poetry in a different way than in philosophical treatises. For oratorical compositions it makes a great difference in what order verbs and names are expressed. For when Cicero wrote ‘For this madness nature gave you birth, your will prepared you, fortune saved you’ it makes a difference that it was said in that way or as ‘for this madness, what gave you birth was nature, what prepared you your will, what saved you fortune’.35 Said like this the impact of the sentence is less and what is prominent in the combination and reveals itself to our minds and ears even without our wanting it now shines out less clearly. Again when Virgil said ‘and on peace to lay tradition’36 he could have kept the metre if he had said ‘and tradition to lay on peace’ but the sound would have been weaker and the line would not be so brilliantly composed with the change of metrical beat. Thus a change in the order of verbs and names has a different impact in oratory and poetry. For when you look at combination you will find a great deal of artistry in word order. But in philosophical treatises where attention to style is not relevant and it is truth alone that is being questioned it is of no importance if the order of verbs and names is in any way changed so long as they retain the same force in their signification. But in them too the same emphasis and signification is not always preserved in every respect when the order is altered. For the negative particle ‘not’ has considerable force and achieves different effects if added in varying positions. For if you say ‘man is not white’ you will make a simple indefinite negation, if ‘man is not-white’37 an indefinite affirmation with an infinite predicate; but if someone proposes ‘notman is white’, he will make an indefinite affirmation with an infinite subject. Again, if one says it in this way, ‘every man is not-just’, this agrees with ‘no man is just’, but if the negative is put with the

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determination of the universal, so as to say ‘not every man is just’, it is no longer a universal affirmation with an infinite predicate agreeing with a simple universal negation, but a simple particular negation. Then do you see how many differences are created by connecting the negative particles with different predications of names. But although this is the case, it is still possible for the same words when put in different positions, to retain the same force and signification. For if the particle ‘not’ placed with its universal is moved around with this same universal, there is no doubt that the same signification is retained. For if one says ‘not-every man is white’, it is a simple particular negation. But if someone says ‘man not-every is white’, the signification is the same; nor if ‘man white not-every is’ does this depart from the previous signification; nor if you change it a bit more to ‘man white is not-every’ does this disagree with the previous signification. Similarly whatever changes are made, so long as the determination remains with its universal, whatever other changes of order are made, the same signification is necessarily retained. Similarly the same signification is kept if the same particle ‘not’ is often moved around joined to another name or verb, as when we say ‘man just is-not’, ‘man is-not just’, ‘is-not man just’. For this reason if the negative particle is moved around on its own and not predicated in the same order, it will produce a number of different propositions. But if it is, as we have said, moved around quite frequently when joined to another name, the same signification will remain in all the transpositions. Then after making these points we should look at Aristotle’s argument that names and verbs when transposed always have the same force and signification. For he says ‘when names or verbs are transposed they signify the same thing, e.g. “man is white”, “white is man”’; for this keeps the same signification when the names and verbs have been transposed; for in one ‘white’ is first and ‘man’ comes after, in the other ‘man’ is first and ‘white’ comes after. But if this is false and they are not the same but are different from each other something impossible and improper is happening. For a single affirmation will have two negations, which is impossible. For it is clear that one negation belongs to one affirmation. Then let us now see, if the affirmations ‘man is white’ and ‘white is man’ are not the same but different, how one affirmation has two negations. First of all put them down like this: man is white white is man Then the negation of ‘man is white’ will be ‘man is not white’; for you cannot reasonably find any other which could serve the purpose. Then put them down again as before, the first one with its negation.

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man is not white

Then if ‘man is not white’ is the negation of ‘man is white’, if ‘white is man’ is to be different from ‘man is white’, its negation will be different. Then you should make it either ‘white is not not-man’ or ‘white is not man’. Again then put down the two primary affirmations separately. Then opposite the first put the negation we agreed upon and opposite the second write down the two negations we mentioned. man is white white is man

man is not white white is not not-man white is not man

Now in this list ‘white is not not-man’ cannot be the negation of ‘white is man’, for it is the negation of ‘white is not-man’ which has an infinite subject. Similarly too if you suggest any other negation, it will certainly be found to have a different affirmation. So it happens that ‘white is not man’ is the only negation left for it. Thus the negation of ‘white is man’ is ‘white is not man’. But ‘white is not man’ is also the negation of ‘man is white’. This is proved by the fact that they make a distinction of true and false, for if it is true that man is white, it is false that white is not man. But if truth is found in any proposition, it is known through the definition of the proposition rather than through the form of the negation, so they are opposed more by their determination than by their quantity. This is demonstrated by the fact that if ‘every man is not white’ is opposed to ‘every man is white’, it is clear that they distinguish between truth and falsity; for one must be true, the other false. So too if the determinations are removed, the same opposition remains although it is indefinite. For just as when ‘every’ and ‘not every’ are removed from ‘every man is just’ and ‘not every man is just’ we are left with the opposed affirmation and negation ‘man is just’ and ‘man is not just’, so too where ‘every’ and ‘not every’ has been removed we have ‘man is white’ opposed to ‘white is not man’, for if you add the determinations one is always true, the other always false. But we said that the negation of the affirmation ‘man is white’ is ‘man is not white’. Then the affirmation ‘man is white’ has two negations, ‘man is not white’ and ‘white is not man’. This is the case if the negations ‘white is not man’ and ‘man is not white’ are different from each other. And this depends on the fact that we laid down before that ‘man is white’ is different from ‘white is man’. But if it is impossible that one affirmation should have two negations and it is clear that the affirmation ‘man is white’ has opposed to it two negations, ‘man is not white’ and ‘white is not man’, these are not different from each other, agree with each other, and differ only in the change of position of a name but are in every

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other respect identical. But if these negations are identical, their affirmations are also identical. Then it was right to say that when verbs and names are transposed they keep the same force and signification. This is the continuous meaning of the passage, following the order of his own words: When names or verbs are transposed they signify the same thing and he gives as an example ‘man is white’, ‘white is man’. For here the names have been transposed. For if this is not the case, i.e. if the transposed verbs and names do not signify the same thing, it is something impossible and improper; for there will be many negations of the same thing, i.e. there will be many negations of the same affirmation. But this is impossible, for it is clear that one affirmation has one negation. Then that two negations are opposed to a single affirmation, if the transposed verbs and names do not signify the same thing, he proves as follows: for the negation of the affirmation ‘man is white’ is ‘man is not white’ (this negation is correctly opposed to the affirmation) and the negation of ‘white is man’, i.e. of the other affirmation if it is not the same as ‘man is white’, i.e. if it is different from the first proposition ‘man is white’ and is not the same as it, the equivalent of saying if it does not agree, will be either ‘white is not not-man’ or ‘white is not man’ or any other negation one may propose that can be shown not to be the negation [of the given affirmation ‘man is white’] by the one argument by which this one is refuted. But this is refuted as follows: But one of these is the negation of ‘white is not-man’, the other of ‘man is white’; for of the posited negations ‘white is not not-man’ and ‘white is not man’, ‘white is not not-man’ is the negation of the affirmation with the infinite subject ‘white is not-man’, whereas the other ‘white is not man’ is the negation of ‘man is white’. For it distinguishes true and false along with this proposition. Thus one affirmation has two negations. But this is impossible. Then it is clear that if the name or verb is transposed the same affirmation or negation is produced, thus confirming with this concluding sentence the previous argument. He made this syllogism in the second hypothetical mode which he calls undemonstrable, as follows: if a, then b; but not b; therefore not a, i.e. if propositions do not remain the same when verbs and names have been transposed, one affirmation has two negations; but this is impossible; therefore propositions are not different when verbs and names have been transposed. Chapter 11

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20b12-22 But to affirm or deny one thing of many or many of one, is not one affirmation or denial, if it is not one thing composed of many. I mean one not in the sense that one name is given but that there exists one thing composed of many, e.g.

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man is perhaps animal, two-footed and tame, but one is produced out of these, but one thing is not produced from white, man and walking. Therefore if someone affirms some one thing of these, it is not a single affirmation, but is one spoken sound, but many affirmations, nor is it one affirmation if affirmed of one thing, but in the same way more than one affirmation. The obscurity of this passage is such as to cause so much confusion that many were unable to follow properly and explain what Aristotle meant. But we have already said above38 that the leaders of the Peripatetic school took great pains to distinguish a single from a multiple affirmation or negation. For these are not recognised by the sound of the spoken utterance or the number of terms. For it is possible for one thing to be predicated of a single thing and not to be a single affirmation. And it can happen that several things are predicated of one or one of several, but that a single affirmation is produced from all of these. They took great care that where a clear rule occurred it should not be left concealed. For if someone says ‘a dog is an animal’ it is not a single statement; for a dog signifies many things. But if someone says that a man is a rational mortal or that a man is a rational, mortal animal, these are single statements because some one single thing can come to be out of many. For man as a single thing is made from animal, mortal and rational joined together at the same time. And there are other things which are predicated as plural, from which some one thing cannot be made or constituted. A single affirmation or negation is produced neither if they are predicated of something nor if another thing is predicated of them, but as many statements are made as there are things which are either predicated of one or of which one thing is predicated, e.g. when we say ‘the bald philosopher Socrates is walking’, no one thing is formed from baldness, philosophy and walking, in such a way that these, as it were, form the species of something. Thus whether these are predicated of one thing or one thing of them, it cannot be a single statement. And this interpretation applies in general to any proposition. Let us now turn to Aristotle’s words. He says: but to affirm or deny one thing of many or many of one, is not one affirmation or denial, if it is not one thing composed of many. If, he says, you predicate many things of one, e.g. Socrates is a snub-nosed bald philosopher’, or when you predicate one thing of several, e.g. ‘Socrates the snub-nosed philosopher is bald’, if some one thing is not produced from the several things which you predicate or attach, in the way that one thing can come about from what we predicate as a living sensible substance, i.e. an animal, then a single negation or a single affirmation is not produced, when several things are predicated or attached without any single species coming into existence from their combination. But if someone predicates one thing of one thing where the single name signifies

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more than one thing and where some one thing is not produced from the plurality, again there is not a single affirmation or negation. For if someone says ‘a dog is an animal’, the name ‘dog’ signifies the kind that barks, the constellation and the sea-dog39 and when these are joined together no one thing is produced. Thus because some one thing cannot be formed from a plurality of this kind, so too a single affirmation and a single negation does not come about from a single name which when it is predicated or attached signifies a number of things that cannot form a single thing. This is what he means when he says I mean one not in the sense that one name is given but that there exists one thing composed of many. For it can happen that one name is predicated of one thing, but if the one thing signifies a plurality from which a single thing is not produced, then we don’t have a single affirmation or a single negation. For a single spoken sound does not make a statement, but the simplicity of what is signified, even if it is a plurality, has the power to make some one single thing from what is gathered together. The example of this which he added has deceived a number of people, e.g. man is perhaps animal, two-footed and tame, but one is produced out of these, but one thing is not produced from white, man and walking. Now some thought that he spoke this way to show that he had given this sort of definition as an example, in case anyone should think he had meant this as some kind of exact definition of man as a two-footed tame animal. And, they maintain, he said man is perhaps animal, two-footed and tame in case anyone should think that he, Aristotle, thought that the definition of man was like this. But others do not accept that this is how it was meant, but that it was meant to be taken in conjunction with a reading of Aristotle’s sentence as ‘e.g. man is equally animal, two-footed and tame, but one is produced out of these’ which is to be understood as meaning that man is in himself just as much ‘man’ as he is a two-footed tame animal. Thus if to say ‘man’ is identical and the same as saying ‘two-footed tame animal’, then whenever this plurality is predicated of one thing, i.e. two-footed tame animal of man, because it equals ‘man’ and man is one, it must be the case that you predicate some one thing although you seem to be predicating three spoken sounds. But none of these understood the passage at all. Porphyry’s interpretation is better. Aristotle, he says, intending to show what is and is not a single affirmation, first of all said that to predicate several things of one or attach several things to one does not lead to a single statement, unless some single thing comes to be from the plurality. Then seeing that so far it looked as if several affirmations were being made even when there was a plurality of predications out of which a single thing could be produced, he then said man is perhaps animal, two-footed and tame. And this I take to mean that it is clear that, if several things are predicated of one and these cannot form one thing or if several things are attached to one and these cannot form one

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thing, there isn’t a single affirmation or negation. But now let us deal with a plurality from which some one thing can be formed; for we will find that in these too several and not one statement is sometimes found because of the way in which we make the statement, although some one thing could be formed from the plurality. For if someone says ‘man is a mortal rational animal’ joining together mortal rational animal at the same time, because it was said continuously and some one thing is formed from them, there is a single affirmation. But if there is an interval between them so that one says ‘man is a mortal’ then ‘rational’ and after a little pause ‘animal’, it is not a single affirmation or negation. For the intermissions create several statements. Again if ‘man is a mortal and rational and animal’ is said with conjunctions, then we again have many statements. Nor does saying it with pauses or with conjunctions separating the words differ at all from saying ‘man is an animal, man is rational, man is mortal’ and these are clearly several propositions. Aristotle then, seeing this, said man is perhaps animal, two-footed and tame. He says perhaps at this point with the meaning: one thing is formed from man, two-footed and tame, but it is perhaps sometimes the case that there are several propositions when their actual conjunction in a sense separates and parts them; for perhaps there will be ‘man’ and ‘animal’ forming one proposition, [‘man’ and] ‘two-footed’ a second and [‘man’ and] ‘tame’ a third. But out of these some one thing is formed so that when they are expressed continuously there is a single proposition because some one thing is created from them. But the same does not happen in all of them. For one thing is not produced from white, man and walking. For if someone says ‘The white man Socrates is walking’, it is not a single affirmation, because a species cannot at all be formed from man, whiteness and walking. Thus the conclusion is that there is no single affirmation even if some one thing is predicated of a plurality which does not form one thing. E.g. because a barking land dog, the constellation and a sea-dog do not form one thing and one thing is predicated of them, namely ‘dog’, which is the sort of name which signifies several things which do not form one thing (if it is predicated of something else or attached to another) a single affirmation or negation is not formed, but there will be a single spoken sound and several affirmations. For if one thing is predicated of several things which do not form one thing, or several things of this kind are predicated of one, or if one thing is predicated of one thing which when predicated signifies several things which do not form a single thing, or if that one thing is added as a predicate to another, there is no possibility of there being a single affirmation or negation. The whole is as follows. There is a single affirmation if either two terms signify single things or if more terms are so predicated of one thing or attached to one thing that a single thing can be formed from them, or if one name which when either predicated or attached signifies the

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kind of plurality which can somehow come together as a whole to form a single species. 357,1

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20b22-30 Then if a dialectical question requires as an answer either the proposition or one side of a contradiction, whilst the proposition is part of a single contradiction, there will be no single reply in these cases; nor will the question be one even if it is true. These things have been discussed in the Topics.40 It is similarly clear that ‘what is it?’ is not a dialectical question either. For the question ought to allow one to choose which part of the contradiction one wishes to express because the questioner ought to decide whether man is this or not this. Whoever employs a dialectical question either asks a simple question putting just one proposition in his question so as to evoke a single reply or puts his question in a double form to which there is no simple reply but a single whole proposition forms the reply. For if someone puts the question ‘is Socrates an animal?’, the answer is either ‘yes’ or ‘no’. But if you put the question in the form ‘Is Socrates an animal or not?’ there is no single reply. For if you reply ‘yes’, it remains unknown to which you are assenting, the affirmation or the negation. Again if you reply ‘no’ it is unclear what you are want to deny, the affirmation or the negation. Thus to questions of this kind the whole proposition has to be given as a reply, i.e. one side of the contradiction or the entire affirmation or entire negation, so that you say either ‘Socrates is an animal’ or, if this is not your view, you reply that ‘Socrates is not an animal’. Then when a question is formed from multiple statements which do not form a single thing, a single answer is open to criticism. For anyone making a question from things that cannot form a single thing, is asking a number of questions. If a simple reply is given, even if that particular reply is true, yet it is rightly open to criticism. For there ought to be a multiple reply to a multiple question. For if you put the question ‘Is Socrates a philosopher and does he read and go for walks?’, because it can happen that he is a philosopher and reads but does not go for walks or goes for walks but does not read or it can happen that he both reads and goes for walks, there can be no single answer to this kind of question. For anyone who put the question in the form ‘Is Socrates a philosopher and does he read and go for walks?’ either framed his question awkwardly or as a trick. If Socrates does happen to be a philosopher and reads and goes for walks, if ‘yes’ is given as an answer to the question, this reply too can be criticised. For a single answer should not be supplied to several questions even if the single reply gives a right answer, as here, if in fact he is a philosopher and both reads and goes for walks. Thus if a dialectical question requires an answer by which a proposition is

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produced, e.g. when someone asks ‘is it day?’ and the answer ‘no’ is given, then from this the negation ‘it is not day’ is produced or of course one side of a proposition when the question is put in the form ‘is it day or not day?’. Thus, it is appropriate to reply that it is day, or that it is not day, which is a whole proposition. Questions that are composed of a plurality and so put that they do not form a single thing, are not simple questions. Therefore a simple reply must not be given to them. Aristotle recalls that he had spoken about these in the Topics. Again, because a dialectical question requires as an answer (as we explained above ) either the proposition or one side of a contradiction, which will be explained a little later, it is a mark of ignorance to put the question in the form ‘what is an animal?’ or ‘what is the soul?’. If you want to ask a dialectical question you must give in the question the choice to the respondent whether he wants to give an affirmation or negation in answer. But someone who puts the question such that he wants the respondent to say what something is, is not asking a dialectical question. And this is how some people put questions: ‘do you think the soul is fire?’ When the reply is ‘no’ he will add, ‘do you think there is something between fire and air, a median body which is soul?’ When the reply to this is also ‘no’, he continues ‘perhaps you think the soul is water or earth?’ When he agrees that the soul is neither earth nor water, then tired out by the questions they put the question in the form ‘what then is the soul?’ But this is not a dialectical question, but rather the kind of question that a student who wants to learn something puts to his teacher. For someone who wants to learn something asks the person who can teach him about the thing he is unsure of. But the dialectician, as we have said, ought to put a question in a way that a choice is given to the respondent to reply in an affirmation or negation as he wishes. And one ought to know that every question requires an answer, but the dialectical question requires not any answer but what stands as a choice on either side. Therefore ‘what is this?’ is not a dialectical question. For one ought to put the question in such a way that the respondent can choose one side of the contradiction from the question. For the questioner ought to define in precise terms whether what is being said is or is not, e.g. ‘is man an animal or not?’ Then the reply must be either an affirmation or a negation. When he says that the dialectical question requires as an answer either the proposition or one side of a contradiction, he means that whoever puts a question in the affirmative form expects his listener either to make the same reply or a contradiction. For example, if someone put the question ‘is man an animal?’, if the answer is ‘yes’ a proposition is given in answer, the one proposed in the question. But if someone asks whether man is an animal and the reply is given that he isn’t, it will appear that a contradiction has been given as a reply. For the

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question was put in the affirmative, but the reply was a negation, which is a contradiction. Again if a question is put in the form of a negation and the reply is a negation, the same proposition will be given in reply as the questioner had put in his question. But where one person asks in the negative and the reply is an affirmation then the response is a contradiction. This is then what he means when he says that a question requires a response and explains ‘response’ with either the proposition, if the reply is the same as the question, or one side of a contradiction if a negation is given as reply to an affirmative question or an affirmation is given as reply to a negation in the question. According to the Peripatetics there are two kinds of question. A question is either dialectical or not dialectical. And there are two kinds of non-dialectical question according to the teaching of Eudemus.41 One kind is where we take an accident and ask what it belongs to, e.g. when we see Cicero’s house, if we ask ‘who lives there?’; or when we take the actual subject and thing, then ask what is happening to it, e.g. if someone sees Cicero himself and asks where he is going off to. This is one kind, a non-dialectical accidental question. The other kind is when we put forward a name and ask what is its genus or difference or definition. For example, if someone asks what an animal is or when we take a definition or one of the things just mentioned and ask what they belong to, e.g. if someone asks what the definition ‘mortal rational animal’ belongs to. 20b31-21a3 Since of things predicated separately some are predicated in combination so that the entire predicate is one, others not; what is the difference? For it is true to say of a man that he is separately an animal, separately two-footed, and as one; and man and white, and these as one. But if he is a lyre-player and good, he is not also a good lyre-player. For if because each of two is the case, both together are also the case, there will be many absurdities. For it is true to say of a man that he is a man and white, therefore the whole too [is true]. And again if white, then the whole too. Therefore there will be a ‘white white man’ and so on to infinity. And again there will be a ‘walking white musician’; and the same things compounded many times. Further if Socrates is Socrates and a man, then Socrates will be a man Socrates, and two-footed, he will be a two-footed man. There are many things which are true when predicated on their own and which continue to be predicated truly if they are joined together and predicated. But there are others, which are true if they are predicated for themselves and unconnected, but if they are said jointly, become untrue in predication. One ought then to know the

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difference between these. For if someone says Socrates is an animal, he has said something true. If again someone says in predication that Socrates is two-footed, this too is true. And if these are joined and expressed as ‘Socrates is a two-footed animal’, there is no departure from the appropriate truth. And this is here said of the genus and Socrates’ substantial differentia. But it can happen just the same way if it is also said of an accident. For if someone says ‘Socrates is a man’, it is true, and again ‘Socrates is bald’, this is also true. If the two are joined as ‘Socrates is a bald man’, a true predication is produced from the combination. And here what was said truly when separate, is also predicated truly when combined. But there are other things which are predicated truly when separate, but lose their quality of truth when combined. E.g. if you say ‘Socrates is good’, it is true, and again ‘Socrates is also a lyre-player’, suppose this to be true as well. It does not follow of necessity that these belong together to make it true that Socrates is a good lyre-player. For he can be a good man and though a lyre-player, not good at it, but good in another respect and with respect to the former only knowledgeable in lyreplaying but not perfect in it. And this will become clearer in the following example. If you say that Tiberius Gracchus is bad, it is true; and again that Tiberius Gracchus is an orator, this too is true. If you join them and say ‘Then Tiberius Gracchus is a bad orator’ you are wrong, because he was an excellent orator. But in case someone should think that in putting it this way we are forgetting that the definition of an orator is a good man skilled in speaking,42 our words are meant in a different context, as an example rather than referring to reality. And this is what is put forward by Aristotle, whose actual words are to be understood as follows: since some are predicated linked and in combination so that a single predicate is formed from what was said truly when separate, but others which when said separately and apart are truly predicated but when combined do not amount to a true predication, we must ask what the difference between them is. Examples are then given. The following is an example of what is truly predicated when separate and does not lose its truth when combined. It is true to say of a man that he is both an animal and two-footed; and it is again true to say of the same man that he is a two-footed animal, e.g. of Socrates. Of the same Socrates too it is true to say that he is separately a man and white, if that is the case, and to predicate of him that he is a two-footed animal does not depart from the truth. And these are predicated truly when said separately and apart, and they are true when combined. But if you predicate of someone that he is a lyre-player, and it is true, and again that he is good, and it is true, it is not necessarily true to say that he is a good lyre-player. For he can be just a lyre-player but a good man. That is how he explained things so far. But because some people seemed to think that everything predicated truly when separate, is

