Classical Backgrounds

Abstract

This chapter sketches the origin as well as the further development of the disciplines of dialectic, logic, and rhetoric in antiquity. For the beginnings of dialectic and logic, the chapter turns in Sect. 2.2 to Zeno’s reductio technique and Plato’s three forms of dialectic, for those of rhetoric to the Sophists and the educator Isocrates.

The chapter discusses Aristotle’s contributions to all three disciplines mentioned. In Sect. 2.3 Aristotle’s theory of dialectic is discussed. The fundamental features of the ancient discussion procedure are explained, the construction of argumentation by means of topoi (argument schemes), and tactical issues concerning debates. Sect. 2.4 is devoted to Aristotle’s fallacy theory. The theory of topics of Cicero and Boethius is discussed in Sect. 2.5. Sect. 2.6 explains Aristotle’s syllogistic – a precursor of predicate logic. Sect. 2.7 deals with Stoic logic – a precursor of propositional logic.

Aristotle’s systematic reflections on rhetoric as the art of finding the appropriate means of persuasion are the topic of attention in Sect. 2.8. Sect. 2.9 deals with the classical system of rhetoric, which developed after Aristotle’s time. The system is illustrated by going systematically through the consecutive tasks a speaker has to accomplish in preparation of the actual performance of a speech. In Sect. 2.10, finally, the ancient achievements are tied in with later developments and shown to relate to the various approaches to argumentation developed in present-day argumentation theory.

2.1 Dialectic, Logic, and Rhetoric

A great many of the theoretical concepts as well as a large part of the terminology used in present-day approaches to argumentation are adopted from or inspired by the classical disciplines of dialectic, logic, and rhetoric. In this chapter, we shall discuss the origins as well as the further development of these disciplines in antiquity, i.e., in the period stretching from the fifth century BC up until the seventh century AD.

In Sect. 2.2, we discuss the beginnings of dialectic, logic, and rhetoric in ancient Greece. As far as dialectic and logic are concerned, we shall concentrate on the contributions made by Zeno of Elea in his paradoxes and those made by Plato in his dialogues. Regarding the beginnings of rhetoric, we shall pay attention to the contributions of the sophists as well as the views manifest in the teachings of Isocrates of Athens and in the anonymous Rhetoric to Alexander.

The next three sections are devoted to classical dialectic. In Sect. 2.3, we discuss Aristotle’s conception of dialectic as put forward in his Topics. After a reconstruction of Aristotle’s views on the structure and goals of dialectical debates, we shall turn to the central notion of a topos and discuss some of Aristotle’s instructions on the proper conduct of a debate. Our discussion of Aristotle’s dialectic continues in Sect. 2.4 with a description of his list of fallacies as put forward in the Sophistical Refutations. In Sect. 2.5, the last section on classical dialectic, we present a reconstruction of the contributions of Cicero and Boethius to the theory of topics.

In the two subsequent sections, we shall elaborate on the ancient roots of two important logical theories of argumentation. In Sect. 2.6, we expound Aristotle’s highly influential theory of the syllogism, a forerunner of predicate logic. In Sect. 2.7, we call attention to the relatively unfamiliar but intriguing notions developed in Stoic logic, a forerunner of propositional logic.

The next two sections will be devoted to classical rhetoric. Since Aristotle is the first to systematically reflect on the phenomenon of persuasion, we shall first give an exposition of his contributions to the art of rhetoric. This is done in Sect. 2.8. After Aristotle, rhetoric slowly developed into a teachable system of instructions for the production of a persuasive speech. Various classical authors have contributed to the system, but instead of discussing their contributions one by one, we demonstrate in Sect. 2.9 the subordinate doctrines developed within the discipline by using as our organizational principle the so-called canons or tasks of the speaker, i.e., the consecutive tasks a speaker will have to accomplish in preparing the actual performance of a speech. In dealing with the various tasks and doctrines, we shall mention the most important classical authors involved in their development.

Finally, in Sect. 2.10, we briefly sketch the further development of the disciplines in the Middle Ages and the Renaissance and conclude the chapter with a brief survey of the relationships between the ancient disciplines of logic, dialectic, and rhetoric and present-day argumentation theory as discussed in this handbook. As an aid to the reader, a chronological table of ancient authors and works has been attached to the last section.

2.2 Beginnings of Dialectic, Logic, and Rhetoric

The ancient Greeks often accounted for the existence of the various arts employed by mankind by attributing the invention of such an art to a god, a hero, or a person that had lived in the past. As far as dialectic and rhetoric are concerned, Diogenes Laertius (third century AD) in Lives of eminent philosophers ¹ – one of the most important sources for the history of Greek philosophy – has Aristotle mention Zeno of Elea as the inventor of dialectic and Empedocles of Agrigentum as the inventor of rhetoric. Diogenes Laertius does not provide any information on who invented logic, probably because logic at the time was not considered a discipline of its own separate from dialectic: with the Stoics and in the later ancient tradition, the term dialektikê includes logic.

Taking other sources into account, it appears that attributions of this kind are not always in agreement with one another. As far as dialectic is concerned, Aristotle mentions Zeno, Socrates, and Plato as inventors of this art and also claims that he himself is the first to give a theoretical account of it. As far as rhetoric is concerned, there is the story, also adhered to by Aristotle, that two lawyers from Sicily, Corax and Tisias, invented it.

The attributions being as discrepant as they are, one important difference between the beginnings of dialectic and that of rhetoric stands out: dialectic developed within contexts of private gatherings where philosophers discussed the nature of reality and mankind, while rhetoric developed within contexts of the public life where citizens delivered speeches regarding judicial and political issues in front of a judging audience.

In this section, we first provide an overview of the beginnings of dialectic and logic as they are manifest in the paradoxes of Zeno and the dialogues of Plato. Reflecting the fact that, at the time of their early development, no clear distinction was drawn between dialectic and logic, in the present description of their beginnings, we treat these disciplines as one. Next, we provide an overview of the beginnings of rhetoric as they are manifest in the teachings of the sophists, Isocrates of Athens, and the anonymous Rhetoric to Alexander.²

2.2.1 The Beginnings of Dialectic and Logic

Zeno of Elea (probably about 490–430 BC) is famous for having left us a number of paradoxes. These have not come down to us directly but via the work of others who have reported on them. From what can be reconstructed from these reports, it appears that Zeno in some of these paradoxes employs a method of refutation that consists in deriving from a standpoint to be refuted two consequences that contradict one another. In later writings on dialectic and logic, this method is described as the argumentative technique of reductio ad absurdum or reductio ad impossibile.

An example of such a report can be found in Plato’s dialogue Parmenides. In one of the passages of this dialogue, Socrates and Zeno discuss the latter’s attempt to defend the monistic ontology that “being is one,” put forward by Zeno’s teacher, Parmenides of Elea (floruit about 500 BC), against attacks by other philosophers who propagated the pluralistic ontology that “being is many”:

[Socrates:] “Zeno, what do you mean by this: if things are many, they must then be both like and unlike, but that is impossible, because unlike things can’t be like or like things unlike? That’s what you say, isn’t it?”

“It is,” said Zeno.

“If it’s impossible for unlike things to be like and like things unlike, isn’t it then also impossible for them to be many? Because, if they were many, they would have incompatible properties. Is this the point of your arguments – simply to maintain, in opposition to everything that is commonly said, that things are not many? And do you suppose that each of your arguments is proof for this position, so that you think you give as many proofs that things are not many as your book has arguments? Is that what you’re saying – or do I misunderstand?” (Plato 1997, Parmenides 127e–128a)

Following on Zeno’s affirmative response to this question, Socrates accuses him of having presented his view on the nature of reality as an original one, whereas in fact it is the same one as his teacher Parmenides held. According to Socrates, to show that reality does not consist of many things is the same as to show that reality consists of only one thing. Zeno then denies the accusation and explains the aim of his philosophical work in more detail:

[Zeno:] “The truth is that the book comes to the defense of Parmenides’ argument against those who try to make fun of it by claiming that, if it is one, many absurdities and self-contradictions result from that argument. Accordingly, my book speaks against those who assert the many and pays them back in kind with something for good measure, since it aims to make clear that their hypothesis, if it is many, would, if someone examined the matter thoroughly, suffer consequences even more absurd than those suffered by the hypothesis of its being one.” (Plato 1997, Parmenides 128c–d)

Whereas Socrates suggests that Zeno is aiming at proving the standpoint that reality is one (demonstratio per impossibile), Zeno himself explains that he is only aiming at showing that the standpoint that reality is many leads to absurdity (reductio ad absurdum) and impossibility (reductio ad impossibile).

This and other reports of Zeno’s paradoxes indicate that he was famous for employing the argumentative technique of reductio in order to refute a standpoint. From later developments in dialectic – especially from Plato’s specimens, in his early dialogues, of debates featuring “Socratic refutation” or “elenchus” (Greek: elegchos) and from the dialectical procedure that underlies Aristotle’s Topics and Sophistical refutations – it becomes clear that this way of refuting a standpoint is central to the discipline. It may therefore be assumed that it is for Zeno’s excellence in using the argumentative technique of the reductio that later authors endowed him with the status of being the “inventor” of dialectic.³

Whereas Zeno employed an argumentative technique that can only retrospectively be labeled as “dialectical,” Plato was the first one to explicitly use the term dialectic as a technical term. In general, throughout his dialogues, he presents dialectic as the outstanding “method” of philosophizing, i.e., as a way of finding and expounding philosophical truths by means of conducting discussions. Most scholars agree that Plato gives three different accounts of what this method entails. In some of the dialogues generally labeled as the “early” dialogues – esp. in the Apology, Lesser Hippias, Euthyphro, Laches, Lysis, Charmides, Protagoras, and Gorgias – dialectic takes the form of the “Socratic refutation debate .” In some of the “middle” dialogues – esp. in the Meno, Phaedo, Republic, and Parmenides – dialectic takes the form of the “method of hypothesizing.” And finally, in some of the “late” dialogues – esp. in the Phaedrus, Sophist, Statesman, and Philebus – dialectic takes the form of the “method of collection and division.”⁴ Below, we shall briefly describe these three different forms of dialectic as they manifest themselves in the dialogues just mentioned.

The Socratic refutation debate is a type of debate prominent in Plato’s early dialogues in which Socrates (as the Questioner ) aims to refute the standpoint of his interlocutor (the Answerer) . Prototypically, Socrates introduces the subject of the debate by asking an opening question. By responding to the question, the interlocutor takes up a standpoint with regard to the subject at issue. Socrates then asks a number of follow-up questions. By responding to these questions with “Yes” or “No,” the interlocutor commits himself to a number of concessions. At the end of the debate, Socrates then tries to refute the standpoint of the interlocutor on the basis of the concessions that are made. The refutation can be direct, in which case Socrates derives from the concessions a standpoint that is the opposite of the interlocutor’s answer to the opening question, or indirect, in which case he shows that the interlocutor’s set of opinions, consisting of the standpoint and the concessions, is internally inconsistent.

The Socratic refutation debate has a striking resemblance with another type of debate occurring in Plato’s early dialogues, the so-called eristic debate as the sophists practiced it. As in the Socratic refutation debate, the aim of the Questioner in an eristic debate is to refute the standpoint of the Answerer on the basis of the concessions made. In the examples Plato provides of this type of debate, the Questioner realizes his aim by making use of ambiguous terms. Having elicited a concession in which a certain term has a specific meaning, the Questioner at the end of the debate derives a conclusion in which the term has a different meaning.

A passage in the Euthydemus, in which Plato describes Socrates’ response to a question containing such an ambiguous term, makes it clear that the procedural problem that impedes the Answerer to properly defend his thesis in an eristic debate is that he is only allowed to say “Yes” or “No” and does not have the right to ask for a clarification of the terms used by the Questioner:

[Euthydemus:] And do you know by means of that by which you have knowledge, or by means of something else?

[Socrates:] By means of that by which you have knowledge. I suppose you mean the soul, or isn’t this what you have in mind?

Aren’t you ashamed, Socrates, he said, to be asking a question of your own when you ought to be answering?

Very well, said I, but how am I to act? I will do just what you tell me. Now whenever I don’t understand your question, do you want me to answer just the same, without inquiring further about it?

You surely grasp something of what I say, don’t you? he said.

Yes, I do, said I.

Then answer in terms of what you understand.

Well then, I said, if you ask a question with one thing in mind and I understand it with another and then answer in terms of the latter, will you be satisfied if I answer nothing to the purpose?

I shall be satisfied, he said, although I don’t suppose you will.

Then I’m certainly not going to answer, said I, until I understand the question.

You are evading a question you understand all along, he said, because you keep talking nonsense and are practically senile.

I realized he was angry with me for making distinctions in his phrases, because he wanted to surround me with words and so hunt me down. (Plato 1997, Euthydemus 295b–d)

If the Answerer had been allowed to ask for clarification of the meaning of terms used in the question at issue, he would have been able to avoid being refuted in an unreasonable manner. By revealing an underlying mechanism of the eristic debate, Plato criticizes the sophists for exploiting the rules of the game of the elenchus in order to win the debate at the cost of philosophical reasonableness.

In his middle dialogues, Plato describes a second form of dialectic, the so-called method of hypothesizing. While the aim of the Socratic refutation debate is to find out whether a standpoint is tenable in the light of certain concessions made, the aim of the method of hypothesizing is to actually show that a standpoint is tenable. The method is derived from mathematical practice. First, the discussants derive from the standpoint – the “hypothesis” – certain other points of view that follow from it, the “consequences.” Then, in case the set of consequences is internally consistent, the hypothesis is accepted, and in case the set of consequences is internally inconsistent, the hypothesis is abandoned. In the latter case, the discussants may finally arrive at an acceptable standpoint by modifying the initial hypothesis in such a way that the set of consequences derived from the adapted hypothesis does comply with the condition of being internally consistent.

In search of a method that arrives at the ultimate philosophical truth, Plato in the Republic defines dialectic as a method that leads the discussants to an understanding of an “unhypothesized” first principle called “the idea of the Good”:

[…] whenever someone tries through argument and apart from all sense perceptions to find the being itself of each thing and doesn’t give up until he grasps the good itself with understanding itself, he reaches the end of the intelligible, just as the other reached the end of the visible.

Absolutely.

And what about this journey? Don’t you call it dialectic?

I do. (Plato 1997, Republic 532a–b)

Because this form of dialectic, according to Plato, enables the discussants to reach the highest possible philosophical knowledge, in his educational program for the future ruler of the state, he places dialectic “at the top of the other subjects like a coping stone” (Plato 1997, Republic 534e).

In his late dialogues, Plato describes a form of dialectic that is rather different from the Socratic refutation debate as well as from the method of hypothesizing. This form of dialectic is called the method of collection and division , and it is aimed at arriving at a philosophically adequate definition of a certain term. Although nowhere in the dialogues Plato gives a clear description of the method of collection and division, the method can be reconstructed as consisting of two parts. In the first part – the collection – the term that is to be defined is brought together with related terms in order to decide which of the collected terms is the most comprehensive. In the second part of the method – the division – the most comprehensive term is divided into species and subspecies until the discussants have arrived at the term that is to be defined. In the Sophist Plato gives an example of such a division. Starting from the comprehensive term expertise, the subsequent divisions of the term are aimed at finding a definition of the term angling.⁵ The debate resembles other forms of dialectic in that there is a Questioner and an Answerer, but in this case the Questioner does not aim at refuting the standpoint of the Answerer but expounds his own views on the matter in a didactical way:

VISITOR: If every expertise falls under acquisition or production, Theaetetus, which one shall we put angling in?

THEAETETUS: Acquisition, obviously.

VISITOR: Aren’t there two types of expertise in acquisition? Is one type mutually willing exchange, through gifts and wages and purchase? And would the other type, which brings things into one’s possession by actions or words, be expertise in taking possession?

THEAETETUS: It seems so, anyway, given what we’ve said.

VISITOR: Well then, shouldn’t we cut possession-taking in two?

THEAETETUS: How?

VISITOR: The part that’s done openly we label combat, and the part that’s secret we call hunting.

THEAETETUS: Yes.

(Plato 1997, Sophist 219d–e)

At the end of the discussion, the definition is given by summing up in the right order all the species and subspecies that link the term to be defined with the most comprehensive term.

Enabling the discussants to find definitions of things in terms of genus -species relationships, the method of collection and division can be characterized as a method that is aimed at gaining philosophical knowledge about the interrelations of the “ideas” or “forms.” Since the quality of the knowledge thus arrived at strongly depends on the skills of the interlocutors in dividing the terms in the correct manner, Aristotle criticized the method for not being deductive in the strict sense (Prior Analytics 46a31–37 and Posterior analytics 91b12–27). Following up on this criticism, Aristotle in his own writings uses the term dialectic to designate the art of debate rather than the ultimate method for reaching philosophical or scientific truth.

Of the three different forms of dialectical discussions described in Plato’s dialogues, the Socratic refutation debate probably reflects the philosophical debates as they were conducted in Plato’s school – the Academy. Aristotle, who studied and taught in the Academy for a period of 20 years, claims to be the first to provide a theoretical account of this type of dialectical discussions, which we will discuss in Sects. 2.3 and 2.4. Later, Cicero and Boethius elaborate on an important part of Aristotle’s account, the doctrine of the “topics.” We will discuss these later developments in Sect. 2.5.

2.2.2 The Beginnings of Rhetoric

Like the beginnings of dialectic and logic, those of rhetoric are not clearly marked. Ancient sources attribute the “invention” of rhetoric to figures as different as the Sicilian lawyers Corax and Tisias and the philosopher Empedocles.⁶ There is some evidence that already in the fifth century certain handbooks on the composition and the presentation of an effective speech (technai logôn) were in circulation. Both Plato (Phaedrus, 266d–267d) and Aristotle (Rhetoric I.1, 1354a11–1355a20, and III.13, 1414a37–b7) give a critical account of these handbooks, from which it can be learned that they may have contained examples and/or instructions regarding the parts of a speech, the use of stylistic devices, and the use of emotion as a means of persuasion. Other citations by Plato (Phaedrus, 273a–b) and Aristotle (Rhetoric II.24, 1402a17–20) indicate that the handbooks may also have contained illustrations of logical means of persuasion, in particular of the argument from probability (eikos).

Around the same time, a number of thinkers, generally referred to as the sophists, started to manifest themselves as teachers of rhetoric.⁷ Among the most famous of them are Protagoras of Abdera, Gorgias of Leontini, Prodicus of Ceos, and Hippias of Elis. Although the sophists are referred to as a group, they operated individually. Travelling from city to city, they presented an educational program intended to prepare young people for a future role in public life. Their teaching concentrated on skills regarding the composition and presentation of an effective speech. It did not take place by means of presenting the rules of the art but rather by means of providing the students with model speeches (epideixeis, singular: epideixis) for them to imitate. Among the surviving model speeches are The encomium of Helen and The defence of Palamedes, both written by Gorgias, and the Tetralogies, attributed to Antiphon of Rhamnus (ca. 480–411 BC).⁸

One of the underlying assumptions of the teaching of the sophists is the relativistic idea that there are always two sides to every issue and that ultimate truth is not to be found.⁹ Another important assumption is the idea that in order to persuade, the speaker does not necessarily have to be an expert on the subject. Plato criticizes this idea in his Gorgias, in a passage where Socrates denies the rhetoric of the sophist Gorgias the status of a true art and describes it as a form of “flattery” that is comparable to “pastry baking”:

Pastry baking has put on the mask of medicine, and pretends to know the foods that are best for the body, so that if a pastry baker and a doctor had to compete in front of children, or in front of men just as foolish as children, to determine which of the two, the doctor or the pastry baker, had expert knowledge of good food and bad, the doctor would die of starvation. […] So pastry baking, as I say, is the flattery that wears the mask of medicine […] what pastry baking is to medicine, oratory is to justice […] You’ve now heard what I say oratory is. It’s the counterpart in the soul to pastry baking, its counterpart in the body. (Plato 1997, Gorgias 464d-465d)

The upshot of Plato’s critique of the rhetoric of the sophists is that it teaches speakers to persuade by telling the audience what is pleasant rather than what is the best thing to do. Within the context of political or deliberative debates, this may lead to making wrong decisions. In Plato’s view, a speaker should not try to gain or maintain political power by deceiving the audience in this way but should promote the general interest by sincerely trying to convince the audience of the best decision to take. Rather than acting like a cook who presents his audience with tasty but unhealthy dishes, the speaker should act like a physician, providing his audience with a bitter but healthy medicine.

