The Term and Its Meaning

‘Induction’ in English derives from a Latin noun apparently first used by Cicero to render the Greek noun ἐπαγωγή – probably as found in some Hellenistic work of Greek rhetorical theory.¹ The Latin noun denotes the action expressed by the verb inducere, as the Greek that of the corresponding verb ἐπάγειν. Using ‘induction’ to render either ancient term can cause confusion if one means by it uncritically any of a number of modern conceptions referred to with this word. For this reason, among others, modern scholars will speak of epagoge rather than induction to signal an appreciation of one or more differences between the ancient and modern understandings.² Variations in meaning important for understanding ancient induction, however, are already present as ambiguities in either ancient term.³ In this study ‘induction’ will be used interchangeably with ἐπαγωγή and inductio, i.e., with an unavoidable amount of ambiguity, rather than to express any arbitrary conceptual difference over against or between these.

In its non-philosophical uses, ἐπαγωγή can refer to the military action of drawing troops forward in orderly formation; some scholars have thought to explain its philosophical usage thence, and the metaphor may well play some part in its story.⁴ But both it and the related adjective ἐπαγωγός will at least as often refer to a mysterious psychological attraction – not unlike the effect the literary Socrates has over certain interlocutors. The philosophical term may for this reason be partly understood in relation to Socrates’ ‘obstetric’ and ‘cathartic’ methods of instruction, as set forth in Plato’s Theaetetus and Sophist, respectively.⁵ Aristotle will in any case have been aware of this primarily psychagogic dimension of the term when he appropriated it to refer to a dialectical process. It is conceivable that Plato and Xenophon’s avoidance of the noun is to be understood in relation to this background, but that Aristotle deliberately adopted it to associate his own with their distinctive conception.⁶ He certainly knew the related Platonic use of ἐπάνοδος and ἐπαναγωγή in reference to a cognitive movement ‘upward’, toward principles in general and especially the good, so that the image of an upward path onto which someone entices or forces a dialectical partner so as to bring him to see something in a new light is one Socratic-Platonic background against which Aristotle necessarily developed his own use of ἐπαγωγή.⁷

The noun seems to have been given a technical sense first by Aristotle, who uses it to refer to an argumentative movement from what he calls ‘particular’ (καθ᾿ ἕκαστον, κατὰ μέρος) to something he opposes to this, calling it ‘universal’ (καθόλου). Exactly what he may have meant by these expressions in such a connection is not immediately clear.⁸ What is more, neither he nor any other ancient philosophical source offers an explanation of the noun itself so used, leaving it to moderns to speculate about this unaided. That it in some way depends on the meaning of the verb ἐπάγειν (‘to induce’ or ‘lead toward’) is agreed, but during the nineteenth century Fr. Adolf Trendelenburg understood this to signify primarily the fact that one arguing inductively adduces, or brings to bear, particular exemplary cases on behalf of a universal point, while Theodor Waitz held that it referred to the way one leads an interlocutor from particular facts toward a universal insight. Rudolf Eucken subsequently suggested that neither explanation alone could account for Aristotle’s complex usage, which several scholars since have tended to view as comprising both significations.⁹ But philosophical treatments of induction in Aristotle have still tended to emphasize one or the other aspect to the virtual exclusion of the other, according to whether writers have chosen to focus on induction as a means for establishing universal conclusions, or prefer to see it as a method of discovery, for forming concepts or generating universal principles.¹⁰

Confirming while cutting across this complexity is a grammatical variation, by which Aristotle will use the verb in the active and passive voices to express either the introduction of paradigmatic examples or an ascent to what is universal, but also in the middle voice to refer to a speaker’s metaphorically appealing to the testimony of similar cases as witnesses for an argumentative point.¹¹ Already before this, we find Xenophon using the verb in its middle voice in reference to Socrates’ appeal to images, while Plato may have been the first to use the active to signify leading someone from a state of ignorance to knowledge. Both strains probably inform the complex meaning of ἐπαγωγή as adopted by Aristotle, for which reason some have sought to see it as a response of some kind to the view found in some Platonic dialogues that learning is a kind of recollection.¹²

Appreciative of such distinctions in usage, scholars have sought to distinguish two general meanings for the term, calling these philosophical or dialectical on the one hand, and rhetorical or pedagogic on the other.¹³ This modern opposition is not quite identical with another distinction, explicitly posited by Aristotle, between induction (ἐπαγωγή) and paradigm or example (παράδειγμα), paralleling his coordinate distinction between syllogism (συλλογισμός) and enthymeme (ἐνθυμῆμα). According to Aristotle, syllogism and induction are the two kinds of argumentation found in dialectic, and paradigm and enthymeme are (viz., analogously) for rhetoric what induction and syllogism are for dialectic. Although the rhetorical variants were recognized first, the dialectical forms seem theoretically primary, since he calls enthymeme a rhetorical syllogism and paradigm a rhetorical induction. But his criteria for the broader distinction are somewhat ambiguous. His enthymeme is conventionally seen as an imperfect syllogism in the way it typically leaves one or more premisses to be understood; from a similar perspective, paradigm can seem satisfied with a single case for comparison, while induction usually relies on more than just one.¹⁴ But there is reason to think that such variation conceals deeper differences, such as the way Aristotle’s enthymeme seems to rely on likelihoods or signs, and his paradigm differs from induction in moving between similar particulars, rather than from particular to universal.¹⁵ In such contrasts induction is understood primarily in terms of a peculiarly Aristotelian logico-metaphysical position. Since the dialectical induction of which Aristotle speaks moves from particular to universal, it would seem that paradigm or example cannot be any kind of induction, properly speaking, since things universal are not, in Aristotle’s view, similar to things particular falling under them.¹⁶ To say that paradigm is a rhetorical induction, then, is not to oppose rhetorical and philosophical kinds of induction in the sense some scholars have.