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also said correctly when combined, he gives them the answer that there will be many absurdities and impossibilities if someone maintains that everything predicated truly when separate is predicated truly when combined. For it is true to say of a man that he is a man. For it is true to say of Socrates who is a man that he is a man. Again it can be truly said of him that he is white. Thus if you also combine the two and predicate them as one, it is true to say of a certain man that he is a white man. But it is true to say of the man who is white that he is white. Therefore if you combine this too, you will get the predication Socrates is a white white man. For it was true to say of Socrates that he is a white man. But it is true to say of a white man that he is white. When these are joined they make ‘a white white man’. But if you want white to be predicated again of the same white man, it is true. Thus if you combine them again, you will have the predication ‘[Socrates] is a white white white man’ and so on to infinity. Again suppose you say of a certain man that he is a musical man, that this is true and you add that the same man is walking, then it is true if you combine them to say that he is a walking musical man. But if it is true to predicate of a certain man that he is a walking musician, and it is true to say of the walking musician that he is musical, that man will be a walking musical musical man. But it is true to say of the same man that he is walking. Therefore it will be true to say of him that he is a walking walking musical musical man. Moreover Socrates is Socrates and also a man. Therefore Socrates will be a man Socrates. But he is also two-footed. Then Socrates will be a two-footed man Socrates. But it is true to say of Socrates that Socrates is a two-footed man. But when I referred to him as a man, I have already called him two-footed; for every man is two-footed. Therefore it is true to say of him that he is two-footed. But it was true to say that Socrates is a two-footed man Socrates. Therefore that Socrates is a two-footed two-footed man will be a true predication. But I have said ‘man’ again and have named a further ‘two-footed’ (for every man is two-footed). Therefore Socrates is a two-footed two-footed two-footed man. And by extending this to infinity one produces a superfluous chain of chatter. Then it cannot happen that whatever is said separately is in every case also truly predicated when combined. 21a5-18 It is clear that many absurdities happen to be said if one lays down that compound [predicates] come about without qualification. We explain now how it should be put. Whenever predicates and what is predicated are said by accident either of the same thing or one thing of another, they will not be one, e.g. ‘man is white and musical’, but ‘white’ and ‘musical’ are not one; for they are both accidents of the same thing. Nor, if it is true

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to say that the white is musical, will the ‘musical white’ form some one thing; for the musical is white accidentally and so the white will not be musical. Therefore neither will a lyre-player be good without qualification, but an animal will be two-footed [without qualification]; for he is not so accidentally. Further whatever is in another will not be [one]. Therefore ‘white’ is not repeated nor is man an ‘animal man’ or ‘a two-footed man’; for ‘two-footed’ and ‘animal’ are in ‘man’. He now gives more specific and clearly argued details on the subject matter of the previous section. He mentions only those predicates which are truly predicated when separate but cannot form a single true predicate if they are combined and which are accidents of the same thing or one is accident of the other in the sense that one accident is predicated of that as an accident. For if someone says of Socrates that Socrates is a lyre-player and again that Socrates is good, if both predicates are true, he has predicated two accidents of the one subject, Socrates. Thus it is not possible for these to make a single predication so as to give ‘Socrates is a good lyre-player’. Again if ‘musician’ is predicated of Socrates (let us assume that Socrates is musical) and if ‘white’ is predicated of ‘musician’, and this is also true, it is not, however, necessary that ‘musician’ is white. For if Socrates is a musician and if white is predicated of the same musician, ‘musician’ is predicated of the subject ‘Socrates’, and ‘white’, one accident, is predicated of ‘musician’ which is an accident. Therefore we don’t have here a single true proposition declaring that ‘Socrates is a white musician’. For it can be that he is not always a white musician, but it is the nature of accidents to come and go. So if the man who is a white musician should stand in the sun and the heat tans his skin, he will not be white though he is a musician. Therefore the predication was correct neither at the time when Socrates was truly described as being a white musician nor when he was tanned. For an accident does not have that permanence of nature that permits it to be always truly predicated. He expresses the argument as follows. If someone says that combinations occur without qualification in any way one wants, i.e. what you had proposed separately, you now propose combined and joined together, many absurdities happen to follow. For many impossibilities are involved as he demonstrated above when he reduced the constant repetition of the same names to excessive pleonasm. For these reasons we are now saying how it should be put, i.e. we are now saying, says Aristotle, how what is said truly when separate ought to be predicated when combined. Everything, he says, which is predicated of another thing and also the things of which the others are predicated are of two kinds. They are either accidents or substances. Some predications are accidental, whenever either two accidents are

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predicated of a substance or an accident of an accident belonging to a substance; another type is not accidental wherever something is said substantially of something. Then where things are said accidentally, if there are either two accidents and they are predicated of the same thing or one accident is predicated of another accident, they cannot form a single proposition nor can they be one if they are joined. For a man is both white and musical, but ‘white musical’, since they do not coalesce in one form, do not make a single proposition; for ‘white’ and ‘musical’ are not the same. Both of these are accidents of the same thing, but are not themselves the same. Nor, if we predicate ‘white’ of ‘musical’, i.e. one accident of another, even if this is true, is it necessarily the case that what is ‘musical’ is ‘white’. For it is not some one thing; for what is musical is accidentally white. For ‘musical’ is said to be ‘white’ because that of which ‘musical’ is an accident is white. And ‘white musical’ is not one thing. Then for the same reason it holds that [the words] ‘good lyre-player’ cannot be one thing and when joined to form one body do not make some single thing, although they are truly predicated when separate. But if someone predicates something substantially and says two things separately, what is truly predicated substantially when separate and apart, can be reduced to one proposition. For since a man is both an animal and two-footed, he is a two-footed animal and one proposition is formed from them. For neither ‘animal’ nor ‘two-footed’ is accidental to ‘man’. He demonstrates this with the words but an animal will be two-footed; for he is not so accidentally. He also adds that incorrect predication occurs when the predicates are concealed or contained in the expression of any of the terms which have been posited in the proposition. For ‘white’ should not be said of ‘white man’ so as to produce the predication ‘white white man’, because ‘white’ is already contained in ‘white man’. And again ‘two-footed’ ought not to be predicated of ‘man’ because even though it is unexpressed, nevertheless whatever is a man is also two-footed. But if someone does predicate ‘two-footed’ of ‘man’, he predicates ‘two-footed’ of a thing which has two feet and of the differentia that it is ‘two-footed’. In this case too then man will be ‘two-footed two-footed’; for ‘man’ contains ‘two-footed’ within itself and when you say ‘man’ you say it with its differentia. If then you predicate ‘two-footed’ of it, you have predicated ‘two-footed’ of a thing which has two feet. A man will then be ‘two-footed two-footed’. But one should not predicate in this way, for ‘two-footed’ is contained in ‘man’ and if you predicate ‘two-footed’ again of it, you will create an extremely awkward repetition. This is what he means by further whatever is in another will not be [one]. They are contained either in the expression, e.g. ‘white man’ (white is contained in it, because it has already been mentioned in the expression) or potentially and by the force [of the signification], e.g. where ‘two-footed’ is contained in ‘man’, although it is not actually mentioned at all.

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21a18-24 But it is true to speak of a someone even without qualification, e.g. that some man is a man or some white man is white; though not always, but when in the addition there is some opposite which yields a contradiction, it is not true, but false; e.g. to call a dead man a man. But when there is no opposite in it, it is true. This problem is the opposite of the previous one. For there the problem was whether separate predicates remain always the same when they are predicated as combined and joined together, whereas here the same problem occurs in reverse, whether what is truly predicated when combined can be truly predicated when separate. For after Socrates’ death we can say that this corpse is a dead man and by joining ‘man’ and ‘dead’ make a single true predication out of them. But it is not true that the corpse is just a man. Again it is true to say of Socrates when he is alive that he is a two-footed animal and it is true to say separately that he is an animal. Then the problem is what is the difference in predication here that when things are said in combination and predicated truly of subjects, some can also be said truly when separate, whilst others are false if they are said on their own without being combined. And he said this as though in doubt. For it ought to be read as though expressing a doubt: is it true to say something combined and joined together about an individual, e.g. about a man that he is a man or about someone white that he is white, in such a way that any of these things can also be predicated without qualification or at least sometimes? And he gives us a rule by which to recognise whether what is said truly in combination can also be said at all separately. For whenever things that are predicated with another are such that they do not contain in themselves a contradiction when predicated, they can be truly said separately as well. But if things that are truly predicated and stated when in combination do contain some contradiction in themselves they cannot be truly predicated separately. when someone says a corpse is a ‘dead man’ he speaks truly whereas he cannot truly say just ‘man, because previously he has predicated in combination when he said ‘dead man’; and ‘dead’ which is attached in addition to the predicate ‘man’ (for ‘dead’ is a predicate along with ‘man’) stands in contradiction to ‘man’; for man is an animal, but ‘dead’ is not an animal; therefore ‘dead’ and ‘man’ contradict each other; for one is an animal, the other not an animal. Therefore, because there is a certain contrariety between them, ‘man’ when separated is not said on its own of ‘dead man’. It is the same too when you say that a statue has a marble hand. This is true, but it is false to say that what the statue has is just a ‘hand’. For a ‘hand’ is able to give and receive, but a ‘marble hand’ cannot. Thus there is a certain contradiction between ‘hand’ and ‘marble hand’, because one can give and receive, the other

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cannot; for these are contradictory opposites. Therefore wherever there is a predication like man of corpse where something is joined and added to form a contradiction with the predicate (as here ‘dead man’ is added and predicated simultaneously of ‘corpse’ so that it makes a contradiction with ‘man’ itself and contains the contradiction in itself) one predicate cannot be separated off to be said on its own. But if there is no contradiction of that kind, it can be separated; e.g. in ‘Socrates is a two-footed animal’ there is no contradiction between ‘animal’ and ‘two-footed’. Thus ‘animal’ and ‘two-footed’ can be said of it separately and without qualification. This is the sense, but the order [of the text] is as follows, for he spoke in a questioning way: but it is true to say of a someone jointly in combination and without qualification, e.g. that some man is a man or some white [man] is white or that they are sometimes, but that when in what is added, i.e. what is said additionally in predication with something, there is any opposition which is followed by a contradiction, i.e. where a contradiction immediately follows the opposition, as the opposites ‘man’ and ‘dead’ are followed by the contradiction ‘animal’ and ‘not animal’, in these circumstances, it is not true to predicate without qualification, but it is false; e.g. you can predicate ‘dead man’ truly when they are combined, but if you predicate the same ‘man’ separately it is false. But when this kind of opposition is not present in the predicates, what you predicated in combination you can also rightly predicate without qualification. But an addition has been made where this sort of opposition sometimes occurs, as in ‘dead man’ where ‘dead’ is added to ‘man’; for otherwise it is not possible for ‘man’ to be properly predicated of ‘corpse’. 21a24-30 Or even when it [opposition] is present, it is always not true, but when it is not present, it is not always true; e.g. Homer is something, a poet; then is it the case that he always is or not? For ‘to be’ is predicated accidentally of Homer; it is because he is a poet, not in its own right, that the ‘is’ is predicated of Homer. Therefore insofar as in predicates there is no contradiction if definitions are put instead of names, and predication is for itself and not accidentally, in these cases it will be true to predicate without qualification. But it is not true to say that what is not, because it is thought about, is something; for what is thought about it is not that it is, but that it is not. He had said before that when there is a contradiction in what is added it is not true to predicate without qualification, but when there is no contradiction it is true to say without qualification what was said in combination. But since it now appeared that this is not true in certain cases, he modifies it accordingly. For he says that what he had said before is true, that whenever there is some contradiction in

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the addition, it is not true to predicate without qualification what was said in combination, but that when there is no contradiction it is not always true to predicate without qualification what was said truly in combination, but that it is sometimes true and sometimes false. An example of this is when I say ‘Homer is a poet’; here I have predicated ‘is’ and ‘poet’ together of Homer. But if I say ‘Homer is’, it is false, although there is no contradiction between ‘is’ and ‘poet’ and in ‘is’ there is no opposition of the kind which is followed by a contradiction. The reason why this occurs is that we predicate ‘poet’ primarily of Homer when we say that Homer is a poet, but ‘is’ we predicate primarily of ‘poet’ and in the second place of ‘Homer’; for we don’t predicate ‘to be’ because Homer is, but because he is a poet. Then if we remove what was predicated primarily [of Homer], i.e. ‘poet’, then although ‘is’ which is attached to ‘poet’ does not stand in contradiction to ‘poet’, we do not make a true predication when we say ‘Homer is’; for it is predicated accidentally, not primarily. And when the primary predicate is removed, what was predicated accidentally is immediately found to be false.43 The next sentence Therefore insofar as in predicates there is no contradiction if definitions are put instead of names, and predication is for itself and not accidentally, in these cases it will be true to predicate without qualification has the following import. He gathers together in one formula what he has said above, by saying that whatever is predicated in such a way that it contains no contradiction in the names or in the appropriate definitions, is predicated truly when apart and without qualification, e.g. ‘dead’ and ‘man’ in ‘dead man’; these have no contrariety or contradiction in their names, but if the definitions are taken in place of the names, contradictory opposition is immediately recognised; for if you give the definition of man, you say ‘mortal rational animal’, and of ‘dead’ you say that it is to be a body which is deprived of life and inanimate; and from this the total force of the contradiction becomes apparent. Therefore if definitions are taken in the place of names and there appears to be a contradiction in them or if something is predicated accidentally, as ‘is’ of Homer, since it is predicated primarily of ‘poet’, then what was predicated in combination will not be correctly predicated without qualification. But if there is no contradiction and predication is not accidental but in itself, then whatever is said truly in combination is predicated truly without qualification. But since there were some who claimed that what ‘is not’ is and composed a complete syllogism with the following propositions: what is not, is thought about; but what is thought about is; therefore what is not is, he says the following: if it is true to predicate of what is not that it is thought about, we are predicating ‘is’ of what is thought about; but we predicate ‘is’ accidentally of ‘what is not’; for since what is not is thought about, we predicate ‘is’ in the second place of ‘what

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is not’. Therefore we cannot say without qualification that what is not is; for it is thought about because it ‘is not’ since if it ‘existed’ it would be knowable rather than thought about, just as Homer is said ‘to be’ because he ‘is a poet’, not because he ‘is’ in itself. But of course Homer is said to be a poet because his poetry exists and survives, just as we say that some people often live in their children. Then what is not is said to be thought about because its being thought about ‘is’, but not because what is not can be something in itself. Then with these preliminary constructs and ordered definitions he turns the treatment and discussion of propositions to modal propositions, a most useful topic for dialectic. It remains now to discuss the modes of propositions and oppositions. For there has been a great deal of doubt and discussion as to whether propositions posited non-modally are the same type as those which are determined by their own modes. And he begins his own questioning about these matters as follows. Chapter 12

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21a34-7 Having cleared up these points we must consider how negations and affirmations about the possible to be and not possible, the contingent and not contingent,44 the impossible and necessary relate to each other; for there are some queries here. Every statement is expressed either non-modally and simply, e.g. ‘Socrates walks’, ‘it is day’ or whatever is predicated simply and without any qualification. But there are others that are expressed with their proper modes, e.g. ‘Socrates walks quickly’. For a mode has been added to Socrates’ walking when we say that he walks quickly. For our predicating ‘quickly’ of his walking signifies how (in what mode – quomodo) he walks. And similarly if someone says that Socrates was well taught, he has shown how he was taught and has not said simply that he was taught, but attaches also the mode of Socrates’ schooling. But because there are other modes according to which we say that something can be, something is, it is necessary for something to be, something happens, the enquiry concerns how contradictory opposites are formed in these as well. For it is easy to recognise the point of contradiction in propositions which are predicated without qualification and non-modally. For the negation of the affirmation ‘Socrates is walking’, if it is put with the verb as ‘Socrates does not walk’ has, when the opposition has been correctly formed, separated ‘walking’ from Socrates. Again if you put the negation of the proposition ‘Socrates is a philosopher’ with the verb ‘is’, you will form a perfect negation saying ‘Socrates is not a philosopher’. For it cannot happen that in simple affirmations the negation is put with anything other than the verb which contains the force of the entire

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proposition. For if someone maintains that the negation of ‘man is white’ is not ‘man is not white’ but man is not-white’, this is shown to be false as follows. If a stone is put in the proposition and the question is put whether that stone is a white man and if he denies it using ‘is a not-white man’ as the negation of ‘is a white man’, let it be said to him: if ‘is white man’ is not a true affirmation about this stone, then the negation ‘is not-white man’ will be true. But this too is false; for a stone is in no way a man and so ‘is not-white man’ cannot be predicated of it. But if neither the affirmation nor the negation concerning it is true and it is impossible for contradictory affirmations and negations when predicated of the same thing to be both false, it is clear that ‘man is not-white’ is not the negation of ‘man is white’, and ‘man is not white’ is. Thus in propositions predicated without qualification and non-modally the negation must never be put anywhere other than with the verb which contains the whole proposition. But we have already said enough about this above. But in modal propositions the question is whether the negative particle is put with the modal word or keeps its place with the verb, as was in fact the case with simple and non-modal propositions. For if the negative particle maintains its position of being placed with the verb, that which makes a contradiction falls away and does not distinguish true and false. For whenever we say it is possible for something to be or necessary to be or things of this kind, there is a mode of doing something. Thus if someone says that I can walk and forms its denial by putting the negative with the verb ‘walk’ and says that I can not-walk, the contradictory affirmation and negation will be found to be true about the same subject at the same time. For it is clear that I can both walk and can not-walk. But if in this modal expression of possibility the negative particle is not rightly joined with the verb and even in propositions where it makes no difference whether the negative is put with the modal word or the verb, one should keep the kind of opposition which belongs to the type of proposition that is expressed modally. in the proposition ‘Socrates walks quickly’ it will appear to be almost the same whether you make the denial by putting the negative with the verb, ‘Socrates does not walk quickly’ or by attaching the negative particle to the modal word, ‘Socrates walks not quickly’. For in whatever way the negation is applied it distinguishes truth and falsity when taken with the affirmation. But because there are many modal forms where if the negative particle is joined to the verb, you don’t get the negative of the previously stated affirmation, one ought to keep the opposition in all forms of modal proposition, so that all their opposites may be said to come about in one and the same way, so that in simple sentences the negation denies the fact, in modal sentences it denies the modality, e.g. in ‘Socrates walks’ that the proposition ‘Socrates does not walk’ should deny and abolish the actual fact, that he walks, but in

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modal sentences it upholds the fact and denies the modality, e.g. in the proposition ‘Socrates walks quickly’ the negation says ‘Socrates walks not quickly’, so that it makes no difference whether he is walking or not, but the negation established in opposition removes the modality, i.e. of walking quickly. However this is not the case in some instances where the thing, too, perishes together with the modality; e.g. in ‘Socrates can walk, Socrates cannot walk’, when the negative particle is attached to the modality it destroys both the modality and the thing. But this happens only in those cases where something is said not to come about and the modality of its activity is added but the modality of doing something in the future, e.g. if someone says that Socrates can walk, not because he is walking now, but because it is possible for him to walk. If the negative is joined to this possibility, it will appear to do away with the very thing of which the possibility is predicated. But if someone says that Socrates walks quickly, he is saying that he is doing something and attaches the modality to the action so that anyone can know how he is doing the thing which he is said to be doing. Here the thing survives, but the modality is destroyed, as we said above. Or shouldn’t it be much more correct to say that propositions of this kind always remove the modality, but do not destroy the thing of which the modality is predicated? It is clear that, both where a fact is stated, e.g. ‘Socrates walks quickly’, and where the present action is itself predicated as happening and being performed, the modality is done away with but the thing which is said to happen continues, as when we say ‘Socrates walks not quickly’, that he walks is not removed, but the negation just disconnects speed from the walking. But in propositions which posit through modality the possibility of doing something in the future, no action is posited at all, but only modality. When the negative is attached to this modality it destroys the modality but the thing of which the modality was predicated does not endure, because even then at the time when it was predicated, it was not proposed that something would come to be or be done along with the modality. Thus if someone says that it is possible for Socrates to walk, a modality has been posited, but the thing has not been established in action. For it has not been said that he is walking, but that it is possible for him to walk. Then the negation removes the possibility in the proposition ‘it is not possible for Socrates to walk’, but in the same proposition the thing of which the modality was said does not survive either. And this happens because the thing of which the modality is predicated is not even stated in the affirmation. And so the thing has not been removed by the negation, because the negation did not find it posited there in the first place, but only the modality which was constituted by the affirmation. But it makes a great difference whether the negation is put with the modality or with the verb. For if I put it with the verb, the predicate is separated

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from the subject, as in ‘Socrates does not walk’; for he is not walking because the predicate has been divided from the subject, Socrates. But if it is put with the modality, the predicate is not divided from the subject, but rather the modality is separated from the predicate, as in ‘Socrates walks not quickly’, the proposition has not separated walking from Socrates, but speed from walking, i.e. the modality from the predicate. And this is seen more easily and clearly, whatever is predicated * * *45 and to come about. But we ought to define what the possible, the necessary and ‘to be’ are and to show their significations because it will help us to understand the subtleties of the passage we are dealing with, what was said earlier about contingents will become even clearer and it will make accessible to us in the clearest light the meaning of the Analytics. In On Communication Aristotle distinguished four modalities. For it is said that something either is, happens to be, can be or is necessary to be. Of these ‘to happen to be’ and ‘to be possible to be’ signify the same and there is no difference between saying that ‘it is possible for there to be races tomorrow’ and ‘there happen to be races tomorrow’, except only where what is possible can be removed by privation, whereas this does not happen to the contingent at all. For both the negation of possibility, ‘not to be possible’, and the privation, ‘to be impossible ‘, are sometimes set against what is said to be possible; for ‘to be impossible’ is the privation of possibility. But in the case of the contingent, although it has the same meaning, only the negation is set against it and no privation is found. Thus in the case of the contingent, if we want to do away with it, we say that it does not happen and this is the negation, but no one would say ‘incontingent’ which is the privation. Then although to be contingent and to be possible signify the same thing, there is, according to Porphyry, a great difference between necessaries, which signify simply ‘to be’, and contingents or possibles. For what is said ‘to be’ something is judged by the present; for if something is now in something else, ‘is’ is predicated; but what ‘is’ in such a way that it is always and never changes, is said necessarily to be, like the movements of the sun and the eclipses of the moon when the earth intervenes. But where things are said to be contingent or possible, we do not regard their occurrence in terms of the present or of changelessness of any kind, but we regard them only to the extent the proposition of their contingency promises. For what is said to be able to be or to happen, is not yet, but could be. And the proposition is said to be contingent or possible, because something can be whether it occurs or does not occur. For propositions of this kind are not judged by the event, but rather by their signification. For example, if someone says that there can be races tomorrow, the affirmation is possible and contingent. But if there are races tomorrow, it is not that anything has been changed in the action of the contingent or possible

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affirmation, so that what the former promised as a possibility seems to have been necessary. And again if the races do not take place, still nothing has changed at all so that it might seem to have been necessary that they would not take place. For these things, as we said, are not determined by the outcome, but rather by the promise in the actual proposition. For what does someone mean when he says that ‘there can be races’? I think he is saying that whether they take place or not, they are not however precluded by any necessity from taking place. Therefore two of the four modalities, the contingent and the possible, are the same, but they differ from the remaining two and the remaining two also differ from each other. For a possible and contingent proposition differs from one which says that something ‘is’. For the former makes an affirmative proposition with respect to possibility in a future time, but the other with respect to action in the present. But both, the one which signifies that something ‘is’ and the one which signifies that something can or happens to be, differ from a necessary proposition. For necessity requires that something not only is present, but is also unchangeably present, so that what we say is cannot ever not be. Thus the implications of the list are quite clear. For what is necessary cannot be said without what is or happens to be or can be; for whatever is necessary both is and can be, or if it cannot be, would not be at all. But if it were not, it would not be said to be necessary. Therefore everything necessary both is and is possible. But not everything that is, is necessary (for there can be some things where it is not necessary for them to be, e.g. that Socrates walks or the other things expressed with separable accidents). Nor again what happens to be or is possible to be, necessarily is. Thus ‘to be’ and possibility follow necessity, but necessity does not follow ‘to be’ and ‘possible to be’. Again ‘to be able’ follows every instance of ‘to be’; for what is can also be; for if it could not be, then doubtless it would not be. But being does not follow possibility; for what is possible, can also not be, e.g. it is possible for me to go out now, but this is not actually occurring for I am not going out. Thus gradually we have the whole range of implications. For being and possibility follow necessity, possibility follows being, but neither being nor necessity follow possibility. It remains then that there are two kinds of possibles, one which closely follows necessity, the other which necessity itself does not follow. For when I say it is necessary that the sun is now moving, this is also possible, whereas when I say it is possible for me to pick up this book now, it is not necessary. Thus Aristotle was right to question a little later whether what agrees with necessity is also possible. But when we come to that passage,46 we will learn what these two similar kinds of possibility mean or how they can be distinguished. But now since we have explained the implications of affirmative propositions, let us explore the implications of the negations.