Plato at the end of the Gorgias (503a–b) preludes on the development of a type of rhetoric that avoids the pitfalls of sophistic rhetoric. In the Phaedrus, he expounds the conditions for such a philosophically legitimate type of rhetoric.¹⁰ As the following passage shows, this type of rhetoric presupposes the type of dialectic called the method of collection and division as a method for teaching or persuading one’s audience of the truth in an effective way:

First, you must know the truth concerning everything you are speaking or writing about; you must learn how to define each thing in itself; and, having defined it, you must know how to divide it into kinds until you reach something indivisible. Second, you must understand the nature of the soul, along the same lines; you must determine which kind of speech is appropriate to each kind of soul, prepare and arrange your speech accordingly, and offer a complex and elaborate speech to a complex soul and a simple speech to a simple one. Then and only then, will you be able to use speech artfully, to the extent that its nature allows it to be used that way, either in order to teach or in order to persuade. This is the whole point of the argument we have been making. (Plato 1997, Phaedrus 277b–c)

Distinct from this philosophically legitimate type of rhetoric, Isocrates of Athens (436–338 BC) developed an educational program that resembled that of the sophists in being intended to teach students how to successfully operate in public life. However, for several reasons, Isocrates is not considered a sophist. First of all, unlike most sophists, he did not travel around but taught in a school he had opened in Athens. Second, Isocrates supposedly never delivered a speech himself, since he was better as a writer of speeches than as a presenter of them. Twenty-one of these written model speeches have survived. Third, his teaching of rhetorical skills was embedded in a larger educational program that also consisted of ethics and political philosophy. And fourth, most importantly, he taught his students rhetoric not only by providing model speeches for them to imitate but also by explaining to them the principles of the art. An example of the latter can be found in a passage in which Isocrates, for the first time in the history of rhetoric, mentions invention , arrangement , and style, which were later incorporated into rhetorical teaching as the three most important of the five “tasks of the speaker ” (officia oratoris ) or “ canons of rhetoric”:

But to choose from these elements [out of which we make and compose all discourses] those which should be employed for each subject, to join them together, to arrange them properly, and also, not to miss what the occasion demands but appropriately to adorn the whole speech with striking thoughts and cloth it in flowing and melodious phrase – these things, I hold, require much study and are the task of a vigorous and imaginative mind. (Isocrates 1929, Against the sophists 13, 16–17)

A final important contribution to the early development of rhetoric is a handbook that came down to us as the Rhetoric to Alexander, written somewhere around 34 BC. Since it starts with a letter in which Aristotle dedicates the work to Alexander the Great, some have assumed that Aristotle wrote it. However, Quintilian (Oratorical education III.4.9) seems to identify Anaximenes of Lampsacus (ca. 380–320 BC) as the writer of the treatise.

Unlike other handbooks, the Rhetoric to Alexander does not only contain models or examples for imitation but also more or less systematically organized collections of rules (or instructions) pertaining to different types of speech. Starting from the distinction between deliberative, epideictic, and juridical speeches (the three basic genres), the author distinguishes seven types of speech: exhortation, dissuasion, praise, blame, accusation, defense, and investigation.¹¹ Having presented the subject matters specific to each of these types (1–6), the author gives a general analysis of arguments (7–17), strategic maneuvers (18–20), and style (21–28). The work is concluded with an overview of the structures specific to each of the seven types of speech (29–37).

As we have explained, the contributions of the sophists, Plato, Isocrates, and those in the Rhetoric to Alexander are to be seen as the start of the development of rhetoric as a coherent and didactically effective set of instructions for the production and delivery of a persuasive speech. The first author to systematically reflect on these instructions was Aristotle, whose Rhetoric we shall discuss in Sect. 2.8. In the centuries after the fourth century BC, Greek and Roman writers modified and extended the rhetorical instructions, resulting into what is now commonly referred to as the system of classical rhetoric, which we shall discuss in Sect. 2.9.

2.3 Aristotle’s Theory of Dialectic

As we already mentioned, students and teachers in Plato’s Academy took part in philosophical debates that were closely related to Socratic refutation debates. Aristotle (384–322 BC), who studied and taught in the Academy for a period of 20 years, was the first to write extensively on the aims, structure, rules, and strategies of such debates. His handbook of philosophical debates, known as the Topics (Topica),¹² consists of eight books. The Topics together with the single book Sophistical refutations (Sophistici elenchi)¹³ – a supplementary volume that is sometimes catalogued as its ninth book – can be regarded as the first extensive work on dialectic (including logic). The work was obviously inspired by Plato’s rendering of the Socratic refutation debates in his early dialogues, but these dialogues do not yet constitute a treatise about dialectic. Aristotle himself claimed, at the end of Sophistical refutations (in a passage that also refers to the Topics), that, in contrast to the situation in rhetoric, his dialectical investigations had to start from scratch:

[…] as far as our inquiry is concerned, it is not the case that some work had been done before, while some had not; rather, there was nothing at all. (Aristotle 2012, Soph. ref. 34, 183b34–36)

In one sense of the word dialectical, all debates, being conversations, are dialectical. However, Aristotle’s inquiries pertain to a specific type of debate, between a Questioner and an Answerer, whom the Questioner tries to refute. Unfortunately, no learner’s guide to these debates has been left to us. Aristotle just assumes that his audience or readership is familiar with the basics. We shall therefore first give a reconstruction of the way in which such debates may be supposed to have proceeded.¹⁴

2.3.1 The Dialectical Procedure

Basically the Athenian philosophical debate (henceforth, dialectical debate) is a regimented version of the Socratic refutation debate we discussed in the preceding section. There are two participants, each of whom has a different role to play: the Questioner (erôtôn, punthanomenos) and the Answerer (apokrinomenos, erôtômenos, êrôtêmenos). Generally, the debate takes place in front of an audience. In what, in a pragma-dialectical vein, may be called the opening stage of the debate, it is first determined which participant will play which role. The Questioner then proposes an issue (problêma) for debate by putting forward a propositional question: a question which offers a choice between two contradictory propositions, such as “Is the universe infinite or not?” or “Is virtue teachable or not?” The Answerer selects either the positive or the negative answer as his thesis. The contradictory of the Answerer’s thesis counts as the thesis of the Questioner. This concludes the opening stage.

The primary aim of the Questioner is to construct a refutation (elegchos) of the Answerer , i.e., a deductive argument or deduction (sullogismos) consisting of (at least two) premises and a conclusion that is to contradict the thesis of the Answerer, and therefore to be identical to the Questioner’s own thesis. The notion of a deduction is defined as follows:

Now a deduction is an argument in which, certain things being laid down, something other than these necessarily comes about through them (Aristotle 1984, Vol. 1, Topics I.1, 100a25–27)

With respect to its linguistic structures, this notion of deduction is clearly not limited to what we would now call “syllogisms.” But, in other respects, Aristotle’s notion of a deductive argument is more restricted than contemporary notions of deduction. For one thing, according to the Aristotelian view, there is no such thing as an invalid deduction. What we would be inclined to call by that name would simply be no deduction at all (though it could still be an argument (logos)). Further, the Aristotelian notion does not admit deductive arguments in which there are not at least two premises, or in which the conclusion is equal to one of the premises or in which one of the premises is not needed to obtain the conclusion.

Notice that it is not upon the Answerer to construct a refutation of the Questioner or, what comes to the same, to defend his thesis by argument: only the Questioner is to argue. The primary aim of the Answerer is to uphold his thesis, i.e., to avoid being refuted.

In order to construct a refutation, the Questioner is to obtain premises/propositions (protaseis, singular: protasis ) that allow him to deduce his thesis. It is not upon the Questioner to decide which premises he may use, because the Answerer first needs to agree with any premise the Questioner proposes. To obtain such an agreement from the Answerer, the Questioner uses again propositional questions (called protaseis as well), which are however formulated in a way slightly different than that used for introducing the issue for debate, for instance: “Has the universe come to be?” or “Is virtue knowledge?” If the Answerer answers such a question either affirmatively or negatively, he has granted a premise.¹⁵ But the Answerer is not in all circumstances obliged to give immediately either a positive or a negative answer: he is allowed to first ask for clarification of the question, or he may object to it, for instance, because the question contains an ambiguity that must first be resolved.

Now it may seem that the Answerer could always win the debate by simply objecting to any premise the Questioner might ask for. But this he cannot do, since in dialectical debates, unless they are degenerated into eristic debates, the audience expects the discussants to display reasonable behavior and to cooperate to some extent in their common enterprise (koinon ergon) of producing good arguments. Therefore, an Answerer refusing to concede acceptable (plausible, reputable) premises (endoxa , singular: endoxon) would be frowned upon by the audience and might even make a fool of himself.¹⁶ An Answerer who persistently uses such tactics would be showing himself ill-tempered (duskolos), which is certainly no compliment. Answering by conceding the opposite of what the Questioner wants him to concede would make matters even worse because if the premise asked for is true, the opposite must be false and if this premise is acceptable, the opposite must be unacceptable. Thus, the ill-tempered Answerer would weaken his position by getting entangled in falsehoods and implausibilities. All the same, it is not easy for the Questioner to find acceptable premises to support his own thesis. Facilitating this task was precisely one of Aristotle’s main purposes when he wrote the Topics. A large part of the Topics is devoted to the description of about 300 topoi (Rubinelli 2009, p. 29), which may, according to some scholars, be compared to what nowadays are known as argument (or argumentation) schemes.

In some cases, considerations of acceptability and pressure from the audience will be enough to make the Answerer willing to concede a certain premise (suggested by a topos), but often it is necessary to argue for the premise. Since the argument for the premise may be again deductive, it may be necessary to argue in a sub-deduction for a premise needed for the ultimate deduction of the Questioner’s thesis and again to argue for premises of these sub-deductions, and so on. This makes the dialectical procedure of debate a recursive one. But, though the ultimate argument for the Questioner’s thesis is supposedly required to be deductive, not all arguments of which the Questioner may avail himself to obtain premises need to be so. It is also permitted to argue for premises in a non-deductive way: induction (epagôge) can be used to get a universal premise admitted and arguments from likeness (homoiotês) to go directly from case to case, skipping the establishment of a universal.

The first of these non-deductive ways of arguing for premises, induction, is defined as follows:

[…] induction is a passage from particulars to universals, e.g. the argument that supposing the skilled pilot is the most effective, and likewise the skilled charioteer, then in general the skilled man is the best at his particular task. (Aristotle 1984, Vol. 1, Topics I.12, 105a13–16)

When the particular cases that function as the premises of the induction have been admitted, the Answerer is expected to also admit the universal conclusion – in the example above: “For each task a man skilled in that task is best at that task.” The only escape would be to object not to a premise but to the induction itself by presenting a counterexample – in the example above, a particular task such that people skilled in that task are not the best in it. If the Answerer admits the particular cases and fails to present a counterexample, but still refuses to admit the universal conclusion, he would appear to be “ill-tempered.”¹⁷

About the second non-deductive way of arguing for premises, making use of arguments from likeness, Aristotle says:

Moreover, try to secure admissions by means of likeness; for such admissions are plausible, and the universal involved is less patent; e.g. that as knowledge and ignorance of contraries is the same, so too perception of contraries is the same; or vice versa, that since the perception is the same, so is the knowledge also. This argument resembles induction, but is not the same thing; for in induction it is the universal whose admission is secured from the particulars, whereas in arguments from likeness, what is secured is not the universal under which all the like cases fall. (Aristotle 1984, Vol. 1, Topics VIII.1, 156b10–17)

After having obtained the premises of his ultimate deduction (the final step in his refutatory argument), the Questioner proceeds to deduce his conclusion. He then claims to have refuted the thesis of the Answerer by having deduced its contradictory. To this the Answerer may still object by trying to show that the alleged refutation is fallacious on some account (see the discussion of Aristotle’s theory of fallacies in the next section).

How does a dialectical debate end? If the Questioner has succeeded in constructing an unobjectionable refutation, we may say that the Questioner has won and the Answerer has lost. If the debate ends for some reason or other before the Questioner has succeeded, the Answerer has won and the Questioner has lost. There are some indications that these debates had a fixed time limit.¹⁸ However, winning or losing in this way does not give the whole picture: it is also important how one has won or lost. And this depends on the quality of one’s contribution to the debate relative to the difficulty of one’s task (Moraux 1968, pp. 285–286).

2.3.2 Goals of Dialectical Debates and of Other Types of Dialogue: Their Argumentative Character

Aristotle is not very explicit about the goals served by dialectical debates. The goal of a kind of activity should not be confused with the aims of the participants as they pursue the activity. In dialectical debates, the aim of either party is to win the debate and to do so in an impeccable way. But by this observation, the question why people would enter into such altercations at all is not answered.

At the start of Topics VIII.5, Aristotle distinguishes three types of dialogue by their different goals: (1) the truly dialectical debate, which is concerned with training (gumnasia), with critical examination (peira), or with inquiry (skepsis); (2) the didactic discussion, concerned with teaching; and (3) the competitive (eristic, contentious) type of debate in which winning is the only concern. Elsewhere, Aristotle distinguishes four domains of argument that are characteristic of these types of dialogue (though the connection need not be exclusive)¹⁹:

In discussions there are four domains of argument: didactic, dialectical, critical and eristic. Those arguments are didactic that deduce on the basis of the principles appropriate to the discipline in question and not on the basis of the views of the answerer (for the student should rely on them). Those arguments are dialectical that, on the basis of acceptable views, constitute a deduction of a contradictory. Those arguments are critically examining that are based on views of the answerer or on things that must be known by anyone who purports to have scientific knowledge […]. And those arguments are eristic that, based on points that appear acceptable without being so, constitute a deduction or appear to constitute a deduction.²⁰ (Aristotle 2012, Soph. ref. 2, 165a38–b8)

The (critical) examination dialogue (peirastic) is concerned with the critical examination (peiras), by the Questioner, of a (would-be) expert (the Answerer). Is the expert really knowledgeable about the things he claims to know? Aristotle sometimes speaks about the examination dialogue as a separate type of dialogue but mostly subsumes it under dialectical debate. The examination dialogue starts from a difference of opinion about the question whether the Answerer is knowledgeable in a certain field and uses arguments to resolve the difference and therefore constitutes a kind of argumentative discussion.²¹ Also, the eristic debate , though it is focused on letting people wrangle rather than on obtaining a resolution, is an argumentative activity in as far as it starts from a difference of opinion and uses arguments. It is a type of debate that is dangerously close to the dialectical debate, since in a dialectical debate eristic moves always threaten to slip in. On the other hand, didactic discussion, which is concerned with the presentation of demonstrations (proofs) by a teacher to his students, constitutes a primarily informative kind of discussion.

In Topics I.2, Aristotle briefly discusses the ways his treatise can be of use; doing so he also throws light on the goals of dialectical debates:

Next in order after the foregoing, we must say for how many and for what purposes the treatise is useful. They are three – intellectual training, casual encounters, and the philosophical sciences. That it is useful as a training is obvious on the face of it. The possession of a plan of inquiry will enable us more easily to argue about the subject proposed. For purposes of casual encounters, it is useful because when we have counted up the opinions held by most people, we shall meet them on the ground not of other people’s convictions but of their own, shifting the ground of any argument that they appear to us to state unsoundly. For the study of the philosophical sciences it is useful, because the ability to puzzle on both sides of a subject will make us detect more easily the truth and error about the several points that arise. It has a further use in relation to the principles used in the several sciences. For it is impossible to discuss them at all from the principles proper to the particular science in hand, seeing that the principles are primitive in relation to everything else: it is through reputable opinions about them that these have to be discussed, and this task belongs properly, or most appropriately, to dialectic; for dialectic is a process of criticism wherein lies the path to the principles of all inquiries. (Aristotle 1984, Vol. 1, Topics I.2, 101a25–b4)

The first kind of use mentioned in this passage is training (gumnasia). It was also mentioned in Topics VIII.5 (see above). Practicing dialectical debating will make people more adept at constructing and criticizing arguments.

The second kind of use mentioned occurs in casual encounters (enteuxeis). The description given presents us with a kind of mirror image of the examination dialogues: just like the latter, dialectical debates in such casual encounters take place between an expert and a layman, but now the expert is the Questioner, who tries to correct the layman and to convince him of the truth of something by arguing from the latter’s own convictions rather than from scientific principles, which would be beyond him.²² The passage does not mention the use of dialectical debates in other kinds of encounters, such as encounters leading to an examination dialogue or encounters with scholars from a competing philosophical school who need to be answered and could be enticed into taking a position in a dialectical debate. In each case of this second kind of use, there will be a difference of opinion and a use of arguments, and so the discussion will be argumentative.

The third kind of use regards the study of the philosophical sciences (hai kata philosophian epistêmai). This use corresponds to the earlier mentioned goal of inquiry (skepsis). When discussants together investigate a scientific problem, they do not necessarily have a difference of opinion, and therefore a discussion of this type is probative and explorative rather than argumentative. But since the participants may at any time take distinct positions about some issue, it is likely to have embedded argumentative parts. There are actually two kinds of use to be considered under this head. First, by dialectical debates, one may find out what counts for and what against a particular thesis and thus discover the truth about something. Second, dialectical debates may offer a way to (or a way to examine) the first principles of science.²³

We may conclude that dialectical debates are of use in various ways and that discussions following their rules are often, though not always, argumentative, so that the study of these debates is a part of argumentation theory concerned with a special context of argumentation.

2.3.3 The Topoi

Whereas Book I of the Topics introduces fundamental concepts and instruments for the dialectical debate and Book VIII gives strategic advice for debaters, Books II through VII, the so-called middle books, are devoted to the description and discussion of topoi. The core meaning of the Greek word topos (plural: topoi) is “place,” but in the context of dialectic and rhetoric, it has a technical meaning, which is in English sometimes conveyed by the Greek word topos and sometimes by the term topic. There has been much debate among experts about what precisely a topos is supposed to be.²⁴ Yet it seems clear that the function of topoi is to help in the construction of arguments. Since it is not immediately clear how “places” would help in constructing arguments, the technical use of the word may be supposed to involve some metaphor. Most likely it derives from the mnemonic art, a memorizing technique in which data to be remembered are, in one’s mind, stored at determinate locations (topoi) in a mental representation of a complex and ramified site.²⁵ Rubinelli (2009, p. 13) suggests a link with a fourth century military use of the term topos, mentioned by Ritoók (1975, pp. 112, 114), in which it denotes a location from which power can be deployed. Indeed, one could say that, similarly, a topos in argumentation would be a point of view from which to construct an argument attacking one’s opponent.

Using another metaphor, Brunschwig, in his introduction to his translation of the Topics, characterizes a topos as une machine à faire des prémisses à partir d’une conclusion donnée [a machine to produce premises starting from a given conclusion] (Aristote 1967, p. xxxix), since the function of a topos is, given a certain conclusion to be reached, to enable the Questioner to find premises from which this conclusion can be deduced. Just as a machine consists of a number of parts, a topos consists of a number of distinct elements.²⁶

In his Rhetoric, Aristotle characterizes a topos as “something under which many enthymemes fall” (Rhetoric II.26, 1403a19, as translated by Slomkowski 1997, p. 43). Since enthymeme (enthumêma) is what in rhetoric corresponds to deduction (sullogismos) in dialectic, we may presume him to hold that a topos in dialectic can be characterized as something under which many deductions fall.²⁷ This characterization stresses the generality of topoi: a lot of deductions exemplify one and the same topos. In this respect, topoi resemble contemporary argument(ation) schemes. Indeed the system of topoi may be looked upon as an ancient system of argument schemes.²⁸

The central part of a topos is a general law (a universal proposition) that can be used in many similar deductions. One may propose that this law be identified with the topos itself, but then, of course, it must still be explained how this law figures in the search for (other) premises.²⁹ Another important part of a topos is an instruction telling the Questioner that if the conclusion to be reached has certain features, he should investigate whether the prerequisites are fulfilled for deducing the given conclusion by means of the general law provided by the topos.³⁰ Below, we give some examples with comments:

(1) A topos from contrary terms ³¹: Again, if there be posited an accident which has a contrary, look and see if that which admits of the accident will admit of its contrary as well; for the same thing admits of contraries. [Take, for example, the case that] he [the Answerer] has asserted that the faculty of desire is ignorant [an accident]. For if it were capable of ignorance, it would be capable of knowledge [the contrary accident] as well: and this does not seem to be so – I mean that the faculty of desire is capable of knowledge. For purposes, then, of overthrowing a view you should proceed as we have said; but for purposes of establishing one, though the rule [topos] will not help you to assert that the accident actually belongs, it will help you to assert that it may possibly belong. For having proved that the thing in question will not admit of the contrary, we shall have proved that the accident neither belongs nor can possibly belong; while on the other hand, if we prove that the contrary belongs, or that the thing is capable of the contrary, we shall not indeed as yet have proved that the accident asserted does belong as well; our proof will merely have gone to this point, that it is possible for it to belong. (Aristotle 1984, Vol. 1, Topics II.7, 113a33–35 and 113b3–14)

The description of this topos starts with an instruction giving strategic advice to the Questioner: if the Answerer’s thesis predicates an accident P of a subject S (“S is (accidentally) P”), then the Questioner is to check that P has a contrary (say Q) and to investigate whether S could also be Q.³² The instruction is followed by the general law (“the same thing admits of contraries”), which provides also the justification for giving this kind of strategic advice. Next there follow two examples (of which we quoted the second) and some more detailed discussion of the way this topos can be applied. This order – first the instruction and then the law followed by examples and further comment – is the usual one in the Topics, but, as we shall see, not all these elements are always present. The law can be formulated as follows:

• If P and Q are contrary accidents, and if S is P or S can be P, then S can be Q.

This law (which is presumed to be acceptable and therefore to be admitted by the Answerer) can be used as a major premise to deduce either “S is not-P” or “S cannot be P,” but only if the minor premise “S cannot be Q” will also be admitted by the Answerer. As Aristotle notices, it can also be used to construct a deduction for “S can be Q” if the Answerer admits either “S is P” or “S can be P.”