Indeed, neither Aristotelian basis for distinguishing example from induction does justice to the way these are used and explained in a competing, technical tradition. The teaching peculiar to the latter can be hard to make out and trace to its authors, since it is attested mainly in later derivative sources exhibiting contamination with Aristotelian conceptions. Scanty philosophical testimonies to the alternative understanding have been preserved via digests of what is now called middle Platonism, viz. the mainly doxographic tradition of Roman times prior to the advent of what moderns have come to call neo-Platonism. These place it alongside that of Aristotle. Thus Albinus distinguishes without further explanation two kinds of induction: one from similar to similar and another from particular to general. Remarks preserved in Diogenes Laertius are fuller and more tantalizing, but his source appears to confuse inductive with deductive argumentation, and even appends a distinction between rhetorical and dialectical kinds of induction on distinctly Aristotelian criteria. The result seems a somewhat muddled account that has defied attempts to bring its teaching on induction into harmony with Aristotle’s.¹⁷ The Greek rhetorical tradition reflects a similar choice – or confusion – between the same two views of induction.¹⁸ Nonetheless, the evidence suggests that there existed from some relatively early time an understanding of induction that differed significantly from Aristotle’s – most notably in making no recourse to a distinction between particular and general, but instead characterizing it as an argument from one or more familiar things to something further that is similar to these.

Inductive Argumentation and Socrates

On either ancient account, the dialectical process called induction seems to have been associated with the persona of Socrates from the outset, with the association assuming two corresponding forms. In the earliest of these, Socrates appears dramatically as someone in command of the art of eliciting agreement about something in question from unsuspecting or unwilling interlocutors by making a preliminary appeal to one or more similar cases about which they will not feel similar qualms. When Cicero wants to exemplify inductive argument in his Topics, he appeals to one of the dialogues of the Socratic Aeschines, in which Socrates described Aspasia leading both Xenophon’s wife and Xenophon himself to appreciate a central requirement of their marriage by first securing their assent to some propositions about their attitudes toward things they desire to possess. Evidently, in this and other such nearly contemporary literary works, Socrates (or one of his fictional mouthpieces) was regularly depicted employing a method of convincing people of things they might otherwise hold unlikely by referring them to other, similar things that they were more prone to accept as being so.¹⁹ Cicero calls the argumentative method these passages depict inductio, characterizing it as a form of argument that gains agreement to a doubtful proposition by first securing agreement to some uncontroversial facts that it resembles. According to this understanding, induction has certain affinities with rhetorical appeals to example (παράδειγμα), but it is not the same thing as these.

Cicero claims to have modelled his Topics on Aristotle’s work of the same name, but any such idea is clearly in need of significant qualification, inasmuch as Cicero’s work is primarily one of rhetorical theory, while Aristotle’s treatise is on dialectic, seen as complementary to, but distinct from rhetoric. Still, it is in the Topics that an Aristotelian definition of induction is to be found, rather than in the Rhetoric. Aristotle does not in this context mention Socrates, but his schematic illustration will remind any reader of Xenophon or Plato of the Socratic character of such argumentation.²⁰ Closer comparison reveals an important difference, however, inasmuch as Aristotle’s illustration concludes with a general proposition, where otherwise parallel passages in Socratic literature tend to aim at a particular conclusion – albeit of a different order from the argumentative examples adduced for its sake.²¹ One thus sees Aristotle both defining and exemplifying inductive argumentation in terms more abstract than those in which it normally appears in Socratic literature.

In a different kind of context in the Metaphysics, Aristotle goes a step further, crediting Socrates with having made, in the course of his primarily moral inquiries, two contributions to a science of metaphysical principles: artistically inductive speeches (τοὺς . . . ἐπακτικοὺς λόγους), and universal definition (τὸ ὁρίζεσθαι καθόλου) aimed at isolating ‘The what is it?’ (τὸ τί ἐστιν). Aristotle’s choice of an adjective deriving from ἐπάγειν but ending in -ικός means that he too attributes to Socrates, not inductive arguments per se, but a technically competent handling of such arguments. The last phrase in this passage refers to Aristotle’s category of substance (οὐσία), which he thereby seems to associate with Socrates’ practice of posing ethical problems in this form.²² But the reference to universal definition evidently does not refer to the goal of Socrates’ inductive arguments, but to a distinct contribution flowing from his dialectical practice in the realm of morals.²³ According to this understanding in its developed form, Socrates – perhaps only inadvertently – introduced, or crucially developed, a method of inductive argumentation for theoretical purposes. The same estimate has recurred in a modified form in modern historical scholarship since the time of Friedrich Schleiermacher.²⁴

Socratic induction in Xenophon

In a way resonant with Aristotle’s claims about Socrates’ contributions to metaphysics, Xenophon recalls him leading people to new insights through lists of exemplary cases, and mentions Socrates’ persistent questioning of the form, ‘What is each of the things that are?’ (τί ἕκαστον εἴη τῶν ὄντων Mem. 4.6.1). He also cites the dialectical art as one among various virtues in respect of which Socrates improved his companions, prefacing several depictions he gives us of such conversations by saying that Socrates held that dialectical activity was named from people’s coming together and taking counsel in common by distinguishing, or sorting, things in accordance with their kinds (διαλέγοντας κατὰ γένη τὰ πράγματα Mem. 4.6.12). Xenophon’s depictions specifically of Socrates’ dialectical influence on his companions do not prominently feature generalizations inferred from lists of exempla, but the chapter ends with an illustration of his method when confronted with an interlocutor who contradicted him ‘having nothing clear to say and without respect for proof’ (ἄνευ ἀποδείξεως Mem. 4.6.13). In these cases, he says, Socrates ‘would draw the entire discourse up toward its hypothesis in some such way as follows . . .’ (ἐπὶ τὴν ὑπόθεσιν ἐπανῆγεν ἂν πάντα τὸν λόγον κτλ. ibid. Cf. Plato Prm. 142b2f.). His illustration depicts Socrates conversing with an interlocutor who disagreed with him on evaluating a certain man as a good citizen. Socrates directs him to the prior question of the function of a good citizen – a move we find also in Plato (the Meno, for instance). He does this by asking him a series of analogous questions about men in special political roles: financial, martial, diplomatic, demegoric. By their similarities, these point somewhere or other, we are presumably to understand. But the generalization implied in the list is left inexplicit, and the implied application to the particular case at issue never specified in Xenophon’s description. To end the chapter, he remarks that Socrates conducted his argumentative discussions on the basis of things most agreed upon, which Socrates himself characterized in reference to Odysseus as ‘leading the discourses through things seeming to be the case to men’ (διὰ τῶν δοκούντων τοῖς ἀνθρώποις ἄγειν τοὺς λόγους Mem. 4.6.15), i.e., things corresponding to ordinary opinion.²⁵