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For the four propositions formed from ‘to be’, ‘necessary to be’, ‘possible to be’ or ‘happen to be’, the four negations are ‘not to be’, ‘not necessary to be’, not possible to be’ or ‘not happen to be’. But just as the affirmations ‘happen to be’ and ‘possible to be’ were the same and similar in signification, their negations too are the same. For there is no difference between saying ‘it is not possible’ and announcing ‘it does not happen that’. And the implications for the affirmatives are as follows. Possible propositions and those signifying that something is follow necessary propositions; those saying something is are followed by the same possibles, but neither do propositions signifying that something is nor those that are necessary agree with the possibles. But in negatives it is the reverse. For the negation of a necessary proposition and of one signifying that something is follow negation of possibility, but neither the negation of what is nor the negation of what is possible to be follow the negation of a necessary proposition. Arrange them all in the following fashion: possible to be happen to be to be necessary to be

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not possible to be not happen to be not to be not necessary to be

We must briefly recap the implications of the affirmations to make it clearer how the converse occurs in the negations. Possibility and contingency follow ‘to be’, but ‘to be’ does not follow possibility and contingency; ‘to be’, possibility and contingency follow ‘necessary to be’, but neither ‘to be’ nor necessity follow possibility and contingency. The reverse occurs in the negations. ‘Not to be’ follows ‘not possible to be’ and ‘not happen to be’, for what cannot be is not; but ‘not possible to be’ does not follow ‘not to be’, for what is not is not altogether precluded from being possible to be. For I don’t now see the Forum of Trajan, but it is not necessary that I do not see it. It can happen that I will go nearer to it and see it. Again ‘not to be’ and ‘not necessary to be’ do not follow ‘not possible to be’ and ‘not happen to be’, for it does not seem that one can rightly say of what cannot be that it is not necessary that it is, but rather that it is necessary that it is not. But neither ‘not to be’ nor ‘not possible to be’ follows the negation of necessity, i.e. it is not necessary to be; for when I walk, it is not necessary that I walk; for it is not of necessity that someone walks. Nor again is it the case that what is not necessary cannot be. For when someone walks, it is not necessary for him to walk, but he can walk. And so what is not necessary to be is not at all precluded from being able to be. The same argument applies to contingents. Then negative convertibility differs from that in the affirmations. For in the affirmations being and possibility followed necessity, and possibility also followed being, but being or necessity did not follow

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possibility nor necessity being; but in the negations ‘not to be’ and ‘not necessary to be’ follow ‘not possible to be’, but neither does ‘not to be’ follow ‘not necessary to be’ nor does the negation of possibility, which proposes that something cannot be, follow either of these. Or should we rather say that it is the same in the negations as in the affirmations, as Theophrastus very acutely observed? For the implications in the affirmations were that possibility and ‘to be’ follow necessity, but ‘to be’ and necessity do not follow possibility. The same too will appear in the negations if you consider them deeply. For when a negation comes along in something necessary and makes a negation declaring ‘it is not necessary to be’ it breaks the force of necessity and leads the entire proposition to what is possible. For when the rigour of necessity is broken what is not necessary to be is brought to possibility. But neither ‘to be’ nor necessity followed possibility. Then neither ‘not to be’ nor ‘not to happen to be’ rightly follow necessity when it has been broken and led to possibility and means ‘it is not necessary to be’. Again the man who says ‘it is possible to be’, if the disjunction of the negative is added to it, removes the possibility, and the negative form, ‘it is not possible’, recalls the entire proposition back to the permanence of necessity. For what cannot come into being is not able to be, but what cannot come to be so that it is, must necessarily not be. Thus the proposition in which we say that something cannot be contains a certain necessary force. But being and possibility followed necessity. Yet ‘not necessary to be’ looks to possibility. Then it is right that ‘not necessary to be’, which already involves possibility, follows the proposition ‘it cannot be’, which involves necessity. Thus there the propositions have a different arrangement but the same force, so that everything follows necessity, but necessity does not follow possibility. But here arises a little problem. For if possibility follows necessity and ‘not necessary’ is related to possibility, why does ‘not necessary’ not follow necessity? For if possibility follows necessity and ‘not necessary’ follows possibility, what we predicate as ‘not necessary to be’ ought to follow necessity. The solution is as follows. Although ‘not possible to be’ has the force of necessity, it does differ from necessity in that the latter has an affirmative specification, the former a negative. ‘Possible to be’ and ‘not necessary’ also are different, simply in that one is affirmative, the other negative, though the force of their signification is the same. But the affirmation of possibility and contingency followed necessity. Yet although ‘not necessary to be’ imitates possibility and agrees with it, it is still a form of negation. Then it is right that the negation in which we state that it is not necessary for something to be does not follow the affirmation that it is necessary to be. This is the solution to the problem reported by the most learned Theophrastus. But now we have cleared this up let us proceed to what follows.

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For there are many problems here, as Aristotle himself says. But first of all we give the entire text of the argument. Although it is long, I will find no difficulty in citing it so that the meaning will not be cut short. 21a38-b32 For if of combined expressions those are the contradictory opposites of each other which are arranged in accordance with ‘to be’ and ‘not to be’; for example the negation of ‘to be a man’ is ‘not to be a man’ and not ‘to be a not-man’, and of ‘to be a white man’ is not ‘to be a not-white man’ but ‘not to be a white man’; for if there is in every case either an affirmation47 or a negation, it will be true to say that a log is a not-white man; and if this is so, even where ‘to be’ is not added, what is said instead of ‘to be’ will have the same effect, e.g. the negation of ‘a man walks’ is not ‘a not-man walks’ but ‘a man does not walk’; for there is no difference between saying that a man walks and a man is walking; then if this is so in every case, the negation also of ‘possible to be’ is ‘possible not to be’ and not ‘not possible to be’. But the same thing seems to be ‘possible to be’ and ‘possible not to be’; for everything which can be divided or walk, can also not walk and not be divided. But the reason is that everything which is possible in this way is not always actual and so the negation will also attach to it. Therefore what is capable of walking can also not walk and what is capable of being seen can also not be seen. But it is impossible for opposite expressions about the same thing to be true. Then this is not the negation; for it follows from the above that either they affirm and deny the same thing at the same time about the same subject or that the opposed affirmations and negations are not produced in accordance with ‘to be’ or ‘not to be’. Then if the former is impossible, we must choose the latter. Therefore the negation of what is possible to be is ‘not possible to be’. And the same argument applies also to what happens to be; for its negation is ‘not happens to be’. And it is the same in the other cases too, i.e. with what is necessary and what is impossible. For just as in the previous cases ‘to be’ and ‘not to be’ are additions whilst the subject matter is ‘white’ and ‘black’, so here too the subject is ‘to be’ whilst ‘to be able’ and ‘to happen’ are additions which determine the possible and not possible in the case of ‘to be’ just as in the former ‘to be’ and ‘not to be’ determine the truth. In this subtle discussion by Aristotle one ought to recognise that there is a great difference between defining the force and nature of possibility itself or embracing it within the specific characteristics of its own epistemological level and deciding what sort of thing a possible statement ought to be. For in recognising what is possible it is noted only whether what is said to be possible can come about when

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there is no external circumstance to prevent it. But even if something should happen to occur, it does not affect the previous state of possibility. Discerning a statement of real possibility is, however, much different, as can be seen straightaway from the actual discussion of statements of possibility. For just as it is not the same to give as the answer to a question the definition of man and to include that definition in another defining term, similarly it is not the same to deal with a statement of possibility and what is in reality possible. Hence it happens that, although the possible and the contingent are the same in their significations, there seems to be a difference in their statements. For above we laid down that possibility and contingency had the same signification, so that what happens to come about is the same as what can come about, what is possible the same as what happens. But a possible statement is not the same as a contingent statement. For if someone proposes a possible affirmation and puts a contingent negation as its opposite, he will not form a correct contradictory. For if someone says that something is possible and another says in answer that that thing does not happen, although it cancels out the previous possibility as far as the signification is concerned, one cannot say that it is a contradictory in which the terms expressed in the affirmation and negation are different; for a possible affirmation ought to have a negation of possibility not of contingency. The same too applies in contingents. For if someone should say that something happens, a negation of possibility should not be set as its opposite, although it is the same thing that is possible and contingent. Thus we can agree that there is a considerable difference in principle between discerning the modality itself and its statement, which is predicated with the modality and its quality. Hence it happens that, although possibility and contingency are the same in signification, they are expressed by Aristotle as somehow different in the arrangement of their modality. And we should not forget that the Stoics thought that there was a more universal difference between the possible and the necessary. For they divide statements as follows. Some statements are possible, others are impossible; of possible statements, some are necessary, others not necessary; again of those that are not necessary, some are possible, others are impossible. Thus in a foolish and reckless manner they make the possible both the genus and a species of the not necessary. And Aristotle recognised both the possible that is not necessary and the possible that can be necessary. For you cannot apply to them in the same way that it is not possible for a transition to be made sometimes from truth to falsity or from falsity to truth. Just as when someone says now, that it is day, he has said what is true, and if he makes the same statement at night time, it is false, and the truth here has been transformed into falsity; so too there are certain possibilities, that happen to be and not be, where what has a change-

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able nature is not described in the same way as those which we call necessary. For example if someone says that the sun moves or it is possible for the sun to move, this can never be changed from truth to falsity. But now we must say no more about this disagreement between Aristotle and the Stoics. The only thing we have to look at carefully is where the negation is to be placed in propositions where a modality is predicated of something to produce a statement of possibility. Possible, contingent and necessary propositions, and any with modality, are properly said to be modal propositions where in the signification a quality is found of the existence of the thing which is predicated. E.g. when I say Socrates speaks well, a modality of speaking is attached to Socrates. Thus, just as in propositions which express the substance of some thing, the negation is put with the substance itself (for example, when we say ‘Socrates is’ the negation is attached to ‘to be’ to form the negation ‘Socrates is not’), so too in propositions which express the modality of a substance the negation should be put with the modality which seems to be attached to the substance. E.g. when we say ‘Socrates speaks well’, the modality of the thing itself is ‘well’; then the negation should be put with this modal word and quality. And we say those propositions are possible or contingent in which the modality is itself evident and is said of ‘to be’, rather than ‘to be’ of the modality. For when we say ‘possible to be’, we say something ‘is’, but then there is added how it is, i.e. possible, so that it does not need to be described in any other way than in accordance with possibility. Thus ‘to be’ is the subject, and the predication is the modality, whether contingent, possible, necessary or whatever else. And modal propositions are defined as those in which there is no question about the substance, but the concern is solely about the modality and determiner. But if the modality is made the subject and ‘to be’ is predicated, then the question concerns the substance of the thing and not the modality. E.g. if someone says that ‘it is possible’, meaning that the possibility itself is in the things, no modality has been added to this proposition. For when we say ‘possible to be’ possesses modality, we do not mean that it has it in itself, but as a phrase separated from its proposition. For we regard it as a modality as if it were joined with a proposition. When we have joined it to its appropriate proposition, the modality of its predication also becomes clear. For when we say ‘it is possible’ the particle ‘is’ forms part of the predication in order to signify the modality. If we make a proposition by adding this to its own body we then know what the modality is expressing. Then let us now add ‘it is possible’ to the other predicates and so produce a single statement; let us say ‘it is possible for Socrates to walk’. Don’t you see the modality of possibility in the proposition, so that anyone can see that whether Socrates is walking or not walking, he still can walk in accordance with the actual modality of the proposition? Then

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by removing in this way the part, we regard it as being a possible statement as though it were a whole proposition, just as is our practice with words which quantify a plurality, where we hesitate whether to put ‘no’ or ‘not every’ as the opposite of ‘every’, we regard these words, which are clearly determinations, as though they were integral propositions. We must, then, in conclusion say that in propositions in which a modality is predicated everything else acts as subject matter, whether ‘to be’, ‘to walk’, ‘to read’, ‘to speak’ or anything else which is said to come about with some modality; but where the modality itself is predicated so as to make a complete proposition,48 the proposition is not with a modality, but in this case concerns only the existence of the modality. E.g. if someone says ‘it is possible’, he is saying that something in the things is possible, if he says ‘it is contingent’, he is saying that there is something in the things that is contingent, and if he says ‘it is necessary’, he is saying that there is something in the things that is necessary. Here the concern is not with the modality, but only with its being. Therefore whenever ‘to be’ is the subject and the modality is the predicate, e.g. when we say ‘it is possible for Socrates to walk’,49 the negation must be added to the modality, whereas when the modality is the subject and ‘to be’50 is a predicate, the negation must be put with ‘to be’. E.g. when we say ‘it is possible’, because we mean the equivalent of ‘there is a possibility’, and when we say ‘it is contingent’ the equivalent of ‘there is a contingency’, the negation must be placed with ‘to be’ and we must say ‘it is not possible’ which has the same force as saying ‘there isn’t a possibility’. It is the same with contingency. But if you don’t look at it carefully it looks as if the subject ought always to be the same as is said to be found in the first place, the predicate identical with what is predicated in the second place. For it is true in some cases, but in others we draw our conclusions as to what is the subject, what the object term, rather from the signification of the propositions. For when I say ‘man is an animal’ I must first say ‘man’ and afterwards predicate ‘animal’; and so ‘man’ is said as subject whilst ‘animal’ is predicated. But where a modality is added, e.g. when we say ‘Socrates speaks well’ it has the same force as saying ‘Socrates is speaking well’ and here ‘well’ is said first and ‘is speaking’ second;51 and ‘well’ appears to be the subject, ‘is speaking’ the predicate. But this is wrong. And because of this anyone hearing the sentence ‘Socrates is speaking well (Socrates well is speaking)’ could well understand it as meaning everyone knows that Socrates is speaking, whereas the modality contains the force of the proposition as a whole. For the mind should concentrate on this and not on whether he is speaking. For this is not in doubt; for if you say he is speaking well, you admit that he is speaking. Thus the mind must concentrate on the modality, on the word ‘well’. For unless ‘well’ occurs in the sentence, ‘is speaking’ is not adequate to express what

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is said in ‘Socrates is speaking well’. Thus the modality contains the whole proposition. But the predicate contains the proposition. Therefore the modality is rather the predicate in these propositions. Then the universal conclusion is drawn that every modal contradiction occurs not with respect to the verb nor the verb containing ‘to be’ as part of itself, but rather with respect to the modal expression. ‘Speaks’ is an example of a verb which is said to contain ‘to be’ as part of itself; for it is the equivalent of saying ‘is speaking’. Thus with any propositions which contain any modality in themselves, there can be no doubt that it is not correct to attach the negation to the subject but that it should be put rather with the modality in which something is expressed as being or coming to pass. For every modal affirmation is such that the listener ought not to concentrate on what it is said to be but on how it is said to be. E.g. when we say ‘Socrates speaks well’ we should not look at ‘speaking’, but the attention should be directed to how he is speaking; for this seems to contain the whole proposition. Thus the negation ‘ not possible to be’ and not ‘possible not to be ‘is the opposite of ‘possible to be’. In the same way the negation ‘not happen to be’ and not ‘happen not to be’ is the opposite of ‘happen to be’. It seems that the same should be done in the case of necessities and impossibles, which Aristotle in his accustomed brevity has omitted. But since the virtue of a commentary is not only to express the impact of the meaning in general but also to join that to the wording and order of the text itself, everything that has been said above in a disorganised way let us now organise in the order presented by Aristotle’s own words. Having cleared up these points we must consider how negations and affirmations about the possible to be and not possible, the contingent and not contingent, the impossible and necessary relate to each other; for there are some queries here.52 We must consider, he says, how affirmations and negations seem to be opposed in modal propositions, e.g. in propositions that are possible, contingent, necessary, impossible, true, false or where anything is predicated as well or badly or by some quality. For there are some queries here he says, and he immediately adds what the queries are. For if of combined expressions those are the contradictory opposites of each other which are arranged in accordance with ‘to be’ and ‘not to be’. The meaning of this is that in the whole series of propositions the relevant opposition is that determined by ‘to be’ and ‘not to be’, e.g. when we say ‘a man is’ the negation is ‘a man is not’, and not ‘a not-man is’. And again the negation of the proposition ‘there is a white man’ is ‘there is not a white man’ and not ‘there is a not-white man’. This issue, that the negative of ‘there is a white man’ is not ‘there is a not-white man’ but ‘there is not a white man’, he proves as follows: For if there is in every case either an affirmation or a negation, it will be true to say that a log is a not-white man. It is expressed concisely, but I think it can be explained as follows. Take a log, he

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says, as the subject of a proposition about which two statements are to be made. And suppose it is clear to us that in every case if the affirmation is true, the negation is false, and its contradictory, if the negation is true, the affirmation is false. Then suppose we say of this log, ‘this log is a white man’. This is false. Then if this affirmation is false, its negation ought to be true. Then if the negation of the affirmation ‘there is a white man’ is ‘there is a not-white man’, then the correct negation to be predicated of the log would run ‘this log is a not-white man’. But this cannot be the case; for it is clearly false that a log is a not-white man. For what isn’t even at all a man cannot be a not-white man. Therefore both are false, the affirmation which says that the log is a white man and the negation which says that it is a not-white man. But if they are both false, this is not the negation of this affirmation. Then we will have to find another to distinguish true and false with it. In this respect the only other opposite to be found to ‘there is a white man’ is ‘there is not a white man’. For if ‘there is a not-white man’ is the negation of the affirmation ‘there is a white man’, it will be the case that where the affirmation about the log was false the negation is true and it will be true to say of the log that this log is a not-white man; but this is impossible. Therefore we agree that the proposition ‘there is a not-white man’ is not the negation of the affirmation ‘there is a white man’ and ‘there is not a white man’ is the negation of the same affirmation ‘there is a white man’. Don’t you see then that in virtually everything affirmations and negations are produced in accordance with ‘to be’ and ‘not to be’? For one said that white ‘is’, the other denied ‘white’ saying ‘it is not’. Again one says that man ‘is’, whilst the other denies it, saying that man ‘is not’. And it is the same way with the others. And if this is so, even where ‘to be’ is not added, what is said instead of ‘to be’ will have the same effect, e.g. the negation of ‘a man walks’ is not ‘a not-man walks’ but ‘a man does not walk’. For there is no difference between saying that a man walks and a man is walking. And this doesn’t only happen, he says, in propositions arranged with ‘to be’ and ‘not to be’, but also in those contained in the kind of words that have the force of ‘to be’, e.g. in ‘a man walks’, ‘walks’ contains ‘to be’ in itself; for ‘walks’ is the same as ‘is walking’. Then the negation is to be attached to verbs which contain ‘to be’. For if every contradiction is formed with ‘to be’ or ‘not to be’ and these verbs contain ‘to be’ in their own signification and because these verbs are placed just as though ‘to be’ itself were being placed, it is clear that the negation ought to be placed with the verbs which contain ‘to be’ in accordance with their similarity to propositions which, in the way we explained above, are opposed to each other in terms of ‘to be’ and ‘not to be’. Then once this has been said in preamble he follows up any peculiarity which follows as a consequence. Then if this is so in every case, the negation also of ‘possible to be’ is ‘possible not to be’ and not ‘not possible to be’. But the

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same thing seems to be ‘possible to be’ and ‘possible not to be’; for everything which can be divided or walk, can also not walk and not be divided. It has been shown above how oppositions are formed with ‘to be’ and ‘not to be’ in combined statements. Now he says that if the contradictories of every proposition are to be stated with ‘to be’ and ‘not to be’, then, too, in propositions which state something possible to be, the negation will have to be posited not to form ‘not possible to be’, but will have to be arranged on the modal of ‘not to be’ so as to produce ‘possible not to be’ as the negation of ‘possible to be’. But if we say this, he says, the contradictory affirmation and negation do not distinguish true and false between them; for everything which can be, can also not be; for what can be divided, can also not be divided and what can walk, can also not walk. He now draws the consequences from this to explain what sort of possibility it can be whereby when something is said to be capable of coming about, it still remains that it can also not come about: but the reason is that everything which is possible in this way is not always actual and so the negation will also attach to it. Therefore what is capable of walking can also not walk and what is capable of being seen can also not be seen. But it is impossible for opposite expressions about the same thing to be true. Then this is not the negation. The reason, he says, why what is said to be able to be, can also not be, is that we pronounce everything we declare possible, to be not always actual, i.e. it is not necessary. For everything which is always actual is necessary, e.g. the sun is always moving; therefore its movement is always taking place. But if someone says that I can walk, since my walking motion is not always taking place and it is in me sometimes not to walk, it also belongs to me that it may be truly said of me that I can not walk, although it is true to say that I can walk. Therefore whatever is not always actual possesses the capability of being and not being. Then both what is capable of walking, i.e. what can walk, can not walk, and what is capable of being seen, can not be seen. Then it seems that ‘can not be’ is not the negation of ‘can be’, because both are true where, he says, things are not always actual. For one of two conclusions follows that either they affirm and deny the same thing at the same time about the same subject, with the consequence that the affirmation and negation are the same and agree with each other, if a contradiction is formed in every case with ‘to be’ and ‘not to be’, e.g. ‘to be able to be’ and ‘to be able not to be’ (for both are the same and agree with each other and if someone says that it is a contradiction he is saying that the contradiction agrees with itself) or that the opposed affirmations and negations are not produced in accordance with ‘to be’ or ‘not to be’ in all negations; i.e. that a contradiction is not formed in every negation by placing ‘to be’ or ‘not to be’ or verbs that contain ‘to be’. Then if the former is impossible, we must choose the latter. He had postulated above two consequences of the arguments

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he gave there, either that they affirm and deny one and the same thing of the same thing at the same time, i.e. the affirmation and negation have been predicated identically of the same thing at the same time and agree with each other, or that a contradiction is not formed with ‘to be’ and ‘not to be’. But both seem to be as it were somewhat absurd, since while one of them is impossible, that an affirmation and negation should agree, the other, that opposites are not formed with ‘to be’ and ‘not to be’, is out of line with other propositions in which contradiction is clearly formed in this way. So now he says that both are awkward, but one of them will have to be chosen and that we must choose the one that is less impossible. But it is less impossible that opposites are not formed with ‘to be’ and ‘not to be’. For there is nothing to stop this, but that an affirmation and negation should agree is more impossible. Then our choice will have to be that modal propositions do not have opposites formed on the model of ‘to be’ and ‘not to be’ but opposites where the modal word is qualified. But he didn’t mean is more impossible in the sense that the alternative is also impossible, but he adverted rather to the fact that both are awkward but that one of them is without doubt impossible. He then gives a particular example of modally expressed propositions which are put in the negative form, when he says therefore the negation of what is possible to be is ‘not possible to be’, where he adds the negation, of course, not to the verb ‘to be’ but to the modal word ‘possible’. He says that the same argument also applies to contingents. For the negation of ‘happen to be’ is ‘not happen to be’. He says he thinks the same occurs with the necessary and the impossible. What the nature of this opposition is which has formed the subject of our long discussion has been expressed briefly but very correctly by Aristotle. But if anyone looks more deeply into it, he could accompany his own understanding of the passage with my exposition which proceeds step by step. 21b26-32 For just as in the previous cases ‘to be’ and ‘not to be’ are additions while the things which are subjects are ‘white’ and ‘black’, so here too the subject is ‘to be’ while ‘to be able’ and ‘to happen’ are additions which determine the possible and not possible in the case of ‘to be’ just as in the former ‘to be’ and ‘not to be’ determine the truth. He calls predications ‘additions’. Thus he says that in non modal propositions ‘to be’ and ‘not to be’ or verbs which contain ‘to be’ are always predicated, whilst things act as the subjects of which they are predicated, e.g. ‘white’, when we say ‘white is’, or ‘man’ when we say ‘man is’. And so because in these cases the predicate contains the whole proposition and the predicate determines truth and falsity, and ‘to be’ or something containing ‘to be’ is predicated, contradicto-