(2) A topos from contradictory terms : […] you should look among the contradictories of your terms, reversing the order of their sequence, both when demolishing and when establishing a view; and you should grasp this by means of induction. E.g. if man is an animal, what is not an animal is not a man; and likewise also in other instances of contradictories. For here the sequence is reversed; for animal follows upon man, but not-animal does not follow upon not-man, but the reverse – not-man upon not-animal. In all cases, therefore, a claim of this sort should be made, (e.g.) that if the honourable is pleasant, what is not pleasant is not honourable, while if the latter is not so, neither is the former. Likewise, also, if what is not pleasant is not honourable, then what is honourable is pleasant. (Aristotle 1984, Vol. 1, Topics II.8, 113b15–24)

The general law of this topos, which is not stated by Aristotle, but indicated by the examples, can be formulated as follows³³:

• A is B if and only if not-B is not-A.

This law (or the relevant part of it: either “If A is B, then not-B is not-A” or the converse implication) can be used as a major premise to construct deductions for “A is B” and for “not-B is not-A” (as well as for their negations), but, again, only if the corresponding minor premise will be admitted by the Answerer. For instance, if the conclusion to be reached is “A is B” (e.g., “What is honorable is pleasant”), the minor premise needed would be “not-B is not-A” (“What is not pleasant is not honorable”). If this minor premise will be admitted by the Answerer as an acceptable premise, the Questioner may complete his deduction. The instruction provided by this topos (which is expressed rather concisely) tells the Questioner to investigate if a suitable minor of this kind is available.

(3) A topos from greater and lesser degree: […] see whether a greater degree of the predicate follows a greater degree of the subject: e.g. if pleasure is good, see whether also a greater pleasure is a greater good; and if to do a wrong is evil, see whether also to do a greater wrong is a greater evil. Now this rule [topos] is of use for both purposes; for if an increase of the accident follows an increase of the subject, as we have said, clearly the accident belongs; while if it does not follow, the accident does not belong. You should establish this by induction. (Aristotle 1984, Vol. 1, Topics II.10, 114b38–115a6)

Here the general law states that “if an increase of the accident follows an increase of the subject […] the accident belongs; while if it does not follow, the accident does not belong.” It can be formulated as follows:

• A is B if and only if a greater degree of A is a greater degree of B.

Given an appropriate minor premise, this law can be used to construct deductions “for both purposes,” i.e., for obtaining “A is B” or “a greater degree of A is a greater degree of B” and for obtaining their negations.

(4) Another topos from greater and lesser degree: […] if one predicate is attributed to two subjects, then supposing it does not belong to the subject to which it is the more likely to belong, neither does it belong where it is less likely to belong; while if it does belong where it is less likely to belong, then it belongs as well where it is more likely. (Aristotle 1984, Vol. 1, Topics II.10, 115a6–8)

The general law of this topos can be rendered as

• If it is more likely that A is B than that C is B, then if A is not-B, C is not-B, and if C is B, A is B.³⁴

There is no instruction or example accompanying this topos, but it is not hard to see what the Questioner should investigate.

(5) A topos from the division of a genus into species: Again, if no differentia belonging to the genus is predicated of the given species, neither will the genus be predicated of it; e.g. of soul neither odd nor even is predicated; neither therefore is number. (Aristotle 1984, Vol. 1, Topics IV.2, 123a11–14)

This topos depends upon the theory of predicables , which tells us there are four ways a predicate B can be predicated of a subject A. If A is B, B can be predicated of A (1) as A’s definition, which gives the essence of A (“Man is by definition a rational animal”); (2) as (2a) A’s genus (“Man has animal as genus”), which gives only part of the essence, or (2b) A’s differentia ³⁵ specifying A within its genus (“Man has rationality as differentia”), which also gives only part of the essence; (3) as a property ³⁶ of A, which does not give (a part of) the essence of A but nevertheless characterizes A by being coextensive with it so that A also belongs to B (“Man has the property of being a featherless biped”); (4) in other cases as an accident.³⁷ The general law of this topos can now be formulated as follows³⁸:

• If genus G is divided into species by exactly the differentiae D ₁,…, D _n and for each D _i (1 ≤ i ≤ n) S is not-D _i , then G is not the genus of S.

Again there is no further instruction, but there is a brief example in the passage cited. We may supplement the example by the supposition that the thesis of the Answerer is that number (G) is the genus of soul (S). Numbers, however, can be divided into odd numbers (D ₁) and even numbers (D ₂). But soul is not odd, nor is it even. Getting these three premises admitted will enable the Questioner to refute the Answerer by means of the general law provided by the topos.

2.3.4 Debate Instructions

Having provided a list of topoi enabling the Questioner to find the premises he needs to construct the final deduction of his thesis, Aristotle in book VIII of the Topics gives some instructions on how to proceed in the actual debate.³⁹ The need for giving these instructions follows from the observation that unlike someone who merely thinks for himself, someone who acts as a Questioner in a dialectical debate will have to obtain the premises needed for his conclusion from the Answerer, who is assumed to be reluctant to concede premises that clearly lead to the refutation of his thesis:

Any one who intends to frame questions must, first of all, select the ground from which he should make his attack; secondly, he must frame them and arrange them one by one to himself; thirdly and lastly, he must proceed actually to put them to the other party. Now so far as the selection of his ground is concerned the problem is one alike for the philosopher and the dialectician; but how to go on to arrange his points and frame his questions concerns the dialectician only; for in every problem of that kind a reference to another party is involved. Not so with the philosopher, and the man who is investigating by himself: the premisses of his reasoning, although true and familiar, may be refused by the answerer because they lie too near the original statement and so he foresees what will follow if he grants them; but for this the philosopher does not care. (Aristotle 1984, Vol. 1, Topics VIII.1, 155b4–14)

Aristotle advises the Questioner to conceal as carefully as possible in what way and from what premises he will draw his conclusion. This general strategy of concealment (krupsis) entails tactics concerning the invention, the arrangement, and the formulation of the questions.

As to the invention, Aristotle advises the Questioner not to restrict himself to asking for concessions upon which the deduction of the conclusion is based – the so-called necessary premises (hai anagkaiai (protaseis)) – but to also ask for concessions that do not directly contribute to the refutation of the Answerer’s thesis. Of these there are four kinds: premises for induction, premises for adding weight or ornament to the argument, premises specifically for concealment, and premises for clarification (Topics VIII.1, 155b20–24, 157a6–13).

As to the arrangement of the questions in an actual debate, Aristotle then advises the Questioner not to ask all of the necessary premises right in the beginning of the debate but rather to keep these at a distance by asking for “more remote” concessions, from which the necessary premises can be derived in a later stage (Topics VIII.1, 155b29–30, 156b27–30). Nor should one ask to be granted, one after the other, the premises leading together to one and the same (intermediate) conclusion, but one should mix them with premises for another conclusion in order to confuse the Answerer as to which conclusions one tries to deduce (Topics VIII.1, 156a23–26). Aristotle also advises to take into account the propensity of most Answerers to deny a proposed premise at the beginning of the debate and to more easily admit things later. For this reason, the Questioner should ask for the most important premises at the end of the debate. However, as he remarks, with some Answerers , namely, those that are ill-tempered (duskulos) or think themselves to be smart (drimus), it is the other way round: since they get more and more reluctant to concede anything, the Questioner should ask for the most important premises at the beginning of the debate (Topics VIII.1, 156b30–157a1).

As to the formulation of the questions, Aristotle notes that the Answerer will probably be less hesitant to concede a premise (1) when the question regarding that premise is formulated in terms of likeness, (2) when the Questioner has increased his credibility by mentioning now and then an objection to his own thesis, and (3) when the Questioner remarks, in addition to asking a question, that a certain answer is commonly accepted (Topics VIII.1, 156b10–23). According to Aristotle, it may also help when the Questioner hides what concession he would like to obtain (the proposed premise or its contradictory) or how important a specific answer is in view of the construction of the final deduction (Topics VIII.1, 156b4–9). As to the conclusion of this final deduction, which is the opposite of the thesis the Answerer tries to uphold, Aristotle urges the Questioner not to put forward the conclusion in the form of a question, in order not to give the Answerer the possibility of escaping from being refuted:

The conclusion should not be put in the form of a question; otherwise if he rejects it, it looks as if the deduction has failed. For often, even if it is not put as a question but advanced as a consequence, people deny it, and then those who do not see what follows from the previous admissions do not realize that those who deny it have been refuted; when, then, the one man merely asks it as a question without even saying that it follows, and the other denies it, it looks altogether as if the deduction has failed. (Aristotle 1984, Vol. 1, Topics VIII.2, 158a7–13)

Some of these tactics are also listed in Sophistical refutations 15, together with some others, such as that you should go fast in order to prevent people from seeing where you are heading and that you should try to incense the Answerer so as to make him less attentive. Perhaps these latter tactics are only meant for purely competitive (contentious, eristic) discussions – which Aristotle does not really champion, but into which truly dialectical discussions may degenerate – but the ones listed in Topics VIII.1 seem rather intended for a kind of dialectic interchange of which Aristotle approves.

That Aristotle recommends these tactics does not mean that in dialectic anything goes: the truly dialectical debate, where there is a common aim in view, remains distinct from the merely competitive (contentious, eristic) kind of debate:

The principle that a man who hinders the common business is a bad partner, clearly applies to an argument as well; for in arguments as well there is a common aim in view except with mere contestants, for these cannot both reach the same goal; for more than one cannot win. It makes no difference whether he effects this as answerer or as questioner; for both he who asks contentious questions is a bad dialectician, and also he who in answering fails to grant the obvious answer or to accept whatever question the questioner wishes to put. (Aristotle 1984, Vol. 1, Topics VIII.11, 161a37–b5)

Having given instructions about how the Questioner may further his aim in a dialectical debate, Aristotle gives (in the Chaps. 5–8 of Book VIII of the Topics) a number of instructions about what kind of things the Answerer is obliged to grant in order to operate in a correct manner. Here he is at first more focused upon the “common business” (koinon ergon) of the discussants to produce good arguments than on the particular aim of the Answerer of upholding his thesis. Thus, he instructs the Answerer not to concede a premise that fails to be more acceptable than the conclusion to be reached by the Questioner, for if he would do so, this would deteriorate the quality of the argument the Questioner is going to construct (Topics VIII.5).⁴⁰ Since these instructions actually require the Answerer to assist the Questioner in constructing a good argument, and thus to contribute to his own refutation by a good argument, they can be interpreted as rules that the Answerer has to comply with in order for the dialectical debate to be carried on as a maximally cooperative and non-eristic pursuit.

Some of the instructions for the Answerer, however, seem to be intended as tactical advice for the Answerer to accomplish his aim – opposed to the aim of the Questioner – of maintaining his thesis and avoiding refutation, albeit in a truly dialectical (i.e., a noncontentious, non-eristic) way.⁴¹ For instance, Aristotle urges the Answerer to make use of his right to ask for clarification in case he does not understand the question and to withdraw concessions made earlier in the debate in case he did not notice, at the time it was asked, that the question contained an ambiguity (Topics VIII.7). Further, Aristotle advises the Answerer to prepare for an upcoming debate by exploring the ways in which the thesis he wishes to defend can be attacked (Topics VIII.9). By doing so, the Answerer may find out how to oppose the premises from which the Questioner in the actual debate will try to deduce the opposite thesis.

Once the Questioner has obtained his premises, the Answerer may still attempt to prevent the Questioner from drawing a conclusion. In Chap. VIII.10 of the Topics, Aristotle mentions four ways in which the Answerer may try to do so: (1) He may try to do so by “demolishing the point on which the falsity that comes about depends” (Aristotle 1984, Vol. 1, Topics VIII.10, 161a2), namely, by showing why the reasoning would be fallacious (this is called giving a solution ).⁴² (2) He may try to do so by “stating an objection directed against the questioner” (ibidem, 161a2–3), namely, by, though not giving a solution, making it impossible for the Questioner to continue with the argument. (3) Further “one may object to the questions asked” (ibidem, 161a5), namely, by pointing out that as yet no conclusion follows (whereas a conclusion might follow with an additional premise): in this case, the Questioner may continue. (4) “The fourth and worst kind of objection is that which is directed to the time allowed for discussion; for some people bring objections of a kind which would take longer to answer than the length of the discussion in hand” (ibidem, 161a9–12). Aristotle seems to favor the first of these possibilities: “There are then, as we said, four ways of making objections; but of them the first alone is a solution: the others are just hindrances and stumbling-blocks to prevent the conclusions” (ibidem, 161a13–5).

There is an obvious tension in Aristotle’s instructions for the Questioner and the Answerer mentioned above. Sometimes these instructions seem to set a standard of reasonable and cooperative behavior; at other times they propound quite unreasonable and competitive tactics that are more appropriate for eristic wrangling than for a philosophical enterprise. Since Aristotle distinguishes between truly dialectical and eristic discussions, and considers those discussants that are uncooperative and contentious in their behavior as “bad dialecticians,” one may wonder why he chose to admit so much contentiousness in his truly dialectical debates. The bottom line, however, is that some contentious (competitive) elements are unavoidable:

Those [propositions, protaseis] which are used to conceal the conclusion serve a contentious purpose; but inasmuch as an undertaking of this sort is always conducted against another person, we are obliged to employ them as well. (Aristotle 1984, Vol. 1, Topics VIII.1, 155b26–28)

How much contentiousness you need may depend on the circumstances of the debate and on the character of your opponent (who may only be thinking of himself as smart or could be highly ill-tempered). But in a debate you need to apply some contentious tactics, just because you are not the only person involved. As a good dialectician, you would not use more contentious means than necessary, so as not to become yourself the one who spoils the debate.

If the Questioner commits a fallacy when pretending to draw a conclusion from certain premises, the Answerer will not behave contentiously at all if he uses the first of the four ways mentioned above of trying to prevent the Questioner from drawing a conclusion, by giving a solution. To expose the fallacy would indeed be a matter of justified self-defense and would at the same time contribute to the quality of the debate. Aristotle elaborates on this kind of situation by presenting a list of fallacies and discussing their solutions.

2.4 Aristotle’s Theory of Fallacies

Aristotle was the first to make a systematic study of fallacies. He devoted a whole volume to the subject, Sophistical refutations,⁴³ the core of which consists of a list of thirteen types of sophistical refutation with explanations, examples (we counted 131 of them), and solutions. Another list of nine types can be found in Rhetoric II.24 (see Sect. 2.8).⁴⁴ Since Sophistical refutations is closely related to the Topics, Aristotle’s theory of fallacies as presented in Sophistical refutations is part and parcel of his theory of dialectic, and the fallacies he discusses must be interpreted in a dialectical context.⁴⁵

2.4.1 Aristotle’s Concept of Fallacy

What concept of fallacy does Aristotle have? He speaks of incorrect argument (pseudês logos), paralogism (paralogismos), sophistical/eristic deduction (sophistikos/eristikos sullogismos), sophistical refutation (sophistikos elegchos), eristic argument (eristikos logos), etc. These terms are not synonymous, but neither are the distinctions between them always clear. In Topics VIII.12, however, we are told that an argument can be incorrect (pseudês) on four accounts:

• (1) Inconclusiveness (eristic deductions,⁴⁶ yielding sophistical refutations): the argument merely seems to reach a conclusion. Most fallacies of Aristotle’s list of 13 belong to this group.

• (2) Irrelevant conclusion (which also yields sophistical refutations): the argument reaches a conclusion, but not the conclusion required in the circumstances.⁴⁷ For instance, if a thesis T is to be refuted, the conclusion is similar to, but not identical to, a denial of T. Or the argument correctly derives an impossibility from T and some other conceded premises, but is mistaken in blaming T for it, so that the impossible conclusion is irrelevant. These fallacies correspond to examples of secundum quid (or of ignoratio elenchi) and of non-cause on Aristotle’s list (see Fig. 2.1).

• (3) Wrong method (another kind of eristic deduction⁴⁸): the argument reaches a relevant conclusion, but by a wrong method, seeming to be using the right method. This group comprises (a) arguments that seem to be in accordance with a scientific discipline, but are not, for instance, arguments that merely seem to constitute a medical (or a geometrical) argument but actually use concepts or principles that are foreign to the discipline (see Soph. ref. 11), and (b) arguments that merely seem to be dialectical, for instance, because some of their premises merely seem to be acceptable.

• (4) False premise: even if an argument reaches a relevant conclusion by the right method, there could be one or more false premises (the concept of being in accordance with a scientific discipline is not to be understood as excluding all error, and of course “acceptable premises” could be false). Examples are false proofs in geometry in which one uses geometrical methods but draws a wrong line somewhere.

Fig. 2.1

Aristotle’s list of fallacies

Incorrect argument appears to be Aristotle’s most general term in this context. The incorrect arguments of groups (1), (2), and (4) are also called paralogism s.⁴⁹ It may also be seen that eristic or sophistical arguments or refutations comprise groups (1), (2), and (3) and thus overlap with the paralogisms.⁵⁰ Most of the exposé in Sophistical refutations deals with the fallacies of groups (1) and (2) (Aristotle’s list). In this chapter, we shall limit ourselves to a brief discussion of these fallacies.⁵¹

2.4.2 Aristotle’s List

The items on Aristotle’s list are types of sophistical refutation: they seem to be refutations, but are not really refutations. A refutation (elegchos), in this context, is a deductive argument from conceded premises that concludes to the contradictory of the thesis of the Answerer in a dialectical exchange. A deductive argument or deduction (sullogismos) is defined as in the Topics: not only must the premises necessitate the conclusion, but also none of them may be superfluous and all of them must be different from the conclusion. An alleged refutation then may either be based on a non-deductive argument (which seems to be deductive) or have a wrong conclusion (which seems to be the required conclusion) or have a premise of the wrong kind (which premise, however, seems alright). This division assigns each sophistical refutation to either group (1), (2), or (3b) above. Aristotle, however, classifies the sophistical refutations in a different way: those that depend on the “use of language” (lexis) and those that do not. Distinctive for the fallacies of the first group seems to be that their deceptive character is due to matters of formulation. According to Hamblin, they result from the imperfections of natural language:

What does distinguish the refutations dependent on language is that they all arise from the fact that language is an imperfect instrument for the expression of thoughts: the others could, in theory, arise even in a perfect language. (Hamblin 1970, p. 81)

According to Aristotle, it can be shown by induction and by deduction that there are exactly six kinds of sophistical refutations that belong to this group (Soph. ref. 4, 165b27–30). Besides, there are seven kinds that do not depend on the way language is used. These 13 types of fallacy are listed in Fig. 2.1, together with their Greek and Latin names.

The fallacies that depend on the use of language arise because one utterance can carry more than one message. Consequently, the Questioner ’s conclusion may only seem to have been deduced from the propositions granted by the Answerer – if the Questioner interprets the Answerer’s utterances in a way different than the Answerer does – or only seem to be the contradictory of the Answerer ’s thesis. Such discrepancies may be brought about on two accounts⁵²: either (a) because an utterance corresponds to two (or more) different sentences (fallacies of composition, division, and accent) or (b) because – even though the utterance may correspond to only one sentence – this sentence is ambiguous (fallacies of equivocation, amphiboly, and form of expression) (Soph. ref. 6, 168a23–28). The fallacies may originate at the level of morphemes, of words, or of sentences.

• (1) Equivocation. This is a type of fallacy of group (b), originating at the level of words. By using an ambiguous term in a question, the question itself will become ambiguous, and the Answerer may grant the premise asked for taking the question in one sense, whereas the Questioner uses it in another sense as he deduces his conclusion. If the ambiguous term occurs in the theses of the Answerer and of the Questioner, it may be that it has a different sense in each thesis, so that there is no real contradiction.

• (2) Amphiboly. If a sentence contains no ambiguous words, it may still be an ambiguous sentence because it allows two ways of being parsed. The fallacy of amphiboly is the corresponding fallacy of group (b) originating at the level of sentences.

• (3) Composition. The fallacies of composition (or combination) and division in Sophistical refutations are markedly different from their contemporary namesakes, which are fallacies of reasoning from parts to wholes and vice versa.⁵³ Here they are fallacies dependent on the use of language and concern the groupings of words. For instance, in an utterance of “[he is] being able to walk while sitting” (Aristotle 2012, Soph. ref. 4, 166a23–24), words can be grouped either as “[he is] ((being able to (walk))(while sitting))” (divided reading: “while sitting” is placed at the same level as “being able to”) or as “[he is] (being able to ((walk) (while sitting)))” (composed reading: “while sitting” is brought into the scope of “being able to”). Aristotle considered these two readings not as readings of an ambiguous sentence but as two different sentences. Therefore, the fallacies of composition and division are fallacies of group (a) and must be distinguished from the fallacy of amphiboly – even though they all originate at the level of sentences. In the present example, the divided reading is unproblematic, whereas the composed reading is absurd and can be misused by the Questioner. A Questioner’s shifting from the divided to the composed reading, then, constitutes the fallacy of composition.

• (4) Division. Conversely, a Questioner’s shifting from the composed to the divided reading constitutes the fallacy of division. So here the composed reading will be unproblematic and the divided reading will be absurd.

