Going Through Aporiai: The Critical Use of Aristotle’s Dialectic

Gabriela Rossi

1. Introduction

The ‘aporematic’ or ‘diaporetic’ procedure is one of Aristotle’s distinctive methodological contributions, and is usually counted among the alleged philosophical applications of his dialectic.¹ One of the main grounds for considering this sort of discussion as dialectical in nature is a conspicuous passage in Topics 1. 2, where Aristotle indicates the philosophical utility of the treatise:

[i] πρὸς δὲ τὰς κατὰ ϕιλοσοϕίαν ἐπιστήμας, ὅτι δυνάμενοι πρὸς ἀμϕότερα διαπορῆσαι ῥᾷον ἐν ἑκάστοις κατοψόμεθα τἀληθές τε καὶ τὸ ψεῦδος· [ii] ἔτι δὲ πρὸς τὰ πρῶτα τῶν περὶ ἑκάστην ἐπιστήμην. ἐκ μὲν γὰρ τῶν οἰκείων τῶν κατὰ τὴν προτεθεῖσαν ἐπιστήμην ἀρχῶν ἀδύνατον εἰπεῖν τι περὶ αὐτῶν, ἐπειδὴ πρῶται αἱ ἀρχαὶ ἁπάντων εἰσί, διὰ δὲ τῶν περὶ ἕκαστα ἐνδόξων ἀνάγκη περὶ αὐτῶν διελθεῖν. τοῦτο δ᾿ ἴδιον ἢ μάλιστα οἰκεῖον τῆς διαλεκτικῆς ἐστιν· ἐξεταστικὴ γὰρ οὖσα πρὸς τὰς ἁπασῶν τῶν μεθόδων ἀρχὰς ὁδὸν ἔχει. (Top. 1. 2, 101^a34–^b4)²

[i] It is also useful in relation to the philosophical sciences, because, if we are able to go through the difficulties on either side, we shall more readily discern the true as well as the false in each subject. [ii] Furthermore, it is useful in relation to the primary things in any individual science. For if we reason from the principles proper to the science in question, it is impossible to say anything about these things (since these principles are the first of all), and it is through accepted opinions about each that it is necessary to discuss them. But this is unique, or at any rate most proper, to dialectic since, being apt for examination, it offers a way towards the principles of all studies.³

I shall assume that this passage states an indirect utility of the Topics, in so far as what is used in philosophical investigations is properly the skills (cf. 101^a34–5: ὅτι δυνάμενοι …) obtained through dialectical exercise, for which the Topics is a manual. It is these skills that, once acquired, are—or can be—used in philosophical investigation.⁴

Aristotle introduces two different ways in which his treatise on dialectic may be of indirect use to philosophy or to theoretical enquiry in general.⁵ In [i] the philosophical utility of this study is that it enables one ‘to go through the difficulties on either side’, an activity that would make it easier to see distinctly the true as well as the false. In [ii] Aristotle seems to suggest that the utility of the study (and practice) of dialectic is that, through learning how to deal with accepted opinions (endoxa) and by practising examination, it enables the dialectician to investigate the (indemonstrable) principles of each science. I shall not tackle this much-discussed second aspect of the relation between dialectic and philosophy here. My focus instead will be on the first one, which alludes to aporiai.

An important and distinctive part of the dialectical training described in the Topics consists in arguing for opposed theses (or for and against the same thesis), which seems to be exactly what happens in Aristotle’s discussions involving aporiai. As a result, it is widely accepted that the skill involved in [i] is the capacity of arguing for p and for not-p (or arguing for and against a thesis p).

The thesis of this paper, in a nutshell, is that this is not the only dialectical aspect involved in Aristotle’s treatment of aporiai, at least as an ideal. I claim that there is another argumentative skill that is obtained through the dialectical exercise as well, whose utility is essential in diaporetic procedures: the critical analysis of arguments. This skill is involved in the dialectical procedure of resolution that Aristotle introduces in Topics 8. 10 and further examines in the Sophistical Refutations.⁶ I contend that the way out of aporiai ideally involves critical analysis similar to that involved in dialectical resolution.

My argument is organized as follows. In Section 2 I discuss some preliminary matters concerning the difference between refutation (elenchos) and resolution (lusis). I shall focus on the latter, in order to reveal its specific nature as well as the extent of its use in Aristotle’s investigations in the scientific and metaphysical treatises. Section 3 is dedicated to arguing against an interpretation of the third use of the Topics just mentioned above. According to this reading, the search for a resolution of an aporia would proceed by arguing for or against conflicting theses in order to refute one of them. I argue that this reading is not satisfactory and suggest that it is based on several assumptions which I seek to undermine in Sections 4 and 5. The main purpose of the fourth section is to argue that an aporia at the logical-methodological level presupposes not just conflicting theses but conflicting arguments for those theses as well. In Section 5 I assess the role of dialectical resolution within the discussion of aporiai, and in Section 6 I draw conclusions about the dialectical skills involved in diaporetic procedures and point to further consequences for the critical use of dialectic in Aristotle’s philosophy.

2. Some preliminaries⁷

(a) Dialectical roles and skills

In this subsection I introduce a number of terminological and conceptual distinctions to demarcate two basic critical dialectical procedures that Aristotle employs in the philosophical treatises. These distinctions are particularly evident when we focus on the different tasks performed by the participants in the dialectical encounter, namely, the questioner and the respondent. Let me start, then, by outlining these tasks.

