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.

This paper reexamines the intertextual connection between Lucretius and Ennius from a multi-medial angle. Ennius’ tragedies were regularly revived in the late Republic, and selections from his epic Annals appear to have been recited in public contexts as well. These performances seem to have stood in a relationship of reciprocal influence with wall paintings, as stagings inspired painters, and their artwork influenced actors in turn. Accordingly, Lucretius treats Ennius’ works as particularly influential expressions of a harmful philosophy that threatens Epicurean ataraxia in a variety of contexts. Analyzing familiar points of contact between the two authors in Book One of On the Nature of Things and highlighting a number of as-yet undiscussed allusions, I argue that Lucretius equips his readers with the tools to challenge Ennius in all three of the relevant media, be it on the page, on the stage, or in images.

After the return to the defense, Simmias and Cebes raise objections to Socrates’ kinship argument, Socrates warns them to avoid misology, and then he responds to Simmias’ objection. These objections and this warning simultaneously serve as the climax of the first half of the dialogue and set the agenda for the second. I argue that misology is a more specific problem than it is typically taken to be, a problem that aspiring philosophers (like Socrates’ companions) are especially at risk of suffering, one that involves not merely becoming cynical about arguments but positively hating them. I then turn to Simmias’ objection and Socrates’ response to it. I argue that, as Socrates interprets Simmias’ theory that the soul is a harmonia, it makes the soul a properly fitted together composite, not the formal structure possessed by such a composite. This means that Socrates is not arguing against a type of supervenience theory or epiphenomenalism, as is frequently claimed. Socrates’ arguments against Simmias’ theory highlight how it cannot explain basic ethical features of the soul that the kinship argument’s account can explain.

Socrates provides here an eschatological account that is thoroughly integrated into a novel cosmology. I argue that the Phaedo’s cosmology draws on and reflects the account of forms and ordinary objects that Socrates presented over the course of the Phaedo. The result is a distinctly Platonic account of the cosmos and the afterlife, one that treats the best parts of the cosmos as form-like and the worst parts as the source of flux. How we live now determines whether after death we will live in a more form-like or flux-like area; this dwelling, in turn, determines whether our souls are benefited or harmed in the afterlife. Since Socrates does not suggest in the Phaedo that any god is responsible for the cosmos, I argue that he avoids needing to explain why our souls can be harmed in the afterlife. In the secondary literature, this section of the dialogue is universally called “the myth,” which has led to treating the entirety of his account as having the same epistemic status. I argue instead that the account has five distinct stages, only the fifth of which Socrates calls a “myth” (muthos).

In this chapter, I examine to what extent Epicurus’ message was still relevant as such in the late Roman Republic and to what extent it had to be adapted to the new ideological and political circumstances. An analysis of books 1 and 2 of Cicero’s On Ends shows that Cicero had perfectly appropriated the Greek philosophical tradition and that he basically thought along the lines of the age-old school discussions. A typically Roman context seems to have had only limited influence on his argument: his conception of virtue, for instance, or his stress on the importance of the brilliant achievements of famous ancestors, though illustrated with many Roman examples, are borrowed from traditional Greek arguments. His attack on Torquatus’ inconsistency between words and deeds is clever and convincing, but rests on a theoretical construct. All in all, the Epicureans of Cicero’s day saw no major problems in adapting their philosophical convictions to the complex world of the Roman Republic.

This famous argument is important for understanding how, according to Socrates, we can inquire without the senses: the knowledge is already within us; the senses are merely necessary for triggering the beginning of inquiry. I argue that Socrates treats recollecting as an extended process. His claim is that learning is a type of recollecting that begins when we first perceive something and continues until we acquire knowledge of the relevant form. Moreover, I argue that Socrates is interested in a type of recollecting that involves perceiving one thing and bringing to mind another, which is the very standard by which one can judge the first. Socrates does not provide here an argument for accepting “Platonic forms,” where these are understood as including all of Plato’s central commitments about the forms. Instead, his argument highlights one key difference between ordinary objects and forms: that the latter do not change over time, whereas the former do.