• (5) Accent. Ancient Greek was a tone language and the accents of words were tones, not stresses: a difference of pitch could suffice to distinguish two words. In some cases, two words that were indistinguishable when written, or sloppily pronounced, could be distinguished by their different accents, if pronounced correctly. Consequently, if an utterance of a sentence S would contain such a word, the utterance could sometimes be taken to correspond also to another sentence S’, and thus to carry two distinct messages: S and S’. If the Questioner takes advantage of this fact by shifting from one message to the other one, he will commit the fallacy of accent, which is a fallacy of group (a), originating at the level of words.

• (6) Form of expression. This is the only fallacy originating at the level of morphemes. According to Aristotle, it is a fallacy of ambiguity (group (b)). But whereas in fallacies of equivocation and amphiboly there are – from the point of view of linguistics – two legitimate readings involved, examples of the fallacy of form of expression usually display a legitimate and an illegitimate reading. Ancient Greek has many morphemes that allow one to infer that a designated entity belongs to a specific category (e.g., the category of individuals, of qualities, of quantities, of actions, of affections (states of being affected), etc.). For instance, verbs with active endings denote actions, and verbs with a passive ending denote affections. There are, however, many exceptions, so that interpretations based on such features can yield an illegitimate reading. Furthermore, the general inclination to regard each entity as an individual makes people misinterpret phrases referring to entities of other categories as referring to individuals. Take the following example:

  “If what someone has he later does not have, he has lost it. For someone who has lost one die alone, will not have ten dice.” (Aristotle 2012, Soph. ref. 22, 178a29–31)

  This tersely expressed example may be reconstructed as follows:

  If someone no longer has what he once had, do we say that he has lost it?

  Yes, thus we may define what it means to lose something.

  Suppose, John has ten dice and loses just one of them. In that case, wouldn’t

  John no longer have ten dice, whereas he once had them?

  Exactly.

  So, according to our definition, John would have lost ten dice?

  Certainly.

  But we supposed he lost just one of them!

  Good grief! (Adapted from Krabbe 2012, p. 246)

  The fallacy hinges on misinterpreting “ten dice” as an individual instead of a quantity. Since “what” and “it” in the premise “If someone no longer has what he once had, he has lost it” refer to the category of individuals, substituting the term “ten dice” for them requires this term to be interpreted as denoting an individual.⁵⁴

  The six fallacies discussed thus far are those that depend on the use of language. We now turn to the fallacies that are independent of the use of language.

• (7) Accident. This is a fallacy of deduction. If it is granted that some entity x has property y (y is called an accident ⁵⁵ of x) and y has property z, one would commit this fallacy if one pretended to deduce from these premises that x has property z. For instance, if Coriscus (x) is a man (y) and man (y) is different from Coriscus (z), it does not follow that Coriscus (x) is different from Coriscus (z). Similarly, from the premises x has property y and x has property z, one cannot deduce that y has property z. For instance, if Socrates (x) is a man (y) and Socrates (x) is different from Coriscus (z), it does not follow that man (y) is different from Coriscus (z).⁵⁶

  Another example of the fallacy of accident⁵⁷ can be found in Plato’s Euthydemus. The speakers are the eristic debater Dionysodorus (D) and a spectator named Ctesippus (C):

  D: You will admit all this [among other things that Ctesippus’ father is a dog], if you answer my questions. Tell me, have you got a dog?

  C: Yes, and a brute of one too.

  D: And has he got puppies?

  C: Yes indeed, and they are just like him.

  D: And so the dog is their father?

  C: Yes, I saw him mounting the bitch myself.

  D: Well then: isn’t the dog yours?

  C: Certainly.

  D: Then since he is a father and is yours, the dog turns out to be your father, and you are the brother of the puppies, aren’t you? [Quickly to keep the other from cutting in:] Just answer me one more small question: Do you beat this dog of yours?

  C (laughing): Heavens yes, since I can’t beat you!

  D: Then do you beat your own father?

  (Adapted from Plato 1997, Euthydemus 298d–e)

  The fallacy is committed when D says: “[…] since he is a father and is yours, the dog turns out to be your father […]” With some effort, it can be reconstructed in terms of the schemas given above: this dog (x) is this father (y) and this dog (x) is yours (z), therefore (fallacy of accident) this father (y) is yours (z); in other words, this father is your father and (since this dog is this father), by a second fallacy of accident, this dog is your father.

• (8) Secundum quid . The phrase secundum quid translates the Greek pêi (in a certain respect, with a qualification), but as can be seen from Fig. 2.1, the full name of the fallacy is longer. It can be rendered as the “fallacy of saying things with or without adding a qualification.” If, for instance, the Answerer has granted that a black man is white of teeth, he is held to have admitted that a black man is both white and nonwhite.⁵⁸ But it is incorrect to omit the qualification “of teeth.” Adding a qualification can also be incorrect: “[…] illness is bad, but not getting rid of illness” (Aristotle 2012, Soph. ref. 25, 180b20–21). Here “getting rid of x” is a qualification that is incorrectly added if one assumes that who admits that illness is bad has also admitted that getting rid of illness is bad. The fallacy may not only lead to a deduction that only seems to be based upon the premises admitted by the Answerer but also to one that only seems to yield the contradictory of the thesis of the Answerer.

  In the later tradition, the designation secundum quid has shifted its meaning so as to denote illicit reasoning from instances to universal propositions, also known as hasty generalization. It is an example of a fallacy label that has been kept in use, while its contents changed beyond recognition.⁵⁹

• (9) Ignoratio elenchi . The phrase translates the Greek tou elegchou agnoia (ignorance of refutation). It is the fallacy of presenting an argument that seems to be a refutation of the Answerer’s thesis but actually violates one of the conditions of the definition of refutation (which include those of deduction). Most examples Aristotle adduces here are similar to those that illustrate secundum quid. For instance:

  Some people, omitting one of the things mentioned, appear to give a refutation, for example, the argument that the same thing is the double and not the double. For two is the double of one, but not the double of three. Or if the same thing is the double and not the double of the same thing, but not in the same respect – double in length, but not double in width. Or if it is the double and not the double of the same thing, in the same respect and in the same way, but not at the same time; because of that it is an apparent refutation. (Aristotle 2012, Soph. ref. 5, 167a28–34)

  The given characterization of ignoratio elenchi permits Aristotle to reduce (in Soph. ref. 6) all other sophistical refutations of his list to special cases of this fallacy by linking them to specific conditions of the definition of refutation. A similar analysis brings him (in Soph. ref. 8) to claim completeness for his list (which no longer includes ignoratio elenchi)⁶⁰:

  Thus we should know on how many grounds fallacies come about, for they could not depend on more; they will all depend on those mentioned. (Aristotle 2012, Soph. ref. 8, 170a9–11)

  In the later tradition, the designation ignoratio elenchi has shifted its meaning so as to denote arguments with an irrelevant conclusion (those of group (2) of the incorrect arguments described in Topics VIII.12). This modern notion extends beyond a context of refutation in a dialectical discussion between a Questioner and an Answerer. On the other hand, it does not encompass all kinds of sophistical refutation.

• (10) Consequent. The fallacy of consequent is, according to Aristotle, a subspecies of the fallacy of accident . It comprises not just the fallacy of asserting the consequent but also denying the antecedent, universally generalized versions of these two fallacies, and in general any conversion of the relation of consequence. Examples are:

  […] since the soil’s being drenched follows upon it having rained, we take it that if the soil is drenched, it has rained. But that is not necessary. And in rhetoric, sign-proofs are based on the consequences. For, wanting to show that someone is an adulterer, they seize on the consequence: that he is nicely dressed or that he is seen roaming around at night. However, these things apply to many people while the accusation does not. Similarly with deductive arguments, for example, the argument of Melissus that the universe is unlimited, having secured that the universe has not come to be (for nothing can come to be from what is not) and that what comes to be comes to be from a beginning; now, if the universe has not come to be, it does not have a beginning either, so that it is unlimited. However, this does not necessarily follow. For it is not the case that if everything that comes to be has a beginning, then also everything that has a beginning has come to be, just as it is not true that if someone who has a fever is hot, then also someone who is hot must have a fever. (Aristotle 2012, Soph. ref. 5, 167b6–20)

• (11) Begging the question. The definition of deduction does not allow any premise to be identical to the conclusion. Aristotle does not give any examples in Sophistical refutations, but from a discussion in Topics VIII.13, it is clear that begging the question is not limited to the case of a premise being identical, or equivalent by substitution of synonyms, to the conclusion. It may also be that there is some other relation of equivalence, or that the premise expresses a special case of what the conclusion universally asserts, or conversely that the conclusion expresses a special case of what the premise universally asserts, or that the premise asserts a conjunctive part of the conclusion. Not all of these cases would nowadays be deemed fallacious.

• (12) Non-cause. The name of this fallacy does not refer to physical causality but to logical grounds. It refers to a fallacious use of a reductio ad absurdum (or ad impossibile)⁶¹ argument in which (1) an impossibility is derived from a number of conceded premises, but (2) the wrong premise is blamed for yielding the impossibility and consequently denied.⁶² This may occur when the impossible conclusion does not depend at all on the premise blamed and denied, as in the following example:

  … soul and life are not the same. For if coming to be is the contrary of passing away, then also a form of coming to be will be the contrary of a form of passing away. But death is a form of passing away and contrary to life, so that life is a coming to be and to live is to come to be. That, however, is impossible. Therefore soul and life are not the same. Surely this has not been deduced, for the impossibility follows even if one does not say that life is the same as soul, but only that life is the contrary of death, which is a form of passing away, and that coming to be is the contrary of passing away. (Aristotle 2012, Soph. ref. 5, 167b27–34)

  The premise to blame is probably that life (instead of birth) is contrary to death.

• (13) Many questions. The Questioner is to obtain his premises by asking the Answerer to either affirm or deny certain propositions. These propositions are each to ascribe one attribute to one thing (“Does S have attribute P?”) and not several attributes to one thing (“Does S have attributes P and Q?”) or one attribute to more than one thing (“Do S and T have attribute P?”) (Soph. ref. 30, 181a36–39). The latter two kinds of question are improper and a refutation that depends on them would be sophistical. So would a refutation depending on the following question:

  … concerning things of which some are good and others are not, ‘Are all of them good or not good?’ (Aristotle 2012, Soph. ref. 5, 168a7–8)

2.4.3 Solutions of Fallacies

The second half of Sophistical refutations is concerned with tactics for the Answerer. Aristotle concentrates in particular on the question of how the Answerer should react when confronted with a sophistical refutation. Ideally, the Answerer should provide a solution on the spot, i.e., he should point out the fallacy and provide an explanation of what went wrong – Aristotle realizes that this may be difficult in the heat of the debate (Soph. ref. 18, 177a6–8).

There is a strict concept of solution , solution directed at the argument (pros ton logon), and also a more relaxed concept, solution directed at the Questioner or at the person (pros ton erôtônta, pros ton anthrôpon). According to the strict concept of solution, there is for each case a unique theoretically grounded solution (Soph. ref. 24, 179b18, 23–24). Further, “arguments depending on the same point have the same solution” (Aristotle 2012, Soph. ref. 20, 177b31–32), and a true solution must be such that if the denial of the solution of an argument is added to the premises, the resulting argument becomes unsolvable (Soph. ref. 22, 178b16–21).⁶³ According to the more relaxed concept, showing the conclusion to be false without pinpointing and blaming any particular premise can be a solution (Soph. ref. 18, 176b40). Also there may sometimes be more than one solution (Soph. ref. 30, 181b19).

The concept of a solution directed at the person rather than at the argument is, according to Nuchelmans (1993), one of the four Aristotelian roots of the argumentum ad hominem, which is nowadays mostly regarded as a kind of fallacy.⁶⁴ As we saw, in Aristotle, the ad hominem solutions need not be fallacious but constitute inferior tactics for defusing fallacies.

2.5 Cicero and Boethius on Topics (Loci)

After Aristotle, the tradition of dialectic continued in commentaries on the Topics and Sophistical refutations as well as in contributions of a more original character.⁶⁵ Several heads of the Peripatetic school founded by Aristotle showed an interest in dialectic. Among them are Theophrastus of Eresus (ca. 371–287 BC) and Strato of Lampsacus (ca. 335–269 BC), of which philosophers we do not possess any specific writings on dialectic, and Alexander of Aphrodisias (floruit AD 200), whose commentary on the Topics, entitled In Aristotelis Topicorum libros octo commentaria [Commentaries on the eight books of Aristotle’s Topics], has been of considerable influence on later scholars and who presumably also wrote a commentary on Aristotle’s Sophistic refutations.

The most important works on dialectic after Aristotle have, however, been written by two Roman scholars. The first one is Cicero (106–43 BC), who was born in Arpinum (in Latium) and later went to Rome, where he became a successful lawyer and politician. He was murdered, after having been declared an enemy of the state, by his political rivals Mark Antony and Octavian (Augustus). His head and hands were nailed to the rostra, the place in Rome where he used to deliver his speeches. A great many of his works – speeches, philosophical and rhetorical works, and letters – have survived.

The second scholar who has written influential works on dialectic is Boethius (ca. 480–ca. 525). Boethius was born in Rome and reached the rank of consul in 510. After a successful career in public life under the protection of King Theodoric the Ostrogoth, he was later suspected by the King of conspiracy and put to death. Apart from the famous Consolation of philosophy, Boethius wrote treatises on theology, mathematics, music, and logic. As to the latter subject, he also produced translations of and commentaries on most of Aristotle’s works on logic, on Porphyry’s Isagoge [Introduction], which is an introduction to Aristotle’s Categories, and on Cicero’s Topica [Topics]. Boethius has had an enormous impact on medieval philosophy.

Given the importance of the notion of a topic (Greek: topos, Latin: locus) in the dialectical as well as the rhetorical tradition, we will now discuss Cicero’s and Boethius’ views on the topics in more detail. Cicero mentions the term locus in an unfinished treatise, entitled De inventione [On invention]. He discusses Aristotle’s topics at greater length in De oratore [On the orator] as well as in his Topica. In our description of Cicero’s view on the loci, we shall focus on the latter two works. Boethius wrote two treatises on the subject. The first one is a fairly elementary work entitled In Ciceronis Topica [On Cicero’s Topics], which is a commentary on Cicero’s last treatise about the subject. The second one is a concise but more advanced study entitled De topicis differentiis or De differentiis topicis [On topical distinctions]. In our description of Boethius’ view on the loci, we shall focus on the latter work.

2.5.1 Cicero’s View of Loci

In Cicero’s treatise De oratore, loci are defined as “the dwelling places of all arguments” (II, 162). As to the application of loci, it is noted that the speaker may use them to find arguments in a wide variety of contexts: “But Aristotle, whom I admire most of all, laid out certain loci from which all argumentation may be found, not just for discussions among philosophers, but also for the kind of speech we use in court cases” (II, 152). In the same treatise, Cicero provides a list of loci consisting of two main types: those “derived from the essential nature of the matter at hand” and those “taken from outside” (II, 163–173). The first main type is further divided into four subtypes, whereas the second main type remains unspecified. Since the list in De oratore is almost identical to the one Cicero provides in his Topica, we will continue our discussion with a reconstruction of his view on the loci as they are presented in the latter work.

Unlike De oratore, Cicero’s Topica is specifically dedicated to the loci. The Topica can be characterized as a manual for finding arguments. It consists of a general introduction of the subject, a concise treatment of the loci, a more elaborate treatment of the same loci, an explanation of different types of questions in juridical disputes, and an explanation of the application of the loci in relation to these types of question as well as in relation to the rhetorical doctrines of finding the appropriate reaction to an accusation (status theory) and the parts of a speech (partes orationis).

The fact that the loci are treated twice – first concisely and then more elaborately – has led scholars to think that Cicero wrote the work in a hurry and did not pay much attention to its composition. This impression is reinforced by the fact that some parts of the Topica seem to be taken from earlier writings. The concise treatment of the loci is a somewhat extended version of his treatment of the same subject in De oratore, and the explanation of different types of questions is adumbrated in De oratore III, 111ff. as well as in Cicero’s Partitiones oratoriae [Arrangements of rhetoric], 61ff.

The Topica is dedicated to the jurist Trebatius, to whom Cicero in the beginning of the work explains how loci are of help in finding arguments as well as judging them. Since the passage is of historical as well as terminological interest, we quote it in full:

Every systematic treatment of argumentation has two branches, one concerned with invention of arguments and the other with judgement of their validity; Aristotle was the founder of both in my opinion. The Stoics have worked in only one of the two fields. That is to say, they have followed diligently the ways of judgement by means of the science which they call dialektikê (dialectic), but they have totally neglected the art which is called topikê (topics), an art which is both more useful and certainly prior in order of nature. For my part, I shall begin with the earlier, since both are useful in the highest degree, and I intend to follow up both, if I have leisure. A comparison may help: It is easy to find things that are hidden if the hiding place is pointed out and marked; similarly if we wish to track down some argument we ought to know the places or topics: for that is the name given by Aristotle to the “regions”, as it were, from which arguments are drawn. Accordingly, we may define a topic as the region of an argument, and an argument as a course of reasoning which firmly establishes a matter about which there is some doubt. (Cicero 2006, Topica 6–8)

As to the loci themselves, Cicero makes a basic distinction between “internal” and “external” loci. The internal loci are “inherent in the very nature of the subject under discussion” (Cicero 2006, Topica 8). They include four different classes: (1) those that are drawn from the subject as a whole; (2) those that are drawn from the parts of the subject; (3) those that are drawn from the etymology of the subject; and (4) those that are drawn from things somehow related to the subject. The external loci are “brought in from outside” the subject. They pertain to arguments from external circumstances, i.e., arguments “that are removed and widely separated from the subject” (Cicero 2006, Topica 8; Fig. 2.2).

Fig. 2.2

Cicero’s basic classification of loci

Most of the examples that Cicero gives of these different types of loci are taken from the field of law. The locus drawn from the subject as a whole is specified as definitio (definition ); it is similar to what is nowadays called “argumentation from definition.” Cicero provides the following example: “The civil law is a system of equity established between members of the same state for the purpose of securing to each his property rights; the knowledge of this system of equity is useful; therefore the science of civil law is useful” (Cicero 2006, Topica 9). Our reconstruction of Cicero’s example below makes clear how the locus of definition may be used in order to construct an argument for defending the standpoint “The science of civil law is useful:”

1. Standpoint	The science of civil law is useful
2. Reason	The knowledge of the system of equity established between members of the same state for the purpose of securing to each his property rights is useful
3. Premise linking (1) and (2)	The civil law is defined as a system of equity established between members of the same state for the purpose of securing to each his property rights

The locus drawn from the parts of the subject is specified as partium enumeratio (listing the parts). This locus may be used to construct arguments that are based on the division of a whole into its parts. Cicero’s example is as follows: “So-and-so is not a free man unless he has been set free by entry in the census roll, or by touching with the rod, or by will. None of these conditions has been fulfilled, therefore he is not free” (Cicero 2006, Topica 10). In this case, the locus drawn from the parts of the subject is used in order to construct an argument for defending the standpoint that a certain person is not a free man:

1. Standpoint	So-and-so is not a free man
2. Reason	So-and-so has not been set free by entry in the census roll, nor by touching with the rod, nor by will
3. Premise linking (1) and (2)	Only if so-and-so has been set free by entry in the census roll, or by touching with the rod, or by will, will he be a free man

The locus drawn from the etymology of the subject is specified as notatio (meaning). Cicero provides the following example: “Since the law provides that an assiduus (tax-payer or freeholder) shall be vindex (representative) for an assiduus, it provides that a rich man be representative for a rich man; for that is the meaning of assiduus, it being derived, as Aelius says, from aere dando (paying money)” (Cicero 2006, Topica 10).⁶⁶ The argumentation in this example serves to support the standpoint that a representative for the defendant ought to be a rich man. Since in the days of Cicero the meaning of assiduus as “rich man” turned obsolete, the argumentation includes the mentioning of the etymology of the term as put forward by an authority. The example can be reconstructed as follows:

1. Standpoint	A representative for the defendant ought to be a rich man
2. Reasons (2a)	The defendant is a rich man and (2b) the law provides that a representative for a rich man ought to be a rich man
3. Reason supporting (2b)	The law provides that a representative for an assiduus ought to be an assiduus
4. Premise linking (3) and (2b)	The meaning of assiduus is “rich man”
5. Reason supporting (4)	The meaning of assiduus is derived from aere dando (paying money)
6. Reason supporting (5)	Aelius says so

The last type of internal loci, those drawn from things somehow related to the subject, is further divided into 15 subtypes.⁶⁷ We will discuss two of these subtypes in more detail: those two for which Cicero does not only provide the name but also its law, i.e., “the principle which provides the inferential strength” (Rubinelli 2009, p. 128).