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ries are in these cases rightly posited with ‘to be’ or ‘not to be’. But where a modality is predicated, ‘to be’ or verbs containing ‘to be’ are the subject, whilst the modal word alone in a sense acts as predicate. For where something is said just ‘to be’ without any modality the substance of the thing itself is expressed and the question somehow is whether it ‘is’; thus its affirmation lays down that it ‘is’, whilst the negation says that it ‘is not’. But where there is a modality, we do not say that something is, but with what quality it is, so that neither the affirmation nor the negation cast any doubt about the being, but its quality, i.e. how it is, then becomes a subject of doubt. And so whilst one person lays down that ‘Socrates generally speaks’, the negation does not claim that ‘Socrates does not speak generally’ but that ‘Socrates does not generally speak’53 because the listener’s mind is drawn not to ‘to be’ or verbs containing ‘to be’ which do not form the proposition as a whole, but to the modal word, when an affirmation proclaims that something is. Then if these contain the force of the proposition as a whole and if what contains the force of the proposition is predicated and always forms opposites with respect to what is predicated, the force of the negation is correctly put only with the modal words. Once he has established this by argumentation he next explains that not only is ‘to be able to be’ and ‘not to be able to be’ not a contradiction, but also that modal propositions have negations attached to ‘to be’ though they are not really negations but affirmations. For other negations can be found for them. For he says the negation of ‘what is possible to be’ is ‘not possible to be’. There is, he says, no contradiction between ‘possible to be’ and ‘possible not to be’ insofar as ‘possible not to be’ is proved not to be a negation but rather an affirmation. But an affirmation is never contradictorily opposed to an affirmation. But ‘possible not to be’ seems to be an affirmation because a negative is found for it, ‘not possible not to be’. At the same time he adds that although there seem to be two negations of the proposition ‘something can be’, namely ‘possible not to be’ and ‘not possible to be’, which of these is the contradictory of the affirmation ‘possible to be’ is recognised in that the one which together with it distinguishes truth and falsity, can be its contradictory rather than the one that agrees with it. But ‘able not to be’ agrees with ‘able to be’ as I have already shown;54 if ‘not able to be’ is false, ‘able to be’ is true; if the latter is false, ‘not able to be’ is true; therefore these distinguish truth and falsity, which could easily be shown in individual examples. For suppose someone says I can walk and he told the truth, if someone then says I can’t walk, he has told a lie. Again if someone says the sun can stand still, he is telling a falsehood; but if he says the sun cannot stand still, no one would doubt the truth of the statement. Thus ‘able to be’ and ‘not able to be’ distinguish truth and falsity,

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whereas ‘able to be’ and ‘able not to be’ imply each other. Therefore propositions which agree are not contradictories, whereas those which distinguish truth and falsity between them, are to be considered more likely to be contradictories. This is what he means by therefore they seemed to imply each other.55 He tells us which propositions follow each other for it is possible for the same thing ‘to be’ and ‘not to be’. He then shows why they follow each other by adding for they are not contradictories of each other. For if they were contradictories, they would never follow each other. But he declares what contradictories are when he says but ‘possible to be’ and ‘not possible to be’ are never simultaneous. And he does not pass over in silence why they are never simultaneous with the explanation for they are opposed. For they are never simultaneous and distinguish truth and falsity because they are opposed. He also lays down that ‘not able not to be’ is the negation of ‘able not to be’. This point can be made from the following words: but ‘able not to be’ and ‘not able not to be’ are never simultaneous which show that the former is the affirmation, the latter the negation. For wherever what one affirms universally, the other removes from the same thing, provided that one is an affirmation, the other its negation and no equivocation or determination of the universals stands in the way, they are found opposed to each other in a contradictory way. The rest are now, he says, so self-explanatory that there is no need of a long exposition, except that some things are mixed together in their order to show more clearly the self-evident. For he deals with the rest of the modalities in a similar way explaining which propositions are and are not the negations of which affirmations. And in order to demonstrate that the propositions he says are not negations are affirmations, he adduces other negations as opposites. And similarly, he says, the negation of ‘necessary to be’ is not ‘necessary not to be, but rather ‘not necessary to be’. 56 For the former is an affirmation as he proved by immediately citing its negation. He goes through everything in the same way, explaining that the negation of ‘necessary not to be’, which as he had said above is not the opposite of ‘necessary to be’, is ‘not necessary not to be’. For propositions which have a negation attached to ‘to be’ are to be considered to be affirmations, if they are modal. The negation of what is ‘impossible to be’ is not ‘impossible not to be’ but ‘not impossible to be’. For the former does not have the negative particle attached to the modal word and the latter with the affirmation distinguishes true and false. The negation of the proposition ‘impossible not to be’ which has the negative particle attached to ‘to be’ and which is clearly an affirmation, is ‘not impossible not to be’. He also briefly concludes what he has just proved by saying:

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22a8-11 And universally, indeed, as has been said, one should put ‘to be’ and ‘not to be’ as subjects and add these to one [subject]57 to make a negation and an affirmation; and one ought to consider these as opposite expressions We say universally, he says, as has already been said above, in propositions with modal additions ‘to be’ and ‘not to be’ act rather as subjects, whilst the modal expressions are predicated and so affirmation and negation always ought to be produced with respect to any ‘one’ modality, i.e. in one respect, e.g. just as the predicated modality contains the affirmation, so too the negative particle when attached to the modality contains the whole negation. And he sets out what he thinks are the opposed expressions in the following way: possible contingent impossible necessary

not possible not contingent not impossible not necessary

The addition true/not true is relevant to including all the modalities; for ‘truly’ is a modality just as are well, quickly, happily, gravely, and any other modalities; the contradictory is formed as follows: it is true, it is not-true, but not it is not true; to walk quickly, to walk not quickly, but not not to walk quickly. To sum up then, the negation must always be attached to the modal word. For propositions which have negative particles attached to their predicates are always opposed to each other, as has already been said. And the predicates in these sentences are modalities, as we have already demonstrated above. Thus the negative when attached in these propositions to the modality creates a perfect contradictory force. Having dealt with modal opposites a careful and useful treatment of the implications and agreement of the propositions will be given. Thus if ‘possible to be’ is said in an unqualified way, there would appear to be a simple and easy agreement of propositions and no mistake could be made in their implications. But since it is now expressed in a double sense, the implications of the propositions are not the same with respect to the different modalities. What I mean is as follows. The possible has two aspects. One which can be whenever it is not, the second which is predicated as being possible because it already is. The first one belongs to the corruptible and changeable. For Socrates can be amongst mortals when he was not, just like mortals themselves who now are what they formerly were not. For a man can speak when he is not speaking and walk when he is not walking. Thus this aspect of possibility is stated in terms of what is not yet, but can be. The other aspect is stated in terms of what already is something not potentially but actually and is appropriate

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to both natures, both eternal and mortal. For what [actually] is in eternals, can be, and again what is in mortals does not lack this possibility of existing either. The only difference is that what is eternal does not change at all and must necessarily always be, whilst a mortal thing could both not be and need not necessarily be. For when I write, writing is in me and therefore it is possible for me to write, but because I am a mortal this possibility of writing is not necessary; for I do not of necessity write. But when we say there is movement in the heavens, there is no doubt that it is necessary that the heavens move. Thus when some mortal thing is, it both can be and it is not necessary that it is, whereas amongst eternals, what is necessarily is and, because it is, it is possible for it to be. Thus the possible has in principle two aspects, one whereby something can be when it is not, the other which is said of what already is something actually and not just potentially. And the latter kind of possibility which is already actual yields from itself two species: one which, though it is, is not necessary, the other which, though it is, has also the characteristic that it is necessarily so. And it is not just Aristotle’s subtle mind that discovered this. In fact Diodorus also defined the possible as ‘what is or will be’. Hence Aristotle thinks that Diodorus’ ‘will be’ is the aspect of possibility which can be when it is not, and his ‘is’ is what is said to be possible because it already actually is. We have laid down that this latter kind of possibility has two aspects, one we called necessary, the other we described as not necessary. But the not necessary kind also has two aspects, one which moves from potentiality to actuality, the other which was always actual from the first moment of existence of the thing which possesses possibility. And the one which moves from potentiality to actuality is open to contradiction on both sides, e.g. I, who am now writing, have moved from potentiality to actuality and whilst actually writing can write. For before I was writing, the potentiality of writing was in me, but I came from the potentiality of writing to the actuality of writing. Thus both, not writing and writing, fit my situation; for I can not write and I can also write, which is a sort of contradiction. And so whatever has come from potentiality to actuality, can both do and not do, be and not be. E.g. take a man who speaks; because he was able to speak before he does speak and now can speak because he is speaking, he both can speak and can not speak. But the other kind of possibility, which was never in potentiality beforehand but always actual from the first moment of existence of what is said to be something potentially, is suited for one thing only. E.g. fire was never potentially hot so that it afterwards was felt to be actually hot, nor was snow potentially cold before, and then actually so afterwards, but fire was actually hot from the time it came into being, and snow actually cold from its first existence. Therefore these possibilities are not suited to both; for fire cannot

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inflict cold nor snow make anything hot. Then from the outset a division of the following kind should be made: one type of possibility is where something can be when it is not, the other where what actually is, is for this reason said to be possible; for if it were not possible, it wouldn’t be at all. This kind of possibility which is stated modally in terms of what already actually is, may be subdivided into two types: one in terms of what we say is of necessity, the other when we think of something as not being of necessity though it is. And non necessary possibility has two further subdivisions: one which, because it moves from potentiality to actuality, possesses the capacity of being or not being, the other, because it never ceases being in act from the first moment of the existence of what is said to be possible, is suited and possible in respect of one side only, namely that aspect which its activity always puts into effect, e.g. heat in fire, cold in snow, hardness in adamant, liquidity in water. But no one should think that where we say that certain activities were never potentially in certain things, e.g. heat in fire, these are to be included in the class of necessary possibility; for fire itself can be extinguished, whereas in necessaries not only ought the quality never leave the subject thing, which seems to the case even in fire, which never loses its own quality of heat, but the very subject should apparently be an immortal substance, which is not the case with fire. For the Peripatetic school considers the sun and the other bodies of this universe which are above in the heavens to be immortal and so is self-consistent in saying that the sun necessarily moves, because not only does movement never leave the sun, but not even the sun itself ever ceases to be. Then after these preliminary remarks we must now turn to what they served as an introduction, to the careful examination of the implications of the propositions.

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Chapter 13 22a14-23 The implications find orderly expression if they are put as follows: ‘happen to be’ follows ‘possible to be’, and the reverse, and ‘not possible to be’ and ‘not necessary to be’[follow these]; ‘not necessary not to be’ and ‘not impossible not to be’ follow ‘possible not to be’ and ‘happen not to be’; ‘necessary not to be’ and ‘impossible to be’ follow ‘not possible to be’ and ‘not happen to be’; ‘necessary to be’ and ‘impossible not to be’ follow ‘not possible not to be’ and ‘not happen not to be’. But what we mean may be seen from the following table. This is what Aristotle now adds concerning the implications of propositions in accord with what we have said in our introductory remarks. And although they are obvious if you look at them carefully, we will run through them with a very brief explanation so that we will not

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appear to have made no contribution to this passage also. First of all he wanted to show that whatever is said about possibility can also very properly be said in the same form of contingency. And so he says that ‘happens to be’ follows ‘possible to be’. And so that there would not seem to be anything discordant between them, he adds and the reverse to help us understand that whatever is possible, is contingent, and whatever is contingent, is possible. Thus any propositions which are convertible with each other, are equal and identical. Then whatever can be said to be within the possible, can be described as being within the contingent. Then these, the possible and the contingent, he said are followed by those which say ‘not impossible to be’ and those which deny necessity, i.e. predicate of something ‘not necessary to be’. For he says ‘ ‘happen to be’ follows ‘possible to be’, and the reverse, and ‘not possible to be’ and ‘not necessary to be’ which is the equivalent of saying that contingency follows possibility and these are convertible, but ‘not impossible to be’ and ‘not necessary to be’ follow these. No one is unaware that this has been put correctly. For what is possible to be and happens to be, is not impossible to be. For if it were impossible, it would not be said to be possible for it to be, because the meaning of impossibility would compel it not to be. Therefore what can be, is not impossible to be. Similarly what is said to be able to be, must not necessarily be. And this occurs because what we predicate as being possible, turns easily in either direction. For it can come about that it is or that it is not. But necessity and impossibility are bound in with one or the other. For what is impossible can never be. But further what is necessary can never not be. Therefore what we say is not impossible to be, we make agree with possibility. And to what we say is not necessary we again assign a force of possibility. To put it more clearly, it should be stated as follows. What is possible, could both be and not be; again what is impossible, cannot be; what is necessary cannot not be. Thus if we break a statement of impossibility by the addition of a negative to say ‘not impossible to be’, we attach to it the type of possibility whereby something is said to be able to be. But if we lessen the rigour of a necessary proposition with a negative to say ‘not necessary to be’, it turns out that we attach the necessary proposition also to a type of possibility, the one whereby something can not-be. Therefore ‘not impossible to be’ follows possibility because what is possible can come about. Again the proposition ‘not necessary to be’ follows possibility because what is possible, could also not be. We can say the same in a different way. It is not true to say of what is possible that it is impossible, because it can be. Again it is not true to say of what is possible that it necessarily is. For what is possible to be can also not be. Therefore if it is not right to predicate impossibility and necessity of possibility, their negations, ‘not impossible to be’ and ‘not necessary to be’, will agree with possibility. But we should recall that the

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same applies in every case to the contingent and the possible, of the possible that when it still is not, it yet could be or not be. The rest of the implications he describes as follows: ‘not necessary not to be’ and ‘not impossible not to be’ follow ‘possible not to be’ and ‘happen not to be’. He said that these implications too are due to the same cause. For he says that ‘to be not necessary not to be’ and ‘to be not impossible not to be’ agree with ‘possible not to be’ and ‘happen not to be’. And this is so because what can not be, can also be, and again what happens not to be, happens also to be. But in fact what is necessary not to be, cannot be, and what is impossible not to be, could not not be. Therefore both depart from possibility. For because possibility promises that something can be, that which declares that it necessarily is not has the contrary sense. Again because possibility has in itself the power to bring it about that what can be can also not be, it differs from and disagrees with the proposition that it is impossible not to be. But if ‘it is necessary not to be’ and ‘it is impossible not to be’ disagree with possibility, it is surely right to think that their negations agree with possibility. And I mean by propositions of possibility those which either in affirmation or negation indicate some possibility where one side is not excluded, e.g. ‘it is possible not to be’ is not excluded by ‘it is possible for something to be’ or if someone says that it is possible for something not to be this does not prevent it from being able to be. And so I call an affirmation of possibility one which predicates ‘to be able to be’ and equally one which says that something can not-be. And in the propositions stated by Aristotle in the form ‘possible not to be’ he does not seem to be speaking as though he meant to say that he wanted it to mean that something is ‘impossible to be’ when what he says is ‘possible not to be’. For he puts the proposition in this form not to remove it from possibility, but to say that it is possible for something not to be. For one has to understand and add to ‘possible’ the verb ‘to be’, so when he says ‘possible not to be’ we understand ‘is possible not to be’, i.e. it is possible that it is not. The third implication he mentions is where he says ‘necessary not to be’ and ‘impossible to be’ agree with ‘not possible to be’ and ‘not happen to be’. This is so clear as not to require an explanation. For what is not possible, cannot be; what cannot be, necessarily is not, and what necessarily is not, is impossible to be. Thus it is right to say that ‘something cannot be’ and ‘does not happen to be’ are followed by those propositions which deny being in combination with ‘it is necessary’ and affirm impossibility. The final implications, in which ‘necessary to be’ and ‘impossible not to be’ follow ‘not possible not to be’ and ‘not happen not to be’, do not present any obscurity. For what is not possible not to be, is impossible not to be. For what we say is ‘impossible to be’ has the same force as saying ‘not possible to be’. For what the negative does in the communication ‘not possible’, the

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privation does in ‘impossible’. But it is quite clear that what is impossible not to be, necessarily is. Therefore what is not possible not to be, clearly is necessary to be. The same too must be said about the contingent as well. He puts them in a table as follows so that they may be understood not only by the mind and reason, but also might be easier to understand by being put before the eyes. And we will put them in two columns to make our explanation clearer. In the first column we have put the leading propositions and in the second those which follow so that there is plenty of opportunity for those who look at the table to understand what follows what, even if they don’t understand just by their reasoning.

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Then when we have made this table, Aristotle’s general and universal treatment of propositions should not be unclear to anyone looking at it with care. But because we do not want to exhaust the reader, the rest of his discussion about their individual implications will be the subject matter of book six. BOOK 6

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This sixth book brings to an end my long commentary which will reach completion after considerable labour and expenditure of time. For many people’s ideas (sententiae) have been gathered here together and I have spent almost two years sweating continuously over my commentary.58 And I do not think, as some wrongly interpret, that it was done out of vainglory so that in the desire to display my learning I stretched out what could be said in a few words, not so much assisting the reader’s understanding as wearing him out with my prolixity. I would say in reply to them that they would not interpret my work so falsely if they were to read through the short first edition. For the troublesome lack of clarity of [Aristotle’s] extremely concise expressions could not be explained in fewer words and it becomes clear how much is missing for a full understanding of this book. But I think that one could very easily work out what each

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edition could usefully provide its readers from the fact that as soon as someone has laid hands on the second edition he is thrown into confusion by the wide variety of the subject matter so that he longs for the brevity and simplicity of the first edition when he is unable to concentrate on the more extended treatment. But if the reader goes to the two books of the first edition, he will think that he has gained some understanding, but will understand how many things he did not comprehend in the first edition when he finally gets to know the second edition. And a long work should not deter men from reading it because of the labour involved when it did not stop me from writing it! But lest our introduction appear to be too long drawn out as well, let us return to Aristotle’s order of the text and his careful explanations of the implications of propositions. In the above descriptions of the propositions themselves he has laid out in a general and universal way the considerations that were to be made about all propositions and their mutual implications; he now deals in a careful treatment with the individual features in each case. This is what he says. 22a32-7 Therefore ‘impossible’ and ‘not impossible’ follow ‘contingent’, ‘possible, ‘not contingent’ and ‘not possible’ contradictorily but conversely; for the negation of ‘impossible’ follows ‘possible to be’, and the affirmation the negation; for ‘impossible to be’ follows ‘not possible to be’; for ‘impossible to be’ is an affirmation, ‘not possible to be’ a negation. The implications of the propositions have been made, as the previous table shows, in terms of the possible and the necessary. And it also followed that contingent and impossible propositions and their implications had to be discussed. For since a contingent agrees with a proposition of possibility in direct modality, the impossible must also agree in converse order, as we will show a little later. Therefore he considers how a possible contingent and an impossible relate to each other or what implications they have and lays it down as follows when he says: ‘impossible’ and ‘not impossible’ follow ‘possible’ and ‘not possible’ contradictorily, but conversely. This means that we know that ‘impossible to be’ is a privative affirmation whose negation is ‘not impossible’ and again that ‘possible to be’ is an affirmation of possibility whose negation is ‘not possible to be’. Thus the negation of impossibility follows the affirmation of possibility. For what is possible is the same as what is not impossible. Otherwise, if ‘it is not impossible’ does not follow possibility, the affirmation follows, i.e. ‘impossible to be’. Then what is possible is impossible, which cannot be the case. But if impossibility does not follow possibility, ‘not impossible to be’ follows possibility. But the affirmation of impossibility follows the negation of possibility. For what is not possible, is impossible. For the negation in a proposition has the same force as

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the privation. And it is the same with the contingent. For what happens is not impossible. For if the contingent and the possible follow each other and ‘possible’ and ‘not impossible’ agree, then the contingent and ‘not impossible’ designate the same thing. Again the ‘not contingent’ and ‘impossible’ could appear the same, if you look at it, because ‘not contingent’ and ‘not possible’ mean the same. But ‘not possible’ agrees with impossibility. Therefore ‘not contingent’, too, also denotes that something is impossible. It happens then that an affirmation of impossibility follows the contradiction of possibility, but not that the affirmation follows the affirmation, nor that the negation follows the negation, but conversely, i.e. that the affirmation agrees with the negation, the negation with the affirmation. For the negation of impossibility ‘not impossible to be’ follows the affirmation ‘possible to be’ and the affirmation of impossibility ‘impossible to be’ follows the negation of possibility ‘not possible to be’. And the same can be said of the contingent. For the negation of impossibility follows the affirmation of the contingent, the affirmation of impossibility follows the negation of the contingent. For in every respect what is proposed of possibility holds also for contingents. Then lay them out as follows. First the affirmation of impossibility and opposite it the negation of impossibility; and underneath the affirmation of impossibility are to be placed the negations59 of the contingent and possible, which impossibility itself follows; under the negation of impossibility, the possible and contingent propositions with which the negation of impossibility agrees, as follows:

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It is obvious then that the contradictories agree with other contradictories. And in this respect it is clear that the affirmations agree with the negations, the negations with the affirmations. That is the general meaning, but the details of the wording are as follows. ‘Impossible’ and ‘not impossible’, which form a contradiction, follow the two contradictions, ‘contingent’, ‘possible, ‘not contingent’ and ‘not possible’ contradictorily (for the single contradiction of impossibility follows two contradictions, contingent/not contingent, possible/not possible) but although one contradiction follows another, they agree, however, with each other conversely. For the negation of ‘impossible’ follows ‘possible to be’, as the diagram above shows, and the affirmation of impossibility the negation of possibility. For what is not possible agrees with what is impossible. And the affirmation of impossibility is ‘impossible to be’. And although the form of expres-

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sion is complicated, if you return to Aristotle’s actual words in the light of our explanation and make up from it what is missing, the meaning is crystal clear and logical. 22a38-b2 But we must consider how the necessary [behaves]. It is clear that it is not the same but contraries follow, and the contradictories are separated. For ‘not necessary to be’ is not the negation of ‘necessary not to be’; for they both happen to be true of the same thing; for what is necessary not to be, is not necessary to be. By our comparison of the impossible and the possible we have just laid down that the negation of impossibility follows the affirmation of possibility and the affirmation of impossibility agrees with the negation of possibility. So now when he asks about the implications of possible and necessary propositions, he says they do not turn out the same way as the implications which arose from the comparisons of possible and impossible propositions. For in the latter, opposing contradictions followed opposing contradictions, so that affirmation followed negation, negation affirmation. But in the case of the former, i.e. necessary and possible propositions, it is not the same, but contraries follow, whereas contradictories and opposites are separate and do not follow. And let us first set out what are the contraries and the contradictories. The proposition ‘not necessary to be’ is the contradictory of ‘necessary to be’, but ‘necessary to be’ is not the contrary. E.g. if someone says that it is necessary that the sun moves, the opposite contradictory is that it is not necessary that the sun moves, but the contrary is that it is necessary that the sun does not move. Thus the contradictory of necessity follows a proposition of possibility, whereas necessity does not follow the contradictory of possibility (which would happen if in these propositions opposites followed each other), but rather the contrary of necessity. Well then let us see what of necessity agrees with the proposition ‘possible to be’. ‘Necessary to be’ cannot agree with it; for what is possible can be and not be, but what is necessary could not not be. Therefore if necessity does not follow possibility, the contradictory of necessity does follow it. Thus ‘possible to be’ is not followed by ‘necessary to be’. Therefore the proposition of possibility is followed by the contradictory of necessity, ‘not necessary to be’. But necessity does not agree with the contradictory of possibility. For we cannot say that ‘not possible to be’ is followed by ‘necessary to be’, but rather by the contrary of necessary, ‘necessary not to be’; for when something is not possible, it is necessary that it is not. Then set out the propositions which follow each other and put the proposition of necessity under these. Then label which is a contradictory, which a contrary.