Xenophon here reports a flexible dialectical approach not unlike the one set forth in the Aristotelian Topics. In this work Aristotle assumes something resembling the main teachings of the logical works preceding it in the later grouping called the Organon, while seeking common ways of establishing conclusions dialectically, as opposed to apodeictically. The difference amounts to rather more than one between uncertain and certain premisses, as might appear on a casual reading. While it is true that Aristotle has dialectical syllogisms beginning from ordinary opinions (ἔνδοξα), rather than from scientifically certain first principles, he is also interested in the former for their utility within commonplaces (τόποι), as distinct from logically universal scientific principles. As Aristotle explains in the Rhetoric, τόποι are argumentative forms that can be used in common (κοινῇ), and similarly across different realms of discourse, with premisses likewise designated common (κοινούς), so distinguishing them from others that are proper (ἰδίας). Here ‘common’ (κοινόν) is a concept broader than ‘universal’ (καθόλου). Where universal principles have application only to the specific matters falling under them, commonplaces are lines of argument one can use in a wider variety of situations. The difference is closely connected with their distinct aims: where apodeictic seeks to demonstrate a conclusion one already possesses by identifying suitable premisses, dialectic is concerned rather to convince an interlocutor, or to refute an antagonist.²⁶ Dialectical method necessarily presupposes a conversation between two parties.²⁷ An important consequence of this is that a dialectical process leaves room for discovery, or invention, in a way that apodeictic normally cannot, for the cooperative or antagonistic encounter tends to yield results unanticipated by either party to the discussion. Dialectic is in this regard more akin to rhetoric than to apodeictic. Aristotle opposes syllogistic to inductive argumentation separately for dialectic and apodeictic, further specifying enthymeme and paradigm as their rhetorical counterparts. These analogous pairings in a sense themselves reiterate the opposition just specified, inasmuch as syllogistic reasoning is more rigorous, and as such more forceful and influential with educated people, while inductive reasoning is useful for addressing people less adept, and needing to be led to see an unaccustomed or unpalatable conclusion via a path from things similar to it but more familiar or acceptable to them. And something similar holds for antagonists who, for one reason or another, prove impervious to demonstration.²⁸

The passage from Aeschines adduced by Cicero illustrates the kind of induction addressed to cooperative, but less able interlocutors; the passage in Xenophon illustrates the kind directed at more able antagonists. In Aeschines, Aspasia induces the married couple to acknowledge their desires for inanimate possessions like those their neighbours might have, which only afterward are made parallel to their conjugal relationship itself. So viewed, however, this focal case now appears to contravene the injunction not to covet one’s neighbour’s spouse. This unpleasant possibility then allows Aspasia to frame the inverted perspective of partners seeking to deserve each other, thus leading the married couple toward a more congenial and constructive view of their conjugal relationship.²⁹ In Xenophon, Socrates presents an irrationally resistant interlocutor with a series of particular activities – money management, war, ambassadorship, public debate – sharing a pattern of striving toward improvement he means to apply to the case of the good citizen generally conceived. Common to all is what Xenophon refers to as ‘what underlies’ (τὴν ὑπόθεσιν), viz. an implied account embodying an adequate answer to the question, ‘What is the task (ἔργον) of the good citizen?’ The series of illustrative cases functions to allow the interlocutor to see (or perhaps, as here, to induce an antagonist to acknowledge) the methodically prior, more general account in terms of which his and Socrates’ assessments of their respective candidates must ultimately be judged.

Induction in Plato’s dialogues

In the tradition stemming from Aristotle, an inductive argument is supposed to produce a universal conclusion based upon one or more paradigmatic cases that we often term ‘examples’. An example in this sense is primarily a model on which one bases some kind of production or action: an artist’s model, for instance; or a living exemplar for a young person still to be formed morally. Thus we still say that a teacher can set a pupil an example – although today one is more apt to speak in terms of a dramatic metaphor by calling the teacher a ‘role model’ for the pupil. We also speak of a writer’s exemplar in a similar way. Such models are said to be ‘paradigmatic’ or ‘exemplary’. Likewise, an example offered to illustrate a precept is thus meant primarily as a model for the pupil to imitate in his own productive, or poetic, activity.

Within the Greco-Roman rhetorical tradition, a παράδειγμα or exemplum also bears one of two more restrictive senses. In the branch of the tradition stemming from Aristotle’s Rhetoric, a παράδειγμα is – as already noted – a rhetorical version of induction. In an alternative, likely pre-Aristotelian branch, a παράδειγμα is some past act with which to compare something that has happened or is being contemplated in the present. For this reason, certain instances of what Aristotle calls a παράδειγμα are liable to confusion with what the alternative tradition calls a τεκμήριον (‘token’).³⁰ Thus, when Euthyphro appeals to the Hesiodic account of Zeus’ maltreatment of Cronus as a model for his own prosecution of his father, he calls it a μέγα τεκμήριον (Euphr. 5d–6a). In redirecting Euthyphro’s attention to the single form (εἶδος, ἰδέα) that is the object of his questioning, Socrates instead says that he wants to be able to use that form, not some mythical story, as his παράδειγμα for judging action pious or impious (Euphr. 6d–e). His usage in this context is conventionally construed relative to a hypothetical evolution and decay of a ‘realist’ Platonist metaphysics reflected in an equally hypothetical ordering of the Platonic dialogues.³¹ This circumstance renders it necessary to stress that, read more historically, it suggests that Socrates is seeking a quasi-visible outward form (literally, a ‘look’) by which to judge rather than an ‘example’ in the standard rhetorical sense.³² To appreciate this in the way requisite for the present investigation may require that we at least temporarily forget what we seem to know about Platonic ideas.