From Topics 1. 1 we learn that the questioner should be able to construct an argument about any problem proposed: that is, in the ideal situation, an argument which concludes with the contradictory of the thesis maintained by her opponent at the beginning of the dialogue. This involves finding endoxastic premisses from which the desired conclusion follows (cf. 100^a19–20), identifying the appropriate topos with which to launch the attack (i.e. the argument against her opponent: cf. Top. 8. 1, 155^b4–5), and posing questions strategically so that she can obtain her opponent’s assent to the requisite premisses (cf. 155^b5–7). Thus, construction of an argument, refutation, or, in the case of peirastic dialectic, a peirastic argument, all belong to the role of the questioner. And skill in constructing arguments for or against theses is acquired by practising that role. Needless to say, this is a fundamental skill for philosophical investigation, and in fact until they find the topos, the investigations of the dialectician and of the philosopher are alike (155^b7–8).

The respondent, for his part, should be able to answer questions asked by his opponent without granting anything that contradicts the proposition he maintained at the beginning (Top. 1. 1, 100^a20–1). For this purpose he must be able to foresee the possible consequences of each question and answer (which the questioner will do her best to conceal).⁸ In addition, once the questioner has drawn a conclusion, the respondent should be able to resolve (luein) that argument whenever it contains some kind of incorrectness (Topics 8. 10).⁹

In what I have just described there are two argumentative procedures which are connected to different roles in the dialogue and involve specific skills, but whose difference has not been sufficiently emphasized in the literature, with the result that they are frequently interchanged and confused, especially when they appear in the treatises.¹⁰ These are refutation (elenchos) and resolution (lusis).

Aristotle defines a refutation as a special kind of deductive argument (sullogismos) produced in dialogue: ‘A refutation is an argument whose conclusion involves a contradiction’ (SE 1, 165^a2–3);¹¹ cf. SE 6, 168^a36–7; Pr. An. 2. 20, 66^b4–17; Rhet. 3. 9, 1410^a22–3. The refutation is the questioner’s argument, the attack, and its conclusion is the contradictory of the proposition maintained by the respondent at the outset of the dialectical encounter. From this definition and the description of dialectical practice, then, it is clear that a refutation is an argument against a proposition or thesis.

A resolution, on the other hand, is characterized in a passage of SE as follows:

… ἦν γὰρ ἡ λύσις ἐμϕάνισις ψευδοῦς συλλογισμοῦ παρ᾿ ὃ ψευδής. (SE 24, 179^b23–4)

… the resolution consists in exposing an incorrect argument,¹² by showing on what its incorrectness depends.

This would be a last line of defence. Once he has granted all the answers, and the questioner has already managed to construct her argument to refute him, the respondent can still attempt to undo that argument. If he successfully resolves the questioner’s argument, the respondent is no longer compelled to accept the conclusion of that argument, and therefore he can no longer be seen as refuted and thus defeated in the dialogue. To do this in the right way, one must be able to pin down the cause that makes the opponent’s argument incorrect or somehow faulty.

This is not the same as refuting an opponent via argument. On the contrary, this task demands a specific skill, different from what is involved in questioning: it is a critical skill, namely, the capacity to analyse an argument and detect the causes of its incorrectness. The resolution is thus a move against an argument.

The difference between putting a thesis to the test and the critical analysis of arguments is not merely a relevant conceptual distinction. It also has importance specifically for the analysis of Aristotle’s ideal outline of diaporetic procedure that I shall develop in this article. If I am right, Aristotle clearly observes the distinction between these two critical procedures.

(b) Resolution (lusis) and its philosophical use

In the last subsection I drew attention to a crucial difference between refutation (elenchos) and resolution (lusis) within the dialectical context: a refutation is an argument against a single proposition or thesis, while a resolution is aimed against an argument. Throughout this article, I shall consistently use the terms ‘refutation’ and ‘resolution’ with this precise meaning.

In this subsection I first examine the main modes of resolving arguments presented by Aristotle. Then I provide evidence that the term ‘resolution’ is used consistently to designate a different procedure from refutation not only in the dialectical context of the Topics (and SE), but in Aristotle’s scientific treatises as well.¹³

(i) The main modes of resolution. Resolution is first introduced in Top. 8. 10, and it is treated in more detail in the second part of SE, as a natural sequel to the study of incorrect (sophistic and eristic) arguments. In this passage of SE 18 Aristotle introduces two main ways of carrying out a resolution:

ἐπεὶ δ᾿ ἐστὶν ἡ μὲν ὀρθὴ λύσις ἐμϕάνισις ψευδοῦς συλλογισμοῦ, παρ᾿ ὁποίαν ἐρώτησιν συμβαίνει τὸ ψεῦδος, ὁ δὲ ψευδὴς συλλογισμὸς λέγεται διχῶς ([1] ἢ γὰρ εἰ συλλελόγισται ψεῦδος, [2] ἢ εἰ μὴ ὢν συλλογισμὸς δοκεῖ εἶναι συλλογισμός), … ὥστε συμβαίνει τῶν λόγων τοὺς μὲν συλλελογισμένους ἀνελόντα, τοὺς δὲ ϕαινομένους διελόντα λύειν. (SE 18, 176^b29–36)