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No one can doubt that the negation of necessity follows the affirmation of possibility, and that the contrary of the necessary rather than the necessary follows the negation of possibility. For since the contradictory of necessity, i.e. ‘not necessary to be’, follows ‘possible to be’, then the contradictory of possibility, ‘not possible to be’ is not followed by necessity itself but by its contrary ‘necessary not to be’. That then is the general sense whereas the actual word order is as follows. But we must consider how the necessary [behaves], i.e. what implications it has. He first of all states the conclusion: it is clear that it is not the same, where we have to understand, as in the case of possible and impossible propositions, but contraries follow, and the contradictories are separated and do not follow. For the contradictory of possibility was not followed by the contradictory of necessity, but as we explained above, by its contrary. For in implications of necessity a contradictory did not agree with a contradictory. For ‘not necessary’ followed possibility, and ‘necessary not to be’, not ‘necessary to be’ followed ‘not possible’. But again ‘to be necessary not to be’ and ‘not necessary to be’ are not contradictories, but ‘not necessary to be’ is the negation of the necessary, whereas ‘to be necessary not to be’ is the contrary of necessary. But contradictories are not opposed to each other; for they can be found in one and the same thing at the same time. And this is what he means by for they both happen to be true of the same thing; for what is necessary not to be, is not necessary to be. For example, because it is necessary that a man is not four-footed, it is not necessary that he is four-footed. For if this is false, it will be necessary that a man is four-footed, since it is necessary that he is not. Therefore it is clear that the propositions ‘not necessary to be’ and ‘necessary not to be’ can sometimes be found together. Since this is so, they are not contradictories. In giving the reason why the same could not occur in the case of necessary propositions as in the comparison of posssible propositions where the implications were rendered in terms of contradictories, he says the following: 22b3-10 The reason why the implications are not the same as the rest is that impossible and necessary have the same force when applied in a contrary way. For if it is impossible ‘to be’, it is necessary for this not ‘to be’ but ‘not to be’. And if it is impossible ‘not to be’, it is necessary for this ‘to be’. Thus if the former follow in the same way the ‘possible’ and ‘not possible’,

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these follow in a contrary way; for necessary and impossible signify the same thing, but, as we have said, in a contrary way. The reason, he says, why the implications are given in this way, is that the necessary always agrees with the impossible in a contrary form. For what is impossible to be, is necessary not to be, and again what is necessary to be, is impossible not to be. Therefore there is a contrariety. For when impossibility has ‘to be’, necessity has ‘not to be’, and when necessity has ‘to be’, impossibility has ‘not to be’. Therefore impossibility and necessity have the same force given in a different way; if necessity is given in terms of ‘to be, then impossibility is in terms of ‘not to be’; if impossibility is in terms of ‘not to be’, then necessity is in terms of ‘to be’. Thus their agreement occurs in a contrary way because where it is impossible to be, there it is necessary not to be; but ‘impossible to be’ and necessary not to be’ agree; therefore ‘not possible to be’ and ‘necessary not to be’ agree. Thus no one can doubt that ‘necessary not to be’ follows the negation of possibility because impossibility which follows the negation of possibility agrees with ‘necessary not to be’. And this is so because impossibility and necessity have the same force, as I have said, if they are proposed in a contrary way. Thus what is said is as follows. The reason why the implications are not the same as the rest, i.e. propositions formed with possible and impossible is that impossible and necessary have the same force, i.e. impossibility has the same force as necessity when given and expressed in a contrary way. For if it is impossible ‘to be’, it is necessary for this not ‘to be’ but necessary for it ‘not to be’, i.e. it is impossible for it to be. Thus no one would say that it is necessary to be, but rather that it is necessary not to be, which is the equivalent of saying: if it is impossible to be, it is necessary for this not to be, but one should not think that ‘necessary to be’ is ‘impossible to be’. Again if it is impossible for something not to be, it must be. Thus impossibility has the same force as necessity when rendered conversely and in a contrary manner. But if impossibility is related in implication to the possible by a similar contradiction and convertibility of contradictories, and impossibility and necessity have the same force when predicated in a contrary manner, no one can doubt that the implications in this case are quite rightly contraries and not opposites. Then it is to be explained as follows. Because in the implicational relationship of propositions of the impossible and not impossible to those of the possible and not possible, ‘something is impossible’ followed ‘not possible’, and the impossible has the same force as the necessary in a contrary way, it is clear that if they are similarly related, i.e. in the way said, the impossible following the possible and not possible, the impossible is in agreement with the ‘not possible’ and that what has the same force in a contrary way, i.e. ‘necessary not to be’ follows the proposition which impossibility also

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followed. And ‘necessary not to be’ has the same force as impossibility in a contrary way and impossibility follows ‘not possible to be’. And ‘necessary not to be’ therefore follows ‘not possible to be’, so that the sense is as follows. Since the impossible can be the same as the necessary in a contrary way, then the relational implications of the impossible to the possible and not possible stand in a similar relationship, i.e. in the way explained. * * * 60 22b10-28 Or perhaps it is impossible for the contradictories in the case of necessity to be placed in this way? For what is necessary to be, is possible to be (for if not the negation would follow; for one must either affirm or deny; then if it is not possible to be, it is impossible to be; therefore what is necessary to be, is impossible to be, which is absurd). But ‘not impossible to be’ follows ‘possible to be’, and ‘not necessary to be’ [also follows]. Thus it happens that the necessary to be is not necessary to be, which is absurd. But in fact neither ‘necessary to be’ nor ‘necessary not to be’ follow ‘possible to be’; for with this both may happen. But whichever of the others is true, these will not be true. For it is at the same time possible to be and not to be; but if it is necessary to be or not to be, both of them will not be possible. It remains then that ‘not necessary not to be’ follows ‘possible to be’. For this is true of ‘necessary to be’ also. For this is the contradictory of what follows ‘not possible to be’; for it is followed by ‘impossible to be’ and ‘necessary not to be’ whose negation is ‘not necessary not to be’. Therefore these contradictories, too, follow in the way stated and there is nothing impossible when they are placed in this way. The conversion of the propositions has been set out in such a way above that the negation of necessity follows a proposition of possibility. And if they are placed in this way, it does not happen that a contradiction follows a contradiction nor that they follow when reversed, which did happen where we were considering the implications of possible and impossible propositions, because the contradiction of necessity, i.e. ‘not necessary to be’, followed the proposition of possibility, and not necessity but the contrary of necessity followed the contradiction of possibility. Now wanting to change this, his intention is to devise the implications in such a way that a contradiction agrees with a contradiction in a similar way, but conversely. And he sets it out in this way when he says: I probably made a mistake in that I traced the consequence of the necessary and possible from the possible and not from the necessary as a measure of their agreement. For he put ‘possible to be’ as the leading proposition and ‘not necessary to be’ as agreeing with it. And this is what he

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did first, but now he changes his mind and asks whether, perhaps, he had succumbed to an error when he established the consequences by putting ‘possible to be’ first and then adding as a consequence the negation of necessity, ‘not necessary to be’. Is it not more true to put necessary first and then attach possibility as agreeing with it? For it seems that possibility follows every necessary proposition. But if someone denies this, we will have to declare that the negation of possibility follows necessity. For in all propositions there is either an affirmation or a negation. Then if possibility does not follow a necessary proposition, the negation of possibility follows. Then the correct sequence is expressed as follows: what is necessary to be, is not possible to be. But we have only just said that impossibility agrees with ‘not possible to be’.61 But ‘not possible to be’ follows necessity, and therefore impossibility follows necessity. Therefore the correct sequence of propositions will be: if something is necessary to be, it is impossible for it to be; but this cannot be the case; then if impossibility does not follow necessity, and the proposition that indicates something cannot be follows a proposition of impossibility, then the negation of possibility ‘not possible to be’ does not agree with the proposition of necessity. But if this does not agree with the statement of necessity, the affirmation will agree. Therefore possibility follows necessity. The correct implication of the propositions will be as follows: if it is necessary to be, it is possible to be. But again other problems arise from this. For if someone says that a possible proposition agrees with necessity, then because ‘not impossible to be’ and again ‘not necessary to be’ agree with possibility, as our previous arrangement has already shown, it will turn out that ‘not necessary to be’ agrees with the proposition of necessity. Then the correct implication will be: if it is necessary to be, it is not necessary to be. But this again is impossible. But if this is so, something in the propositional implications of possibility has to be changed so as to establish self consistency. And so either the initial statement that the negation of necessity followed a possible affirmation, i.e. that ‘not necessary to be’ follows ‘possible to be’, was wrong, or we were not right to think that the necessary agrees with a possible proposition. But because this is absurd (for no one would say that possibility is the contrary of necessity; for it would happen that what is necessary, could not be) and the appropriate consequence would be ‘if it is necessary, it is possible’, it happens that the negation of necessity does not follow a possible proposition. But when this is said, it can be understood that possibility follows necessity so that what is necessary is said also to be possible, but what is in itself possible is not in every case necessary. For if it is necessary, it cannot be the case for it not to be, but what is possible, can also not be. Therefore what is possible is not necessary. But I mean that the proposition which is the complete contrary of necessity does not

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follow possibility. For ‘necessary not to be’ is the contrary of necessity. No one would force this proposition to agree with possibility. For what is necessary not to be, cannot be, but what is possible, can both be and not be. Therefore necessity in the proposition which is predicated with ‘to be’ does not follow possibility because possibility can also not be, whereas necessity predicated with ‘to be’ cannot not be. Again necessity which is predicated with ‘not to be’ is different from possibility and does not follow it, because the necessity which is said with ‘not to be’ cannot be, whereas the possible can both be and not be. Then possibility is followed neither by the opposed negation of necessity, ‘not necessary to be’, nor by the necessary affirmation ‘necessary to be’, nor by its contrary ‘necessary not to be’. But there will be clearly four in this list; for the necessary affirmation ‘necessary to be’ is opposed to ‘not necessary to be’ and the necessary affirmation ‘necessary not to be’ is again opposed to necessity, and to this is opposed the proposition ‘not necessary not to be’, as the following table makes clear. is not necessary to be is necessary not to be

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is necessary to be is not necessary not to be

Then if neither what is necessary to be nor its opposite ‘is not necessary to be’ nor its contrary whose meaning is ‘is necessary not to be’, agrees with possibility, it remains that the fourth proposition ‘is not necessary not to be’ agrees with it. This fourth proposition agrees to some extent also with necessity itself, whereas necessity does not agree with possibility. For everything which is necessary to be is also capable of being and it is not necessary that it is not. And the proposition ‘is not necessary not to be’ agrees with necessity because ‘is necessary not to be’ is the contrary of necessity, and ‘is not necessary not to be’ is the opposite of ‘is necessary not to be’. Therefore the contrary proposition agrees with its opposite affirmation. This is easy to understand if you look carefully at and return to what we have written above. Thus if ‘is possible’, as we have said, is followed by the proposition ‘is not necessary not to be’, the negation of possibility is followed by its opposite ‘necessary not to be’ and the consequence will be as follows: if it is possible, it is not necessary that it is not; again, if it is not possible, it is necessary that it is not. Thus this is the reverse of the consequence which was contradictory but converse, as given above in the case of possibles . For here the negation ‘is not necessary not to be’, predicated with ‘not to be’, which cancels out necessity, follows a possible affirmation, and a necessary affirmation predicated with ‘not to be’ follows the negation of possibility. Thus, there is here the same conversion, so that a contradictory follows a contradictory, but conversely, so that an affirmation agrees with a negation, a negation with an affirmation.

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I think that this will become clearer if it is presented visually and the arrangement of the diagram impresses on us in the clearest way the meaning of the subject matter.

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The meaning as a whole and the way in which it is expressed is as follows. After saying about the consequence of possible and impossible propositions that contradictories agree with contradictories, but conversely, i.e. that the affirmation agrees with the negation, the negation with the affirmation, we must see, he says, how the same consequence occurs in necessary propositions. Then after consideration, he does not find the same situation in necessary propositions. For although he had said that the negation of necessity agrees with possibility, a necessary affirmation does not agree with the negation of possibility. In giving the reason for this he argues that impossibility when stated in a contrary manner has the same force as necessity. This is what he says in his wish to change this: Or perhaps it is impossible for the contradictories in the case of necessity to be placed in this way? so as to say that the negation of necessity agrees with possibility. And he adds a doubt which is self-evident. For what is necessary to be, that, without doubt, is possible to be; for if not, i.e. if what is necessary is not possible, the negation of possibility would follow; for one must in every case either affirm or deny; for in all things either the affirmation or the negation is true. Then if it is not possible to be, i.e. if what is necessary to be, is not possible to be, and the proposition ‘is not possible to be’ is followed by ‘is impossible to be’, something becomes impossible, in his words what is necessary is impossible to be. But this is absurd. Thus he shows here that possibility followed necessity. But he now adds something else. Because he said above that the negation of a necessary affirmation agrees with a possible proposition, he now expresses a doubt, saying But ‘not impossible to be’ follows ‘possible to be’. For what is possible, is not impossible, but what is not impossible to be, is not necessary to be. Therefore, if ‘not impossible to be’ follows possibility, and ‘not impossible’ is followed by ‘not necessary to be’ and a possible proposition is followed by ‘not necessary to be’, then no one can doubt that if possibility follows necessity, the negation of necessity follows a necessary affirmation. Thus it happens that the necessary to be is not necessary to be, which is absurd. Therefore, it is agreed that a possible affirmation is not followed by the negation which is the opposite of a necessary affirmation, because it has to be rejected.

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Either, as we said above, the negation of necessity should not follow an affirmation of possibility, or possibility should not follow necessity. What should be rejected, as it is completely impossible, is that the negation opposed to necessity follows a possibility. Therefore, ‘is not necessary to be’ does not follow possibility. And because he had passed over all of these in silence in the middle of the argument, he adds to what he said above but in fact neither ‘necessary to be’ follows ‘possible to be’ including in the formulation that the necessary does not agree with possibility, and not only this but nor ‘necessary not to be’. He shows clearly what the situation is with this. For with this, i.e. the possible, both may happen, i.e. to be and not to be. But whichever of the others, i.e. the necessary with ‘to be’ and the necessary with ‘not to be’, is true, these will not be true. This he explains himself. For he says of both aspects of the possible: for it is at the same time possible to be and not to be (namely with this both may happen); but if it is necessary to be or not to be, i.e. if it cannot not be and cannot be both of them will not be possible, so that if it is necessary to be, it could not not be, or if it is necessary not to be, it could not be. Therefore the three propositions ‘not necessary to be’, ‘necessary to be’ and ‘necessary not to be’ do not follow possibility. It remains then, i.e. the fourth proposition which, stated as the opposite of the necessary that is affirmed with ‘not to be’, follows possibility, namely that ‘not necessary not to be’ follows ‘possible to be’. But because the possible agrees with the necessary, this too agrees with the necessary. For this is what he means when he says for this is true of ‘necessary to be’ also. For what is necessary, must not not be. Thus the proposition ‘is not necessary not to be’ is the contradictory of the affirmation which follows the negation of possibility, ‘not possible to be’. For since the affirmation ‘possible to be’ is followed by the negation of necessity with ‘not to be’, ‘is not necessary not to be’, the negation of possibility, ‘is not possible to be’, is followed by the necessary affirmation with ‘not to be’, ‘is necessary not to be’, and ‘not possible to be’, which is the negation of possibility, is followed by the affirmation of impossibility, ‘impossible to be’. This is what he means by for this is the contradictory of what follows ‘not possible to be’. For since a possible affirmation is followed by the negation of necessity with ‘not to be’, ‘is not necessary not to be’, this necessary negation with ‘not to be’ is the contradictory of the proposition which follows the negation of possibility. For it, i.e. the negation of possibility, is followed by what is impossible. For since the negation of possibility is ‘not possible to be’, it is followed by ‘is impossible to be’ with which ‘is necessary not to be’ agrees. Thus the negation of a possible proposition is followed by ‘necessary not to be’ whose contradictory is ‘is not necessary not to be’. Then it happens here too that a contradictory follows a contradictory, but conversely. This is what he means when he says therefore these contradictories, too, follow in the way

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stated, i.e. so that an affirmation follows a negation, a negation an affirmation, and there will be nothing absurd or impossible if the consequences are stated in this way, so that a possible affirmation is followed by the negation of necessity with ‘not to be’, and the necessary affirmation with ‘not to be’ agrees with the negation of possibility. Once he has explained these things he again throws in other questions.

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[22b29-36 Someone will raise the question whether ‘possible to be’ follows ‘necessary to be’; for if it does not follow, the contradictory ‘not possible to be’ follows. And if someone says that this is not the contradictory, one must say that ‘possible not to be’ is. But both are false of ‘necessary to be’. On the other hand the same things seem capable of being cut and not being cut, of being and of not being; and ‘necessary to be’ will be ‘to happen not to be’; but this is false.] He arranged the consequences above in such a way that possibility followed necessary preceding it. He now has doubts about this. For whether someone makes the possible agree with the necessary, or denies it, either seem odd, since if someone says that possibility does not agree with necessity, he is saying that the negation of possibility agrees with the proposition of necessity. For if someone denies that ‘possible to be’ agrees with the proposition that something is necessary, he cannot then deny that the negation of possibility agrees with necessity; and the full implication will be: if it is necessary to be, it is not possible to be, seeing that the sequence ‘if it is necessary to be, it is possible to be’, is false. But if it cannot be the case that the negation of possibility agrees with the affirmation of necessity, then it is true that the affirmation of possibility agrees with necessity. But here lurks an even greater difficulty. For everything which is possible to be, is possible also not to be. But if possibility follows necessity, it will be the case that what is necessary can be and can not be according to the nature of possibility which agrees with necessity itself. But this is impossible. Therefore possibility does not follow necessity. But if possibility does not follow necessity, the negation of possibility ‘not possible to be’ follows and there again occur the absurd consequences which we mentioned just now when dealing with the passage. But if someone wants the negation of possibility to be ‘is possible not to be’ rather than ‘not possible to be’, although he is not attaching the affirmation to the negation in the correct arrangement and we have said above that in modal propositions the negation ought always to be put with the modality rather than with the verb, we must, nevertheless, yield to it so that when we have demolished their argument as false, after making a concession which could appear to some useful for its defense, the truth is established with greater

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depth and profundity. Thus if ‘possible not to be’ is, as they want, the negative of possibility, it, too, still does not agree with necessity. For if someone says that ‘possible to be’ does not follow the necessary, then the contradictory of possibility follows necessity. But if someone makes ‘is possible not to be’ the contradictory of the possible and thinks that it agrees with necessity, the appropriate implication according to him will be: if it is necessary to be, it is possible not to be. But this cannot be the case; for what is necessary to be, cannot not be. Then if possibility does not follow necessity (for what is necessary will be contingent, for the contingent and the possible have the same force), the negations of possibility, whether ‘not possible to be’ or the idea ‘is possible not to be’, follow necessity. But both of these are impossible. But if these do not follow, their affirmation, i.e. possibility, follows. But this is also not possible as we have often demonstrated. Then this question is solved by him in the following passage. Since that is the nature of the question as we have given it, let his own words and order of argument appear for itself. This is what he says. Someone will raise the question whether ‘possible to be’ follows ‘necessary to be’, i.e. if possibility agrees with necessity. For if it does not follow, i.e. if someone denies that possibility follows necessity, the contradictory follows, i.e. the contradictory of possibility. For because possibility does not follow, the contradictory of possibility ‘not possible to be’ follows. And he omits to say that it cannot follow. But it is the case that if possibility does not follow necessity and the contradictory of necessity agrees, the appropriate implication is: if it is necessary, it cannot be, which is absurd. And if someone says that this is not the contradictory, i.e. if someone says that ‘not possible to be’ is not the contradictory of possibility, one must say that the contradictory of possibility is ‘possible not to be’. But both are false of ‘necessary to be’. For of what is necessary it cannot be the case that it cannot be and again of what is necessary it cannot be the case that it is possible for it not to be. On the other hand the same things seem capable of being cut and not being cut. For possibility is common to affirmation and negation. For what is said to be possible is capable both of being and of not being. But this is false, i.e. as predicated of what is necessary. For if it is necessary, it could not not be; if it is not, it does not happen at all. But if someone says that possibility follows necessity, this possibility agrees with the contingent and ‘necessary to be’ will be ‘to happen not to be’; i.e. ‘necessary to be’ will be contingent. For if what is possible, can not be, and what can not be, happens not to be, there can be no doubt that if possibility follows necessity, then its consequence also follows it. But we can say of a contingent in negation that it happens not to be. Therefore, what is necessary, happens not to be. But this is false. And the sequence of ideas here is involved and concise. For the external form of the

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statements is one thing, another is what is missing that gives the implicit and unobvious meaning. But the meaning of his thought will become more completely clear if anyone should connect our orderly exposition with Aristotle’s words, separate out with the distinctions and analysis of our exposition what in the text is confused because of the external form and make up from our commentary what is lacking in Aristotle’s text. But now since he has put a question, he follows it up straightaway in the following words. 22b36-23a6 But it is clear that not everything capable of being or walking is also able to do the opposite. But there are cases where this is not true, firstly where things are capable in a non-rational way, e.g. fire can heat and has a non-rational force. Thus the same rational capabilities are capable of more things, even of contraries, but not all irrational powers [are like this] but, as has been said, fire is not able to heat and not [heat], nor are the other things that are always active. But some things even with irrational capabilities are at the same time capable of opposites. But this has been mentioned because not every capability is for opposites, not even those which are said to be of the same kind. Since he had raised a question about the implications of the possible and necessary, and since, if possibility with necessity, did, which was absurd, or, if again possibility followed necessity, necessity itself, with which possibility agreed, took to itself to be and not to be, he has now solved this inconsistent ambiguity with a rational argument, by saying: I was not afraid that possibility, in following necessity, would cancel the very nature and rigour of necessity so that what was necessary would be turned into contingency. For not everything that is possible to be, is also possible not to be. For there are many things which have only one force and are in no way fitted for its negation, as in the capabilities which an irrational activity effects. For although it is possible for fire to heat, it is not possible that it should not heat. Thus this capability cannot do the opposite. For if any capability can do the opposite, it both can be and not be, act and not act, whereas what cannot do the opposite, is capable of only one thing, which just allows the affirmation and rejects the negation. Then, if someone makes possibility agree with necessity, that is no reason why it is immediately necessary that necessity is changed to contingency, which agrees, of course, with possibility. For, he says, not every thing that is capable is capable of both, i.e. both to be able to be and to be able not to be; and thus not everything possible agrees with contingency. He lays this down where he says that where things are capable in a non-rational way, the capability mentioned is not able to do the opposite, e.g. that fire

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heats is due to something irrational. For there is no reason why fire heats; for there is no reason in any of the things that come about naturally. Then things whose capability is irrational cannot do the opposite, as fire cannot heat and not heat. For if they can do both, they can do the opposite; for to heat and not to heat are opposites. Then, since irrational capabilities do not have the capacity to do opposites, those with reason will be able to be led equally to effect either opposite, so that whatever has been devised as a result of will and reason can go in either direction, e.g. it is possible for me to use a medicine and it is possible that I will not or similarly with walking. For what anyone wants through rational thought or desire, is said to occur as a result of reason. And in all of these there is the capability that can apply itself to both, i.e. to affirmation or denial, so that something is or is not. But with irrational capabilities, although it can happen only in them that the irrational capability is not also able to do the opposite, yet not every irrational capability is not able to do the opposite, e.g. water both freezes and is moist; thus it can easily freeze and be liquefied, but when it is changed into hot water it cannot then have the power of freezing, though it cannot lose the power of becoming liquid so long as it remains water. Thus not every capability can do the opposite, but a capability that achieves its action by reason can do the opposite, whereas a capability that cannot do the opposite is found only in irrational capabilities, though not in all. For there are irrational capabilities which can do both, e.g. what we have said about water freezing. That is the general meaning of the passage. We now explain the way in which it is expressed. But it is clear that not everything capable of being or walking is also able to do the opposite. What is here said to be clear is not that we are to think that everything which can walk or which can be could not do the opposite, i.e. could not not be; for the passage seems to declare this, but should not be understood by anyone in this way, but rather seems to say that it is clear that not everything is capable of doing the opposite, in the frequent usage of the word ‘capable’ when we say ‘capable of walking’. For it is not the case that every capability agrees with its affirmation and negation, but there are some which can do only one, as we have already said above. And this is more clearly understood if we say it is clear that not everything possible also achieves its opposite, because we often predicate ‘possible’ of being and walking. If you consider it this way it is easier to understand the meaning of the actual text, though you must also patiently and sympathetically add as support to the obscure meaning what you expect is required to express the sense of the writer even though it is not there in the actual argument. When this is done it is clear that not all capabilities can effect the opposite, but that there are some where this is not true to say, that they effect the opposite. He gives as an example firstly where there is an irrational capability, i.e. not in