What came to be called Plato’s forms or ideas are characterized in a few places in his dialogues as serving as stable models (παραδείγματα) for the transient things of the world of generation and corruption. His use of the term in the Euthyphro need bear no such sense; but since Socrates’ search for moral definition, or focus, is also there presented as a search for an idea or form of some kind, one is led to look for some continuity between the near-rhetorical use of παράδειγμα found in the Euthyphro and the distinctly metaphorical use found in other, more ‘metaphysical’ dialogues. At least one possibility for a meaning underlying such a unity comes to sight in Cicero’s invocation of Plato’s ideas at the beginning of his Orator. Faced with the question who was the finest orator – there were competing schools of thought – he proposes to depict as best an orator of such a quality as has perhaps never existed (in summo oratore fingendo talem informabo qualis fortasse nemo fuit Or. (2) 7). To explain, he compares the exemplary case of Phidias, whose productions were the finest one might ever see, but were nevertheless modelled by the artist on some superlative look within the artist’s mind (in mente . . . species . . . eximia quaedam ibid. (2) 9) to which he looked as his model in reproducing a similar look in a work of art. He adds that just as it is with forms and figures, viz. that there is some perfect standard to which we refer deficient instances, so too we have in our minds a quasi-visual form (species, later a standard translation for εἶδος) of oratory with reference to which we seek aurally to judge practical instances. He says that Plato called such forms of things ideai, and held that they did not come into being but are always, being comprehended by reason and intelligence, while other things undergo generation, corruption, and unstable change. Cicero proposes, in short, an approach at the same time rhetorical and philosophically Platonic to the question of the best form of oratory. What follows is the classic Ciceronian rhetorical work on elocution. Ancient writers like Cicero for some reason lacked access to modern conclusions about Plato’s metaphysical development. One value of testimony like Cicero’s is thus as a reminder of a radically alternative way of reading Plato’s use of εἶδος and ἰδέα that would have been natural in antiquity. Fortunately, it is unnecessary for this reading entirely to supplant assumptions geared to a post-medieval debate on universals in order for the more rhetorical usage to enhance our understanding of the development of dialectical argumentation between Socrates and Aristotle. The fact that any metaphysical status of a moral εἶδος or ἰδέα is there left ambiguous, for example, suggests that the question may well be irrelevant to a properly dialectical understanding of the Euthyphro.

On the other hand, an overarching orientation toward paradigmatic forms or ideas in the sense just specified enters into the dialectical practice represented in the Platonic dialogues, including their use of induction.³³ This fact requires one not only to read individual arguments in the light of their greater dramatic and dialectical contexts, but also invites observation of an additional layer for interpretation, insofar as Plato’s literary art exerts an inductive influence on his readers through his dramatization of the dialectical process. Success at this level of interpretation necessarily involves a certain sympathy for Plato’s dialectical orientation. For such reasons, although the Platonic Socrates employs argumentation superficially like that exemplified in Xenophon and theorized in Aristotle, addressing it to interlocutors cooperative and resistant alike, the task of isolating an underlying logical form for his arguments can in either case be frustrating.³⁴ The analytical school of modern interpretation has in recent times been the most energetic in the effort to lay such forms bare. This has given rise to complaints of modernizing among adherents of other approaches, but the analysts can claim later ancient readings of Plato as precedents, for these too sought to identify a logical form for properly dialectical arguments found in the Platonic dialogues. There exists more than one kind of ancient analysis along such lines, however.

A useful example of one kind is provided by the tradition of later Platonic commentaries on the Alcibiadesi, one of numerous conversations in which Socrates begins by bewildering a promising but initially resistant interlocutor with refutative techniques, following these up with a more cooperative phase of argumentation. Later Platonists sought to identify syllogisms informing dialectical passages in the dialogue, and also inductions by which certain premises within these are established. In this effort, which they undertook to show how Socrates instructed Alcibiades, they were guided by the Peripatetic logic they had long since incorporated into their philosophy.³⁵

A complementary tendency is evident in the Aristotelian commentator Alexander of Aphrodisias, who, in commenting on the Prior Analytics, extracts an argument from a Platonic dialogue to illustrate Aristotle’s statement that syllogistic premises can themselves be established syllogistically or inductively. According to Alexander, in the course of arguing against Thrasymachus, Socrates does just this toward the end of Republic 1, as he is completing his refutation of Thrasymachus’ thesis that the unjust life is better.³⁶ In the greater argument of which this forms a part, Alexander explains, Socrates argues from two premises: first, that (1) one seeing fit to have more than his unlike but the same as his like is wise; and second, that (2) the just man sees fit to have more than his unlike but the same as his like (shorthand hereafter: ‘discriminates appropriately’). According to Alexander, the conclusion following from these premises is that the wise man is just. That he seems to have without warrant converted the valid conclusion (viz., that the just man is wise) is curious, but does not here concern us. Certain features of his finer analysis do, for he says that the first premise is established via an induction from the cases of the doctor and musical man, but the second via syllogism: a man prone to distribute equitably discriminates appropriately, but the just man is prone to distribute things equitably, so the just man discriminates appropriately.³⁷ The argument as it is found in Plato (Rep. 1.349b–350c) seems to be of a rather different character. Its main steps might be outlined as follows:

In his reading of the clearly inductive section of Socrates’ refutation, Alexander not only inverts the order of the examples, but appears to have converted the constituent propositions: Socrates establishes inductively in (6) not that discriminating men are wise, but that knowledgeable men are discriminating. As to the syllogism Alexander lays out as the basis for understanding the rest, even its middle term (the man who is prone to distribute things equitably) is nowhere explicit in Socrates’ argumentation. In fact, his second main premise seems not to be argued for at all, being instead readily conceded by Thrasymachus toward the outset, in (1) (cf. Rep. 1.349b2–d2 with 1.350b6–c2). Can Alexander so thoroughly have missed the flow of this argument?