The first one is the locus a genere (argumentation from the genus). Cicero gives the following example: “Since all the silver was bequeathed to the wife, the coin which was left in the house must also have been bequeathed. For the species is never separated from its genus, as long as it keeps its proper name; coin keeps the name of silver; therefore it seems to have been included in the legacy” (Cicero 2006, Topica 13). The reconstruction below clarifies the argumentative function of all the elements mentioned in the example including the sentence “the species is never separated from its genus, as long as it keeps its proper name,” which is the law associated with this topic:

1. Standpoint	The coin (nummus/argentum) which was left in the house must have been bequeathed to the wife
2. Reason	All the silver (argentum) was bequeathed to the wife
3. Premise linking (2) and (1)	The coin (nummus/argentum) belongs to all the silver (argentum)
4. Reason supporting (3)	Coin (nummus/argentum) keeps the name of silver (argentum)
5. Premise linking (4) and (3)	The species is never dissociated from the genus as long as it keeps its proper name

The second subtype is the locus ex comparatione (argumentation from comparison). For this subtype, Cicero provides three examples, each of which includes a description of the law associated with the locus at issue. We discuss the third one, which resembles what in pragma-dialectics is called “similarity argumentation” or “argumentation based on a comparison.” Cicero specifies this particular topic as the locus ex comparatione parium (argumentation from the comparison of equals). He gives the following example: “What is valid in one of two equal cases should be valid in the other; for example: Since use and warranty run for two years in the case of a farm, the same should be true of a (city) house” (Cicero 2006, Topica 23). Like with the former locus we discussed, the law of the present locus can be reconstructed as a linking premise, be it that in this case the law operates on a different level in the argumentation:

1. Standpoint	Use and warranty of a city house should run for two years
2. Reason	Use and warranty of a farm run for two years
3. Premise linking (2) and (1)	What is valid in one of two equal cases should be valid in the other

Unlike the internal loci, which are divided into four subtypes, the external loci are not further divided into subtypes. From Cicero’s description, it follows that they can be used to construct what nowadays would be called “argumentation from authority”: “Extrinsic arguments depend principally on authority […] Since Publius Scaevola has said that the ambitus of a house is only that space which is covered by a roof put up to protect a party wall, from which roof water flows into the home of the man who has put up the roof, this seems to be the meaning of ambitus” (Cicero 2006, Topica 24). Since Cicero does not provide a law for the locus corresponding to argumentation from authority, the reconstruction of this example only contains the standpoint and the reason given in its defense:

1. Standpoint	The ambitus of a house is only that space which is covered by a roof put up to protect a party wall, from which roof water flows into the home of the man who has put up the roof
2. Reason	Publius Scaevola has said so

As to the application of the internal and external loci, Cicero remarks that they are not all equally suitable in all situations. In some cases, particular loci are more appropriate than others. In the remaining sections of his Topica, Cicero provides an explanation of their application by relating the use of the various loci to other aspects of the composition of a speech, such as the type of question the speaker addresses, the type of speech he is giving, the type of standpoint he is defending, and the different parts of the speech.

2.5.2 Boethius’ View of Loci

Of the two works Boethius devoted to loci, In Ciceronis Topica and De topicis differentiis, the latter is meant to be his definitive treatment. We therefore concentrate our discussion of his view on loci on De topicis differentiis. The treatment consists of an introduction with definitions and discussions of key terms (Book I), an exposition of the views on dialectical loci of the fourth century orator and philosopher Themistius (Book II), an exposition of Cicero’s view on dialectical loci with a comparison and reconciliation of the divisions of the two authors (Book III), and an explanation of rhetorical loci followed by a comparison of dialectical and rhetorical loci and a discussion of the nature of rhetoric (Book IV).

It is noteworthy that Boethius defines an argument as something that is supposed to change the doxastic attitude of the addressee towards the standpoint: “An argument is a reason (ratio) producing belief regarding a matter [that is] in doubt” (Boethius 1978, 1174D). This definition indicates that Boethius’ treatise is intended to be a manual for the production of belief in the context of dialectical disputations and rhetorical speeches rather than a manual for the production of valid arguments in the context of logical proofs or philosophy. Because loci are generalizations of reasons on the basis of which the arguer may find the concrete reasons needed for the defense of his standpoint, they play an important role in disputations and speeches. The function of loci is reflected in Boethius’ definition of a topic: “A topic is the seat of an argument, or that from which one draws an argument appropriate to the question under consideration” (Boethius 1978, 1174D).

Boethius distinguishes between two types of loci: a locus of the first type he calls a “maximal proposition” (maxima propositio) and a locus of the second type a “difference of maximal propositions” (differentia). These notions are difficult to interpret. In the following, we provide a separate reconstruction of both of them and clarify their respective functions (if any) in finding and justifying arguments.

By a locus of the first type – the maximal proposition – Boethius means a locus in the sense of a self-evident truth that may function as a justification of something that is in doubt:

There are some propositions which not only are known per se but also have nothing more fundamental by which they are demonstrated, and these are called maximal and principal [propositions]. And there are others for which the first and maximal propositions provide belief. (Boethius 1978, 1185A)

This definition leaves open two different interpretations. On the one hand, Boethius may have thought of a maximal proposition as a self-evident truth in the sense of a first principle or axiom from which other propositions can be derived. On the other hand, he can have meant a self-evident truth in the sense of a justificatory principle underlying the link between a given reason (premise) and the standpoint (conclusion) this argument is to support.

From the examples of maximal propositions Boethius provides, it becomes clear that the second interpretation is the most appropriate. For instance, when the standpoint “The Moors do not have weapons” is defended by the reason “They lack iron,” he mentions as the maximal proposition “Where the matter is lacking, what is made (efficitur) from the matter is also lacking” (Boethius 1978, 1189C-D). The following reconstruction shows that in this example, the maximal proposition functions as a justification of the implicit link between the reason and the standpoint, which can be expressed as “If the Moors lack iron, then they lack weapons:”

1. Standpoint	The Moors do not have weapons
2. Reason	They lack iron
3. Implicit premise linking (2) and (1)	(If the Moors lack iron, then they lack weapons)
4. Maximal proposition supporting (3)	Where the matter is lacking, what is made from the matter is also lacking

Apart from an implicit link, a maximal proposition may also justify an explicit link between a reason and a standpoint. Take the following example, where the standpoint “The art of medicine is advantageous” is defended by the reasons “It is advantageous to drive out disease and minister to health and heal wounds” and “If it is advantageous to drive out disease and minister to health and heal wounds, then the art of medicine is advantageous.” Boethius mentions in this case as the maximal proposition: “What inheres in the individual parts must inhere the whole” (Boethius 1978, 1188D). The following reconstruction shows that the argumentative function of the maximal proposition in this example is the same as that in the preceding example, namely, to support the conditional premise that validates the passage from its antecedent to its consequent in a modus ponendo ponens:

1. Standpoint	The art of medicine is advantageous
2. Reason	It is advantageous to drive out disease and minister to health and heal wounds
3. Explicit premise linking (1) and (2)	If it is advantageous to drive out disease and minister to health and heal wounds, then the art of medicine is advantageous
4. Maximal proposition supporting (3)	What inheres in the individual parts must inhere in the whole

In sum, what Boethius calls a maximal proposition can be reconstructed as some kind of generalization of the implicit or explicit link between the reason and the standpoint. As such, the generalization can be used as a heuristic tool for finding a reason in defense of the standpoint. But it can also, when made explicit, function as a “principle” that does not need any further justification and therefore will eventually produce a state of belief with respect to the standpoint on the side of the other party.

The second type of locus Boethius distinguishes is the difference of maximal propositions (differentia). The terminology is confusing, since loci of this type are used as labels for species of loci of the first type: the maximal propositions . the distinction may find its rationale in the fact that it relates to the two distinct types of use of the loci: the “differences” are suitable only for heuristic purposes, i.e., for finding a reason for a given standpoint, whereas the maximal propositions are primarily suitable for justificatory purposes, i.e., for justifying the link between the reason and the standpoint (though they may also be used for heuristic purposes).

Boethius in De topicis differentiis distinguishes between intrinsic, extrinsic, and intermediate differences: “All Topics, that is Differentiae of maximal propositions, must be drawn from the terms in the question, namely, the subject and the predicate, or be taken from without, or be situated as intermediates between the [previous] two” (Boethius 1978, 1186D). The intrinsic differences are those taken from the subject or predicate of the question, i.e., the standpoint that is doubted. An example is the difference called from material cause, of which the maximal proposition we discussed above, “Where the matter is lacking, what is made from the matter is also lacking,” is an instantiation.

A specimen of the extrinsic differences not taken from the terms of the standpoint is the difference called from similar cases. An instantiation is the maximal proposition “if something inheres in a way similar [to the thing asked about] and is not a property, neither can the thing asked about be a property” (Boethius 1978, 1190D). This maximal proposition functions as the linking premise in the following example: “The way four-leggedness inheres in a horse is similar to the way two-leggedness inheres in a man; but four-leggedness is not a property of the horse; therefore, two-leggedness is not a property of man” (Boethius 1978, 1190C-D). The classification of this difference as “extrinsic” is in fact somewhat unclear, since the maximal propositions that can be derived from it do relate to the terms of the standpoint at issue: the way in which something is predicated of the subject in the reason is the same as the way in which something is predicated of the subject in the standpoint. The same holds for the other differences in this group. The only difference that can be called “extrinsic” in an emphatic sense is the difference from judgment, from which an argument from authority can be derived: in this case, a complete proposition is argued to be true because someone says it is true.

Finally, the intermediate differences are those that in one way have to do with the terms of the standpoint at issue and in another way not. An example is the difference that is called from conjugates. An instantiation of this is the maximal proposition “if a just [man] is good, justice is also good” (Boethius 1978, 1192C). Topics of this kind are called “intermediate” since they imply a “certain small change” of the terms involved (Boethius 1978, 1192C).

Like the loci in the sense of maximal propositions, the loci in the sense of differences can be used to find reasons for a given standpoint. The heuristic procedure for this can be described as follows. In order, for example, to defend the standpoint “The Moors do not have weapons,” the arguer might use the intrinsic difference called “from material cause” to find the maximal proposition “Where the matter is lacking, what is made from the matter is also lacking.” This maximal proposition then enables him to construct the reason “The Moors lack iron.” Unlike the loci in the sense of maximal propositions, loci in the sense of differences are not to be viewed as premises justifying the link between a reason and a standpoint. They are labels that express the genera of maximal propositions and can therefore only function as a heuristic tool for the arguer to come up with a maximal proposition that fits the situation at issue.

2.6 Aristotle’s Syllogistic

In the preceding sections, we saw logical issues – such as the structure of the reductio ad absurdum, the definition of deductive argument (syllogismos ), and the various fallacies of deduction – crop up in a dialectical and argumentative context. The further development of logic, making it into an instrument that can be applied for the analysis and evaluation of arguments, was at first undertaken by Aristotle himself and its most famous result was Aristotle’s theory of syllogistic, to which we shall now turn. The principal exposition of this theory is to be found in his Prior Analytics.⁶⁸ For illustrative purposes, we have chosen to treat the small but crucial non-modal part of his theory that is now known as the theory of the assertoric (and categorical) syllogism (AnPr ⁶⁹ I.4–7).⁷⁰ A much greater part of the Prior Analytics has been devoted to modal logic (AnPr I.8–22), but the assertoric syllogisms form the kernel and most influential part of Aristotle’s logic.⁷¹ According to Russell, “any person in the present day who wishes to learn logic will be wasting his time if he reads Aristotle or any of his disciples” (1961, Chap. 22, p. 212), but we think that by studying this central part of Aristotle’s logic, the reader will have an easy access to a number of logical concepts and get acquainted with the very idea of a logical theory. This holds alike for students of logic and of argumentation theory.⁷²

We met the Greek term syllogismos in Sects. 2.3 and 2.4, when we dealt with the Topics and Sophistical refutations, and we there translated it by “deduction” or “deductive argument.” The definition of syllogismos used in these two works reappears almost verbatim in the Prior Analytics (AnPr I.1, 24b18–20), yet in practice the term is used in a much more restricted way, so that in the present context, it will be better to translate it by “syllogism.” The restrictions are due to Aristotle’s specification of the kinds of statements that may appear as premises or conclusions of syllogisms. His theory applies only to arguments that consist of statements that are, or can be reformulated as, statements of these kinds.

2.6.1 The Language of Syllogistic

In order to give precise expression to his theory of the syllogism, Aristotle in De interpretatione (On interpretation)⁷³ and in the Prior Analytics analyzes and regiments a part of the Greek language so as to be able to unambiguously express all statements that figure in arguments to which the theory is to apply. Even though he did not define a formal language, in the way of contemporary logicians, the standard formulations he introduces for different types of statements serve the same purpose. Thus, Aristotle was a pioneer of formal logic. At the same time, it must be understood that his formalization of arguments was not meant to replace the use of natural language in arguments but to give a clear expression to its interpretation.

In the Prior Analytics, Aristotle introduces the following types of statements:

A proposition,⁷⁴ then, is a statement affirming or denying something of something; and this is either universal or particular or indefinite. By universal I mean a statement that something belongs to all or none of something; by particular that it belongs to some or not to some⁷⁵ or not to all; by indefinite that it does or does not belong, without any mark of being universal or particular, e.g. ‘contraries are subjects of the same science’, or ‘pleasure is not good.’ (Aristotle 1984, Vol. 1, AnPr I.1, 24a16–22)

Since each statement must be either affirmative (“affirming something”) or negative (“denying something”) and each statement must be either universal or particular or indefinite, this gives us six types of statements.⁷⁶ This is not to say that Aristotle was not aware of any other type of statements. For instance, he was clearly aware of singular statements, i.e., statements with singular terms, such as “Socrates is white.”⁷⁷ It only means that other types of statements play no role in the theory. Yet, Aristotle was ambitious about the scope of application of the theory, for he seems to argue that, upon analysis, all deductive reasoning and all proof can be reduced to syllogisms in the narrower sense of his theory (Smith 1995, pp. 42–43), so that the restriction to six types of statements would be no real limitation.⁷⁸

Of the six types of statements, the two types (affirmative and negative) of indefinite statements are scantily treated. Mostly, they are said to behave like the corresponding particular statements.⁷⁹ Leaving them out of consideration, we have in Fig. 2.3 just four types of statements left, which are commonly known as categorical.⁸⁰

Fig. 2.3

Four types of categorical statements: the square of opposition

Figure 2.3 regiments a part of the English language in a way that parallels Aristotle’s regimentation of a part of the Greek language. Examples of categorical statements are obtained by substituting distinct⁸¹ general terms (countable nouns in the singular or equivalent phrases⁸²) for P and S in one of the statement forms. The term substituted for S is the subject (term) and the term substituted for P is the predicate (term) of the statement that results. Aristotle’s regimented statements allow for more variation in the form of expression than we have introduced in the English counterpart, where we have stipulated just one statement form for each type of categorical statement . Also, in the statement forms he uses most often, the order of subject and predicate is P–S instead of our S–P, as in “P is predicated of (or: belongs to) every S.” Consequently, some scholars write “PaS,” “PeS,” etc., where we have “SaP,” “SeP,” etc. (e.g., Smith 1995; Boger 2004). Anyhow, no such rendering was Aristotle’s.

Aristotle explains that O-statements are the denials of the corresponding A-statements, and vice versa, so that “Every S is a P” and “Some S is not a P” form a pair of contradictories (of which, necessarily, one is true and the other false). Similarly for I- and E-statements, “Some S is a P” and “No S is a P” are contradictories (De Int. 7, 17b16–20). The relation between A-statements and the corresponding E-statements is a different one. According to Aristotle, they are contraries: “Every S is a P” and “No S is a P,” he says, cannot both be true (but they could both be false) (De Int. 7, 17b20–23). Further it is clear that according to Aristotle, the universal statements are logically stronger than the corresponding particular statements: “Every S is a P” implies “Some S is a P,” and “No S is a P” implies “Some S is not a P.”⁸³

Each of these logical relations between categorical statements seems plausible when taken by itself, but unfortunately the unconditional acceptance of them all has the implausible consequence that for no general term S, the set of all S’s can be empty. For suppose the set of all S’s to be empty, and let P be any other general term, then “Some S is a P” will obviously be false. Since “Every S is a P” implies “Some S is a P,” “Every S is a P” will also be false. Because “Some S is not a P” is the denial of “Every S is a P,” “Some S is not a P” must then be true and, consequently, the set of all S’s will not be empty, against our supposition.

This means that if we wish to keep the relations between categorical sentences claimed to hold by Aristotle, we must restrict the language of syllogistic to general terms that apply to at least one individual (nonempty terms). This is sometimes called a blanket assumption of existential import. It is perfectly possible to go without such an assumption, but then one will get a different logic, not Aristotle’s theory of syllogistic.

Before we turn to reasoning in the language of syllogistic, a further remark must be made about the semantics of the categorical statements. We may assume that with each general term , there is associated a concept as well as a (nonempty) set of objects that fall under the concept. The first is, in contemporary philosophy of language, often denoted as the intension (with an “s”) of the term and the other as its extension. Both are part of the term’s meaning. Thus, corresponding to the term “swan,” there is the concept of a swan, as its intension , and the set of all swans, as its extension . Though there is no reason to suppose that intensions are unimportant (for Aristotle or for us), it is easier, in order to grasp Aristotle’s logic, to take an extensional point of view, that is, to take only the extensions of terms into account. Therefore, we interpret “Every S is a P” as saying that the set of all S’s is a subset of the set of all P’s (there is no S that is not a P) and “No S is a P” as saying that the set of all S’s and the set of all P’s have no element in common. Further we interpret “Some S is a P” as the denial of “No S is a P” and hence as saying that the set of all S’s and the set of all P’s have at least one common element. Finally, we interpret “Some S is not a P” as the denial of “Every S is a P” and hence as saying that there is at least one element in the set of all S’s that is not an element of the set of all P’s.⁸⁴

2.6.2 Deductions by Rules of Conversion

Before discussing syllogisms (taking the term in a restrictive sense), Aristotle discusses the rules of conversion (AnPr I.2). These allow one to derive one categorical sentence from another one while interchanging the two terms. A categorical statement to which such a rule applies is said to be convertible. E- and I-statements are convertible: “No B is a C” is a consequence of “No C is a B,” whereas “Some B is a C” is a consequence of “Some C is a B.” A-statements are only partially convertible , i.e., “Some B is a C” is a consequence of “Every C is a B,” but “Every B is a C” does not necessarily follow. E-statements are not only convertible but also partially convertible: “Some B is not a C” is a consequence of “No C is a B.” O-statements, however, are not convertible at all.

2.6.3 Deductions in the Figures

The core part of Aristotle’s theory of arguments in the language of syllogistic is concerned with the question in which cases two categorical premises (satisfying certain conditions) yield, by virtue of their form,⁸⁵ a categorical conclusion (and which conclusion this is). Equivalently, one could say that Aristotle studies arguments in the so-called syllogistic figures. These figures will be explained shortly. At present it suffices to know that an argument in the figures is an argument (1) with two premises and a conclusion, each of them in the language of syllogistic, (2) using precisely three distinct general terms such that (3) each pair of statements has one term in common. The question is then, which of the arguments in the figures are, by virtue of their form,⁸⁶ syllogisms?⁸⁷

The term occurring in both premises is called the middle term . The other two terms are known as the extremes. Each of the extremes occurs both in one of the premises and in the conclusion. One of them is called the major term and the premise in which it occurs is called the major premise, and the other is called the minor term and occurs in what is called the minor premise. Aristotle’s definitions of “major” and “minor” are somewhat problematic and ad hoc. In the later tradition (sixth century), which we shall here follow, the major term has been defined as the predicate term of the conclusion and the minor term as the subject term of the conclusion.⁸⁸ Here is an example of an argument in the figures that is also valid , i.e., a syllogism⁸⁹:

• (1) No swan is a predator.

• (2) Some bird is a swan.

• Therefore: (3) Some bird is not a predator.

Example 1

A syllogism in the figures

In the argument of Example 1, (1) and (2) are the premises and (3) is the conclusion; “swan” is the middle term, and “predator” and “bird” are the extremes, “predator” being the major term and “bird” being the minor term; (1) is the major premise and (2) the minor premise. The argument form of our example can be rendered as follows:

• (1) No S is a P.

• (2) Some B is an S.

• Therefore: (3) Some B is not a P.

This form can be symbolized as

• (1) SeP

• (2) BiS

• Therefore: (3) BoP

In such symbolic versions, the lower case letters “a,” “e,” “i,” and “o” indicate in an obvious way the type of categorical statement. An example of an argument in the figures that is not a syllogism is

• (1) Every swan is an animal.

• (2) Every swan is a bird.

• Therefore: (3) Every bird is an animal.

Example 2

An invalid argument in the figures

In Example 2, “swan” is again the middle term, and “animal” and “bird” are the extremes; “animal” is the major term and “bird” the minor term. The form of this argument can be rendered as follows:

• (1) Every S is an A.

• (2) Every S is a B.

• Therefore: (3) Every B is an A.

The invalidity of this form of argument can be shown by providing a counterexample (in the sense of an argument displaying this form with true premises and a false conclusion): substituting “swan” for S, “bird” for A, and “animal” for B will give us the true premises “Every swan is a bird” and “Every swan is an animal” but the false conclusion “Every animal is a bird.”