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accordance with any reason, where an explanation of the capabilities cannot be given because their nature is such that an explanation cannot be given, e.g. that fire makes things warm, for this is naturally present in it. And this capability of fire does not effect the opposite since it is irrational whereas the capabilities that are rational and in accordance with reason are capable of more things, even of contraries. For the nature of things where reason is dominant is suited to both opposites so that the same capabilities are capable of more contraries. Thus if it is possible for me to walk, since this depends on my reason and will, it is possible for me not to walk and this is a capability for effecting not one but many things and their contraries. For although ‘to walk’ and ‘not to walk’ are somehow an affirmation and a negation, nevertheless they are arranged by Aristotle as contraries. And it is clear in the case of all rational capabilities that they are capable of more contraries and effect the opposite, whereas those that are irrational, though they do have things which count as opposites, they cannot however effect all of them. For though water has the capability of freezing, which is irrational, it has also another capability of warming when it has itself been heated. But this is not found in all irrational capabilities. For fire, as we have said, seems to have just the one capability of heating. This is what he means by: but not all irrational powers can effect opposites but, as has been said, fire is not able to heat and not. And the general rule is given that those things that always contain a single capability in act are not capable of their opposite, e.g. fire always heats, the sun always moves etc. He says this with the words nor are the other things that are always active. But even some irrational capabilities can effect an opposite, as with our example of water. But he tells us that he has said this so that we might know that no contrary occurs if someone says that a possibility agrees with a necessity. For since not every capability effects its contrary, the capability which does not effect an opposite but always does one thing, agrees with necessity. This is what he means by: but this has been mentioned because not every capability is for opposites, not even those which are said to be of the same kind. The words not even those which are said to be of the same kind mean: not only is not everything which is said to be possible capable of producing contraries, but also some things which are of the same kind are not capable of opposites, e.g. those which have irrational capabilities. For since all irrational capabilities constitute a single kind insofar as they are irrational, not even in all of these, however, can an identical capability for opposites be found, e.g. in fire as we have already explained above. For though its power is irrational, it is not capable of being transferred to an opposite effect. Then it has been rightly said that not even those of the same kind could have the capability of effecting opposites. For although fire is a capability of the same kind, i.e. an irrational capability, along with

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all the other irrational powers, it can, however, never lose its power of opposites. And he has said in advance that this, which could deal with the whole question, does not resolve the problems in the strongest way; but he goes straight on to say what primarily causes the problem and creates the ambiguity. 23a6-18 Some capabilities are equivocal. For ‘possible’ is not said in an unqualified way, either because it is true as being in act, e.g. it is possible [for it] to walk because it is walking, and it is generally possible to be because what is possible is already in act, or because it might be act, e.g. it is possible [for it] to walk because it will walk. This kind of capability is found only in things that change, the former also in things that do not change. In both it is true to say that to walk or to be is not impossible, both what is already walking and what is going to walk. Thus it is not true to assert without qualification the one kind of capability of what is necessary, but of the other type it is true. But since the universal follows the particular, what derives from necessity follows ‘possible to be’, but not in every case. What this idea which Aristotle now puts forward involves, we have already carefully explained in book five and now will briefly explore. For we have taken the trouble to explain this for a second time in the interests of explanation and teaching and not for extending our indulgence in lengthy discourse. Then the general meaning is that the ‘possible’ which we frequently say is in things is not said without qualification, and so because the possible has been rendered by ‘capability’, ‘capability’ too is also itself equivocal. This is clear from the following, that some things are said to be capabilities not because they are being done, but because nothing stops them from being done, as when it is said of someone when sitting, if he has a healthy body and all other potential impediments are removed, that he is capable of walking, not because he is walking, but because nothing at all is stopping him from walking. Whereas some capabilities are so called because they are already in act and being performed, as when someone says of a man walking that he is capable of walking. And so the kind of possibility which is not said to be actualised in any way, but is so called insofar as it can act if not prevented from acting, is called a ‘possibility’ from the capability.62 But the type which is already acting and is in act, act itself, is called ‘possibility’. Thus there are two significations of ‘possibility’, one which designates possibility which is potential and which is not in act, the other which signifies possibility which is already in act. But the possibility which is already in act is either changing from possibility to act or was always naturally actual, e.g. when a man changes from sitting to walking, he is able to walk and so changes from the possibility to the

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actuality, whereas when the sun moves, it does not change from possibility to actuality (for there was never a time when it did not fulfill this movement); nor does fire, so that now it heats, but sometimes does not heat. Thus the possibility which is said to be in act has two sub-species, one which designates the kind of possibility which may not not be and which is called necessary and never changes from possibility to actuality, but remains naturally actual, the other which may also not be and which is not necessary though it is actual. And the kind of possibility which changes from possibility to act is found only in things that have motion, i.e. which can move, and these are corporeal. For we will mention a little later63 the reasons why incorporeals are shown not to have motion. But those which have always remained in act because of their own natural quality, are found both in things that have motion, like fire’s heat which is always in act and was never potential, and in those that have no motion, the incorporeal and divine. Thus the possibility which has moved from possibility to act belongs only to what can decay and is corporeal, whereas that which was always in act is common to divine and corporeal things. Then to encapsulate the whole meaning in a few words we should say that possibility is equivocal and signifies many things; for there is one kind of possibility which though not in act, can however be and thus be predicated as possibility and there is another which is already in act. But the possibility which is already in act, is not equivocal, but a genus; for it has as its own species, the possibility which is in act but has changed from possibility, and the other which is in act but has not changed from possibility. And the latter, which has not changed from possibility, is called necessary and never abandons its subject, while the former, which has moved from possibility to act, is without any hesitation called not necessary because it can sometimes abandon its subject. But these two, i.e. what are called possibilities potentially and actually, could have a common predication if we said that they were both not impossible. For it is true to say both of the man who can walk though he is not walking and of the man who is already walking, that it is not impossible for them to do that which they can do or are doing. Then since there are two things under the signification of possibility, a possibility which is not actual and another which is, and the possibility which is said to be potential is not in conformity with necessity and sometimes cannot agree with necessity, it remains for necessity to be placed under the kind of possibility which is in act. But it too has a species in which there is a change from possibility to act and which is not necessary. Then necessity cannot be placed even in this. It remains then that, because no one denies that what is necessary to be is possible and while what is said to be potential comes under the possible, but necessity is not put under the possibility which is actual and could abandon a subject, necessity is put under the act which cannot abandon its subject, so

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that the possibility which is actual and never abandons its subject is a necessity in that it has never come from potentiality to act. Thus necessity is a kind of species of possibility if it is placed where there is the kind of possibility which is always actual. But because a genus follows a species and where there is a species there cannot fail to be a genus, the appropriate genus, possibility, follows its own species, necessity, but not every genus. The possibility which is only potential and not also actual does not follow necessity, nor that which though actual can abandon its subject, but only that which when actual could never leave its subject. Therefore possibility follows necessity and nothing impossible occurs here, but, as we have said, the kind of possibility which is actual and whose nature is not to cease being in its subject. That then is the general meaning of this passage. The detailed meaning of the actual wording will be as follows. Some capabilities, he says, are equivocal. This is said because not every capability is equivocal; for there is the capability which is a sort of genus, the one predicated in actuality. But how some capabilities are equivocal he explains with the words: For ‘possible’ is not said in an unqualified way, and this is then subdivided, either because it is true as being in act, e.g. it is possible [for it] to walk because it is walking, and it is generally possible to be because what is possible is already in act. This could not be more clearly demonstrated than by saying that what is already in act is possible. But if someone says that it is not possible, he is saying that what is impossible is being done and happening and being; but this exceeds all bounds of rationality. He now gives the other part of the signification of capability with the words because it might be actualised, with the example it is possible to walk because it will walk. Not then because it is already in act but because it might be in act, i.e. because nothing probably stops it from being actualised. This kind of capability is found only in things that change, i.e. the kind of capability which is said to be potential and not actual. And by changing things he means, as we have said, only bodies. The former, i.e. what is in act, are also in things that do not change, i.e. in what is divine. And he makes the addition also in things that do not change so that we do not think that the capability of actuality is found only in divine things but also in mortal and corporeal things. In both it is true to say that to walk or to be is not impossible, both what is already walking and what is going to walk. One predicate, he says, could fit both significations, so that we can say that it is not impossible for what is already walking to be walking or what can walk and is not walking to walk, the latter expressed by what is going to walk. For what is going to walk is what is not in fact walking but could walk. To this he adds thus it is not true to assert without qualification the one kind of capability of what is necessary, i.e. it is not true to predicate without qualification, universally and generally of necessity the kind of possibility which is

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predicated equivocally; i.e. not every capability agrees with necessity. But the other type of capability it is true, i.e. to predicate of necessity the kind of capability which is said to be unchangeably actual. But since the universal, i.e. the genus, follows the particular, i.e. the species, what derives from necessity, which is a species of capability, follows ‘possible to be’, i.e. capability but not in every case. For the capability which is predicated in actuality and can abandon its subject does not follow necessity, but only the capability which when it is in act neither changes from potentiality to actuality nor could abandon its subject. And the kind of things Aristotle meant are what we picked out in our explanation that unchanging things are divine. But that only bodies are called changing things must be briefly demonstrated. It is clear that there are six kinds of motion, as Aristotle has explained in the Categories,64 although he altered this in the Physics.65 But let us now make our pronouncement as though there were six in total. If reasoned argument has declared that divine and incorporeal realities do not move according to any form of motion, the logical consequence is that divine things do not move. Thus they are not born, nor are they destroyed, nor do they grow bigger or smaller, nor do they move from place to place, since they are present everywhere in their entirety66 and none of these ought to be applied to god, nor are they changed with any kind of affection. But if the nature of divine things is not changeable in the sense of any of these motions, it is clear that they are entirely unmovable and these motions occur only in bodies. Let it be enough that we have reached this clarity in our reasonings and arguments in the many things that can be said about this problem. Now because he has told us that not every capability agrees with necessity and has explained which does agree with necessity, Aristotle adds for completeness what ought to be put first, what second in their implications, in the following words: 23a18-26 And perhaps what is necessary and what is not necessary are a principle of everything’s either being or not being and one should look at the others as following from these. But it is clear from what has been said that what is of necessity is actual. Thus if the things that always are are prior, then what is actual is prior to capability. And some things are actual67 without capability, e.g. primary substances, others with capability which are prior in nature, posterior in time, others are never in act but only potential (potestate).68 After explaining what appears to be the case with the consequence of possibility and necessity, he adds these remarks as a sort of correction of the arrangement previously given, so that where previously he began with possibility and led all the other propositions back to the possible and contingent and their agreement, he now has good

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reason to change this so that we must begin from necessity rather than from possibility. For if you look more carefully at the previous list, the possible and contingent is put first and the agreement of everything else is related to them. But this now seems to have been changed. For he says it is probably more correct to begin the consequence of the propositions from necessity. And the general sense is as follows. Because the things that always are are necessary and what always is is the principle of all the other things that are not always, what is necessary must appear to be prior to everything else. Thus the consequences are also to be made in the same way so that necessity is placed first, then possibility and the rest, and the sequence is as follows: necessary to be is not possible not to be

not necessary to be is possible not to be

is necessary not to be not possible to be

is not necessary not to be possible to be

Do you not see, then, that ‘necessary to be’ and ‘not necessary to be’ are proposed first, then, in second place, the rest are related to the agreement and consequence of necessity? This is what he meant by saying that what is necessary is perhaps the principle of everything’s either being or not being, so that the commencement of the consideration of the propositions should be from necessity which establishes the sequential agreement of the other propositions as to being or not being. And because ‘necessary to be’ is put first, ‘is not possible not to be’ agrees with it. Thus necessity is the principle of the proposition ‘is not possible not to be’ which denies ‘not being’ (for it abolishes the modal ‘possible’), and without doubt agrees with it. And again, because ‘is possible not to be’ agrees with ‘not necessary to be’, ‘not necessary to be’ is the principle of the proposition which establishes that something is, i.e. possible. Thus whether necessity is proposed affirmatively or negatively, you see that it is a kind of principle of the rest, and the rest ought to be judged as being in agreement with these, i.e. with the necessary propositions. And this is what he means by and one should look at the others as following from these. Why this turns out so, he shows in the following explanation. Because what is necessary is in actuality, as has frequently been demonstrated, and what is necessary always is, and what always is, is prior to things whose capabilities are not yet in act, it is clear that things that are in act and do not come from potentiality to act are prior. But we are talking about the actuality which does not come from potentiality to act but always remains in act because of the way in which its own nature is established, as in the case of fire warming, the sun moving or the other things that are such as never

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to abandon their act and the act is never absent from them and they never come from capability to this act. Then since they are such as always to be and things that always are are prior to everything, they will also by their own nature be prior to capability. But things that are always prior and necessary, are in act, and it is necessary that what is in act is prior to what is potential. After this Aristotle makes the following division of things. Some things are always in act, of the kind that does not come from potency, and these are the things that do not have potencies but are always in act. Others move from potency to act and their substance and act is posterior in time to their potency, while it is prior in nature. For in everything, what is actual is prior to and nobler than what is potential. For what is potential is still hastening towards actuality, and thus actuality is a perfection, while potentiality is still something imperfect, which is only perfected when it has at some time reached actuality. And it is clear that what is perfect is nobler and prior to what is imperfect. For if things which have come to their actuality from potentiality, were previously potential and then later actual, then the actuality of these things is posterior to their potentiality, if we are to make reference to time, but in reference to their nature it is prior to their potentiality. And this is what he means when he says that there are other things that have potentiality and actuality but have actuality as posterior to potentiality in time, but prior in nature, while there are some things, e.g. infinite number, in which there is only potentiality, and never actuality. For number can increase to infinity and whatever number has been mentioned, a hundred, a thousand, ten thousand and the rest, must be finite. Thus an actual number is never infinite because it can increase to infinity. And for this reason infinite number is only potential. Time is the same. For any time you mention is finite, but because time can increase to infinity, we say that it is infinite because it is infinite potentially, not actually. For nothing actual could be infinite. And where he said above that things that are always actual are primary substances, one should not think that he means primary substances as in the Categories where he calls individuals primary substances. But here he calls things that are always actual primary substances, because, as he has said, things that are always actual are the principles of the all the other things and they must in this way be primary substances.

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Chapter 14 23a27-32 Is the affirmation contrary to the negation and the sentence to the sentence, the sentence ‘every man is just’ to the sentence ‘no man is just’ or ‘every man is just’ to ‘every man is unjust’? ‘Callias is just’, ‘Callias is not just’, ‘Callias is unjust’; which of these are contraries?

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After dealing thoroughly with the consequences of propositions and arranging them with a sophisticated investigation, a question arises which is so useful in itself that it is brought right to the fore of the readers’ attention. For although it is clear that an opposite negation is at odds with its affirmation and a universal negation completely cancels a universal affirmation and that it is not unknown that an affirmation which affirms a contrary also cancels out the proposition of the contrary, the question is which more effectively cancels out and opposes an affirmation, a universal negation or the affirmation of the contrary or of the privation. Suppose that the affirmation is ‘every man is just’. Two propositions cancel this out, the universal negation ‘no man is just’ and the one which predicates in affirmation the privation of justice, ‘every man is unjust’. Then the affirmation ‘every man is just’ is cancelled both by its own universal negation ‘no man is just’ and by the privative affirmation ‘every man is unjust’. Then since it is cancelled out by both and what is cancelled out seems to be the contrary of what cancels it out, and it is cancelled out, as we have said, by two, and there cannot be two contraries of one statement, which of the two propositions which we mentioned above, the universal negation and the privative affirmation, is to be the contrary of the universal affirmation referred to above? No one can be unaware of the usefulness of the question raised here when he considers that had the question not been raised and resolved by Aristotle, there would be great doubt as to whether to accept that there could be two contraries of a single statement, which clearly cannot be the case. For since two cancel out one thing, who is there who would doubt that one thing is opposed to two or that since two things cancel out one thing the question should be asked, which of them seems more likely to be the contrary? But we are now talking about contraries not in the sense in which Aristotle explained them in the Categories,69 but only in the sense that one thing cancels another, one proposition cancels another proposition, so that the question is something like this: what is more effective in canceling out a universal affirmation, a universal negation or a statement that predicates the privation or something else which embodies the force of a contrary from its very opposition? Whence it should also not go unnoticed that no one doubts what is a contrary opposite between a universal privative affirmation and a universal negation. For it has already been said above that a universal negation is the contrary of a universal affirmation, but this is not what is meant here, as we have said, but rather that which more effectively cancels a thing out. For what more effectively cancels something out will appear in the same way to be a more effective contrary. And so not only did he make propositions about universals, but lest anyone might suspect that he is saying the opposite of what he said in the Categories or of what he said above about universal affirmation and negation, he adds propositions about

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particulars which do not have affirmations and negations of their contrary opposite. For if we recall what we correctly understood above a universal affirmation and a universal negation were said to be contraries. Not only this but also in the case of ‘just’ and ‘unjust’ he decided the problem that state and privation are more than any contrariety. Thus, as we said, it has to be understood that the question now is which proposition most closely and effectively destroys and cancels out which proposition. The way he tackles this question is as follows. 23a32-b2 For if what is in spoken sound follows what is in the mind, and there the belief of the contrary is contrary, e.g. ‘every man is just’ is contrary to ‘every man is unjust’, it must be the case that the same holds for spoken affirmations. But if the belief of the contrary is not contrary there, the affirmation will not be contrary to the affirmation, but rather the negation we have mentioned. So we must enquire what kind of true belief is contrary to a false belief, the belief of the negation or the belief that there is an opposite. This is what I mean; there is a true belief about the good that it is good, and a false belief that it is not good, and a further that it is bad. Which of these is the contrary of the true belief? And if they are one belief, according to which is it a contrary? This investigation of what is more effectively the contrary of a universal affirmation, a universal privative affirmation or a universal negation, starts here from the fact that almost every property that must occur in spoken sounds comes from the beliefs which the sounds themselves signify. Then what is to be sought in spoken sounds must firstly be seen in the beliefs. For it cannot happen that the properties of the spoken sounds will not first be found in beliefs, since the significance of the spoken sounds comes from the beliefs which the spoken sounds themselves signify. Thus the enquiry must ask how those things are related in beliefs, so that what has been found in the beliefs can be logically transferred to the spoken sound. The enquiry into beliefs is first made as follows. If the belief of a privative universal affirmation is a more effective contrary of the simple universal affirmation than is the belief of a universal negation, it is clear that a privative universal affirmation more effectively cancels a simple universal affirmation than does a universal negation. But if the argument should hold more weight that the belief of a negative universal more effectively cancels the belief of a universal affirmation than does the belief of a privative universal affirmation, it is then agreed that a universal negation is a more effective contrary of a universal affirmation than is a privative affirmation. But in order to find this out, one must proceed as follows. A particular true belief

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should be posited, and against it two false beliefs, one of which should be a privative affirmation, the other a universal negation. Then whichever of the two false beliefs the argument shows to be the more false will be declared to be the more effective contrary of the true belief. Then let there be three beliefs, one true and two false; and let the true belief be the one which thinks that what is good is good, which Aristotle gives as the belief about the good that it is good. Then one of the false beliefs is that what is good is not good, which Aristotle gives as the false belief about the good that it is not good, and the other that what is good is bad, which Aristotle gives as the belief about the good that it is bad. Then the question is which of these three, one true, two false, is the more effective contrary of the true belief. But because it often happens that both a negation and a privation signify one thing and especially in contraries where no median is found, he adds and if they are one belief, according to which is it a contrary? And the meaning of this is that in contraries where there is no median the negation has the same force as the privation, whereas in those where there is a median a privative affirmation and a negation do not share the same signification. Take ‘to be born’ and ‘to be unborn’ as the kind of contraries that are without a median. Then in contraries without a median the privative affirmation has the same force as the negation, but in those which do have a median the force is not the same. For it is not the same to say of someone that he is bad and that he is not good. For though ‘good’ is denied, the listener’s mind can suppose that there might be something in between. But when ‘bad’ is posited, any supposition of the listener to the contrary is thrown out; and so they do not signify the same thing. But because, as has been said, privation or contrariety agree with negation, whenever the kind of propositions are found in which a privative affirmation does not disagree at all with a negative, the question must be raised, as Aristotle appears to do, in respect of which statement or belief the statement or belief is contrary to the true affirmation or belief. For although they sometimes signify the same thing, they employ the propositions in a different way. For in positing a negation you say of what is that it is not, while in positing a privation you say of what is not that it is. Then since propositions with the same signification somehow have a different starting point and thrust, you have to ask which of them is more effectively contrary to the true proposition and through which mental movement the true proposition is more effectively cancelled. This is what he means by and if they are one belief, according to which is it a contrary? For he does not say that a negation and privation are in every way identical, but in those cases where they are the same, that is in contraries without a median, even when they signify the same thing, because they do not declare the single signification with one mental movement when they propose a contrary or privation and when they

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propose a negation, in respect of which one is the contrary proposition more effective, the privative or the negative proposition? After this he explains what the nature of the contrariety is. 23b3-7 For it is false to think that contrary beliefs are distinguished by being of contraries. For [the belief] of the good, that it is good, and of the bad, that it is bad, are perhaps the same and true, whether they are one or more than one. But they are contrary things. Yet it is not through being [beliefs] of contrary things that they are contrary, but rather because they are in a contrary manner. The meaning is expressed very concisely but is bound up with the most important element of truth in the argument. For since he is talking about contraries, he explains in the very first place how there can be contrary beliefs. For there is a view that contrary beliefs are those which have some contrary thing as their object, but this is proved to be false. For if good and bad is a contrary and someone thinks about good and bad, it is not automatically necessary that contrariety follows. For imagine that someone thinks about good that it is good and thinks also about bad that it is bad. Then although he thinks about good and about bad, that this is good, that is bad, they are still not contrary beliefs. For to think that what is good is good and what is bad is bad is not a contrary; for both are true, whereas contrariety of beliefs is recognised in falsity. But how can beliefs of this kind be contrary, when they arise somehow from the same mental state, i.e. they are beliefs which know that they are true? Thus it is not when someone has a belief of contrary things and has a belief about contraries that contrariety must automatically follow in those beliefs. Therefore contrariety of beliefs is not found in the act of thinking which has contraries as its object and is concerned with contraries, but contrariety occurs in beliefs whenever anyone thinks about one and the same thing in a contrary manner. For example, suppose something good is proposed. If someone thinks in a contrary manner about it that it is good and about the same thing that it is bad, the belief which considers what is good to be good is true, while the other belief which considers what is good to be bad is false; and true and false are contrary. Thus we are right to say that beliefs which truth and falsity distinguish are contrary and not of contraries, but have been formed in a contrary manner about one and the same thing. Thus it was right to say that one ought not to distinguish contrary beliefs because they are beliefs of contrary things, but rather because they consider the same thing in a contrary manner. The way in which he expresses it is as follows. For to think that contrary beliefs are distinguished by being of contraries, i.e. because they are beliefs about contraries, is false. He then declares how it is

