The rejection of the medieval scholastic tradition that characterised the logic of the Renaissance did not imply the rejection of ancient logic. On the contrary, the philological expertise of humanist scholars made it possible to read the writings of ‘practically all classical Greek authors’.1 In particular, Aristotle’s logical writings and many commentaries on them, together with new Latin translations and revised scholastic ones, became widely available not only in manuscript form but also in print.2 This favoured a lively dialogue with ancient logical literature, even when it was tinged with criticism.

In a passage from his New Essays on Human Understanding (4.5.3–11) Leibniz distinguishes between three kinds of truth: propositional, moral, and metaphysical. Propositional truth belongs to true affirmations and negations, and consists in ‘correspondence of the propositions which are in the intellect with the things they are about’. Moral truth or truthfulness consists in ‘talking about things in accordance with the belief of our spirit’. Finally, metaphysical truth ‘is the real existence of things, in conformity with the ideas which we have about them’ and ‘is typically interpreted by metaphysicians as an attribute of being’. In ancient Greek we can find a similar tripartition of the meanings of the noun alētheia and the adjective alēthēs, which at least from the classical age (fifth–fourth century BCE) prevailed over the other terms adopted in the rich Homeric vocabulary for truth. Therefore, in ancient Greek there are three possible meanings of alētheia: (1) truth as opposed to falsehood (pseudos), (2) truthfulness as opposed to lying, and (3) reality as opposed to appearance. The first meaning is what I will call ‘logical truth’ (obviously not in the sense of ‘logical tautology’) and is an attribute of declarative sentences and of the beliefs that they express. The second meaning, moral truth, applies in particular to people, but also to oracles or dreams; in the case of people it is the ethical virtue of those who are sincere in their discourses (en tois logois),2 namely, of those who say what they believe without hiding anything, and is opposed to the moral vice of lying, which belongs to those ‘who hide something in themselves and declare something else’.3 Finally, there is reality as opposed to appearance, which Leibniz calls ‘metaphysical truth’ and which I prefer to call, faute de mieux, ‘ontological truth’; I distinguish this both from Leibniz’s definition and from the definition of it as an attribute of being given by the metaphysicians of Leibniz’s time and later by Heidegger, which Leibniz considered to be ‘a useless and almost senseless attribute’. By ‘ontological truth’ I will thus mean the attributive use of the adjective ‘true’, as applied ‘to each object, if one wants to express that it really is what it should be according to the name given to it’.4

The Greeks invented the philosophical discipline known as ‘logic’, whose core is the study and classification of valid forms of inference. Since its inception Greek logical inquiry was motivated by the need to establish the standards of correctness for philosophical reasoning and argument. Throughout antiquity this inquiry also focused on the identification, diagnosis, and classification of forms of argument that are invalid, unsound, or otherwise problematic. Within these, special attention was devoted to those forms of argument that, despite their deficiency, somehow appear to be valid, and thus can easily induce us in error, or can be exploited ‘sophistically’ to mislead others. To be able to defend oneself, by detecting the fallacies in someone else’s reasoning, was a valuable skill in a context in which philosophical discourse developed in a dialectical setting, and one’s opponents could use, whether consciously or inadvertently, fallacious arguments to (apparently) refute one’s side of the argument and to win the debate. In addition, the study of fallacies was deemed important to avoid errors in one’s own reasoning, which was construed by Plato as a sort of inner, silent dialogue which one entertains with oneself.1

Aristotle is history’s first great logician and Chrysippus is the second. We know more of Aristotle’s work than Chrysippus’ (whose works have been almost entirely lost), but we have enough at hand to identify the principal achievements of each. Aristotle’s logical particles of the syllogistic were ‘all’, ‘no’, ‘some’, and ‘non-’. Chrysippus’ were ‘if-then’, ‘it is not the case’, and ‘or’. This inclines the modern reader to see in Aristotle’s term-logic a precursor of predicate logic, and in Chrysippus’ logic the precursor of propositional logic. Because space is limited, I shall take the ancient logic of this chapter to be Aristotelian and Chrysippean logics.