To organize this part of his research, Aristotle distinguishes three figures, according to the role of the middle term in the premises. In each premise the middle term must be either the subject term or the predicate term (it cannot be both). For two premises, this gives three possibilities: either the middle term functions as the subject term in one premise and as the predicate term in the other (first figure), or it functions twice as the predicate term (second figure), or twice as the subject term (third figure). For each figure, Aristotle investigates which combinations of premises yield syllogisms. When treating the first figure, Aristotle at first (AnPr I.4) restricts himself to arguments in which the predicate term of the conclusion (the major term) is also the predicate term of the premise in which it occurs (the major premise), as is the case in Examples 1 and 2. Thus, he skips syllogisms of forms in which the major term (P) is the subject term of the major premise, whereas the minor term is the predicate of the minor premise, such as:

• (1) No P is an M.

• (2) Every M is an S.

• Therefore: (3) Some S is not a P.

That does not mean that Aristotle is unaware of these syllogisms; with one understandable exception, all kinds of such syllogisms are covered by the Prior Analytics (AnPr I.7, 29a19–27 and AnPr II.1, 53a3–12). The exception is a kind of syllogism in which the conclusion is weaker than the strongest possible conclusion that can be deduced from the premises. Aristotle never deigns to mention such kinds of syllogism. In the later tradition, those first figure argument forms in which the major term is the subject term of the major premise were transposed to a separate fourth figure, giving us the neat system of figures shown in Fig. 2.4:

Fig. 2.4

The four syllogistic figures

Example 1 above belongs to the first figure and the invalid Example 2 to the third.⁹⁰ The argument form (or mood) of Example 1 is nowadays denoted as “EIO-I,” where the three capital letters indicate the types of categorical statements used (in the order: major premise, minor premise, conclusion) and the Roman numeral indicates the figure (in this case the first figure). This mood is also called by a scholastic name: Ferio.⁹¹

Each statement occurring in an argument in the figures can belong to any of the four types of categorical statements, giving us 4 × 4 × 4 = 64 moods in each figure, 256 in total. In 24 of these (6 in each figure), the conclusion follows necessarily from the premises, provided, of course, that the blanket assumption of existential import is fulfilled. If existential import is not assumed, this number drops to 15; of these 15 one finds 4 in each of the first three figures and 3 in the fourth figure. As said above, Aristotle does not discuss syllogisms with a weaker conclusion than would be possible. There are five moods that display this feature, but Aristotle recognizes all other moods; so Aristotle recognizes 19 kinds of syllogism in the figures. Since the fourth figure syllogisms are treated rather on the side, the alleged number of Aristotle’s kinds of syllogisms in the figures gets often reduced to 14.⁹²

2.6.4 Proving Validity

For each syllogism of the second or third figure (and also for cases that later came to belong to the fourth figure), Aristotle provides a proof (at a metalevel⁹³) showing why its conclusion necessarily follows from the premises. For first figure syllogisms (exempting those that came to belong to the fourth figure), no such proof is needed: first figure syllogisms are called perfect, meaning that they “need nothing other than what has been stated to make the necessity evident” (Aristotle 1984, Vol. 1, AnPr I.1, 24b22–24). As an example of a proof, we quote Aristotle’s proof for syllogisms in the mood EIO-II, also called Festino:

• (1) No N is an M.

• (2) Some O is an M.

• Therefore: (3) Some O is not an N.

Aristotle writes:

… if M belongs to no N, but to some O, it is necessary that N does not belong to some O. For since the negative is convertible, N will belong to no M; but M was admitted to belong to some O: therefore N will not belong to some O; for a deduction is found by means of the first figure. (Aristotle 1984, Vol. 1, AnPr I.5, 27a32–36)

Using our formats for categorical statements, we may write this proof as follows:

• (1) No N is an M (premise).

• (2) Some O is an M (premise).

• (3) No M is an N (from (1) by conversion of E-statements).

• (4) Some O is an M ((2) repeated).⁹⁴

• (5) Some O is not an N (from (3) and (4) by the perfect mood EIO-I (Ferio)).

The proof is one based on the rules of conversion and the perfect (first figure) syllogisms by simply chaining these procedures (this is called a direct proof ⁹⁵). But not all syllogisms can be proved in this way: sometimes an indirect proof, i.e., one by reductio ad impossibile, must be given. In these proofs, the denial of the conclusion is supposed to hold, together with the premises; then, by chaining perfect syllogisms and applications of conversion rules, one derives a pair of contradictories. This shows that not all assumptions can be true and hence that if the original premises are true, the denial of the original conclusion must be false and consequently the conclusion itself must be true. To illustrate this procedure, we quote an example that applies the perfect mood AAA-I, also called Barbara, to obtain a proof for syllogisms of the mood AOO-II, also called Baroco. Barbara and Baroco can be rendered as follows:

• (1) Every M is a P.

• (2) Every S is an M.

Therefore: (3) Every S is a P (AAA-I, Barbara).

• (1) Every N is an M.

• (2) Some O is not an M.

Therefore: (3) Some O is not an N (AOO-II, Baroco).

Aristotle writes:

Again if M belongs to every N, but not to some O, it is necessary that N does not belong to some O; for if N belongs to every O, and M is predicated also of every N, M must belong to every O; but we assumed that M does not belong to some O. (Aristotle 1984, Vol. 1, AnPr I.5, 27a36–b1)

In our format:

• (1) Every N is an M (premise).

• (2) Some O is not an M (premise).

• (3) Suppose: Every O is an N (denial of the conclusion to be reached).

• (4) (while supposing (3)) Every N is an M ((1) repeated).

• (5) (while supposing (3)) Every O is an N ((3) repeated).

• (6) (while supposing (3)) Every O is an M (from (4) and (5) by Barbara).

• (7) (while supposing (3)) Some O is not an M ((2) repeated).

Here Aristotle’s proof stops, leaving the rest to the reader: since (6) and (7) form a pair of contradictories, supposition (3) must be false (assuming that (1) and (2) are true) and its denial “Some O is not an N” must be true.

2.6.5 Aristotle’s Method of Contrasted Instances

In logic, showing that certain forms of argument are invalid is as important as showing that forms are valid. Above, when proving the invalidity of the argument form of Example 2, we saw how this can be done by means of a counterexample. Aristotle selected counterexamples in a very efficient way, called the “method of contrasting instances.”⁹⁶

To show, for example, that in the first figure from a pair of premises of the form “Every M is a P. No S is M” no conclusion S–P (P being the major term and S the minor) follows, instead of working through four counterexamples (one for each categorical statement form), it suffices to present two contrasted instances, that is, two ways of substituting terms for P, M, and S, both of which yield true premises, but such that one of them makes “Every S is a P” true, whereas the other makes “No S is a P” true. The first one provides counterexamples that exclude the two negative conclusions, and the second one does the same for the two affirmative ones.⁹⁷ In Aristotle’s words (the order of terms is P, M, S),

… if the first term belongs to all the middle, but the middle to none of the last term, there will be no deduction in respect of the extremes; for nothing necessary follows from the terms being so related; for it is possible that the first should belong either to all or to none of the last, so that neither a particular nor a universal conclusion is necessary. But if there is no necessary consequence, there cannot be a deduction by means of these propositions. As an example of a universal affirmative relation between the extremes we may take the terms animal, man, horse; of a universal negative relation, the terms animal, man, stone. (Aristotle 1984, Vol. 1, AnPr I.4, 26a2–9)

The first assignment of terms is P: animal, M: man, S: horse. This gives us the true premises: “Every man is an animal” and “No horse is a man” but also “Every horse is an animal” is true, so that both “No horse is an animal” and “Some horse is not an animal” are false, giving us the counterexamples needed to show that no negative conclusion S–P follows.

The second assignment of terms is P: animal, M: man, S: stone. This gives us again true premises: “Every man is an animal” and “No stone is a man,” but also “No stone is an animal” is true, so that both “Every stone is an animal” and “Some stone is an animal” are false, giving us the counterexamples needed to show that no affirmative conclusion S–P follows.

2.6.6 The Completeness of Syllogistic

Aristotle reduces all syllogisms in the second and third figures to those in the first figure, that is, he shows them to be syllogisms by a direct or indirect proof using only first figure syllogisms and the conversion rules. A further reduction, in which of the first figure syllogisms only those of the moods AAA-I (Barbara) and EAE-I (Celarent) were used, was also effected by Aristotle. This does not answer the question whether Barbara and Celarent and the conversion rules suffice to give direct or indirect proofs for each syllogism in the language of syllogistic no matter the number of premises. Aristotle claims at least so much, when he announces an even more encompassing reduction:

It is clear from what has been said that the deductions in these figures are made perfect by means of the universal deductions in the first figure [Barbara and Celarent] and are reduced to them. That every deduction without qualification can be so treated, will be clear presently, when it has been proved that every deduction is formed through one or other of these figures. (Aristotle 1984, Vol. 1, AnPr I.23, 40b17–22)

The attempt at a proof in AnPr I.23 is, however, incomplete and in other respects wanting (Corcoran 1974, pp. 120–122). Nevertheless, it has been proven that the question can be answered in the affirmative (Corcoran 1972). This means that as a system for formal (direct and indirect) deduction within the language of syllogistic, the system consisting of Barbara, Celarent, a rule for repetition, and conversion rules – for I-conversion, E-conversion, and partial A-conversion – is indeed complete.

2.7 Stoic Logic

Stoic philosophy is mainly known for its ideas about ethics and the conduct of one’s life, but these ideas were from the beginning supported by the study of logic (including philosophy of language and epistemology) and physics (natural science). In logic, the Stoics continued the tradition of the Megarian school (founded ca. 400 BC by Euclides of Megara), which stood in opposition to Aristotle and the school of Aristotle’s successors: the Peripatetic school. This antagonism was inherited by the Stoic school founded in Athens circa 300 BC by Zeno of Citium, who had been educated in the Megarian tradition by Diodorus Cronus and Stilpo. Thus, for the logical approach to arguments, the Megarians and the Stoics, in particular the Old Stoic school (ca. 300–ca. 130 BC), provide us with a second classical background, besides, and apart from, the Aristotelian one.

However, the outlines of this second background are much harder to discern: in contrast to the Aristotelian corpus, no Megarian or Stoic works on logic have come down to us. That is not to say that no such works were written. Diogenes Laertius mentions in his Lives and opinions of eminent philosophers ⁹⁸ that Chrysippus (circa 280–206 BC), the third head of the Stoic school, wrote 705 books, 311 of them about logic (O’Toole and Jennings 2004, p. 413). Even if one takes into account that it takes usually several ancient “books” to make a work that would nowadays be published as one volume, this is a considerable amount. Unfortunately, we have none of these books (whether on logic or not). We even do not have any of the numerous books called Introduction to Logic (Eisagôgê dialektikê) that Stoic authors were wont to write as much as contemporary logic professors. We must do with descriptions, explanations, summaries of points of view, and some quotations by other ancient authors – writing centuries later – who were not always knowledgeable about logic and often opposed to, or even prejudiced against, the Stoics.

Our main sources are the works of the skeptic physician Sextus Empiricus (circa AD 200) – who wrote Outlines of Pyrrhonism ⁹⁹ and Against the mathematicians ¹⁰⁰ – and the abovementioned popular work by Diogenes Laertius. They are supplemented by important information from a number of other authors, such as Alexander of Aphrodisias, Pseudo-Apuleius, Aulus Gellius, Boethius, Cicero, Galen, Origen, and Philoponus.

Sextus Empiricus is a serious author, but as a skeptic he is ill-disposed towards Stoicism. Diogenes Laertius is notoriously untrustworthy, but less so in the case of Stoic logic, since he could avail himself of the writings of Diocles Magnes (i.e., Diocles of Magnesia, first century BC), “who seems to have had a fair knowledge of Stoic logic” (Mates 1961, p. 9). Since, generally, these sources are insufficient to assign particular views to particular Stoic philosophers, we must assign the views we reconstruct from this material indiscriminately to the early Stoic philosophers (of whom Chrysippus was the most important one), running the risk that we so obtain a set of views that was held by nobody in its entirety (Mates 1961, p. 8). Yet, from these sources, scarce as they may be, the picture arises of a highly original and sophisticated approach to logic that could be appreciated only after the development of logic starting with Boole and Frege had made it possible for Łukasiewicz in 1935 to attempt a new reading of the old texts (Łukasiewicz 1967).

In this section, we can only briefly sketch the Stoics’ philosophy of language, which underlies their logic, the logical operators that they introduced, and their formal system of syllogistic.¹⁰¹ It then will become clear that it is really to be regretted that the Peripatetics and the Stoics were so little disposed to cooperate, for their approaches are apparently complimentary. To put it briefly, the Peripatetics had developed a kind of predicate logic (Aristotle’s syllogistic) and the Stoics a kind of propositional logic. To be fair, it must be said that the Peripatetics, too, worked on a kind of propositional logic: there are some remarks of Aristotle pointing in that direction, and we know that his pupil and collaborator Theophrastus developed a theory of “hypothetical syllogisms” (Kneale and Kneale 1962, pp. 96–100, 105ff). Unfortunately, instead of joining their efforts to the profit of both of them, the two schools stayed apart, each developing its own logical terminology. When in late antiquity their terminologies merged, the creative period for logic was over and the merging of terminologies was confusing rather than profitable.

2.7.1 Signs and Their Signification

The Stoics divided philosophy into logic (dialektikê), physics, and ethics. Of these fields, ethics, in which it is investigated how one can lead a virtuous, harmonious, and happy life, was their main concern. But the achievement of a good life required insight into the natural course of events (physics) and of the ways in which such knowledge can be obtained (logic, in a broad sense: including philosophy of language and epistemology).

The Stoics were materialists: not only the objects of the external world but also each person’s mental presentations (phantasiai) were thought of as corporeal entities. Some of our presentations are rational (phantasiai logikai), which means that their content can be expressed in words. These words are again corporeal: as sounds or written characters, they are part of the physical world; however, the content or meaning expressed by these words was considered to be incorporeal and therefore not said to exist (huparchein) as corporeal entities exist but to subsist (huphistasthai/paruphistasthai).¹⁰² The ontological distinction is similar to the one drawn by Alexius Meinong between existieren (exist) and bestehen (subsist) (O’Toole and Jennings 2004, p. 463).

With respect to horses, for instance, the following four kinds of entities may be distinguished:

• 1. Actual horses in the external world

• 2. Rational presentations of horses in the minds of individuals

• 3. Occurrences of the word “horse” (voiced or written)

• 4. The content of 2 or the meaning of 3

Of these, the first three would be corporeal and exist, whereas the last one would be incorporeal and merely subsist. The Stoic technical term for entities of the last kind was lekton (plural: lekta), a term that can be literally rendered as “what has been said,” or “what can be said,” or more freely translated as “what is meant.” “It is what the Barbarians do not understand when they hear Greek words spoken,” though nothing prevents them from hearing the spoken sounds.¹⁰³ Hearing the word hippos, they will be unable to attach a meaning to it and consequently fail to form a rational presentation of a horse, though they may be perfectly familiar with actual horses.

The lekta divide into two kinds: the complete lekta, which are contents expressed by sentences, and the deficient lekta, which are contents expressed by parts of sentences, especially grammatical predicates.¹⁰⁴ Complete lekta are again divided into various kinds, corresponding to different kinds of sentences, of which they are the incorporeal contents, and to different kinds of speech act: propositions (axiômata), questions, injunctions, prayers, curses, oaths, etc. (O’Toole and Jennings 2004, p. 443). Just as an interrogative sentence expresses a question and can be used to ask a question, a declarative sentence expresses a proposition and can be used to make a statement.

The Stoics defined what they called an axiôma (which we here render by proposition) as “a complete lekton , assertoric by itself.”¹⁰⁵ Their conception has – like all conceptions of propositions – its peculiarities. First, the name should not confuse us: an axiôma is not the same as what we would call an axiom (though axioms are propositions), for a proposition does not need to be true, let alone function as a starting point of a system of deductions. The point is that it is the kind of lekton that can sensibly, and in a primary sense, be evaluated as true or as false.¹⁰⁶ By contrast, it makes no sense to say of questions, injunctions, etc., that they are true or that they are false. Propositions are expressed by declarative sentences (rather than by interrogative sentences or imperative sentences, etc.). Being lekta they are incorporeal.

Thus far the characteristics of the Stoic proposition seem rather similar to those of contemporary notions of proposition, such as Frege’s notion of thought (Gedanke), but there are also remarkable differences. One thing is that Stoic propositions are tensed, whereas we would rather think of tense as a property of sentences. From a Fregean perspective, one would say that “Tomorrow will be John’s birthday” expresses the same proposition today as “Today is John’s birthday” will express tomorrow and “Yesterday was John’s birthday” will express the day after tomorrow. But these three sentences would express different Stoic propositions, because tense is a property of these propositions as well as of the sentences by which they are expressed. A consequence of their being tensed is that propositions can also change their truth-values: each of the three propositions expressed above is true only on one day of the year.

Even more striking is that Stoic propositions may sometimes be destroyed. For example, “This man is dead” – where “this man” refers to a particular person named “Dion” – expresses a Stoic proposition, which however ceases to subsist when Dion dies and “this man” can no longer refer to him. Therefore, the proposition that this man is dead can never be true (for to have a truth-value a proposition must subsist). It is, however, admitted that the proposition that Dion is dead can be true. This latter proposition must therefore count as a different Stoic proposition (Kneale and Kneale 1962, pp. 154–155).

These features move the Stoic propositions very far from the unworldly propositions that inhabit a Fregean or Popperian third realm of being, with which they are often compared. Scholars differ about this comparison. Kneale and Kneale (1962, p. 156) argue that both kinds of propositions are similar also in that they “exist in some sense whether we think of them or not.” But Nuchelmans (1973, pp. 85–87) argues against this. This may not be the place to pronounce on such discussions, but despite these difficulties, it may be clear that the Stoic conception of proposition provides an important background for the notion of “propositional content” figuring in contemporary argumentation theory.

2.7.2 Simple and Complex Propositions

The Stoics divided the proposition s into complex and simple ones, according to whether or not a proposition was constructed from propositions (or from one proposition taken several times) by means of a connective (sundesmos) (Sextus Empiricus, AM VIII.93–95). Evidently, they spoke of the construction of propositions in much the same way as one would speak of the constructions of the declarative sentences by which they are expressed.

Understandably, since a negation does not connect propositions, they did not include negation among the connectives, and therefore negations of simple propositions were again simple propositions. A proposition was supposed to be equivalent to its own double negation (Diogenes Laertius, LP VII.69). Presumably, then, negating turned true propositions into false ones and vice versa. Those simple propositions that were not negations could still be negative in other ways: their subject could be (equivalent to) “no one” or “nothing,” or their predicate could be privative (like “unkind”).¹⁰⁷ Another way of classifying simple propositions is by the nature of their subject: besides being negative (“no one” or “nothing”), the subject could be (1) a demonstrative phrase in the nominative case (“This man is walking”), where the speaker points at a particular person, or (2) indefinite (“Someone is walking”), or (3) a noun in the nominative case (“Dion is walking”). A simple proposition of the first type is true if and only if the predicate belongs to the object indicated by the demonstrative phrase. A proposition of the second type is true if and only if some corresponding proposition with a demonstrative subject is true.¹⁰⁸

Kneale and Kneale (1962, p. 146) remark that there is no simple Stoic proposition that concurs with Aristotle’s universal affirmative statement (“Every human is a rational mortal animal”) and present evidence that the Stoics may have analyzed the universal affirmative as a generalized conditional (“If anything is a man, it is a rational mortal animal”). In that case universal affirmative sentences would express complex propositions.

Complex propositions were distinguished according to their principal connective.¹⁰⁹ Diogenes Laertius lists seven kinds (LP VII.71–73). The most important of them are:

• 1. Conditionals, for instance: “If it is day then it is light.”

• 2. Conjunctions, for instance: “Both it is day and it is light.”

• 3. Disjunctions, for instance: “Either it is day or it is night.”¹¹⁰

Conjunctions and disjunctions are not necessarily restricted to two components but may in fact have any number of components connected by repeated occurrences of “and” or “or” respectively, for instance “It is light, and it is day, and Dion runs, and Socrates walks, and....”

The semantics of conditionals was much debated among the Megarians and the Stoics. Among the proposals discussed, that of Zeno’s contemporary Philo of Megara amounts to the truth conditions of what is now known as material implication : a conditional proposition “If A then B” is true if and only if it is not the case that A is true and B false. Diodorus Cronus (one of Zeno’s teachers), on the other hand, held a conditional “If A then B” to be true if and only if at no time A would be true, whereas B would be false. This presupposes that propositions can have truth-values related to times, so that we can write the Diodorean conditional as “For all times t, if A at t, then B at t.”

The most common view among the Stoics (often ascribed to Chrysippus), however, seems to have been that in a true conditional, there must be some more intimate connection between the antecedent (A) and the consequent (B), so that in circumstances in which the antecedent were true, the consequent also had to be true (O’Toole and Jennings 2004, pp. 484–489). Thus, a conditional “If A then B” was said to be true if and only if the contradictory of B (cB) was “in conflict” with A. The notion of conflict involved here implies that A and cB cannot both be true, but that is not to say that A and cB must be logically inconsistent: it may be that A and cB cannot both be true for physical reasons. Further, to count as conflicting, A and cB must be distinct, and it must be excluded that they cannot both be true merely because one of them is necessarily false (Hitchcock 2002d, pp. 10–11).¹¹¹ In this section, we shall from now on suppose that Stoic conditionals are interpreted in this way.