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false. For [the belief] of the good, that it is good, and of the bad, that it is bad, are perhaps the same, i.e. they are not beliefs contrary to each other, but they are both the same. He then himself adds how they are ‘the same’ with the words and true; for they are ‘the same’ because they are true, whereas contrariety lies, as we have explained, in truth and falsity. Thus if they agree, they will appear to be ‘the same’ in truth and falsity. Number does not make a difference either; for whether they are one or more than one, because they are true, they are ‘the same’. But they are contrary things, i.e. what is found in beliefs. Yet it is not through being of contrary things, i.e. that they are beliefs about contrary things that they are found to be contrary beliefs, but their contrariety arises from the fact that the beliefs are about one thing in a contrary manner. This is what he means by but rather because they are in a contrary manner. For in a contrary manner is here an adverbial expression, the equivalent of saying that they are contraries rather insofar as the beliefs operate in a contrary manner; and we have to complete the meaning with ‘about the same thing’. For if beliefs are not about the same thing in a contrary manner, but about separate things, they could not be contraries. Everyone will easily see this if he looks at it carefully. 23b7-15 Then if there is a belief about the good that it is good, and that it is not good, and that it is something else, something that it is not and cannot be (none of the other [beliefs] is to be taken, that it is what it is not or is not what it is; for both are infinite [in number], the belief that it is what it is not and that it is not what it is. But [we must take only those] in which there is deception. And these are the ones from which comings-intobeing arise; but comings-into-being are from opposites; then cases of deception are also [from opposites]) He has expressed in very few sentences an important idea whose force, to put it briefly, is as follows. Anyone who sought to know about contrariety in propositions, ought first to have established which of the propositions is not infinite and then attach to it the force of contrariety. For in all contraries one is contrary to one. But if there is an infinity in the propositions, the total infinite number of propositions could not be contrary to one proposition. He begins the whole structure of his argument with this assumption and says that in propositions one should expect not only that the false is contrary to the true, but that under all the false propositions the proposition that is one and not infinite is contrary to the true one. But there can be an infinite number of propositions which are also false, but it can only be a finite and false proposition which may be logically posited as a contrary of a true proposition. Therefore since he wanted to establish that the contrary of an affirmation is its negation rather than the

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affirmation which posits a contrary, he says that there is a belief which thinks what is of a certain thing is of that thing. There is another which thinks that a thing is what it is not, a third which thinks that a thing does not possess what the proposed thing possesses in itself, and a fourth which thinks that the proposed thing is not the very thing it is. And that this might become clear through a common example, he took the proposition that something is good to serve as the belief to be considered. So, if someone thinks this good is good, he will think truly. If he thinks that this good is what is not good, he will think falsely. Thus, if someone thinks that the good does harm, that it is useless, that the good is unjust, he will be thinking of the good, things which are not, and this is false. Again if someone thinks that the good does not have what it does have in itself, he will think that the good is not useful, the good is not just, the good is not to be sought; and he too says what is false. But if there is someone who thinks that what is good is not good, so that he does not think that the good is bad, i.e. what it is not, nor that it should not be sought, i.e. what it has in itself, but that the good is not what it itself is, such a man thinks that the good is not good. Thus all the other beliefs are infinite; for we can collect a large number of things which though they do not hold we can nevertheless say of one particular thing, e.g. in the case of the good I can say that it is bad, that it is base, that it is unjust, that it ought to be avoided, that it is dangerous, and the rest of the things that no one will find in the good; and these are infinite in number. I can also say that what the good has are not in the good, e.g. if I were to say that the good is not useful, that the good is not to be sought, that the good is not something that causes increase; and these things are also infinite in number. But when a belief does away with what a thing is, it can do this only once; for nothing else can be brought about by what is good being belief not to be good. Then the rest of the propositions which either consider the good to be what is not or consider it not to be what it has in itself, are false but infinite in number. He is now using ‘good’ as the equivalent of ‘goodness’. If someone thinks that goodness is not a good, he is both wrong and wrong in a definite way. But falsities that are definite and numerically one seem to be more effective and precise contraries of truths; for one thing is always contrary to one thing. Therefore the denial of what is, is rightly regarded as more a contrary than the denial of what a thing has in itself or the affirmation that it doesn’t have it in itself. To demonstrate this he does not use a direct expression but distorts his argument to say something different, which has caused some problems. For when he said that we should not prefer to put infinites as contraries of a true belief, he added but [we must take only those] in which there is deception. And this deception comes from those from which comings-into-being also arise. The idea embraced here is that beliefs in which there is a starting point for deception are

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the ones which ought to be put as contraries to true beliefs. But deceptions arise from the same beliefs which give rise to comingsinto-being; and comings-into-being are found in opposites. What this means is that every instance of coming-into-being arises from a change in what a thing was. For there cannot be coming-into-being unless something has ceased to be what it was before. For everything which comes to be, changes into some other sort of substantial form. Thus when something is no longer what it was, it then comes into being and is something other than what it was; and the deception occurs when someone thinks that something is not what it is. For you are deceived if you think that what is good is bad; but it is not possible for it to become bad unless it were not good; and the same applies to the rest too. Thus deception and the starting point of deception is where someone thinks that something is not what it is. And this deception takes its start from where comings-into-being arise. For every instance of coming-into-being, as I have said, arises from destruction, so that what becomes sweet does not become sweet from white, but from not sweet, and again what becomes white does not become white from hard, but from not white, and all the other instances of coming-into-being arise rather from their negations; and from this arises the first deception. But if the most complete and precise falsity of a true belief occurs where the first deception is found, and these turn out to be opposites, i.e. affirmations and negations, there can be no doubt that the belief of a negation is more a contrary than the belief which in its conception affirms a contrary. That then is the general meaning of the passage. The form of words runs as follows. Then if there is a belief about the good that it is good, which is in fact true, and that it is not good, which is false and definite, and that it is something else, something that it is not and cannot be, i.e. the belief which lays down that something is what it is not, none of all the other [beliefs] is to be taken, that it is what it is not, i.e. the belief that the proposed thing is what it is not, or is not what is, i.e. the belief that denies that the proposed thing has what it does have. He explains in the following words why these are not to be taken as contraries: for both are infinite [in number], the belief that it is what it is not and that it is not what it is. But what should be put in their place? [We must take only those], he says, in which there is deception, i.e. in which there is a starting point for deception. But where does the starting point for deception arise? It takes its start from those from which comings-into-being arise; but where do comings-into-being arise? From opposites. For every instance of coming-into-being, as has been said, is from a thing not being what it was; and this of course comes close to being a negation. Then cases of deception are also [from opposites] and the starting point for deception is found in opposites, where comings-into-being, from which the actual deception arises, are also found.

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23b15-21 Then, if what is good, is good and is not bad, the former in itself, the latter accidentally (for it is accidental to it to be bad), the truer belief about each thing is the one about what it is in itself, and the false one too, if this is so of a true belief. Thus the belief that what is good is not good is a false belief about what is in itself, whereas the belief that it is bad is a belief about what is accidental. Therefore the belief of the negation will be more false than the belief of the contrary. Although we explained all this most diligently in the careful commentary of the first edition, we will repeat the same explanation here too, so that the explanation in this book will not seem short. The argument starts like this. If when a true proposition is proposed there are several false propositions which cancel it, the one among them which is the more false will be the more contrary to the true proposition. Thus we must look for what is the more false under the many false propositions, so that it might be seen as more contrary to the true proposition. But we must say what happens in the case of truth. For since something can be said truly both in itself and accidentally, what is said in itself rather than what comes accidentally possesses the nature of truth to the greatest extent. Thus if someone thinks about the good that it is good, he possesses a true belief according to the thing itself; but if someone thinks that the good is useful, he will think something true, but that truth about the good is accidental to the good. For it is accidental to the good that it is also useful. Thus the proposition which considers the good to be good is true in itself, i.e. it is true in its very self, whereas that which considers the good to be useful is true accidentally. Thus the proposition which considers the good to be good is nearer to the nature of goodness than that which considers the good to be useful. But if this is so, the proposition which is true in itself is truer than the one which is true accidentally. Then once we have established this we must say the same about falsity too. For the false proposition which is contrary to a proposition which is true in itself, is more false than the one which cancels a proposition which is true accidentally. For if a proposition which considers some truth about the nature of the thing itself is truer, then the one which cancels the truer proposition will be more false. But if the one which makes a statement about the accident of a thing, although it is true, is however less true, the one which cancels a less true proposition will also be less false. Once we have established this let us now see what holds in the beliefs or propositions which we have been dealing with. We will use the same example. As we said above, what is good is both good and not bad, but that it is good is according to itself, that it is not bad is accidental to it. For that it is good is good by its nature, that it is not bad is a secondary and in a way accidental. Thus the belief of the good

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that it is good will be truer and closer to its nature than the idea of the good that it is not bad. Then if this is so and the proposition which cancels a truer belief is more false than the one which cancels a proposition which, though true, is less true, it is clear that a negation is more false than the affirmation which posits a contrary. For the negation says that what is good is not good, the affirmation that what is good is bad. The negation, what is good is not good, cancels the essential belief, the good is what is good, whereas the affirmation of the contrary, that the good is bad, cancels the true belief, which holds accidentally of the good, that what is good is not-bad. It is agreed then that the belief that the good is not good is more false than the belief that what is good is bad. But if this is more false, it is more contrary. Thus the belief of a negation is more contrary than that of a contrary affirmation. Then having dealt with the meaning, we must discuss the actual wording. Then, if what is good, is good and is not bad, the former in itself, i.e. that the good is good, the latter accidentally, i.e. that the good is not good, (for it is accidental to it to be bad), the more true belief about each thing is the one about what it is in itself; for what is according to the nature of a particular thing is closer to the thing according to whose nature it is; thus the truth of the thing in itself, because it is closest to the thing, is truer than the truth which is accidental. And this is what he means by the more true belief about each thing is the one about what it is in itself. But if this is so the false one too, i.e. the falsity which cancels a belief or proposition which is true in itself is more false, if the belief true to the nature of the thing itself is truer than one which is true accidentally; this is what he means by if this is so of a true belief. He confirms this exposition with an example: thus the belief that what is good is not good is a false belief about what is in itself, i.e. the belief that what is good is not good is opposed to the belief which was true in itself. This is demonstrated by the words thus the belief that what is good is not good is a false belief about what is in itself, i.e. the belief which denies that the good itself is good is in itself a false belief of the true proposition, i.e. it is opposed to it; for falsity is opposite to truth. Whereas the belief that it is bad is a belief about what is accidental. This is the false belief which considers that what is good is bad and which fits the proposition which is true accidentally, i.e. which considered the good to be bad. Therefore the belief of the negation will be more false than the belief of the contrary, i.e. the negation of the contrary is more contrary than the affirmation of the contrary, if when both are predicated of the good, the negation is found to be more false. But to say that it is accidental to the good that it is not bad, must not be understood in the way we are accustomed to say that something is an accident to a substance. For this can not come about, whereas to be accidental here is to be understood as meaning ‘secondarily’. For

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what is good is said to be good primarily, but said to be not bad secondarily. And this is derived from the similarity of the substance and the accident. For each substance is primarily a substance, and secondarily either white, two-footed, lying or whatever can be an accident to substances. 25b21-5 But he who holds the contrary belief is more wrong in each case; for contraries belong to those things which differ most with regard to the same thing. But if one of these is contrary, yet the belief of a contradiction is more contrary, it is clear that this will be the contrary. The force of the whole argument in brief is that every true thing is true either in itself or accidentally. Therefore everything false must be false either in itself or accidentally. But it is agreed that the truth which is so in itself is truer than that which is so accidentally. Then whoever holds a belief about anything that is contrary to the thing itself, must be most wrong. For there is a contrariety of beliefs whenever there are beliefs about one and the same thing which differ greatly from each other. Then what is more false will also be a contrary falsehood. For what is more distant from the truth will be more a falsehood. But beliefs which differ very greatly from each other are contrary. In beliefs, then, the one which is most false is the contrary. And the one which is most false, as we have said, is the one which is false in itself, i.e. which cancels a proposition which is true in itself. Therefore, for this is a negation, a negation is the contrary of an affirmation rather than an affirmation positing the contrary. This is the meaning expressed in the words but he who holds the contrary belief is the more wrong in each case. For although anyone can be wrong, even if he does not have a contrary belief about the same thing, he is more wrong, however, who does have a contrary belief. He explains how this happens: for contraries belong to those things which differ most with regard to the same thing. For the main reason why contrary falsehoods are held is that contrariety is found only in things that have the greatest disagreement. But if one of these is contrary, i.e. but if it is necessary that one of the propositions which is false in itself or accidentally is a contrary, yet the belief of a contradiction is more contrary, i.e. a negation is more false (this is what he means by more contrary where the sense is the equivalent of saying that the belief of a contradiction is more false, i.e. a negation is more false); he then concludes that if what has been said is the case it is clear that this, i.e. the belief of a contradiction, will be the contrary. 23b25-7 The belief that the good is bad is complex, because the same person must perhaps believe that it is not good.

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After he has proved that the negation is rather the contrary, because this is more false than the affirmation of the contrary, and has shown that the proposition and belief which denies what has been proposed is the contrary because of the way it distinguishes falsity, he now tries to prove the same thing from simple and complex propositions and beliefs. For he says that an affirmation which posits a contrary is complex and not simple. And it is complex because the belief that what is good is bad must also automatically involve the belief that what is good is not good. For a thing cannot be bad unless it is not good. Thus whoever thinks that what is good is bad, thinks both that a good thing is bad and that the very same thing is not good. The belief about the good that it is bad is, then, not simple; for it contains within it the belief that it is not good. But the person who thinks that what is good is not good, must not also think that it is bad. For something can be both not good and not bad. And this comes to an end where a median state can be found. This, too, he added in a very cautious way. Then once it is established that the belief of a contrary is not simple, whereas that of a negation is simple, a simple belief must appear to be the contrary of simple belief. But the simple belief about the good that it is good is true, while the simple belief about the good that it is not good is false. Therefore the contrary of the simple belief about the good that it is good is the belief of the negation that it is not good. The general force of this argument is derived from the fact that whenever there is any true proposition and two propositions which can cancel it, if one of them cancels the true proposition without requiring anything else, but the other cannot cancel the same true proposition without the first, then the one which is self-sufficient and does not require anything else to be able to cancel the proposed proposition, must be said to be more its contrary. And only the self sufficient belief that what is good is not good can cancel the true proposition about the good that it is good and leads to its destruction. The one that considers it to be bad is not sufficient on its own, unless the belief that what is good is not good comes to its aid. For the latter contrary does away with it because it brings the negation along with it. It is clear that the one which is sufficient of itself to destroy the true proposition is rightly seen to be its contrary rather than the one which is not in itself sufficient unless the force of the negative proposition is added to it. 23b27-32 Further if the same thing holds in other cases, it will seem that we have given the right explanation here; for the belief of contradiction is [the contrary] either everywhere or nowhere. But where things have no contraries, there is a false belief about them which is opposite to the truth, e.g. he who thinks a man is not a man is wrong. Then if these are contraries, so too are other beliefs of the contradiction.

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If what we say about these propositions, he explains, is found in everything, then what we are saying ought to be firm. For it is unlikely that negations are contraries in some propositions, but in others affirmations proposing a contrary. But if it is found in all propositions and contradictions that a contradiction is more the contrary, i.e. a negation, than a proposition holding a contrary, there is no doubt that this schema exists everywhere. But if in some the proposition of a contrary is more a contrary than a negation, it is clear that here too the same is the case. For wherever contrariety can be found there is a doubt as to what the contrary is, whether the affirmation of a contrary or the negation of the proposition. Thus where there is no doubt, one must enquire why this is so. And there is no doubt where there is no contrariety, as with substances. For here the only contraries are negations. Thus if the belief about a man that it is not a man is opposed to the belief about a man that it is a man, it is clear that in other cases too where contrariety is found, the negation takes the place of the contrariety.70 For what use is it when we say of man, because it does not have a contrary, that the negation is the contrary, but when of the good, because it does have a contrary, that it is not in the negation but rather in the belief that proposes a contrary? For whatever is converted by a negative ought in every case to keep its own force. Then what is said by Aristotle, to put it briefly, is as follows. If in other cases the negation is the contrary, it is clear that the negation is the contrary here too. But if in other cases it is not so, the same applies in the cases which he mentioned above. But in all the other cases where contrariety is not found, contradiction takes the place of contrariety, and in those where some contrariety is found, it will take the same and no other place. He explains this in the following words. Further if the same thing holds in other cases, it will seem that we have given the right explanation here; for if it must be so in all the other cases, what we have said to hold in the cases mentioned above and what we said there will seem to be right. For the belief of contradiction is [the contrary] either everywhere or nowhere. * * *71 in one place a contrary is found, in another it is not. But where things have no contraries, e.g. in substances where there is no contrary (The Categories showed us this, if we remember correctly), here is a false belief about them which is opposite to the truth, i.e. in these is found a false belief which is opposite to the true belief, but it is clear what it is. For where there is not contrariety, it remains that the belief of a contradiction is the contrariety, e.g. he who thinks a man is not a man is wrong. For this is the only contrariety to be found of the true proposition. Then if these are contraries, so are also those others which are beliefs of the contradiction, i.e. if in those which do not have a contrariety, their negations are contraries (for there must be some contraries), in all the others, too, where there is some contrariety, e.g. in good and bad, the negation takes the place of the contrary.

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23b33-24a3 Further the belief about the good that it is good and about the not good that it is not good are similar; and in addition to these that about the good that it is not good and about the not good that it is good. What then is the contrary to the true belief about the not good that it is not good? For it is not that which says it is bad; for this will sometimes be true at the same time; but a true belief is never contrary to a true one; for there is something not good which is bad; therefore they both happen to be simultaneously true. Nor is it the belief that it is not bad; for these too will hold at the same time. It remains, then, that the belief about the not good that it is good is the contrary of that about the not good that it is not good. Therefore the belief, too, about the good that it is not good is the contrary of that of the good that it is good.

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He now confirms what has been said just before with a stronger argument by ratio. Ratio is in fact the mutual similarity of things to each other. Then if four propositions are made, two of which precede, the other two following, and the first is related to the second as the third to the fourth, it is necessary that the first relates to the third as the second to the fourth. We can understand this very easily and concisely when expressed in numerals. Make the first number II, the second VI, then begin again with IV as three and XII for four. II IV

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So in the diagram the leading propositions are two and four, the following ones six and twelve. Four is to twelve is as two to six. For just as two is a third of six, four is a third of twelve. Therefore just as the preceding four relates to its sequent, so the other preceding number will relate to its sequent. But two is half of the preceding four, and six is half of twelve. Thus one should notice in every ratio that, if with four proposed things, the third is be to the fourth as the first to the second, then the second will be to the fourth as the first to the third. Then transfer the numerical ratios to the force and nature of propositions and put two propositions first, of which one precedes, the other follows, and then another two, one of which precedes, the other follows in the same way, and let there be a similarity. For the first is to be about the good that it is good, then follows that of the good that it is not good. Then make the leading third the proposition about the not good that it is not good, and following this the fourth about the not good that it is good.

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Then work out the similarity of ratio in these. The first, about the good that it is good, is to the second, about the good that it is not good, as is the third, about the not good that it is not good, is to the fourth, about the not good that it is good. For just as the proposition about the good that it is good is true, but that about the good that it is not good is false, so too the proposition about the not good that it is not good is true, but that about the not good that it is good is false. But if this is so and the belief about the good that it is not good relates in the same way to that about the good that it is good, as the belief about the not good that it is not good relates to the belief about the not good that it is good, the first will relate to the third as the second to the fourth. Then just as the belief about the good that it is good relates to that about the not good that it is not good because they are both true, so will that about the good that is not good relate to the belief about the not good that it is good, because they are in fact both false. For the latter are both simultaneously false, as the former are simultaneously true. Therefore the second is to the fourth as the first is to the third. Then now that we have demonstrated these ratios, arrange the same propositions without changing their order [of ratio]. The proposition about the not good that it is not good should be put first and following it that about the good that it is good; then under these in the leading position as third, about the not good that it is good and following this as fourth that about the good that it is not good.

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Then, as has been demonstrated above, the belief about the not good that it is not good relates to that about the good that it is good just as that about the not good that it is good relates to that about the good that it is not good. For just as the former are both simultaneously true, the latter are simultaneously false, and there is the same ratio. Thus the first, about the not good that it is not good will relate to the third, about the not good that it is good, as the second, about the good that it is good, to the fourth, about the good that it is not good. Then we must now ask what is the relationship of the first to the third so that we can work out that of the second to the fourth. I mean that the belief that what is not good is good is contrary to the belief that what is not good is not good. Then place, if it is possible, the belief that what is not good is not good opposite the belief that what is not good is bad. But this is not possible; for contrary beliefs are never both simultaneously true, but these two can be simultaneously true. For if someone thinks that parricide, which is not good, is not good, and also thinks that parricide, which is not good by nature, is bad, he has a

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true belief in both. Therefore the belief that what is not good is bad is not the contrary of the belief that what is not good is not good. Again put the belief that what is not good is not bad opposite the belief about the not good that it is not good. This too is sometimes the case; for it can happen that what is not good is also not bad. For not all things that are not good are automatically bad, but it can happen that some things are not good, but are nevertheless not bad either. If someone, for example, thinks that a stone that is lying there to no purpose, which is in itself not a good thing, is not good, he will have a true belief; and if the same man thinks that the stone lying there, which is not a good thing, is not bad, nothing false enters his belief. And so because the belief about the not good that it is not good is found sometimes to be true both with that about the not good that it is bad and with that about the not good that it is not bad, it is the contrary of neither. It remains then that the belief about the not good that it is not good is the contrary of the belief that what is not good is good, i.e. about the not good that it is good. Thus the belief about the not good that it is not good is the contrary of that about the not good that it is good. But the belief about the not good that it is good related to that about the not good that it is not good as the belief about the good that it is good related to that about the good that it is not good. But the first and the third are contraries; then the second and the fourth, because of the similarity of their ratio, are doubtless also contraries. It can also be more simply understood in the following way. If the belief about the good that it is good and about the not good that it is not good are similar in being true, and that about the good that it is not good and about the not good that it is good are also similar in being false, should one of the true beliefs be found to be contrary to one of the false ones, the remaining false one will be contrary to the other true one; and this is brought about by their similarity alone. But in fact one of the false beliefs is shown to be contrary to one of the true ones, as we explained above, i.e. the belief that what is not good is good is contrary to the belief that what is not good is not good. It remains then that the belief that what is good is not good is contrary to the belief that what is good is good. Thus we conclude that a negation is the contrary of a true affirmation rather than an affirmation stating the contrary. We have explained, then, this complex idea in what we have said above; the actual wording is as follows. Further the belief about the good that it is good and about the not good that it is not good, which are both true, are similar; and in addition to these that about the good that it is not good and about the not good that it is good, both being false. What then is the contrary to the true belief about the not good that it is not good? This is put in the form of a rhetorical question. For it is not that which says it is bad; because it could sometimes be simultaneously true. But this is not the case with contraries. For a

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true belief is never contrary to a true one. But how can it happen that they are both true at the same time? Because there is something not good which is bad; therefore they both happen to be simultaneously true. Nor is it the belief that it is not bad; for these too will hold at the same time, i.e. they can sometimes both be true at the same time, especially where it is a question of good and bad. It remains, then, that the belief about the not good that it is good, which is false and cannot be found to be true at the same time is the contrary of that about the not good that it is not good, which is true. Therefore, he returns to the similarity of relationship stated above, the belief, too, about the good that it is not good is the contrary of that of the good that it is good. But if anyone looks carefully at what was said above, he will not make a mistake about the structure of the doctrine as a whole or about any detail of the arrangement. 24a3-6 But it is clear that there is no difference even if we state the affirmation universally. For the universal negation will be contrary to it; e.g. the belief that none of the things that are good is good [is the contrary] of the belief that everything that is good is good. In the previous argument all the explanations concerned indefinite propositions. But because someone could perhaps have imagined that the same pattern could not be found in definite propositions and that there could be some difference as to whether the same argument applies to definite propositions, he added the comment that it makes no difference with them whether one uses the same argument that he had applied above to indefinite propositions, in the case of universal propositions, which are of course already definite. For if someone arranges definite propositions in the order he gave for indefinite propositions and considered them with regard to their predication, he would find that the contrary of the belief of a universal affirmation is none other than the belief of a universal negation. For there is no difference between indefinite and definite propositions other than that indefinite propositions are without a determination, while definite propositions have the addition of a determination, whether it is universal or particular. This is what he means by there is no difference, even if the affirmation is stated universally. For a universal negation is the contrary of a universal affirmation, e.g. the belief that none of the things that are good is good, i.e. the belief of the universal negation is the contrary of the belief that everything that is good is good, i.e. the belief of the universal affirmation. He then shows why this occurs. 24a6-b1 For the belief about the good that it is good, if it is good universally, is the same as the belief that whatever is good is