Early Greek rhetoricians dealt with a wide range of persuasive techniques: emotional appeals, stylistic ornamentation, slander, and eristic tricks were all part of their repertoire. Notwithstanding this variety, there was a basic understanding that any technique of persuasion has to incorporate elements of genuine argumentation. This is why even early systems of rhetoric came to acknowledge the relevance of notions like proof, sign, probability, contrariety, etc. Still, Aristotle was the first to conceive rhetoric as an endeavour that essentially relies on arguments and, thus, requires some expertise in logic. He strikingly requires the rhetorician, who has to deal with rhetorical proofs or arguments, to be an expert in all sorts of sullogismos, or deductive argument. At the time Aristotle wrote the core of his Art of Rhetoric, he seems to have taken for granted that it is the dialectician who is the expert on all sorts of sullogismoi. The logic that he thus adopts for his account of rhetorical arguments seems to be the same logic that underlies his dialectic, which is unfolded in his Topics and Sophistical Refutations. The underlying logic of these works includes a clear understanding of deductive arguments, the difference between deductive and inductive arguments, and the role of premises, conclusions, and refutations. Most notably, it introduces the so-called topoi, argumentative schemes that enable the dialectician to construct premises from which he can derive the intended conclusion.1 These are the most important tools that Aristotle uses for reinterpreting the terminology of the traditional rhetorical manuals. For example, he takes over the traditional notion of an enthymeme, which had previously been used for condensed and antithetical formulations (see Section II below), and redefines it as a sullogismos that is used for rhetorical purposes. He also tries to adapt the sullogismos as it was defined and used in dialectic to the peculiar circumstances of a public speech, taking into account, for example, that the mostly contingent and variable subject matter of rhetorical arguments seldom allows for necessary proofs. This insight brings the role of the sullogismos, in certain cases, close to the role of the likelihoods and probability arguments, which were prominent in early rhetoric; but, unlike his predecessors, Aristotle is able to clearly distinguish between the modal quality of a premise and the (logical) necessity of a conclusion. Equipped with these logical distinctions he reinterprets the use of likelihoods in traditional rhetoric as a modal modification of the premises of a rhetorical sullogismos.

Aristotelian logic was the basis for various traditions of medieval logic: Greek, Armenian, Syriac, Latin, Arabic, and Hebrew. This chapter will concentrate on just two, the Latin and the Arabic. They are certainly the two great traditions of logic in the Middle Ages and the very different ways in which they use the ancient heritage makes a fascinating comparison. A fuller discussion would certainly include the other four traditions: they are omitted here, not just due to considerations of space, but also because scholarship in these areas has not yet reached the stage to make a survey possible.

Ever since the beginnings of philosophical thought in Greek antiquity, philosophers have made use of modalities. In particular, the concepts of necessity and ‘what must be’ played an important role in Pre-Socratic thought.1 For example, Anaximander maintained that things perish into that from which they came to be ‘in accordance with what must be’ (kata to chreōn).2 Heraclitus held that ‘everything comes about in accordance with strife and what must be (kat’ erin kai chreōn)’.3 In his poem, Parmenides asserts that what is (to eon) is entirely still and changeless because ‘powerful Necessity (Anankē) holds it in the bonds of a limit, which encloses it all around’.4 Among the atomists, Democritus identified necessity with a whirl of atoms, holding that ‘everything comes about in accordance with necessity, inasmuch as the whirl – which he calls necessity – is the cause of the coming about of all things’.5 Finally, Plato in the Timaeus describes the creation of the cosmos as the result of the interplay between divine demiurgic Intelligence and natural Necessity.6

Aristotle’s logical work has been handed down to us as a group of six treatises of variable scope, collected under the title Organon, which means ‘instrument’ or ‘tool’. The collection is opened by the Categories, a short treatise which introduces the ten Aristotelian categories, the classification of the ultimate kinds of being which Aristotle discusses or deploys in virtually all his works, but examines only substance, quantity, relative, and quality, and moves then on to the different kinds of opposition. The second treatise in the traditional order, De Interpretatione (Peri hermēneias, perhaps best translated as On Expression, but normally referred to with its Latin title), deals with language: it defines the name and the verb, and discusses what affirmation and negation are. The third treatise, Prior Analytics, turns to logic in a narrower sense, and offers a thorough and quite technical exposition of deductive arguments – its core is Aristotle’s assertoric syllogistic, the system which has dominated Western logical thought for more than two millennia. A second system, modal syllogistic, is also expounded in detail. The fourth treatise, Posterior Analytics, builds on the theory of syllogism in order to elucidate the notion of demonstration and the structure of a demonstrative science; its second book studies definition and the principles of science. The fifth treatise, the Topics, is a lengthy collection and classification of patterns for dialectical arguments, and the sixth, the Sophistical Refutations, deals with fallacies, i.e. apparently good arguments which are in fact invalid or otherwise defective.1