The Stoic semantics for conjunctions is in agreement with contemporary classical logic: a conjunction is true if and only if each of its conjuncts (the propositions that are connected to construct the conjunction) is true. Together with negation, conjunction yields the full power of expression of contemporary classical propositional logic, which is not to say that the Stoics were in possession of that logic.

About the Stoic semantics for disjunction , the sources differ, but it seems likely that a disjunction was thought to be true if and only if it consisted of a sequence (without repetitions) of connected propositions (its disjuncts), such that distinct disjuncts were in conflict , whereas one of the disjuncts was true (Hitchcock 2002d, pp. 12–14).¹¹²

2.7.3 Arguments

According to the Stoics, an argument (logos) is a system composed of premises and a conclusion (Diogenes Laertius, LP VII.45). Obviously, premises and conclusion must be propositions. Yet arguments are not complex propositions, since the propositions out of which they are composed are not connected by connectives. It is not excluded that the conclusion is identical to a premise, but it is generally excluded that there is only one premise (or none).¹¹³

An argument is valid (sunaktikos, perantikos) if and only if the contradictory of its conclusion conflicts with the conjunction of its premises (Diogenes Laertius, LP VII.77). Given the most common Stoic semantics for conditional propositions, this led the Stoics to the following principle of conditionalization : an argument will be valid precisely when the conditional proposition whose antecedent is a conjunction composed of all the argument’s premises and whose consequent is equal to the argument’s conclusion (the so-called associated conditional ) will be true (Sextus Empiricus, PH II.137).¹¹⁴

An argument is said to be true (alêthês) if and only if it is valid and all its premises are true (as well as its conclusion). An argument is demonstrative (apodeiktikos) if and only if it is valid, and true, and leads from pre-evident premises to a non-evident conclusion. Finally, an argument is a proof (apodeixis) if it is valid, true, and demonstrative and moreover conducts us to the discovery of its conclusion (and, for instance, not merely to an acceptance of the conclusion on the basis of an argument from authority) (Sextus Empiricus, PH II.138–143).

2.7.4 The Stoic Formal System

Some of the valid arguments were called syllogistic. These were the so-called undemonstrated arguments (anapodeiktoi)¹¹⁵ and those arguments that were reduced to the undemonstrated arguments (Diogenes Laertius, LP VII.78). The terms undemonstrated and reduced refer to the formal system the Stoics developed to show that arguments of certain kinds were valid. Evidently, the system was not intended to capture all valid arguments. For one thing, it was restricted to propositional logic (negations, conditionals, conjunctions, and disjunctions), but even within that realm, the system seems to have been incomplete. It is hard to tell whether it was really incomplete, for only part of the system has come down to us.¹¹⁶

Reductions in the Stoic formal system started from a given argument that had to be shown to be a syllogism. By application of a reduction rule, called a thema ,¹¹⁷ this argument was replaced by (one or two) other arguments. Arguments introduced by a reduction rule had either to belong to the one of the five types (listed below) of undemonstrated arguments, which needed no further reduction, or to be further reduced by a reduction rule. The reduction was completed as soon as all arguments that had turned up, but were not further reduced, belonged to the undemonstrated arguments. In that case the argument from which the reduction had started had been shown to be a syllogism. The undemonstrated arguments were obviously valid, and the themata took care of the validity of the other arguments in the reduction.

A completed reduction can also be read as a deduction, with the undemonstrated arguments as axioms, the reversals of the reduction rules as deduction rules, and the given argument as its conclusion. But notice that it would be a meta-deduction, consisting not of propositions but of arguments.¹¹⁸

The five types of undemonstrated arguments have come down to us as short descriptions. More than one argument form may be covered by a description, and the descriptions may admit more arguments than the argument forms here shown.¹¹⁹ We shall here present the descriptions of the types and for each type just one of the argument forms covered by the description. In the argument forms, the Stoics used ordinals as propositional variables, where we use capitals. Premises will be separated from the conclusion by a slash. The descriptions within quotation marks we took from Bobzien (1996, p. 136), substituting “undemonstrated argument” for “indemonstrable” and introducing some minor changes:

(1) “A first undemonstrated argument is an argument that is composed of a conditional and its antecedent (as its premises), having the consequent of the conditional as conclusion.” (Sextus Empiricus, AM VIII.224, Diogenes Laertius, LP VII.80)

Argument scheme: If A then B, A/B.

In the later tradition, this mode of reasoning became known as modus ponendo ponens (the mood that affirms (B) by affirming (A)) or simply as modus ponens.

(2) “A second undemonstrated argument is an argument that is composed of a conditional and the contradictory of its consequent as premises, having the contradictory of its antecedent as conclusion.” (Sextus Empiricus, AM VIII.225, Diogenes Laertius, LP VII.80)

Argument scheme: If A then B, Not-B/Not-A.

In the later tradition, this mode of reasoning became known as modus tollendo tollens (the mood that denies (A) by denying (B)) or simply as modus tollens.

It will be no surprise that the Stoics, who explicitly recognized arguments following the patterns of modus ponens and modus tollens as valid, were also aware of the fallaciousness of arguments following the patterns of denying the antecedent (Sextus Empiricus, AM VIII.432–433, Diogenes Laertius, LP VII.78) and affirming the consequent (Sextus Empiricus, PH II.147–149). Such arguments were said to be invalid because of their being put forward in a bad form.

(3) “A third undemonstrated argument is an argument that is composed of a negated conjunction and one of its conjuncts (as premises), having the contradictory of the remaining conjunct as conclusion.” (Sextus Empiricus, AM VIII.226, Diogenes Laertius, LP VII.80)

Argument scheme: Not both A and B, A/Not-B.

In the later tradition, this mode of reasoning, as well as the one that follows, was at times referred to as modus ponendo tollens (the mood that denies (B) by affirming (A)).

(4) “A fourth undemonstrated argument is an argument that is composed of a disjunction and one of its disjuncts (as premises), having the contradictory of the remaining disjunct as conclusion.” (Diogenes Laertius, LP VII.81)

Argument scheme: Either A or B, A/Not-B.

In the later tradition, this mode of reasoning, as well as the preceding one, was at times referred to as modus ponendo tollens (the mood that denies (B) by affirming (A)).

(5) “A fifth undemonstrated argument is an argument that is composed of a disjunction and the contradictory one of its disjuncts (as premises), having the remaining disjunct as conclusion.” (Diogenes Laertius, LP VII.81)

Argument scheme: Either A or B, Not-A/B.

In the later tradition, this mode of reasoning was at times referred to as modus tollendo ponens (the mood that affirms (B) by denying (A)).

Thus, we have a pretty good survey of what the undemonstrated arguments were. As to the themata (the rules that were used to reduce arguments to other arguments and ultimately to the undemonstrated argument), we are not so fortunate. Presumably, there were four themata, but we have only versions of the first and the third thema (the latter in two quite different versions). We also know that the second and fourth thema were similar to the third one.¹²⁰ Further, there are some arguments that we know to have been syllogisms and many that we may presume not to have been syllogisms. This situation invites attempts at reconstructing the Stoic system from its remains. Hitchcock (2002d, p. 3) lists ten earlier reconstructions, among them one by himself, before proposing a new one. We shall not try to add to this list, but just close off our survey of the Stoic system by describing versions of the first and of the third thema and then present two examples of reductions in which only these themata are used.

The first thema allows one to reduce a given argument with a premise P and a conclusion C to another argument, with as conclusion the contradictory of P (cP) and with the same premises, except that P has to be replaced by the contradictory of C (cC):

• Thema 1: Argument X, P/C reduces to argument X, cC/cP.

Here “X” stands for the other premises.

The version of the third thema that we shall use in the examples allows one to reduce a given argument to two other arguments in the following way:

• Thema 3: Argument X, P/C reduces to arguments X/Q and Q, P/C.

Since the reversals of reduction rules are deduction rules (for deducing arguments from arguments), the themata can also be formulated as follows (which is indeed the way in which they usually are formulated):

• Thema 1: From a valid argument X, P/C, one obtains a valid argument X, cC/cP.¹²¹

• Thema 3: From arguments X/Q and Q, P/C, one obtains a valid argument X, P/C.

As our first example of a reduction in the Stoic system for propositional logic, we shall start from an argument put forward by the skeptic philosopher Aenesidemus: “If the things apparent appear in like manner to all those in similar condition (A), and the signs are things apparent (S), the signs appear in like manner to all those in similar condition (L); and the things apparent appear in like manner to all those in similar condition; but the signs do not appear in like manner to all those in a similar condition; therefore the signs are not things apparent” (Sextus Empiricus, 1933–1949, II, Against the logicians II(=AM VIII).234). It is possible to write down the reduction of precisely this argument, but it is easier to do so for its argument form¹²²:

• 1. If both A and S then L, A, Not-L/Not-S

• Argument 1 reduces by Thema 3 to

• 1.1 If both A and S then L, not-L/Not both A and S (undemonstrated of type two)

• and

• 1.2 A, Not both A and S/Not-S (undemonstrated of type three).

The reduction has been completed. Being reduced to two undemonstrated arguments, the initial argument has been shown to be valid and even to be a syllogism.

Our second example is a little more complicated.¹²³ We only give the argument forms:

• 1. If both if A then B and C then D, If D then E, Not-E, C/Not if A then B.

• Argument 1 reduces by Thema 1 to

• 2. If both if A then B and C then D, If D then E, If A then B, C/E.

• Argument 2 reduces by Thema 3 to

• 2.1. If both if A then B and C then D, If A then B, C/D

• and

• 2.2 D, If D then E/E (undemonstrated of type 1).

• Argument 2.1 reduces by Thema 3 to

• 2.2.1 If A then B, C/Both if A then B and C

• and

• 2.2.2 Both if A then B and C, If both if A then B and C then D/D (undemonstrated of type 1).

• Argument 2.2.1 reduces by Thema 1 to

• 2.2.1.1 If A then B, Not both if A then B and C/Not-C (undemonstrated of type 3).

Since all the unreduced arguments belong to the undemonstrated arguments, the reduction of the initial argument has been completed. This shows the argument to be valid and syllogistic.

Even though it remains unclear which arguments the Stoic system was intended to yield, and whether it did do so, we can still admire the ingenuity and the rigor applied to its construction and recognize its contribution to the study of arguments.¹²⁴

2.8 Aristotle’s Rhetoric

In Sect. 2.2 we mentioned several key figures in the early development of rhetoric. Some of them are credited with the “invention” of rhetoric (Corax, Tisias, and Empedocles), others are known to have taught rhetoric (the sophists and Isocrates), and again others are known to have criticized and further developed the discipline (the handbook writers, Plato, and the anonymous writer of the Rhetoric to Alexander). Although these authors have formulated useful insights regarding the phenomenon of persuasion, Aristotle was not satisfied with their approach, which in his eye was too restricted (Rhet. I.1, 1354a11–18). His Rhetoric contains a new definition of rhetoric, criticisms of the teachings of his predecessors, as well as expositions of important rhetorical concepts. In this section, we shall discuss the main insights Aristotle developed.¹²⁵

2.8.1 The Definition of Rhetoric

According to Aristotle, the art of rhetoric resembles the art of dialectic in that it is not restricted to any particular domain of subjects (as the sciences are in Aristotle’s view), but can be generally applied. Like other arts, it cannot guarantee success, but enables one to see what are real and what are merely apparent means of persuasion (Rhetoric I.1, 1355b7–17).

Unlike his predecessors, who defined rhetoric as the “art of words” or as the “worker of persuasion” (Gorgias’s definition as described by Plato 1997, Gorgias 453a), Aristotle defines rhetoric as follows¹²⁶:

Rhetoric may be defined as the faculty of observing in any given case the available means of persuasion. This is not a function of any other art. Every other art can instruct or persuade about its own particular subject-matter; for instance, medicine about what is healthy and unhealthy, geometry about the properties of magnitudes, arithmetic about numbers, and the same is true of the other arts and sciences. But rhetoric we look upon as the power of observing the means of persuasion on almost any subject presented to us; and that is why we say that, in its technical character, it is not concerned with any special or definite class of subjects. (Aristotle 1984, Vol. 2, Rhet. I.2, 1355b26–35)

Starting from this definition, Aristotle discusses in Book I and II the finding of the material for a speech, which he calls thought (dianoia). In Book III, he discusses the wording of a speech, called style (lexis), the ordering of the different parts of the speech, called arrangement (taxis), and – to a very limited extent – the actual performance of the speech, called delivery (hupokrisis). These concepts are adopted by later authors under the heading of the tasks of the speaker (rhêtoros erga or oratoris opera), i.e., a list of the subsequent procedural steps the speaker has to accomplish in order to produce a persuasive speech. Eventually this list comprised five items: (1) the invention (heuresis or inventio), (2) the arrangement (taxis or dispositio), (3) the wording (lexis or elocutio), (4) the memorizing (mnêmê or memoria), and (5) the performance (hupokrisis or actio) of the speech. In the Rhetoric, Aristotle’s main focus is on the first task of the speaker: the invention of arguments. Books I and II are entirely dedicated to this topic. Some scholars even believe that Book III, which is dedicated to other tasks, was originally a separate work, which was only later combined with Books I and II.

2.8.2 The Modes of Persuasion

As far as the invention of the contents of the speech is concerned, Aristotle makes several distinctions that were later canonized in the system of classical rhetoric (see Sect. 2.9). Among them is a basic distinction between modes of persuasion. According to Aristotle, some of the means of persuasion are nontechnical, i.e., they are not part of the art of rhetoric: they are not construed by the speaker but already present at the outset. He mentions as examples evidence provided by witnesses, evidence given by slaves under torture, and evidence provided by written contracts. Other means of persuasion are technical in the sense that they belong to the art of rhetoric because they are supplied by the speaker in the context of the process of persuading an audience of the acceptability of a certain standpoint with regard to the question at issue (Rhet. I.2, 1355b35–39).

On the basis of the observation that a speech involves a speaker, a subject, and an audience (Rhet. I.3, 1358a36–b2), Aristotle distinguishes three technical means (or “modes”) of persuasion:

Of the modes of persuasion furnished by the spoken word there are three kinds. The first kind depends on the personal character of the speaker; the second on putting the audience into a certain frame of mind; the third on the proof, or apparent proof, provided by the words of the speech itself. (Aristotle 1984, Vol. 2, Rhet. I.2, 1356a1–4)

Interestingly, Aristotle provides a psychological explanation of the persuasive effect of the first two technical modes of persuasion. The effectiveness of the ethical mode of persuasion, when the speaker tries to achieve persuasion by presenting himself as a trustworthy person, is based on the psychological fact that “we believe good men more fully and more readily than others: this is true generally whatever the question is, and absolutely true where exact certainty is impossible and opinions are divided” (Aristotle 1984, Vol. 2, Rhet. I.2, 1356a6–8). When he returns to this means of persuasion in Book II of the Rhetoric, Aristotle remarks that “there are three things which inspire confidence in the orator’s own character – the three, namely, that induce us to believe a thing apart from any proof of it: good sense (phronêsis), excellence (aretê), and goodwill (eunoia)” (Aristotle 1984, Vol. 2, Rhet. II.1, 1378a6–8).

The effectiveness of the pathetical mode of persuasion , when the speaker tries to achieve persuasion by stirring the emotions of the audience, is based on the psychological fact that “our judgements when we are pleased and friendly are not the same as when we are pained and hostile” (Aristotle 1984, Vol. 2, Rhet. I.2, 1356a15–16). For this reason, Aristotle provides in Rhet. II.2–17 several definitions of emotions. Knowledge of these matters enables the speaker to highlight those aspects of the subject at issue that evoke in the audience the emotions relevant for the promotion of his case.

Although Aristotle says in Book I that the personal character of the speaker “may almost be called the most effective means of persuasion” (Aristotle 1984, Vol. 2, Rhet. I.2, 1356a13), his subsequent treatment of the various modes of persuasion focuses on the logical ones. Taking the distinction between deduction and induction made in the Topics and Analytics as a starting point, Aristotle divides in the Rhetoric (I.2) the logical means of persuasion into enthymemes (enthumêmata) and examples (paradeigmata). In enthymemes something is proven in a deductive way by making use of signs (sêmeia) or probabilities (eikota); in examples something is proven in an inductive way. Aristotle observes that in the rhetorical context of a speaker addressing an audience, the deduction employed in the enthymeme does not have to be complete. The members of the audience will usually be able to add the missing parts with the help of their background knowledge regarding the issue at hand: “The enthymeme must consist of few propositions, fewer often than those which make up a primary deduction. For if any of these propositions is a familiar fact, there is no need even to mention it; the hearer adds it himself” (Aristotle 1984, Vol. 2, Rhetoric I.2, 1357a16–19). As to the use of signs, Aristotle makes a distinction between using non-necessary signs, which make a refutable argument, and using necessary signs (tekmêria), which make an irrefutable one.

Aristotle’s distinctions regarding the technical means of persuasion that are available to the speaker are summarized in Fig. 2.5.

Fig. 2.5

Aristotle’s distinctions regarding the means (or modes) of persuasion

2.8.3 The Three Genres

Another important distinction made by Aristotle and adopted by most authors is the distinction (in Rhet. I.3) between three genres (genê, singular: genos) of speeches (or “genres of rhetoric”). Aristotle provides the following rationale for the distinction. When listening to a speech, the audience may either judge whether the standpoint defended by the speaker is made acceptable or observe the rhetorical qualities of the speaker. In the former case, the question at issue may either pertain to acts performed in the past or to acts to be performed in the future. It follows from these considerations that there are three genres of speeches to be dealt with: (1) the deliberative genre (genos sumbouleutikon), in case the audience judges the acceptability of the speaker’s qualification of a future act as (dis)advantageous; (2) the judicial genre (genos dikanikon), in case the audience judges the acceptability of the speaker’s qualification of a past act as just or unjust; and (3) the exhibiting genre (genos epideiktikon), in case the audience observes the rhetorical qualities of the speaker who puts forward a non-controversial standpoint about someone or something to be either praised or blamed. The three genres and their characteristics are summarized in Fig. 2.6.

Fig. 2.6

Aristotle’s description of the three genres of speech

2.8.4 Rhetorical Topoi

As happens in the Topics, the Rhetoric provides descriptions of topoi that may help the speaker in finding arguments for specific standpoints (see Sect. 2.3). Making use of the distinction regarding the genres of speech, Aristotle distinguishes in the Rhetoric between common topoi (koinoi topoi), which can be used to construct enthymemes in all genres, and special topoi (idia), which are based on propositions that belong to sciences relevant to specific genres of speech.

In Rhetoric II.23, Aristotle presents a list of 28 common topoi. As in the Topics, each description of a topos usually consists of the following elements (not all of which are always present): the name of the topos, a general law, instructions for the arguer, some examples, and some further comments. Although the topics mentioned in the Rhetoric overlap with those that can be found in the Topics, the list is not just a shorter version of the material provided in the Topics; it is a selection of those topics that are particularly useful for speakers who are preparing a speech (of any genre). According to Braet, “Aristotle did not arrive at his dialectical topics in the same way as his rhetorical topoi: the former seem to have been devised deductively and the latter inductively, from rhetorical practice,” and this is “one of the reasons that the topics from the Rhetoric, with all the causal types which do not appear in the Topics, is closer to today’s argumentation schemes” (2005, p. 67).¹²⁷

According to Braet, the common topoi mentioned in the Rhetoric can be classified according to the themes they pertain to: opposition, comparison, classification, induction,¹²⁸ authority, and causality (Braet 2007, pp. 168–171). For each theme, Aristotle gives one or more topoi that help the arguer to construct enthymemes that are suitable to persuade the audience.

2.8.5 Rhetorical Fallacies

After having listed the common topoi, Aristotle presents in Rhetoric II.24 ten topoi of merely apparent enthymemes or – as we would say – ten (or nine) types of fallacies. This list, which supposedly originated in rhetorical practice, is at some points markedly different from the list included in Sophistical refutations. Only three of the thirteen types of fallacies treated in Sophistical refutations return, as far as we can tell, unchanged: equivocation, secundum quid, and consequent. Five types of fallacies have been altered, often preserving no more than the name (composition , division , form of expression , accident , and non-cause ), whereas five other types do not return at all: amphiboly, accent, ignoratio elenchi, begging the question, and many questions. Figure 2.7 gives a survey. Of the first two items in the survey, which are commonly counted as subtypes of one type of fallacy, Aristotle says that they are fallacies dependent on the use of language (para tên lexin).

Fig. 2.7

The fallacies in the Rhetoric

2.8.6 Other Contributions

Aristotle’s contributions regarding other tasks of the speaker are less extensive and influential than the contributions regarding the invention mentioned above. As to the arrangement, he discusses in Rhet. III.13–19 the parts of a speech, of which he considers the standpoint and the arguments to be the most important. As to the wording of a speech, which he discusses in Rhet. III.1–12, Aristotle emphasizes the importance of “clarity” and provides accounts of the “simile” and the “metaphor” (Rhet. III.2–4, III.10–11).