To see more clearly the contrast between the two ancient styles of attributing a logical form to arguments in Plato’s dialogues, it will be useful to compare an ancient Platonic reading of this same passage. Proclus’ running commentary on this part of Republic 1 is lost, but fortunately he preserves in outline his interpretation of it in his commentary on the Alcibiades 1.³⁸ He seems to understand the general form of the argument the same way Alexander does, but spells out some assumptions in a way showing a greater appreciation of the dialectical nature of the argument. Most notably, where Alexander has a demonstrative syllogism, he frames the reasoning underlying the minor premise reductively, and thereby more in tune with Thrasymachus’ initially assertive responses to Socrates’ questions: if the just man did try to have more than his like, he wouldn’t be a just man.³⁹ Why the difference? Alexander may have relied upon his own faulty memory of Plato’s Republic. But it is also possible that his Peripatetic outlook leads him to seek or even to supply a syllogism in an obscure context where he believes that it is needed to understand the argument. If so, then the element he found hard to construe as it reads in the Republic will likely have been the argumentative strain both he and Proclus seem to have missed, best seen in the statement that the just man will be of such a quality (τοιοῦτος) as the one he resembles (ἔοικε), and so likewise with the unjust man (Rep. 1.349d4–9). It is on this basis that Socrates in fact argues to the conclusion that the just man must himself be good and wise, since he resembles men good and wise in other pursuits, in respect of seeing fit to try to have more than his unequal but the same as his equal (the middle term in Alexander’s analysis of the larger argument) (Rep. 1.350c2–8).

Where both Alexander and Proclus seem to have supplied logical propositions and terms they think necessary to appreciate Socrates’ argument, a majority of modern scholars have tended to find fault with it, alleging several logical ‘fallacies’ of which Socrates is supposedly guilty. The most common complaint has to do with the role of the clearly inductive phase at 1.349d13–350b2, and alleges that the application of its conclusion (6) is unsound, since Socrates equivocates on πλέον ἔχειν and πλεονεκτεῖν, falsely assimilating the unjust man’s over-reaching in a moral sense to an incompetent’s inability to see the limits of a given art.⁴⁰ This complaint is often framed in terms of Socrates’ illegitimate use of an analogy with the crafts.⁴¹ But an analogy is an identity of relations; thus, e.g., for a father to stand to a son analogously as a mother does to a daughter it is not necessary for fatherhood and motherhood (or sonhood and daughterhood) to be synonymous. The complaint about equivocation seems misconceived, therefore. It is sufficient for the purposes of the argument if an analogy in the proper sense holds for the behaviour of the unjust man relative to that of the just man; it is unnecessary for Socrates to use πλέον ἔχειν and πλεονεκτεῖν univocally, or for him to presuppose that justice and the arts of music and medicine are species of some universal that can be predicated univocally of arts and virtues. It is in this case interesting to note that, although Socrates has hereby been supposed guilty specifically of a fallacya dicto secundum quid ad dictum simpliciter,⁴² W.H.B. Joseph, who also authored the standard textbook on traditional logic of his day, counts among the few modern readers who have judged the argument entirely sound.⁴³

The second main criticism modern scholars make of the argument bears directly on the feature that Alexander seems to disregard in his analysis. When Socrates asks Thrasymachus whether the unjust resembles the wise and good, Thrasymachus (who has earlier claimed that the unjust is wise and good) asks rhetorically how one who is of such a quality as (ὁ τοιοῦτος ὢν) some others can avoid resembling them too (καὶ ἐοικέναι τοῖς τοιούτοις). Socrates reformulates this affirmatively: so each is of the same quality (τοιοῦτος) as the one he resembles (ἔοικε). Thrasymachus finds this unobjectionable, but numerous modern scholars have balked at it as embodying a false conversion: if A is B, A will also resemble B; but if A resembles B, it does not follow that A is B.⁴⁴ This interpretation of the argument is evidently compelling enough that the Kneales can offer it as an example of a logical principle adduced by Plato, the unsoundness of which we cannot be certain he was aware, on account of the dialogue form within which we find it.⁴⁵

One might say at least two things in defence of Socrates’ argument against this second criticism. First, since he and Thrasymachus agree that the just man and artistic adept will both feel free to over-reach relative to their unqualified counterparts, there would presumably be nothing wrong with Socrates’ overreaching relative to Thrasymachus on this occasion – whether as a champion of justice or as the superior in the dialectical art. On a dramatic level, this is what seems to occur. Socrates might be said to ‘get the better of’ Thrasymachus in dialectical speech in this instance. Plato will often in this way have his characters act out the philosophical themes they are discussing (cf. Rep. 1.350a8). The second is that, from another perspective, the argument in the Republic is not fallacious at all, for Socrates does not in fact say something of the form ‘A is B because A resembles B’, but asserts only that ‘A is of the same character as (τοιοῦτος) B because A resembles B’. In the context of this particular argument, ‘is of the same character as B’ means ‘behaves toward its opposite the same way B does toward its opposite’, where the relation consists in differing attitudes toward limits on over-reaching in the general sense specified above in relation to the first complaint. Thus although Socrates’ conversion of Thrasymachus’ rhetorical question (4) into (5) is invalid in a purely formal sense, the meanings of the terms employed are such that it need not vitiate his argument.⁴⁶

The last observation brings out a feature that Alexander too seems not to have noticed, viz. that Socrates’ entire argument – not only the clear use of induction to establish one of its premises – turns on resemblances. This is not only true of the induction underlying the major premise, and the movement from the resemblance viewed as an action (ἐοικέναι) to the predication of the corresponding property (τοιοῦτον εἶναι),⁴⁷ but even of the criterion governing the discrimination shown by the knowledgeable man of each pair (see 1.350b7–9).⁴⁸ The argument thus employs induction throughout, but in more than one sense. In one regard it relies on an inductive path from particular statements falling under it to a general statement in the sense required by Peripatetic logic. But in the way it traces the idea of an equitable distribution from its relatively deficient or distorted reflections in the realm of the special arts back upward to its ‘hypothesis’, viz. the paradigmatic instantiation seen in political justice (cf. Rep. 4.420d1–e1), it is also founded on reasoning from similar to similar, viz., exemplary induction as conceived in the rhetorically attuned philosophical tradition of Xenophon, Cicero and others. And it is the latter argumentative strain that the Peripatetic commentator appears to have tried to supplant with a ‘syllogism’ of his own construction, employing the man who exhibits this political quality as its middle term. But to repeat: the Platonic argument relies on inductive movement throughout: in one sense as the generalizing movement from particular to universal statements, but then also as a movement ascending from posterior to prior instantiations of a feature common to all, if not predicated of them univocally.