Greeks were intensely competitive. Their historians dated events by who had won what in the Olympics (Thucydides 3.8.1, 5.49.1, Xenophon Hellenica 1.2.1, 2.3.1); they would hold athletic contests as we might hold a memorial service (Aristotle Constitution of Athens 58.1); they staged dramas as competitive spectator sport (Aristotle Constitution of Athens 56.3–5); they had beauty contests for both men and women (Athenaeus 13.610a, Andocides 4.42); and when they sneered at competitions, this was to express their own superiority over the winners (Xenophanes DK 21B2, Thucydides 1.22.4). In particular, Greeks had competitions in which competitors strove to outdo one another in reasoning and argument. Protagoras was, according to Diogenes Laertius 9.52, ‘the first … to arrange contests of speeches’, and he declares that he has taken part in many such contests himself (Plato Protagoras 335a).

The topic of demonstration lies at the intersection of logic and epistemology. It is motivated by the following question: what features must an argument possess to be suitable for providing us with knowledge? A first, obvious thought is that it ought to be valid and to have true premises. But some ancient philosophers came to the view that this is not yet sufficient for an argument to grant knowledge of the truth of its conclusion; there are further requirements, concerning the epistemic status of its premises and the relations they bear towards its conclusion.

In considering the place and importance of definitions in ancient logic,1 the most appropriate point of departure is Aristotle’s commendation at Metaphysics 1.6, 987b1–3 of the historical Socrates (as opposed to the character portrayed in the Platonic dialogues) for being the first to focus attention on definitions in the course of his ethical inquiries, an unmistakable reference to early ‘definitional’ dialogues such as the Euthyphro, Laches, Charmides, and Meno.2 None of these works contains any occurrences of Aristotle’s term for definition, horismos, or its close relative, horos,3 but this does not automatically undermine Aristotle’s ascription. In the ethical inquiries represented in these dialogues Socrates typically begins by identifying someone who is reputed to possess expertise concerning one or another of the ethical virtues (viz. temperance, courage, justice, or piety), and then insists that anyone who really possessed such expertise should be able to say what is the object of her alleged expertise. Consequently, Socrates demands that his interlocutors produce defensible answers to questions of the form, ‘What is X?’, (ti esti X;) where appropriate substituends of ‘X’ are names of the individual virtues. For example, when the title character of the Euthyphro informs Socrates that he is prosecuting his own father for murder on a highly dubious factual basis, Socrates declares that to undertake this prosecution Euthyphro must have ‘precise’ (akribōs) knowledge of piety and impiety, and in that case he should be able to answer the questions ‘What is piety?’ and ‘What is impiety?’ (Euthyphro 4e–5d). Inasmuch as this form of question can plausibly be construed as a demand to be told what distinguishes X things from everything else, or in other words, to be given a definition of X, if we assume that Plato’s portrayal of Socrates in these texts is accurate, then they seem to support Aristotle’s historical contention that Socrates sought definitions of the virtues as part of his ethical research program.

This chapter claims that Atticus offers a fruitful case study of Epicureanism in the late Republic and can thereby contribute to broader questions of philosophical allegiance in the ancient world. There has, of course, been valuable discussion of philosophical allegiance in recent years. A reconsideration of Atticus’ Epicureanism will fruitfully extend these debates precisely because he is a not a perfect fit for any of these categories. He was not a professional philosopher; in any case, it is dangerous to assume that the thunderings of Lucretius or Philodemus on the Epicurean wise man map reliably onto the complexities of life, especially in the case of Atticus.

This chapter examines Nature's ultimatum at On the Nature of Things 3.931-962 as a contribution to the much-discussed problem of “deprivation”. This is the problem that death may be bad after all, despite the elimination of sensation, because it deprives us of the opportunity to complete projects that are worthwhile. As I try to show, Lucretius personifies Nature in order to have her argue, in her own words, for a message that Lucretius develops throughout his entire poem: this is the necessity of accepting the natural conditions of our existence. Nature underscores this necessity with the harshness of her words. At the same time, she shows that the conditions themselves are not harsh. Instead, she has provided us with ample opportunity to achieve happiness within a finite lifetime. In sum, she does not deprive us; for she has made it possible for us to flourish fully within the limits she has placed on us.