Since the right resolution consists in exposing an incorrect argument by showing on what kind of question the incorrectness depends, and ‘incorrect argument’ has a double meaning—for it is used either if [1] a false conclusion has been deduced, or if [2] there appears to be a deduction but there is not really a deduction— … it thus comes about that one resolves arguments that are real deductions by eliminating [sc. by rejecting some of the premisses], whereas one resolves those that merely appear to be deductions by making distinctions.¹⁴

The modes of resolution presented are here roughly in accordance with the two general kinds of incorrectness in argument identified in Top. 1. 1, 100^b23–5, and SE 2, 165^b7–8: (1) the argument proceeds from apparently acceptable views (ϕαινόμενα ἔνδοξα), so that it involves a mistake regarding its premisses,¹⁵ or (2) the argument is not deductive (it involves an inferential mistake).¹⁶

Further distinctions are made in SE 18 within (1) the first kind of error: the argument either (a) has a true conclusion, or (b) it concludes in a false proposition (176^b36–8), implying that one of its premisses must be false too.

(1a) In the first case, the conclusion is true, so if there is no inferential mistake, we must assume that the premisses are false.¹⁷ Accordingly, Aristotle says that the resolution of these arguments must proceed by eliminating premisses, i.e. showing that they are false (cf. 177^a1–2). (1b) In the case of an argument with a false conclusion, the resolution may proceed either by eliminating a premiss or by showing that the conclusion is false (cf. 176^b38–40).

This last tactic for resolving arguments, (1b), is surprising if one takes seriously the initial claim that a proper resolution reveals ‘on what kind of question the incorrectness depends’ (cf. also 179^b23–4, quoted above). In other words, the resolution must make clear the cause of incorrectness in the argument (in this case, the cause of its false conclusion). But in arguments of type (1b), which involve no inferential mistake, this cause must be that one or both premisses are false. To this extent, it is hard to see why showing that the conclusion of an argument is false can count as an acceptable resolution.¹⁸

In Topics 8. 10, however, the resolution of arguments of type (1b) receives a somewhat different and more satisfactory treatment. Aristotle claims that this sort of argument must be resolved by eliminating the false premiss upon which the falsity of the conclusion depends (160^b23–5, 33–7). Moreover, it does not suffice to point to any given false premiss: the dialectician must eliminate the false premiss that is the cause of the false conclusion. In 160^b26–33 Aristotle offers the following example. The questioner takes the propositions

(i) Whoever is seated is writing

(ii) Socrates is seated

and draws the conclusion

(iii) Socrates is writing,

which we are informed is false. Assuming that Socrates is not in fact seated, this is a case in which both premisses are false. Aristotle claims, however, that the correct resolution of the argument is not to eliminate (ii), for the argument does not conclude something false because of (ii). And he explains this with a counterfactual: even if someone happened to be seated (but not writing), i.e. even if (ii) were true, the false conclusion would still follow. This counterfactual example just shows that the cause of the false conclusion is not the falsity of (ii), but the falsity of (i). Hence, the correct resolution is to eliminate the false universal premiss (i), since it is not in fact the case that every seated person is writing.

Finally, it can be reasonably supposed that, unless the premiss in question is trivially false, its elimination can be accompanied by an argument proving that it is false. Such an argument could refute the premiss, for instance by showing that absurdities follow from accepting it, a strategy that is followed many times in the treatises. But this does not undermine the special role of resolution as a critical procedure distinct from refutation or, most importantly for my argument, the fact that it is directed against an argument. A resolution may involve the construction of refutative arguments against a premiss, once that premiss has been identified as the one responsible for the argument’s not being correct.

(2) In the case of an argument that is not really deductive, Aristotle says one must produce a resolution by drawing distinctions. It is not immediately clear what this means. Taking into account that this case involves an inferential mistake, one possible reading is that a distinction or ‘division’¹⁹ would rupture the unity of the premisses and the conclusion, by showing that there is no real inferential link between them. Another possible reading, which is less general, is that Aristotle is claiming that one must produce a resolution by distinguishing those respects in which the conclusion (or certain premisses) holds good from those in which it does not. This not only involves clarifying linguistic ambiguities, but also the accidental identities exploited, for example, in the Fallacy of Accident (παρὰ τὸ συμβεβηκός) and the Fallacy of the Consequent (παρὰ τὸ ἑπόμενον).²⁰

Besides these two main modes of resolution, in SE 19–30 Aristotle provides the dialectician with specific resolutions for each of the thirteen kinds of deceptive refutations studied earlier in chapters 4 and 5. To go through a detailed survey of these individual resolutions would exceed the scope of this paper. It is important to mention, however, that these resolutions are not produced solely against eristic or sophistic arguments, but against incorrect arguments in general (i.e. even if they are not intentionally fallacious).²¹

(ii) The evidence from the treatises. In this subsection I briefly review the occurrences of ‘refutation’ and ‘resolution’ outside the Topics and SE, in order to show that Aristotle’s use of these terms in the treatises and the procedures they designate is quite consistent with their characterization in the dialectical writings.