2.9 The System of Classical Rhetoric

Unlike classical dialectic and logic, for which disciplines Aristotle provided the most significant contributions, classical rhetoric has many fathers. From the fifth century BC until the second century AD, various Greek and Roman writers contributed to the development of a systematic set of prescriptions on how to effectively deliver a persuasive speech. Quintilian’s Oratorical education (Latin: Institutio oratoria), written approximately AD 150, is generally viewed as the most elaborate summary of this system of classical rhetoric.¹²⁹

The system of classical rhetoric has various components, most of which can be described as subordinate doctrines addressing specific aspects of the production process of a speech.¹³⁰ Among these components are a doctrine of the subsequent tasks of the speaker (rhêtoros erga; officia oratoris or oratoris opera), a doctrine of the different speech genres or genres of rhetoric (genê tou logou or tês rhetorikês genê/eidê; genera causarum or rhetorices genera), a typology of possible responses to an accusation (stasis theory; status theory), a doctrine of the parts of a speech (logou merê; orationis partes), and many other more or less systematized sets of rhetorical instructions. Since these subordinate doctrines are interrelated, the system of classical rhetoric can be expounded in various ways. One could, for instance, first explain of which parts a speech consists and then explain for each part of the speech what type of persuasive means the speaker should employ. Most rhetoricians have taken either the doctrine of the tasks of the speaker or the doctrine of the parts of a speech as the organizational principle for their didactical exposition of the various components of the system. In our description, we will follow the former organizational principle. The other main components of the system of classical rhetoric can be subsumed under the various tasks of the speaker as shown in Fig. 2.8.

Fig. 2.8

Overview of the various components of the system of classical rhetoric

2.9.1 Invention

The first task a speaker has to accomplish is called the invention (inventio), i.e., the invention of the contents of the speech. This task comprises the invention and analysis of the standpoint, sometimes conceived as a subtask called the noêsis or intellectio , as well as the invention of the arguments supporting the standpoint, the inventio proper.

As to the intellectio, several theories have been developed to classify the standpoints at issue in a speech. One of them is the doctrine of the various speech genres (genera causarum or rhetorices genera) exemplified by the seven types of speeches in the Rhetorica ad Alexandrum discussed in Sect. 2.2 as also in Aristotle’s distinction between the judicial genre (genos dikanikon; genus iudiciale), the deliberative genre (genos sumbouleutikon; genus deliberativum), and the exhibiting genre (genos epideiktikon; genus demonstrativum), discussed in Sect. 2.8. Another example is the doctrine of the degrees of defensibility of the standpoint. This doctrine is, confusingly, also referred to as causarum genera. This time, however, causa refers not to the speech but to the standpoint, specifically to the standpoint as it is judged by the audience prior to the delivery of the speech. If the speaker intends to defend a standpoint that corresponds with the audience’s judgment or prejudice about the issue at stake, the standpoint belongs to the honorable genre (honestum genus). If the standpoint challenges the audience’s sense of justice or truth, it belongs to the doubtful or wavering genre (dubium or anceps genus). And if it shocks the audience’s sense of justice or truth, it belongs to the shocking genre (turpe or admirabile genus). Apart from these three basic classifications, some rhetoricians distinguish the petty genre (humile genus) for standpoints that are completely in accordance with the opinion of the audience and the complex genre (obscurum genus) for standpoints that exceed the cognitive capacities of the audience. The relevance of the doctrine of the degrees of defensibility is based on the fact that the different types of standpoint require different rhetorical strategies to achieve an optimal persuasive effect. For instance, if the standpoint belongs to the shocking genre, the speaker is advised to state the standpoint he wishes to defend not too bluntly at the beginning of the speech, but to introduce it by a detour (insinuatio).

Another important contribution to the intellectio stems from Hermagoras of Temnos (second century BC), who wrote a handbook on rhetoric that contains a theory on the determination of the standpoint at issue – the so-called status (Greek: stasis) theory. Although the handbook is now lost, the theory can be reconstructed from later reports by Cicero, Quintilian, and others.¹³¹ The status theory is different in nature than the theories just mentioned. Whereas the theory of speech genres qualifies the standpoint in terms of the temporal aspects of its propositional content, and the theory of the degrees of defensibility does so in terms of the audience’s initial doxastic attitude towards the subject matter, the status theory qualifies the standpoint in terms of the kind of difference of opinion that arises from the confrontation between two parties in a legal dispute. The theory takes as a starting point that the speech under consideration is a response to an accusation made by the other party. Possible responses to such an accusation are divided into four main categories: (1) denial, (2) redefinition, (3) justification or exoneration, and (4) raising doubt with regard to the legitimacy of the judge.

Depending on the response chosen, the status is the main question the judge will have to answer. In the case of a denial of the accusation, the difference of opinion between the accuser and the defendant concerns the facts. This response generates the status coniecturalis , which means that the judge will, for instance, have to answer the question: “Did he kill someone?” In the case of a redefinition of the accusation, the difference of opinion between the accuser and the defendant concerns the juridical qualification of the facts. This response generates the status definitionis , which means that the judge will, for instance, have to answer the question: “Is the killing to be qualified as murder or as manslaughter?” In the case of a justification of the deed, the difference of opinion between the accuser and the defendant concerns the justifiability of the deed. This response generates the status qualitatis , which means that the judge will, for instance, have to answer the question: “Was the killing justifiable?” The last possible response distinguished within this system is raising doubt with regard to the legitimacy of the judge. This response generates the status translationis , which is of a somewhat different nature than the other ones because it concerns the issue (mostly preliminary in modern law) as to whether the case is brought up in front of the right court.

Although the status theory is especially suitable for judicial speeches, it may be applied – after the necessary adaptations – for the determination of the standpoint of deliberative and exhibiting speeches as well. After Hermagoras, the status theory has been extended and refined by other authors. This applies especially to the status qualitatis, which describes the ways in which the accused may justify his deeds. The most important extension of the status theory is the one proposed by Hermogenes of Tarsus (floruit ca. AD 161–180), who describes in his Peri staseôn [On issues] fourteen different options of choosing a standpoint.

Once the speaker has decided upon the standpoint he is going to defend in his speech, he moves on to the task of finding what to say to get the audience to accept the standpoint – the inventio proper. The first systematic theory of invention was developed by Aristotle, whose distinction between ethical, logical, and pathetical modes of persuasion we discussed in Sect. 2.8. As to the logical means of persuasion, most rhetoricians take over Aristotle’s distinction between the example (paradeigma; exemplum or inductio) and the enthymeme or rhetorical syllogism (enthymêma; argumentum or ratiocinatio). However, the anonymous Rhetorica ad Herennium (ca. 85 BC)¹³² contains an important addition to these types of logical means of persuasion, called the epicheireme (epicheirêma). In this work, the epicheireme is conceived as a combination of the two means just mentioned, involving five elements: the thesis to be defended (propositio), a reason (ratio), a subordinate argument in support of the reason (rationis confirmatio), a further elaboration of the reason (exornatio), and the quintessence of the argumentation (complexio), which may take the form of a résumé (enumeratio) or a conclusion (conclusio) (Rhetorica ad Herennium II.28).

The basic structure of the epicheireme has been adapted by later authors. Some of them do not deem all five elements equally important, or even necessary, for an argumentation to be called an “epicheireme .” Others redefine an epicheireme as an extended syllogism, adding in their examples subordinate arguments for one or both of the premises involved. According to Cicero (De inventione I.67), for instance, the epicheireme consists of the major premise (which is called proposition , although it is not the same as the thesis to be defended), a subordinate argument in support of the major premise (propositionis adprobatio), the minor premise (adsumptio), a subordinate argument for the minor premise (adsumptionis adprobatio), and the conclusion (complexio).

As to the ethical and pathetical means of persuasion, most later rhetoricians follow Aristotle’s definitions. Others took over Cicero’s redefinition in De oratore of these modes as two different forms of emotional appeal. According to Cicero, the ethical means of persuasion make use of the long-term emotion of trust, while the pathetical means rely on short-term emotions like anger.

A second important theory of invention is that of the topoi (loci). Aristotle’s distinction of common and specific topoi was extended and refined by later writers, most notably by Cicero and Boethius (see Sect. 2.5). Whereas some scholars interpret the theory of topoi solely as a theory of the various ways in which an argument may justify a standpoint, others state that it is also a theory of the way in which a speaker may find the appropriate arguments for defending his standpoint. As we explained earlier in this chapter, these interpretations are complementary rather than excluding each other. Depending on their formulation, most of the topoi may be attributed a heuristic as well as a justificatory function.

Some of the topoi are general in the sense that the speaker can use them in all speech genres. Others are specific in the sense of being especially suitable for the construction of arguments in a judicial, political, or exhibiting speech. For example, since political decisions are taken by evaluating the arguments for or against a proposed action or policy, the list of topoi for political speeches consists of typical ways in which such an action can be defended or criticized. The speaker in favor of the action may emphasize that the action is just or legal, that it is expedient or gives pleasure, or that the proposed action is possible, necessary, or easy to perform.

2.9.2 Arrangement

The second task a speaker has to accomplish is called arrangement (dispositio), i.e., the arrangement of the speech. Apart from the contents of the speech, rhetoricians deemed it important in what order the standpoint, the reasons, and the other utterances in support of it are presented to the audience. Their advice on this issue slowly developed into a standard theory of the parts of a speech (merê tou logou; partes orationis). From a didactical point of view, the theory provides an ideal framework for the explanation of other rhetorical instructions. In our discussion below, we will mention for each main part the most important rhetorical instructions that relate to it.

The first part, the introduction (prooimion; exordium, prooemium or principium), is divided into several subparts. The speaker should present an exposition of the problem and the relevant information at hand (diêgêsis; narratio).¹³³ Also, he should present his standpoint with regard to the problem (prothesis; propositio). Finally, he should provide the audience an overview of the remaining elements of the speech (prokataskeuê; partitio or divisio). The main functions of the first part of the speech are to catch the audience’s attention, to make the audience understand the topos at issue, and to win the audience’s goodwill. As to the exposition of the problem and the relevant information at hand, the speaker is advised to present them in a clear, succinct, and plausible manner.

In the second part, the middle part or the proof (pisteis or agônes; argumentatio), the speaker should present his arguments. Most rhetoricians divide this part of the speech into a subpart containing the arguments in favor of the standpoint of the speaker (pistis or apodeixis; confirmatio or probatio) and a subpart containing the arguments against the standpoint of the speaker’s opponent (lusis; refutatio, confutatio, or reprehensio).

In the third and last part of the speech, the epilogue or conclusion (epilogos; peroratio, conclusio or epilogus), the speaker is advised to restate the standpoint as well as the main arguments (anakephalaiôsis; recapitulatio or enumeratio). The function of the last part of the speech is to enhance the audience’s acceptance of the speaker’s standpoint regarding the issue at hand by appealing to the audience’s cognitive as well as emotional capacities.

Rhetoricians disagree about the necessity as well as the relative importance of the parts of the speech mentioned above. According to Aristotle, the propositio and the argumentatio are the only necessary components of a speech (Rhet. III.13). Others mark the propositio as optional, or add a digression (digressio) between the first and the second part. Also, rhetoricians disagree about the relation between the theory of the modes of persuasion and that of the parts of a speech. Some propagate the idea that the speaker should employ ethical means in the beginning of the speech, logical means in the middle, and pathetical means at the end. Others are of the opinion that there is no preferred position for the various modes of persuasion and that the speaker should employ all three of them throughout the whole speech.

The task of arrangement (dispositio) does not only comprise the ordering of the main parts of the speech but also the ordering of the elements within the main parts. The most important of these internal orderings is that of the arguments. According to some rhetoricians, the speaker should place the arguments in an order of increasing strength or in an order of decreasing strength. Others advice to place the weaker argument in the middle and the stronger arguments in the beginning and at the end. This is called the Nestorian order or the Homeric disposition (Quintilian, Oratorical education V.12.14), named after the Homeric hero and commander Nestor, to whom people attribute the invention of the battlefield strategy of placing the weaker parts of the army in the middle.¹³⁴

2.9.3 Wording

The third task a speaker has to accomplish is called the wording (elocutio), i.e., the putting into words of the speech as conceived. Aristotle’s remarks regarding this task had less influence on later authors than those regarding the tasks we have discussed. It was his student Theophrastus who developed a doctrine of the virtues (virtutes) of style that was much later canonized in the system of classical rhetoric . Important later writers on the virtues of style include Dionysius of Halicarnassus (floruit 30 BC), who wrote several works on the subject, and Hermogenes of Tarsus, whom we already met as an author on status theory. Hermogenes distinguishes in his Peri ideôn [On ideas, or: On types of style] seven main categories of virtues of style. Most rhetoricians, however, distinguish only four main categories. The first one is grammatical correctness (hellênismos; latinitas), which is sometimes set apart as a grammatical rather than a rhetorical virtue. The other three are clarity (perspicuitas), embellishment (ornatus), and aptness (aptum or decorum). Of the instructions regarding these virtues, those concerning the embellishment are the most elaborate. They often comprise descriptions of tropes (tropoi; tropi), such as metaphor, hyperbole, and litotes, as well as figures (figurae), such as repetition, ellipsis, anastrophe, and oxymoron.

Theophrastus was possibly also the first one to develop a theory on the kinds of style (genera dicendi). In later works, such as the anonymous Rhetorica ad Herennium and Cicero’s Brutus and Orator, a threefold typology was developed, consisting of a “simple” style (genus subtile), a “middle” style (genus medium), and a “grand” style (genus grande). In Demetrius’ De elocutione (probably first century BC), an alternative typology is described, consisting of an “elevated” style (megaloprepês), a “plain” style (ischnos), an “elegant” style (glaphuros), and a “forceful” style (deinos). The description of the properties of these types of style can be interpreted as a summary of the rhetorical instructions concerning the virtue of aptness.¹³⁵

2.9.4 Memorization

The fourth task the speaker has to accomplish is called memorization (memoria), i.e., the committing to memory of all the elements of the speech. The relevance of this task stems from the fact that in antiquity it was not allowed to let someone else like a lawyer present a juridical speech on your behalf in front of the jury; also it was technically impossible, or at least ineffective, to read a political speech in front of an assembly. Having completed the previous three tasks, the speaker should therefore learn by heart not only the contents of the speech but also its order as well as its wording. For doing so, he could make use of the prescriptions from the “art of memory” or mnemonics. The basic idea of the memorization method is that the speaker should establish symbolic or otherwise meaningful relations between the contents of his speech and a number of objects he imagines to be placed in a familiar space, e.g., his house. By taking, when delivering his speech, a specific imaginary walk through the house and meeting in it the objects in the order they are placed, the speaker recalls the content as well as the wording of his speech.¹³⁶ Mnemonics slowly developed into an art of its own and was less and less considered to be a proper part of the system of rhetoric.¹³⁷

2.9.5 Performance

The fifth and last task the speaker has to accomplish is called performance (actio), i.e., the actual delivery of the speech. Under this heading, rhetoricians collected their advice concerning the nonverbal aspects of delivering a speech, like the use of facial expressions, the voice, and the hands. Like in the case of memorization, later a great many rhetoricians no longer considered this task to constitute a basic part of rhetoric. Some parts of it slowly developed into an art of their own, like the art of facial expressions and the art of gestures.

2.10 The Classical Heritage

After having presented the emergence and development of the classical disciplines of dialectic, logic, and rhetoric in antiquity, we will briefly sketch how they relate to later developments in the Middle Ages, the Renaissance, the modern period, and in present-day argumentation theory.

2.10.1 Dialectic and Logic

During late antiquity, the disciplines of dialectic and logic more and more converged up to the point where they finally merged in the Middle Ages. The main goal of scholars representing the combined discipline, which was mostly referred to as dialectic, was to preserve the insights regarding the validity of reasoning that were developed in antiquity.¹³⁸ Medieval scholars wrote commentaries on Aristotle’s, Cicero’s, and Boethius’ works on the topics and on Aristotle’s treatment of the fallacies.¹³⁹ In teaching, dialectic (now including logic) was considered part of the trivium : the three of the seven liberal arts that were related to language (grammar, dialectic, and rhetoric).¹⁴⁰ The idea behind the trivium and the didactical order of the teaching is that students should first learn how to use language in a correct manner (grammar), then how to reason in a valid manner (dialectic), and finally how to adapt and embellish their reasoning when communicating it to an audience (rhetoric).

In the Middle Ages, dialectical debates evolved into specific types of logical games: the tradition of the obligationes and disputationes.¹⁴¹ In the Renaissance, humanist scholars, such as Ramus and Agricola, revived the tradition of dialectic in the Aristotelian sense, i.e., as the art of conducting a discussion rather than as the art of reasoning.¹⁴²

In the nineteenth century, the discipline of logic transformed into a purely formal discipline, in which reasoning was studied without taking the context of a discussion into account. In philosophical writings of this period, the term dialectic mainly refers to the processes of transformation in ideas, history, and society, as described by Fichte, Hegel, and Marx. In the twentieth century, different interpretations of Aristotle’s theory of fallacies as being either a logical or a dialectical approach are reflected in the modern approaches to fallacies. In most twentieth-century textbooks, fallacies are conceived as mistakes in reasoning rather than as unreasonable discussion moves and thus as an object of study for logic rather than dialectic. Moreover, throughout the intervening centuries, Aristotle’s original list of fallacies in On sophistical refutations scholars had been subjected to all kinds of changes, extensions , and reinterpretations. Sometimes the result was that the ancient and the modern version of a particular type of fallacy had no more in common with each other than the label. By the mid-twentieth century, the study of fallacies was in a sorry state.¹⁴³

Charles Hamblin observed this negative state of affairs in his influential book Fallacies (1970), in which he discusses Aristotle’s list and surveys the history of the study of fallacies since Aristotle. Hamblin surveyed and severely criticized treatment of the fallacies in the introductory logic textbooks of his day (see Sects. 3.5 and 3.6 of this volume).¹⁴⁴ According to Hamblin, Aristotle’s theory of fallacies is part and parcel of his theory of dialectic, and the fallacies Aristotle discusses must be interpreted in a dialectical context. Thus, Hamblin inspired fallacy theorists to return to the classical heritage and take a dialectically oriented approach. See the discussions of the dialectical view of Næss in Sect. 3.8, the formal dialectical approaches in Chap. 6, “Formal Dialectical Approaches”, the dialectical elements in informal logic in Chap. 7, “Informal Logic”, the pragma-dialectical theory of argumentation in Chap. 10, and the dialectical approaches in the study of argumentation and artificial intelligence in Chap. 11, “Argumentation and Artificial Intelligence”.

Apart from the notion of a “fallacy,” several other notions developed within the ancient dialectical tradition still play an important role in contemporary approaches to argumentation. This holds, for instance, for the notion of a topos as a description of the relation between the reason advanced in support of a standpoint and the standpoint. This notion seems to come close to what n present-day argumentation theory is referred to as an “argument scheme” (or “argumentation scheme”). Influential approaches to argument(ation) schemes are discussed in Chap. 5, “The New Rhetoric” on the new rhetoric, Chap. 7, “Informal Logic” on informal logic, Chap. 10, “The Pragma-Dialectical Theory of Argumentation” on pragma-dialectics, and Chap. 11, “Argumentation and Artificial Intelligence” on argumentation and artificial intelligence.

Several of the main present-day approaches to argumentation may even be characterized as being dialectical. This goes for formal dialectics, in which the tools of formal logic are extended by developing formal models of a discussion (see Chap. 6, “Formal Dialectical Approaches”). In the analysis and evaluation of argumentative texts in informal logic, a dialectical perspective often plays an important role, in particular in the contributions made by Finocchiaro and by Walton (see Chap. 7, “Informal Logic”). And in pragma-dialectics, an ideal model of a critical discussion is developed based on a combination of dialectical insights and pragmatic insights (see Chap. 10, “The Pragma-Dialectical Theory of Argumentation”).

2.10.2 Rhetoric

The system of classical rhetoric depicted in Sect. 2.9 was taught in schools since late antiquity. In the Middle Ages, rhetoric was part of the trivium. During the Renaissance and the early modern period, the emphasis within the teaching of rhetoric shifted gradually from inventio to elocutio, in particular after inventio had been included in dialectic. In line with this development, the domain of application of the set of instructions that constitutes the classical system of rhetoric moved away from the production and evaluation of argumentative discourse to literary criticism.¹⁴⁵

In the second part of the twentieth century, the interest in the use of classical rhetorical insights in studying argumentation returned, including the uses of such insights for the purposes of inventio. This interest is notable in Toulmin’s approach to argumentation, which is discussed in Chap. 4, “Toulmin’s Model of Argumentation” of this volume, and much more explicitly in Perelman and Olbrechts-Tyteca’s new rhetoric, discussed in Chap. 5, “The New Rhetoric”, for which the system of classical rhetoric was the major source of inspiration. Much earlier, however, American communication and rhetoric scholars had already put insights from classical rhetoric to good use in their (often case-based) studies of argumentative discourse. Their contributions are discussed in Chap. 8, “Communication Studies and Rhetoric”. In informal logic, exceptionally, Tindale draws attention to the possibilities of using classical rhetoric in the theorizing (see Sect. 7.11).

2.10.3 Classical Works

To close this chapter, we provide a chronological list of the classical authors we discussed or mentioned and their relevant works (Fig. 2.9). For bibliographical information about the translations we quoted from or about the secondary literature we used, see the “References”.

Fig. 2.9

Chronological table of classical authors and works