That the Platonic passage is so designed is also suggested by certain dramatic details. Socrates narrates the course of this argument on the next day, remarking at the end that it did not actually occur so smoothly as his narration depicts, for Thrasymachus put up resistance at numerous points during it, and is exercised enough to blush red at its conclusion.⁴⁹ Socrates gives hints in the main places Thrasymachus might have expressed reservations by the way he reports his responses to questioning. First, in reference to the universal conclusion Socrates draws from the two cases he adduces, Thrasymachus allows that ‘for this much, at least, to hold so is perhaps necessary’ (ἀλλ᾿ ἴσως, ἔφη, ἀνάγκη τοῦτό γε οὕτως ἔχειν). Second, when Socrates draws the conclusion that the just man resembles the good and wise man, he gives his unenthusiastic assent (κινδυνεύει). In the mouth of one less well versed in argumentation, these could be read simply as indications of hesitation about the particular statements at issue. Some have indeed thought that Thrasymachus must be a poor dialectician – if a good rhetorician – since he voices a preference for extended speeches. But a competent rhetorician will have to be familiar with forensic (including cross-examinational) as well as epideictic techniques; and the same predilection does not prevent Protagoras’ conversing dialectically and even offering a criticism of Socrates’ argumentation in another dialogue, in which he points out what seems to be a faulty conversion not unlike the one scholars have alleged to be present in Republic 1. As characterized by Plato’s Socrates, therefore, Thrasymachus would be likely to appreciate the direction in which the argument is going, and to curtail his assent in cases where there are solid grounds for reservation.⁵⁰

From a modern standpoint, he would have his grounds in both cases just mentioned. Two instances might seem to him hardly sufficient to establish a universal conclusion. This is, in a sense, the later problem of ‘incomplete’ induction. An experienced dialectician (or forensic rhetorician) would realize that the inference is less than secure, but also that the only effective refutation of such an induction is a counterexample. Thus his problem may be that, while he fully understands that a respondent is supposed to admit an induction unless he can supply such a counterexample, Thrasymachus thinks that he cannot.⁵¹ Similarly, the resemblance the just man bears to technical men in a certain regard might not in Thrasymachus’ view compel the conclusion that he is describable in corresponding terms qua just man, but the task of articulating just how he differs might be challenging. This resembles the even more modern problem of the so-called craft analogy. There is no sign, on the other hand, that he finds any problem in the move from ‘resembles’ to ‘is of the same character as’ so troublesome to modern scholars.

Platonic vs. Peripatetic universals

The reason Alexander sees the first kind of inductive movement more clearly than he does the second is not far to seek. In commenting on the passage in the Topics where Aristotle defines and illustrates ἐπαγωγή, he remarks in passing that those defining it as a movement from similar to similar are mistaken, since the universal is not similar to the specific instances falling under it.⁵² While he does not specify whom he means, at least Platonists of his own day might have viewed the matter otherwise, since their universals – the ideas – served also as exemplars (παραδείγματα) for the particulars participating in them. Peripatetics like Alexander held that induction moved from particulars to universal but tended to conceive of the latter in terms of Aristotle’s logic, rather than his metaphysics, where ‘universal’ is used also of items occupying a primary position in a hierarchy of things prior or posterior to one another.⁵³ Moreover, for them (i.e., later Peripatetics) such logical universals were to be located in fact only in their particular instantiations, and had no existence besides that of corporeal things, much less a paradigmatic relation to these.⁵⁴ Alexander’s Peripateticism commits him to a radical critique of the Platonic ideas, excluding the possibility of an inductive movement drawing an interlocutor toward the appreciation of a paradigmatic entity, as distinct from a general universal. Hence, perhaps, his attempt to identify a ‘syllogism’ as the basis for his second premise. By contrast, later Platonists, seeking to accommodate Aristotelian logic to Platonic metaphysics, understood even genera and species as occurring within hierarchical structures of the kind Aristotle describes in terms of priority and posteriority, in addition to standing in relations of the kind postulated by Aristotelian logic.⁵⁵ This would have allowed their conceiving an upward movement of the kind seen in the second strain of argument in the Republic passage as inductive in the original, Platonic sense of an ἐπαναγωγή aiming toward universal ‘genera’ in the sense of the concrete entities even Aristotle had admitted could stand at the head of non-univocal but still dependent series πρὸς ἕν or ἀφ᾿ ἑνός.⁵⁶ Later Platonists avoided calling this kind of upward movement ἐπαγωγή, which they reserved for referring to the induction of Aristotelian logic, but used instead the primarily mathematical terms ἀνάλυσις and ἀναλυτική [sc. μέθοδος].⁵⁷ They applied this terminology to various kinds of technical procedures: geometrical analysis of the kind presumably parodied in the Meno, dialectical reasoning corresponding to the fourth segment of the Republic’s Divided Line, and the erotic path up Diotima’s ladder of beauty in the Symposium. Provided that one allows for universals after the Platonist conception of these, all such cognitive movements may be counted inductive in the broader sense of Aristotle’s use of ἐπαγωγή, seen as a development of the Platonic ἐπαναγωγή. This is especially clear in the case of the last, where we can compare a closely parallel movement in the Hippias Major, whereby Plato has Socrates lead Hippias to see the limitations in his own conception of beauty by appealing to examples forming a series similar to that outlined by Diotima in the Symposium.⁵⁸ The comparison incidentally illustrates the way Plato’s literary use of inductive movements moves beyond a simply Socratic phenomenon. Where Socrates in his conversations aimed to prepare his interlocutors for a process of discovery, Plato’s literary dialogues already conduct his readers on this path. Aristotelian logic, by contrast with the dialectic of both Socrates and Plato, aims primarily to convince us of matters once discovered, so that induction here comes to occupy a role subservient to that of syllogistic.⁵⁹