The first thing that draws one’s attention is that there are not many occasions on which ‘refutation’ appears in the scientific treatises (i.e. outside the logical works). One of them, though, is often considered a conspicuous instance of a dialectical argument in philosophical writing: the ‘refutative demonstration’ of the principle of non-contradiction in Metaphysics Γ 3–4. I share Brunschwig’s reservations about this being a merely dialectical procedure; nonetheless, the refutative nature of the argument seems to be uncontested.²² For my purposes, it is pertinent just to observe that this refutation against an imaginary interlocutor is consistent with the characterization of refutation in the Topics and SE in an important respect: the starting point and target of the refutation Aristotle carries out is a thesis, namely, that the principle of non-contradiction does not hold true (1005^b35–1006^a1). Apart from this, there are about eight other passages where Aristotle refers to third-party refutations, and so not refutations carried out by Aristotle.²³ But these third-party refutations also seem to be either against a proposition or against those who uphold it. Overall, the number of refutations is quite small, though, particularly when we compare them with the number of resolutions.

Leaving aside the instances in which they are mentioned in connection with an aporia (which I shall come back to below),²⁴ the Greek term for ‘resolution’, lusis, and its cognates occur more than twenty times outside the logical works, in some twenty passages.²⁵ What is more remarkable is that these uses of the term in the treatises are consistent with its general characterization in the Topics and SE: in these passages the resolution and/or the activity of resolving is always mentioned and/or carried out against arguments.

Further, within these passages there are at least eleven resolutions actually carried out by Aristotle.²⁶ This fits well with the fact that in his investigations Aristotle does not just consider commonsense opinions, but also the theses of earlier philosophers, which are most often supported by arguments. When those theses are disputed, the arguments supporting them must be disarmed through a resolution. Indeed, consistent with the treatment of resolution in the Topics and SE, and partly accounting for the need for this particular critical device in scientific investigations, Aristotle asserts that if one cannot resolve an argument, there is no alternative but to accept the conclusion, however implausible it might be (see EE 1. 6, 1217^a13–14; Metaph. Γ 7, 1012^a18; NE 7. 2, 1146^a24–7).

I shall pick a few of the passages referred to (see n. 25) to illustrate how this procedure is used in the treatises. This survey is meant to cover resolutions for the main types of mistake in argument, the first being a resolution directed at false premisses and the invalidity of an argument, the second exposing invalidity alone, and the third directed solely at false premisses.

The most paradigmatic instance of a resolution is probably the one carried out in Physics 1. 3 on Melissus’ and Parmenides’ arguments claiming that being is one. In Physics 1. 2–3 Aristotle consistently describes the discussion against the Eleatics as a lusis (Phys. 1. 2, 185^a8–9; 185^a14–17; 1. 3, 186^a4–7; 186^a22–4), and he claims, moreover, that their arguments are eristic on the grounds that they assume false premisses (ψευδῆ λαμβάνουσι) and that the conclusion does not really follow from those premisses (asullogistoi, 1. 2, 185^a9–10; 1. 3, 186^a6–8). This recalls the two general kinds of error used to characterize eristic arguments in Top. 1. 1, 100^b23–5, and SE 2, 165^b7–8, which are precisely the two sorts of incorrectness used in SE 18 to define the two main modes of resolution. The discussion against Parmenides in Physics 1. 3 is clearly structured by this initial diagnosis: Aristotle will endeavour to show, in turn, that Parmenides’ argument is flawed as regards both its premisses and the validity of the inference.²⁷

First, Aristotle undertakes to expose the non-deductive character of Parmenides’ argument in 186^a25–31. Then, after stating in 186^a24–5 what he takes to be Parmenides’ false assumption, namely that ‘being’ has just a single (and absolute) meaning, he offers a reductio ad absurdum of that thesis in 186^a32–^b12, followed by another at 186^b14–35.²⁸ Admittedly, taken in themselves these are refutations²⁹ of the starting point of Parmenides’ argument, but this implies nothing against the conceptual difference between a resolution and a refutation. In the first place, this is because identifying a false premiss and refuting it are one, but only one, way to resolve an argument—some arguments can be resolved by being shown to be invalid, without any of their premisses being refuted. In the second place, even in the case where the resolution involves the refutation of a premiss, as occurs with Parmenides’ argument in Physics 1. 3, this is the result of that premiss having been identified as the cause on account of which the argument is faulty, and so the point of the refutation is not merely to show that a particular thesis is false, but to show that the argument was incorrect by showing that thesis to be false. In such cases the refutation is an instrument for resolution.³⁰

Another example can be found in GA 1. 18, this time illustrating a case of invalidity. After presenting several arguments in GA 1. 17 supporting the theory of pangenesis (according to which the sperm comes from all of the body parts), Aristotle states that these arguments are not difficult to resolve.³¹ He then tackles the argument for pangenesis presented in GA 1. 17, 721^b20–4. This argument takes as its starting point the similarities between the parts of a living being and the same parts in its offspring and postulates that the cause of those similarities must be that the sperm stems from all those (similar) parts. Aristotle resolves this argument explaining that there is no necessary implication between the similarity of the parts and its putative cause, more precisely, that one thing is not a valid sign (σημεῖον) of the other (1. 18, 722^a4–5). To make his case, he gives several counter-examples (cf. 722^a6–11), i.e. cases where it is clear that the similarity has causes that, by necessity, are different from the sperm. Thus, the argument is resolved as a non sequitur (i.e. as being asullogistos), without claiming or proving, this time, that its premisses are false.³²