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good. does not differ from the belief that everything that is good is good. And it is the same in the case of the not good. He has gradually brought the indefinite proposition into similarity with the universal. He says that an indefinite proposition becomes a universal if the everyday expression ‘whatever’ is added to it, so that it is in no way different from the proposition which predicates ‘every’ of the thing in affirmation. For example, the belief or proposition about the good that it is good is that the good is good. If we add ‘whatever’ to this to give ‘whatever is good is good’, it is no different from the belief that everything good is good. Therefore the validity of the previous argument in the case of indefinite propositions applies also to universals, which differ only to the small extent that it applies not to the quality or the force of the proposition but to its quantity. For it is the universality of quantity that is stated. That is the general meaning; the wording is as follows. He had stated above that there is no difference whether a proposition is indefinite or universal. Why there is no difference he explains as follows: for the belief about the good that it is good, i.e. an indefinite affirmation, if it is good universally, i.e. if ‘good’ is expressed universally, is the same as the belief that whatever is good is good, i.e. there is no difference from the belief that good is good. And this belief does not differ from the belief, which is clearly stated universally, that everything that is good is good. And it is the same in the case of the not good, i.e. we speak of the not good in the same way. For the proposition or belief that what is not good is not good, if universality is added to it, does not differ at all from the proposition that whatever is not good is not good. And this does not differ at all from the universally stated proposition, everything that is not good is not good. 24b2-6 Therefore, if this is how it is with beliefs, and spoken affirmations and negations are symbols of those72 in the soul, it is clear that a universal negation about the same thing is contrary to an affirmation, e.g. the contrary to ‘every good is good’ or ‘every man is good’ is that ‘no [good is good]’ or ‘no [man is good]’, while ‘not every’ [man] or ‘not every’ [good] are opposed contradictorily. He brings all the previous arguments together and steers the entire thrust of the enquiry to a conclusion. For he had previously said above that negations and affirmations and their contrary relationships should be considered as concerned with beliefs, while now, since he has found the universal negation to be a contrary in beliefs, he applies the same [principle] to propositions, which, it is clear, designate the affections of the soul, because they are spoken sounds

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and significant. For at the beginning of the book he rightly told us that significant spoken sounds reveal the affections of the soul; and now, as though to prove it, he thinks, that because with beliefs the contrary to a universal affirmation has been found to be a universal negation rather than the affirmation of the contrary of a universal affirmation, the same too occurs in spoken sounds, i.e. that it is not the affirmation stating the contrary to a universal affirmation that is its contrary, but the universal negation, while when there is a universal affirmation and a particular negation, they are contradictories. And this is said very clearly and there is no error in the wording. But let us follow the exact wording here too, just as we left nothing ambiguous in the rest of the text. Therefore if this is how it is with beliefs, i.e. that the belief of a negation rather than an affirmation stating a contrary is found to be contrary to the belief of an affirmation, and spoken affirmations and negations are symbols of those in the soul, (for just as there is affirmation and negation in spoken sound, so also is there in belief, when the soul itself affirms or denies something in its thinking, as we have explained carefully elsewhere); therefore because the affirmations and negations in spoken sound are symbols of the affirmations and negations in the soul it is clear that a universal negation about the same thing is contrary to an affirmation. He adds about the same thing so that we do not say that disconnected affirmations and negations are contraries, but that an affirmation and negation universally affirm and deny of one and the same thing; and instances of these are e.g. the contrary to ‘every good is good’ or ‘every man is good’ is that ‘no [good is good]’, which is contrary, or ‘no [man is good]’, while ‘not every’ [man] or ‘not every’ [good] are opposed contradictorily, i.e. ‘not every man is good’ is contradictory to ‘every man is good’ and ‘not every good is good’ is contradictory to ‘every good is good’. Thus it is agreed that among the propositions which he stated above the contrary of the affirmation ‘every man is just’ is ‘no man is just’ rather than ‘every man is unjust’. 24b6-9 And it is clear that it does not happen that a true belief or contradiction is the contrary of a true one. For contraries embrace their opposites and it is possible for the same person to say the truth about the same opposites, but it is not possible for contraries to be in the same thing at the same time. After this he brings the book to an end by a discussion and demonstration with which he tries to prove that two true propositions are not contraries, although this is true and clear to all. The argument starts as follows. Things that are contrary are opposites; but opposites cannot be present at the same time in the same thing; thus contraries cannot be present at the same time in the same thing. But things about which something true can be said at the same time, can

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be present at the same time in the same thing, whereas those which cannot be present at the same time in the same thing cannot be the subject of simultaneously true propositions, an affirmation and a negation. But contraries cannot be in the same thing at the same time. Therefore, statements which say the truth at the same time are not contraries because what can be both affirmed and denied as true at the same time, are in the same thing at the same time. Therefore, statements that are both true at the same time are not contraries. This is the meaning; the wording is as follows. And it is clear that it does not happen that a true belief or contradiction is the contrary of a true one, i.e. that two true propositions cannot be contraries. If a true belief is not the contrary of a true belief, much less so is a contradiction which arises from beliefs. He has put ‘contradiction’ here for contrary, as the question here is not about contradiction. For contraries embrace their opposites, i.e. every contrary is an opposite, and it is possible to say the truth about the same opposites, because there can be a simultaneously true negation and affirmation only about what can be in the same thing at the same time, but it is not possible for contraries to be in the same thing at the same time. Then the conclusion is that because things about which there is a simultaneously true affirmation and negation, can be in the same thing at the same time, and contraries cannot be in the same thing at the same time, statements that are true at the same time cannot be contraries. Our task, too, has now come to rest in a tranquil harbour. For I do not think that anything has been left out which would lead to a full understanding of this book. Then if we have achieved our aim with dedication and application, it will be of use to those who will be gripped by the desire to understand these things properly. But if we have fallen short of our aim to sort out the very abstruse ideas in this book, our work will not be blamed for harming others, even if it does no good.

Notes 1. Note the quite different interpretations of this sentence advanced by Shiel and Ebbesen. Shiel p. 361 (Sorabji, 1990): ‘The textual sequence is obscure and it is supplemented by extremely obscure scholia’; Ebbesen ibid. 376 n. 15: ‘the doctrines of this book are very obscure, and on top of that the manner of presentation is obscure’. These reflect the differing views of the two about the sources available to Boethius, Shiel arguing that he had only scholia, Ebbesen that he had access to full commentary editions, particularly of Porphyry. 2. Shiel (Sorabji, 1990) p. 365 thinks that he is referring here to his Introduction to Syllogisms. 3. 61-3. 4. cf. 115. 5. Literally ‘what can do the same thing’. 6. Int. 16a30-1. 7. Int. 16b11-15. 8. i.e. of verbs at 16b6-7. 9. Int. 16b6-7. 10. cf. 128,13f. 11. An. Pr. 1.46, Int. 19b31f. 12. A reading rejected by Alexander but either found in the text or reported by Herminus and Porphyry with whom Boethius agrees that it makes no difference to the sense. 13. See the full list in 323-4 and the discussion in 294ff. 14. This refers just to the position of the Greek esti (is) which in Greek may naturally be positioned at the beginning of these propositions, whereas the Latin est would have a different meaning if put first and so has to be put at the end of the sentence to translate Aristotle correctly. 15. Int. 16b19. Cf. 71ff. 16. cf. 368f. 17. It should be noted that the reading given here in the lemma is also the one adopted in the translation and there is no mention of the more ‘demanding’ variant in the short commentary. 18. Meiser suggests a lacuna here. What follows gives an objection raised by some unspecified people that the relationship of the following propositions is different and that there is therefore no consistency in them: a privative negation follows a simple affirmation, a simple affirmation does not follow an infinite negation. This objection requires a little more introduction than is given in the MS. 19. cf. 177. 20. 288-302. 21. 276-94. 22. 149. 23. Int. 19b11-12; cf. 256. 24. Added by Meiser. 25. 311.

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Notes to pages 47-93

26. Theaetetus 186B-C. 27. i.e. between ‘is not’ and ‘is not x’; i.e. ‘is’ as an indefinite verb and ‘is’ as definite with the negative attached to the participle. 28. I have changed the MSS correction finitum ‘finite’ back to the uncorrected indefinitum ‘indefinite’. 29. 18,26. 30. Int. 20a1. 31. 150,27f. 32. The order of these two propositions in the Greek text is reversed in Minio-Paluello’s edition. Boethius’ order is found in cod. Ambrosianus (saec. ix) and Ammonius. 33. Added by Meiser. 34. Boethius gives two further word orderings which, though possible in Latin, would be even more misleading in English (‘man white is’, ‘white man is’: homo albus est, albus homo est); I have therefore omitted them from the translation. 35. Cic. in Catilinam 1.10 §25 ad hanc te amentiam natura peperit, voluntas exercuit, fortuna servavit. Alternative version: ad hanc te amentiam perperit natura, exercuit voluntas, servavit fortuna. 36. Virgil Aeneid 6.852 pacique imponere morem. Alternative version: moremque imponere paci. 37. The word order differs in Latin – homo albus non erat, homo non albus est. 38. 178,9f. 39. For the latter see Pliny 9,35.55 canis marinus, and in mythology of the dogs of Scylla Lucretius 5.890 and Virgil, Aeneid 3.432. 40. cf. Top. ch. 8. 41. Eudemus: an emendation of Meiser for the MS audivimus. Courcelle emends to Ammonius, but Shiel p. 357 (Sorabji, 1990) has confirmed the emendation ‘Eudemus’. The point is important as it would remove the only direct evidence that Boethius had access to the works of Ammonius. For Eudemus of Rhodes, a pupil and friend of Aristotle, see Wehrli, Die Schule des Aristoteles 8 (2nd edition 1969), Fr. 25. 42. A standard concept developed, for example, by Cicero in the context of the political realities of Republican Rome. 43. The idea contained in these two sentences is also found in Ammonius in Int. 212,2-6. 44. Ackrill (1963) p.149 translates Aristotle’s endekhomenon with ‘admissible’ to avoid the ‘misleading’ connotations of the traditional translation ‘contingent’. I have, however, retained the latter to echo Boethius’ translation of the Greek word as contingere. 45. Meiser suspects a lacuna in the text at this point. 46. Int. 22b29f. 47. Here dictio. 48. I have followed S2. in deleting the words non enim propositionis. 49. We have to understand to walk and to be here as equivalents, as he has explained above. 50. To be here refers to is in is possible. 51. i.e. in the Latin order which cannot be so well reproduced in English. 52. Int. 21a34-7; Boethius 376. 53. The Latin is Socrates speaks well but this does not display his point in English. 54. 402,12f.

Notes to pages 94-138

143

55. Int. 21b35f. 56. Int. 22a3-4. 57. The Greek text reads to be or not to be. Boethius has neither of the infinitives (M-P’s apparatus notes the omission of the second infinitive in an eighth-century Syriac translation). 58. Note the quite different emphasis and interpretation of Shiel’s translation of this sentence (Sorabji, 1990) p. 361: ‘For there are scholia of numerous points heaped up all together and so I have spent almost two years in a constant sweat of writing comments.’ 59. Adding negationes with F2. 60. Lacuna as Meiser thinks. 61. 423,21-4. 62. The Latin terms possibilitas (possibility) and potestas (capacity) are related. 63. 458,24f. 64. Cat. 15a13ff.: generation, destruction, increase, diminution, alteration, motion. 65. Phys. 260a26-b7 where motion, alteration and increase are listed. 66. cf. Porphyry Sententiae 31 and 32. 67. Thus in Boethius, the Armenian text and cod. Marcianus (saec. x). MinioPaluello reads ‘actualities’. 68. Thus in Boethius, the Armenian text and cod. Marcianus (saec. x). MinioPaluello reads ‘never actualities but only potentialities’. 69. Cat. chs 10-11. 70. I have followed Meiser in deleting several lines here. 71. Meiser notes a possible lacuna here. 72. Either earum ‘of those’ with reference to the affirmations and negations or eorum ‘of things’. Meiser adopts the former reading, although the MSS all give the latter, based on the continuous translation where two MS give earum. This is confirmed by Boethius’ own paraphrase, 501,11-17. The Greek, which is ambiguous, is interpreted by Ackrill as ‘of things’.

Select Bibliography Greek text of Aristotle De Interpretatione: Aristotelis Categoriae et Liber De Interpretatione, ed. L. Minio-Paluello, Oxford 1949. Latin text of Boethius’ second commentary on De Interpretatione: Boetii Commentarii in Librum Aristotelis PERI ERMHNEIAS, pars posterior, rec. Carolus Meiser, Lipsiae 1880. Latin text of Boethius’ first commentary and translation of De Interpretatione: Boetii Commentarii in Librum Aristotelis PERI ERMHNEIAS, pars prior, rec. Carolus Meiser, Lipsiae 1877. Aristoteles Latinus I.1-5, ed. L. Minio-Paluello, Bruges 1961. Ackrill, J.L., Aristotle’s Categories and De Interpretatione, Oxford 1963. Arens, H., Aristotle’s Theory of Language and its Tradition: Texts from 500 to 1750, Amsterdam-Philadelphia, 1984. Chadwick, H., Boethius: The Consolations of Music, Logic, Theology, and Philosophy, Oxford 1981. Courcelle, P., Les lettres grecques en occident, Paris 1948 (2nd edn). Ebbesen, S., ‘Porphyry’s legacy to logic: a reconstruction’, in Sorabji 1990, 141-72. Ebbesen, S., ‘Boethius as an Aristotelian commentator’, in Sorabji 1990, 373-92. Hadot, I., ‘Les introductions aux commentaires exégétiques chez les auteurs néoplatoniciens et les auteurs chrétiens’, in M. Tardieu (ed.) Les règles de l’interprétation, Paris 1987. Heinze, R., Xenokrates, Leipzig 1892 (reprint Hildesheim 1965). Magee, J., Boethius on Signification and Mind, Philosophia Antiqua LII, Leiden 1989. Shiel, J., ‘Boethius’ commentaries on Aristotle’, in Sorabji 1990, 349-72. Sorabji, R. (ed.), Aristotle Transformed, London 1990. Sorabji, R., ‘The ancient commentators on Aristotle’, in Sorabji 1990, 1-30. Tarán, L., Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary, Leiden 1981. Usener, H., Review of Meiser, Deutsche Literaturzeitung 370, 1880. Wehrli, F., Die Schule des Aristoteles 8, Basel 1969 (2nd edn).

English-Latin Glossary addition: adpositio affection: passio affirmation: adfirmatio belief: opinio capability: potestas category: praedicamentum combination: conplexio, conpositio combined: conpositus communication: interpretatio concept: conceptio conjoined: coniunctus conjunction: coniunctio convention, by: positione, secundum placitum defined: definitus definite: definitus denote: designare determination: determinatio disposition: adfectio division: divisio element: elementum equivocal: aequivocus equivocation: aequivocatio essence: esse expression: dictio finite: finitus image: imago imagination: imaginatio, imago indefinite: indefinitus, indeterminatus individual: individuus infinite: infinitus intellect: intellectus name: nomen negation: negatio particular: particular particularity: particularitas

privation: privatio property: proprietas proposition: propositio proprium: proprium quality: qualitas relation(ship): habitudo sense-perception: sensus sentence: oratio separation: divisio sign: nota significant: significativus signification: significatio signify: significare, signare signify, additionally: consignificare simple: simplex single: singulus singular: singularis sound: sonus speech: oratio spoken sound: vox state: habitus statement: enuntiatio statement-making: enuntiativus subject: subiectum substance: substantia term: terminus, vocabulum, verbum, nomen thing: res thought: intellectus univocal: univocal utter: profero utterance: locutio prolatio verb: verbum will: voluntas word: sermo, verbum, vocabulum, nomen, particular

Latin-English Index * indicates that the listed Latin word is used by Boethius for the marked Greek word in his translation of de Interpretatione or Categories or is specially glossed by him. adfectio, disposition, 11,25 adfirmatio (*kataphasis, phasis), affirmation, 13,27 adpositio (prosthesis), addition, 391,18 aequivocatio, equivocation, 39,28 aequivocus (*homonumos), equivocal, 16,12 conceptio, concept, 8,1; conception 21.13 = intellectus coniunctio (*sundesmos), conjunction, 5,7: connecting, 16,31 coniunctus, conjoined, 5,10 conplexio (sumplokê/), combination, 173,8 conpositio (*synthesis), combination, 43,30 conpositus (*sunthetos), combined, 5,10 consignificare, additionally signify, 65,29 contradictio, contradiction, 99,29 (contradictory) contradictorius, contradictory, 199,22 contrarietas, contrariety, 158,1 contrarius, contrary, 19,30 definitio, definition, 4,26 definitus, definite, defined, 62,3 (opposite of indefinitus) designare, denote, 5,17 determinatio, determination, 138,12 dictio (*phasis), expression, 5,7 divisio (*diairesis), division, separation, 43,30 = separatio elementum (stoikheion): element, 4,24 (written letter, sound of a letter, 21,6) enuntiatio (*apophasis), statement, 13,27

enuntiativus (*apophantikos), statement-making, 9,13 esse, essence, 17,31 finitus, finite, 256,8 habitudo (skhesis), relation(ship), 46,6 habitus (hexis), state, 17,17 imaginatio (*phantasia, phantasma), image, mental image, mental imaging, 28,1 imago, image, 35,6 indefinitus (= indeterminatus), indefinite (opposite definitus), 138,3 indeterminatus, 144,17 = indefinitus individuus, individual, 179,7 infinitus (*aoristos), infinite (opposite of finitus), 61,7 intellectus thought 8, 1(*noêma) = conception; intellect, 7,16; comprehension, 9,4 intelligentia, mind, 29,2; thought, 136,9 interpretatio, communication, 6,3 locutio (*lexis), utterance, 5,4 = prolatio negatio (*apophasis), negation, 13,26 nomen (*onoma), name, 8,11; word, 12,27; term, 7,2 nota (*sumbolon, sêmeion), sign, 25,7 opinio, belief, 467,2 oppositio, opposition, 160,26 oratio (*logos), sentence, 8,11, speech, 13,6 particula, word, 48,12 particular, particular, 69,14 particularitas, particularity, 69,4 passio (*pathêma), affection, 25,7

Latin-English Index positione (*thesei): by convention, 23,5 potestas, capability, potentiality, 446,24 praedicamentum (*katêgorêma), category, 4,14 privatio (sterêsis), privation, 17,18 profero, utter, 47,4 prolatio, utterance, 18,10 = locutio propositio, proposition, 12,19 proprietas, property, 138,29 proprium, proprium, 18,32 qualitas, quality, 7,22 res (*pragma), thing, 20,16 secundum placitum (*kata sunthêkên), by convention, 52,29 sensus (aisthêma, aisthêsis): sense perception, faculty of sense perception, a sense perception, 24,17; meaning, 36,24 separatio = divisio, 49,22 sermo, word, 5,6

149

significare = signare (sêmainô, dêloô), signify, 6,14 significatio, signification, 6,24 significativus (*sêmantikos), significant, 5,23 simplex, simple, 7,23 singularis, singular, 135,24 singulus, single, 86,8 sonus (*psophos), sound, 4,26 subiectum (hupokeimenon), subject, 18,6; what underlies, 136,2 substantia, substance, 17,31 terminus, term, 100,5 universalis, universal, 15,28 univocus (*sunônumos), univocal, 16,14 unus, one, 5,9; single, 48,28 verbum (*rhêma), verb, 8,11; word, 13,24; term, 12,6 vocabulum, term, 6.7; word, 56,10 voluntas, will, 34,7 vox (*phônê): spoken sound, 4,18*

Index of Names Alexander, 272,14.28; 274,13; 292,8; 293,19.30; 317,9 Aristotle, passim with reference to de interpretatione Analytics, 264,6.12.; 382,13 Categories, 458,26; 465,31 Topics, 359,6 Aspasius, 293,29 Callias, 464,9.10 Cicero, 361,12.14 In Cat., 344,16 Diodorus, 412,16.18.19 Eudemus, 361,9 Gracchus, Tiberius, 263,22.24 Greeks, 250,21; 293,27 Herminus, 273,1; 275,5.6.31; 276,7; 293,29; 307,29; 310,16.17 Homer, 373,12f.; 374,10f.; 375,17; 376,8 Latins, 250,21

Lyceum, 266,25 Peripatetics, 352,2; 361,6 Plato, 316,13.17 Porphyry, 272,29; 276,7; 293,27; 354,25; 383,6 Roman, 332,7f.; 334,5 Socrates, 253,1f.; 254,1.4; 256,10; 266,10f.; 273,14.15; 332,f.; 334,2f.; 335,13f.; 352,23; 353,5.6.; 357,18.20; 358,2f.; 362,9f.; 363,4f.; 364,13f.; 365,7f.; 366,3f.; 370,20.24; 377,5f.; 381,3f.; 382,1; 384,26; 394,11f.; 396,15; 397,7f.; 406,9; 411,14 Stoics, 261,27; 393,13; 394,3 Syrianus, 321,21; 324,15 Theophrastus, 387,28; 389,19 Trajan, 387,2 Virgil, 344,23

Subject Index actuality/potentiality, 412,9f.; 462,1f. affections of soul, 500,16f. affirmation, 315,19f. beliefs (opiniones) signified by spoken sounds, 467,17f.; 501,12 contraries, 325,7f.; 474,1f.; 502,20f. dialectical question, 357,13f. ‘every’, 314,15f. falsity, degrees of, 484,24f. first and second edition, 250,20f.; 274,25; 421,1f.; 479,6 name, infinite, 256,3; 259,1f.; 275,6f; 337,3f. name, universal and singular, 256,9 negations position of ‘not’, 319,10f.; 345,9f.; 394,5f. relative strength of, 464,13f. two negations cannot produce a syllogism, 316,10f. possibility and contingency, 392,17f. predication and contradiction, 373,24f. connected and unconnected , 362,12f. of ‘is’ as a joined third thing, 314,6f. propositions difference in quality and quantity, 252,10f.; 256,20 indefinite as universals, 498,18f. indefinite categorical, 321,24 infinite (propositions with an infinite subject), 311,24f.; 341,9f. infinite (propositions with infinite names as predicates), 276,16 modal and simple, 377,4f.

modal: capabilities/possibilities, 453,9f.; contradictories, 422,24f.; 433,10f.; four types, 382,9f. necessity, priority of, 460,4f. negative, 378,24f.; 394,5f. possible and necessary, implications of, 447,7f. predicative, total number of, 323,10f. privative, 276,26 sequence of, 298,19f.; 307,30f. (Herminus’ interpretation); 328,1f. simple and privative, sequence of, 278,11f.; (Alexander’s interpretation )292,8f. simple categorical with an infinite name, 252,1f. simple categorical, every subject is a name or equivalent, 255,20 universal, particular and indefinite propositions, 256,16f.; 294,17f. with ‘is’ predicated as a joined third thing, 264,19f. with finite and infinite name, 258,8f. with infinite subject, finite or infinite predicate, 339,20f. singulars, 331,15f. single and multiple affirmation/negation, 351,26f. statement, simple verb always predicated, 255,15 subcontraries, 326,29 transposition of names and verbs, 344,5f. verbs, infinite, 261,15f.