Dialectical induction in Aristotle

Aristotle’s own argumentative practice does not congrue with Aristotelian logic, and it has for some time been acknowledged that Aristotle’s philosophical treatises employ a distinctly dialectical method in developing their themes. The way he regularly begins from commonly held – if not necessarily true – propositions, proceeding from these toward less obvious truths, may fairly be termed inductive in the broader, Platonic sense exposed above.⁶⁰ The question may therefore reasonably be asked, how does Aristotle himself conceive induction as used in dialectical, as distinct from apodeictic, reasoning? Does he recognize only the passage from particular statements to general statements covering these, or would he also accept an argument as inductive that moved up a concrete hierarchy of some kind? The inductive phase in the Socratic argument in the Republic that Alexander recognizes bears a certain resemblance to Aristotle’s own illustration in the Topics, where the particular cases of the knowledgeable pilot and knowledgeable charioteer are adduced in support of the general statement that one who is knowledgeable about each thing is generally best.⁶¹ In his study of the origins of traditional logic, Ernst Kapp compares an exchange at Meno 88a, saying ‘Obviously, Aristotle’s notion of induction may be adequately represented by the part of a Socratic dialogue which I have quoted’, and then adding ‘even his example . . . is nothing but a condensed abstract of some piece of Socratic dialectic’.⁶² Aristotle’s illustration uses the same examples – pilot and charioteer – found paired in other Platonic passages (e.g., at Theag. 123a9ff.), rather than those found in the passage in Republic 1, but these and several other similar arguments purport to establish a general statement about the man who knows on the basis of two exemplary cases. In Socratic contexts, such generalizations are, as a rule, adduced only in relation to some concrete case under consideration. Thus Xenophon reports that Socrates was accused of making the youth disrespect the Athenian regime by saying that it was stupid to choose political rulers by lot when one would never do the same with a pilot, carpenter, flautist, or the like.⁶³ The range of exempla used in arguments reducible to the same basic form suggests that the function of such arguments goes beyond that provided by their purely logical force and, more particularly, that the choice of exemplary cases may make some difference or have an important contextual bearing. Although his inductions do exhibit various conventional groupings of exempla, Socrates as reported by Xenophon seems to have used these largely with a view to their familiarity to his interlocutors. One might equally ask why Socrates chooses the particular examples he does in the induction identified by Alexander, getting much the same kind of answer. But in Plato’s dialogues there is characteristically a greater literary architecture governing such choices. In the present case, the examples of the doctor and musician are not only to do their immediate job of securing Thrasymachus’ agreement to the induction, but they further anticipate the role of music and gymnastic in the preliminary education of the guardians in books 2–3, so serving in an artistic sense also to prepare Plato’s readers for what is to come. Reflection on this larger literary relationship further suggests that even the induction from the two cases of doctor and musician already moves upward in a hierarchy, so that their order becomes important as well.⁶⁴

Since Aristotle in his treatises proceeds in a dialectical, rather than an apodeictic manner, he will vary his own use of inductive movements in analogous ways. A familiar instance occurs at the very beginning of the Nicomachean Ethics:

The inductive form of this opening is evident,⁶⁵ but syncopated enough that it remains somewhat unclear in what sense the particular items adduced combine to build the general statement. The four examples grouped in pairs might be seen as adding up to ‘everything’ in different ways. Does Aristotle mean ‘both art and action’, or alternando that ‘both performance and principle’ aim at some good? Or does he contrive to say both of these at once? In any case, one may notice a movement up a compact hierarchy like that traversed in either strain of Socrates’ argument in Republic 1.

Another kind of inductive opening – more familiar to most ancient Greeks of Aristotle’s day, if less so to us – serves to begin the Eudemian Ethics. Here, we find a traditional, popular kind of list, which modern literary scholars have dubbed the ‘Priamel’, but which in many ways anticipates the induction of the philosophers.⁶⁶ In such lists several less clearly analogous items are more clearly ranked in a hierarchy often explicitly tied to some conventional outlook or other:

It would probably be mistaken to conclude from this difference in the forms of these two openings that one was written earlier than the other. The variation is more likely coordinate with some difference in the literary strategies of the two works. Since the appearance of Werner Jaeger’s influential interpretation of Aristotle, such differences have usually been regarded in the light of a hypothetical evolution in Aristotle’s thought. But it is at least equally possible that they are more rhetorical than doctrinal, being determined mainly by the differing occasions of the two works, or perhaps by the requirements of differing audiences to which they are addressed. The Nicomachean Ethics is palpably more theoretical in tone and method; the Eudemian Ethics follows by contrast the path of a more traditional morality. The poetic quotation at the opening of the latter surfaces in the former as well, but in the Nicomachean Ethics it is relegated to a subsequent chapter in which Aristotle seeks to square a discussion that he has been pursuing theoretically with ordinary opinions. The Eudemian Ethics, by contrast, begins with ordinary opinions and moves from them toward more theoretical considerations. Both methods are inductive, but they are so in relation to differing kinds of audiences, or projects, or both.⁶⁷

To us, as moderns interested in ancient philosophy, it is the Nicomachean Ethics that opens with an induction of the kind better known. Aristotle here also begins by positing a good that is universal in a sense comporting reasonably well with induction as understood in traditional logic. But he immediately moves to qualify this sense by distinguishing instances of good ends within a theoretical hierarchy. The universal good he seeks thus stands not as an abstract generic end to specific or concrete ends, but as a super-ordinate concrete end per se to subordinate concrete ends per alia.⁶⁸ In order to maintain this hierarchical perspective, he later in book I criticizes the Platonists’ resort to an idea of the good, as both an object for theoretical contemplation and also the good in which everything else good participates. Aristotle’s stated view is that there is no such thing forming the subject matter for political theory, since – among other reasons – ‘good’ has various senses coordinate with the senses of ‘being’ distinguished in his ten categories, in which the category of substance is prior to all the rest. Since, then, ‘good’ is used in senses that fall prior and posterior to one another, and the Platonists of Aristotle’s own day posit no ideas for such series of things, there is no ‘common, universal, single’ good. Moreover, ideas are subject matters for single sciences, but sciences of what is good are different even within single categories. He offers some examples: in the category of time, generalship knows what is opportune in war, but in disease, medicine; and in that of quantity, medicine knows what is the right amount of sustenance, but gymnastic of training.⁶⁹ The universal good toward which Aristotle’s opening induction in fact points, then, seems to be some primary sense standing at the head of an organized hierarchy of goods. The Eudemian Ethics covers similar ground in a slightly different way. There, Aristotle seems to explain more clearly his notion of derivatively named things’ being arranged in a structure centred on a single entity prior to all else, but he at the same time appears to neglect to apply the idea explicitly to the hierarchy of human goods. In the course of his argument, he rejects the Platonic idea of the good as a possible subject for the discipline of ethics, but he also does the same for the candidate of a ‘common’ (κοινόν) good, appearing to leave it open whether ethics may not have to concern itself with some ‘proper’ (ἴδιον) subject matter. For whatever reason, Aristotle’s approach seems on this occasion mainly problematic in character.⁷⁰