In the discussion of Zeno’s paradoxes about movement in Physics 6. 9 examples are found where the problem of the argument lies with the premisses: Aristotle claims that Zeno’s arguments are faulty,³³ and he then proceeds to resolve them (cf. 239^b11, ^b26) pointing out in each case the false premiss on which they are respectively based. Thus, Zeno’s first and second argument both depend upon the same false assumption,³⁴ which was discussed previously in Phys. 6. 2, 233^a21–31. In this passage Aristotle claims the assumption that it is impossible to traverse what is infinite is false, since ‘infinite’—he explains—is ambiguous: things can be infinite in extent or infinite by division, and it is only when understood in the first way (which in Aristotle’s view is false) that the aforementioned impossibility follows. In 6. 9, 239^b14–29, he explains that the second argument (Achilles and the tortoise) is based on the same false assumption and so should be resolved in the same way. As for Zeno’s third argument against movement, in Phys. 6. 9, 239^b8–9, Aristotle explains that the problem is that it assumes that time is not a continuum (viz. that it is composed by discrete ‘nows’). It is only under this (false) assumption, he says, that the conclusion follows (239^b30–3). Finally, Zeno’s fourth argument is resolved in 240^a1–4, pointing out that it rests on the false assumption that a body X takes the same amount of time to pass a body Z moving in the opposite direction as to pass a body Y at rest (where Y and Z are of equal size).

The textual evidence examined thus suggests that whenever Aristotle talks about lusis within argumentative contexts in the treatises, we should understand it in the technical sense presented in Top. 8. 10 and examined further in SE, which is not equivalent to elenchos. A resolution is not a refutation.³⁵

To conclude this section and anticipate what follows, I would add that, in addition to the passages mentioned where lusis appears as a critical procedure directed against arguments in the non-logical treatises, lusis and its cognates are usually employed to designate resolutions of aporiai in those writings. I shall argue that this use of lusis in connection with aporiai is often not far removed from that presented in this section.

3. The third use of the Topics as ‘producing arguments on both sides’

In the previous section I argued that resolution and refutation are two different critical procedures that Aristotle defines in the Topics and SE, and I have drawn attention to his terminological consistency in the use of these concepts in his philosophical writings, in which he makes a remarkably extended use of resolutions. Building on this, I shall now look into the ideal role of resolution—i.e. the critique of arguments—in diaporetic procedures.

A good place to start seems to me to be the discussion of the third use of the Topics, where Aristotle refers to this procedure explicitly and connects it with a capacity acquired through dialectical exercise. Recall the passage in question:

[The treatise] is also useful in relation to the philosophical sciences, because, if we are able to go through the difficulties on both sides [πρὸς ἀμϕότερα διαπορῆσαι], we shall more readily discern the true as well as the false in each subject. (Top. 1. 2, 101^a34–6)

The well-known semantic oscillation of the term diaporēsai in Aristotle makes it necessary to clarify, as far as possible, how the term is used in Topics 1. 2. First, I shall distinguish the range of meanings that diaporein has in the most general, even formal, manner possible. Then I shall endeavour to elucidate concretely what the task alluded to in each case is.³⁶

According to the standard description of diaporetic procedure, where the starting point is an aporia and the last step a resolution, the activity of diaporein takes place at some intermediate point between them.³⁷ I shall assume that these two extremes establish the limits, so to speak, of the range of possible meanings of ‘diaporein’, so that depending on how Aristotle uses the term in a given case, we can place the task referred to at times closer to one extreme and at times closer to the other:

(1) One accepted meaning of ‘diaporein’ is close to raising an aporia. In this sense, to diaporēsai is to pose a philosophical problem properly.³⁸

(2) The term can also refer to an activity whose end is just the resolution of the aporia. In this sense diaporēsai aims for a resolution as its final result, whether or not it reaches it de facto. In this sense, to diaporēsai is to go through the aporia, considering and analysing the problem in order to find an answer to it.³⁹

For the sake of clarity I shall call these two very broad senses of the term diaporēsai₁ and diaporēsai₂ respectively.

Prima facie, the use of diaporēsai in Topics 1. 2 seems to correspond to the second meaning, that is, to diaporēsai₂, the procedure that is meant to lead to a resolution. And this is how it is usually understood. A significant hint in this direction is that the capacity to diaporēsai is presented as something which aims at seeing the true and the false in a problem or aporia. To see the true and the false is presumably to resolve the aporia, and this would be easier for us, Aristotle says, if we have some dialectical training in diaporēsai on both sides.

In his commentary on the Metaphysics, Alexander of Aphrodisias connects Top. 1. 2, 101^a34–6, with the diaporetic procedure outlined in Metaph. Β 1, 995^a24–^b6, so that the ability alluded to in the Topics is construed as the ability to find arguments for each conflicting thesis during the search for a resolution:

διὰ δὲ τῶν προειρημένων περὶ τοῦ δεῖν διαπορεῖν πρῶτον εἴη ἂν αὐτῷ δεικνύμενον ἅμα καὶ τὸ χρήσιμον τῆς διαλεκτικῆς πρὸς ϕιλοσοϕίαν καὶ τὴν τῆς ἀληθείας εὕρεσιν· τῆς γὰρ διαλεκτικῆς τὸ διαπορεῖν καὶ ἐπιχειρεῖν εἰς ἑκάτερα. ἀληθὲς ἄρα τὸ ἐν τοῖς Τοπικοῖς εἰρημένον τὸ χρήσιμον εἶναι τὴν διαλεκτικὴν πρὸς τὰς κατὰ ϕιλοσοϕίαν ζητήσεις. (In Metaph., 173. 27–174. 4 Hayduck)

These remarks about the need first of all to work through the aporiai would also show the usefulness of dialectic for philosophy and for the discovery of truth. For it is characteristic of dialectic to work through aporiai and to argue on both sides [of a case]. So what was said in the Topics (1. 2), that dialectic is useful for philosophical enquiries, is true.⁴⁰

Alexander’s reading suggests, then, that diaporēsai₂ consists in finding arguments on both sides: this would be the strategy for resolving an aporia. This reading is nowadays widespread, and it is usually associated with one or more of the following ideas: (1) that an aporia consists in two conflicting or contradictory theses; (2) that arguments for or against each of them are presented in order to find out which one of them is true; and (3) that, accordingly, the ‘way out’ of the aporia would take place through a refutation, or more precisely, taking a pair of conflicting theses, the truth of one would be established through the refutation of the contradictory.⁴¹

In the following pages I shall do two things. On the one hand, I shall challenge the three ideas mentioned in the last paragraph in order to formulate afterwards an alternative account of diaporēsai₂—i.e. as the activity that leads in its final stage to resolution. On the other hand, I shall argue that it is only diaporēsai₁—i.e. to properly raise an aporia—that involves the task of formulating arguments on one or both sides of the problem. This task, however, does not end in a resolution, but in a thorough understanding of the puzzle.

Let me start by arguing against the reading that diaporēsai on both sides (pros amphotera) in Top. 1. 2 is ‘to produce arguments on both sides’ in order to resolve the aporia, in other words, that diaporēsai₂ is a way of arguing for and against a thesis.

We must keep in mind that any interpretation of the capacity to ‘diaporēsai on both sides’ should explain why this procedure makes it easier to discern what is true and what is false in the problem at hand (cf. 101^a35–6), and that Aristotle does not claim that seeing what is true and false is a necessary consequence of diaporēsai.

Now, ‘to produce arguments on both sides’ can mean either

(a) to find arguments for a thesis and its contradictory, or

(b) to draw consequences that follow from a thesis and from its contradictory.

Neither construal produces an entirely satisfactory reading.

(a) This seems to be exactly what the dialectician does when he follows the training recommended in the Topics for gymnastic dialogues. In fact, it is characteristic of dialectic, together with rhetoric, that it produces arguments for and against a thesis, i.e. on both sides (Rhet. 1. 1, 1355^a29–38; cf. also Plato, Phdr. 261 c ff.). In those dialogues the questioner must offer an argument for A or for not-A depending on the proposition asserted by the respondent at the beginning. Hence, in preparation, he should already have in his pocket arguments for A and arguments for not-A, so that he has ample supplies for any discussion he happens to take part in (cf. Top. 8. 14, 163^a36–^b1). It might seem, within this context, that this capacity is what is alluded to in Top. 1. 2, as being put into practice when he, as a philosopher, finds an aporia, supposing an aporia to consist in the opposition of two contrary or contradictory theses.

This reading does not hold up, though. In the first place, it is not clear how following this procedure would make it easier for one to see what is true and false in an aporia. Finding arguments that support a thesis and its contradictory only gives us some information about the truth and falsity of each, if we already know that the set of premisses for one of the arguments is true. But if we find a set of premisses (P₁) for A, and we know that (P₁) is true, ipso facto we know that A is true as well. So the problem is, first, that the activity of diaporēsai in this case would not leave us in a position to ‘more readily discern the true as well as the false’, but rather coincides with knowing something is true, which was instead supposed to be a consequence of this activity. Second, read in this way the activity of diaporēsai would not necessarily be ‘on both sides’ (pros amphotera), as it is not clear why we should find arguments on both sides of an aporia, when finding a single argument for A (or for not-A) from true premisses would suffice to settle the matter.⁴²

(b) It is possible that with ‘diaporēsai on both sides’ Aristotle is instead referring to drawing consequences from both theses, which likewise assumes that the initial aporia consists in the opposition of conflicting theses.⁴³ In this way, the true and the false would be easier to see from the consequences that follow from each. This seems, in fact, the more natural reading of the passage.⁴⁴

Now, we cannot prove that a thesis is true from its consequences.⁴⁵ But the other way around does work: we should discard as false any thesis from which false consequences, not to mention contradictory consequences, can be deduced. And then the remaining thesis of the aporia would stand victorious. This reading goes together not only with the idea that an aporia consists in a conflict between two genuinely contradictory theses, but also with the assumption that its resolution is the refutation of one of them.