Parallel arguments recur once more toward the beginning of the Great Ethics, or Magna Moralia, a third Aristotelian moral work evidently addressed to yet another kind of occasion or audience.⁷¹ But they are here both placed and organized somewhat differently. The work begins with the observation with which the first chapter of the Nicomachean Ethics concludes, and moves from there by way of a historical review to the point with which it began.⁷² Having by this alternative route premised that every science and capacity has an end, and that this end is good, Aristotle here again moves to establish that this good is not something common in the sense of a logical genus, much less in the sense of the idea of the good. But this time he considers the extent to which political science can consider a ‘common’ good. He does this in a way reminiscent of his description in the Metaphysics of Socrates’ two contributions to first philosophy, for he speaks explicitly of this possibility in terms of definition and induction (ὁ ὁρισμὸς καὶ ἡ ἐπαγωγή), rejecting both possibilities.⁷³ He treats the definitional sense first, and then moves to induction. In arguing that political science is unable to speak about ‘what is common via induction’ (τοῦ κατὰ τὴν ἐπαγωγὴν κοινοῦ), he says in advance that the same impossibilities will result as do for a definition of a common good. One may indeed speak of a best good, but this is the good for us, for men. No science can speak about every good, however. Why?

Premising (a) that there is no single science or power of every good, since good falls under all the categories, he next points out (b) that within the category of time, different people will have knowledge, arguing inductively from the cases of the doctor and pilot to a general statement of the form ‘in each science each (sc. special practitioner) will know the ‘when it is good’ that is proper to himself’. Good is a ‘common’ element in all these cases, but no science can speak about a common good within the category of time.

He goes on to say that something similar holds for good in the category of relation, and in all the rest of the categories, with the result that as no science can speak knowledgeably about the good in each (sc. category), neither can political science speak about a common good (sc. simply).⁷⁴

Thus runs one of many curiously parallel passages in the Great Ethics. Most relevant to the present occasion is the way Aristotle here does two things. The first lies in his universal inference from the two particular and familiar cases of the doctor and pilot, which follows the pattern found in Xenophon, Plato, and his own description of induction in the Topics. The other is the greater movement to recognize the special kind of community underlying a non-univocal sense of ‘good’ – both within single categories, and between the categories themselves. Aristotle argues that there is no science of the good as a logical genus or idea, on the grounds that one cannot have a single science of a genus subsuming different species of good, but he does so precisely by following an induction through the cases exhibiting good as a ‘common’ element. In order to do this, he must regard induction from particulars to universal as including the movement from posterior to prior as well as the one from species to genus in the sense required by Aristotelian logic.

Viewed against the contemporary Platonic conception of an idea of the good, this seems to deny a separable pre-eminence to any unitary good as such; but viewed against a hierarchy of ends like the one he sets out at the beginning of the EN directly following the inductive opening quoted above (1.1–2.1094a3–b11), it reflects the kind of structure Aristotle in several other contexts confirms, most notably in the Metaphysics, when he speaks of the subject matter of first philosophy as something that would be universal, inasmuch as first (Met. 6.1.1026a29–32).

Conclusion

Socrates’ characteristic use of series of exemplary cases to establish some similar point developed out of several kinds of focusing device traditional to poetry and rhetoric, a background that must be borne in mind in order to understand the development of inductive argumentation during classical times. Before these or Socrates’ own practices were subjected to theoretical treatment by Aristotle and his successors, Plato, Xenophon, and other Socratic writers made the ethic integral to their dramatic portrayals of his dialectical method, i.e. the pathway by which he would lead his interlocutors on an upward road toward new insights. These portrayals normally do not show Socrates seeking to infer logically universal statements for general scientific purposes, or doing so via attempts at complete enumeration of particular cases falling under such universal statements. They instead show Socrates selecting examples embodying images apt to produce agreement in his interlocutors – and, at least in Plato’s case, the examples Socrates chooses can often be seen to bear, in addition to their rhetorical probability within the immediate dialectical context, a literary significance determined by the larger argument of the dialogue as a whole.

Attribution to Socrates of an inductive method in a logical sense grew out of charitable statements Aristotle makes according him a place in an Aristotelian history of philosophy. An early modern reaction against Aristotle’s unquestioned authority led to the charge of his having acted like a horse-thief, appropriating Socrates and Plato’s method for his own purposes while branding it with his own name and altering its appearance in order to conceal the theft.⁷⁵ There may be some truth in this, but it is too harsh. Not only does Aristotle himself speak about induction in a variety of senses extending beyond the narrow conception traditionally attributed to him, but he himself is seen to employ inductive arguments dialectically, in a way preserving a technical, rather than logical understanding of the relation between his exemplary cases and the point of more universal interest for the sake of which these have been adduced.

This alternative understanding was preserved in the later Platonic tradition of interpretation and a sympathetic rhetorical tradition, while it seems to have been either later Aristotelianism or wholly distinct modern views that have narrowed the conception of induction to include only what has come to be called inductive inference. In order to understand induction as it is actually used in the literary tradition preservative of classical Greek philosophy, including that part represented by the Corpus Aristotelicum, then, it is best to hold in question all such later constructions and instead, through judicious accumulation and consideration of particular instances, develop an appreciation of the enduring phenomenon of Socratic induction itself.