A passage in Top. 8. 14 that is sometimes mentioned in connection with Top. 1. 2 also seems to support this view:⁴⁶

πρός τε γνῶσιν καὶ τὴν κατὰ ϕιλοσοϕίαν ϕρόνησιν τὸ δύνασθαι συνορᾶν καὶ συνεωρακέναι τὰ ἀϕ᾿ ἑκατέρας συμβαίνοντα τῆς ὑποθέσεως οὐ μικρὸν ὄργανον· λοιπὸν γὰρ τούτων ὀρθῶς ἑλέσθαι θάτερον. δεῖ δὲ πρὸς τὸ τοιοῦτον ὑπάρχειν εὐϕυᾶ, καὶ τοῦτ᾿ ἔστιν ἡ κατ᾿ ἀλήθειαν εὐϕυΐα, τὸ δύνασθαι καλῶς ἑλέσθαι τἀληθὲς καὶ ϕυγεῖν τὸ ψεῦδος· ὅπερ οἱ πεϕυκότες εὖ δύνανται ποιεῖν· εὖ γὰρ ϕιλοῦντες καὶ μισοῦντες τὸ προσϕερόμενον εὖ κρίνουσι τὸ βέλτιστον. (Top. 8. 14, 163^b9–16)

And also for knowledge and philosophical wisdom, being able to see (or already having seen) the consequences of either assumption is no small instrument: for it remains to choose one or the other of these rightly. In order to do that one must be naturally gifted, and this is what it is to be naturally gifted with respect to truth: to be able to properly choose the true and avoid the false. This is just what the naturally good are able to do, for it is by loving and hating in the right way whatever is presented to them that they judge well what is best.

The passage claims that it is an important instrument for philosophical wisdom to be able to see or comprehend the consequences of two contradictory theses; for once we have these consequences in sight, all that remains is to choose the right thesis. Let us first consider the immediate context: the chapter is dedicated to giving practical advice to the dialectician as to how to prepare best for dialectical competitions. In the lines prior to this passage Aristotle explains that for each thesis it is convenient to construct arguments against things being such-and-such, and against them not being such-and-such, i.e. refutations for both the thesis and its contradictory.⁴⁷ This preparatory task is meant to supply the dialectician with plenty of material for his actual encounters. Thus far, there is no concern about the truth or falsity of each thesis: the point is just to perform well in the dialectical exercise—that is, to win the discussion. This is probably the reason why the possible utility of this preparatory exercise for philosophy is introduced here as a sort of afterthought, and why Aristotle also points to the necessity of being ‘naturally gifted with respect to truth’. This disposition towards truth is not derived from, or inherent in, dialectical practice, nor is it a purely intellectual capacity of seeing the true and the false, but rather of choosing the true once we have seen it. The ethical connotations of the passage (through the comparison with loving and hating in the right way) reinforce the idea that this choice, and the pursuit of truth, fall outside intellectual dialectical training.⁴⁸ For this training, indeed, choosing the truth is of no relevance. All these considerations seem to bring this passage close to Top. 1. 2, 101^a34–6, where dialectical training in diaporēsai on both sides of a problem should make it easier to discern the true and the false, even though it does not guarantee it. Brunschwig goes beyond merely linking these passages, however, when he claims that in Topics 8. 14 there is a brief but very important appearance of the philosophical use of dialectic ‘that refers to, illuminates, and completes 1. 2, 101^a34–6’.⁴⁹

Now I shall point out some difficulties for reading the passage from Topics 8. 14 as an explanation of how dialectic helps us deal with aporiai, and as a consequence I shall propose some additional qualifications to this reading.

The first problem with taking Top. 8. 14, 163^b9–16, as an illustration of Aristotle’s treatment of aporiai is that the procedure described would work only if the theses involved in the aporiai were genuinely contradictory, since Aristotle refers unambiguously to choosing ‘one or the other’ of the initial hypotheses, and the natural reading is that one of them (the one to be chosen) is true and the other is false. This happens sometimes in the treatises, admittedly—but only sometimes. As we shall see, in many instances this is not the case, and the theses are only apparently contradictory, where the resolution of the aporia does not consist in the refutation of one of them and the acceptance of the other, but rather in an explanation of the way in which each of them involves a partial truth.⁵⁰ The passage at Top. 1. 2, 101^a34–6, can be read, instead, as leaving room for this very possibility. There Aristotle says that it will be easier to discern ‘the true as well as the false in each’ (ἐν ἑκάστοις κατοψόμεθα τἀληθές τε καὶ τὸ ψεῦδος). But this need not mean that the truth is to be identified straightforwardly with one thesis and falsehood with the other.⁵¹ In fact, the Greek for ‘in each’ (en hekastois) might refer, not to each subject matter in general, but to each of the two theses (amphotera) just alluded to, so that truth and falsity might be in both theses at the same time.⁵² This would make the ability to discern the true as well as the false all the more relevant, since they are (or can be) intermingled in each assertion. The advantage of this reading of ‘en hekastois’ is that it leaves room for what, in practice, usually happens when Aristotle considers an aporia. Far from keeping one opinion and discarding the other, Aristotle often shows how they are both true when understood in a certain way.⁵³ Moreover, while he often admittedly draws absurd consequences from one thesis, this is not followed by the affirmation of the conflicting one. Instead, what follows is usually another battery of arguments against the other thesis as well.⁵⁴ But even if ‘en hekastois’ is read in the usual manner as meaning ‘in each subject matter’, this still does not entail that the ‘whole truth’ will be found in just one of the two theses, with the other being completely false.

Taking this into account, it would seem that the passage in Topics 8. 14, far from explaining and completing 101^a34–6, gives at best one possible reading of it. This leads me to the second problem with reading diaporēsai in Topics 1. 2 in the light of Topics 8. 14, i.e. as drawing consequences from both theses in order to refute one of them. If the theses involved in the aporia were genuinely contradictory (as this reading of diaporēsai and of Top. 8. 14, 163^b9–16, demands), the task mentioned in Topics 1. 2, of arguing about both conflicting theses (pros amphotera) thus understood, would become redundant, since it would suffice to consider the consequences of just the false one, if it happened to be the first examined. Why must we argue on both sides of the difficulty, then, in order to find the true and the false, i.e. in order to resolve it?

These are some grounds for weakening the link between Top. 8. 14, 163^b9–16, and 1. 2, 101^a34–6. But there is another. In 163^b9–16 the task of looking for the consequences of each hypothesis is not described as diaporein, nor is the opposition of hypotheses described as an aporia. This is not merely an argument ex silentio. My point is rather that it is only on the assumption that an aporia consists in an opposition of two contradictory hypotheses or theses that the situation described in 163^b9–16 can be identified as an aporia. And I shall argue that this is precisely one of the assumptions that the texts do not permit. Looking ahead slightly to the next section, the textual evidence indicates that an aporia consists not merely in an opposition of theses, but of arguments for those theses, and so there is not much of a basis for simply identifying the initial scenario in Topics 8. 14 with an aporia. In contrast, Top. 1. 2, 101^a34–6, does leave open the possibility of taking an aporia to involve an opposition of arguments, which is just how Aristotle defines it. The connection between both texts can be maintained, I believe, if Topics 8. 14 is taken to express one, but only one, possible way in which a conflict of hypotheses can be dealt with, and not as the complete explanation of Topics 1. 2, nor as an illustration of the diaporetic procedure of finding the resolution to an aporia.

In sum, the reading that ‘diaporēsai on both sides’ in 101^a34–6 should be understood as diaporēsai₂, and that this consists in producing arguments on both sides, does not seem entirely satisfactory under either version (a) or version (b). To conclude this section, let me emphasize once more that on this reading it is implicitly assumed that an aporia consists merely in two conflicting theses, that the truth lies in one of them and falsehood in the other, and hence that the ideal resolution of an aporia consists in producing an argument, a refutation, against one of these theses.

In what follows I shall defend an alternative view of the structure of an aporia which rebuts these assumptions and ultimately supports a different reading of diaporēsai₂ and the use of the Topics in diaporetic procedures. In analysing the structure of an aporia it will also become clearer what diaporēsai₁ (i.e. to raise an aporia) consists in, and that it is only in this sense that diaporēsai can mean ‘to produce arguments on both sides’.

4. Aporia as conflicting arguments

In order to clarify the senses of diaporēsai further it is necessary to spell out what an aporia is, i.e. just what it is that is ‘raised’ through diaporēsai₁ and whose resolution is aimed at through diaporēsai₂.

Aristotle uses the term aporia with more than one meaning: there are at least three meanings of ‘aporia’ corresponding to three different levels.⁵⁵ First, Aristotle uses ‘aporia’ and ‘aporein’ to designate a state of perplexity or philosophical puzzlement, as he notably puts it in Metaph. Β 1, 995^a30–3. This is sometimes called the ‘existential’ meaning of ‘aporia’, thereby alluding to the psychological state of impasse or intellectual puzzlement. Second, Aristotle sometimes uses ‘aporia’ to designate the state of affairs that produces that perplexity or puzzlement, i.e. the philosophical problem itself.⁵⁶ Finally, ‘aporia’ often designates a method of exposition or discussion. In this sense, an aporia has a certain logical structure that involves a conflict of opinions. I shall call this the ‘logical-methodological’ meaning, and I shall be interested mainly in this structure.

A passage in Topics 6. 6 spells out the relation between the intellectual puzzlement and the ‘methodological’ or logical meaning of ‘aporia’, and is often invoked when explaining this notion. Frequently, though, not all its implications are taken seriously enough. In this chapter of the Topics Aristotle first offers a tentative definition of an aporia as ‘the equality [ἰσότης] of contrary arguments’ (145^b1–2), which seems to pick out the logical-methodological sense of the term. But he then explains that this definition is unsatisfactory, for aporia is not something that belongs to contrary arguments (145^b5), as that definition suggests, but rather:

… τῆς ἀπορίας δόξειεν ἂν ποιητικὸν εἶναι ἡ τῶν ἐναντίων ἰσότης λογισμῶν· ὅταν γὰρ ἐπ᾿ ἀμϕότερα λογιζομένοις ἡμῖν ὁμοίως ἅπαντα ϕαίνηται καθ᾿ ἑκάτερον γίνεσθαι, ἀποροῦμεν ὁπότερον πράξωμεν. (145^b17–20)

… an equality between contrary arguments seems to be what produces the aporia: for it is when we argue on both sides, and it seems to us that everything turns out alike in each case, that we are puzzled [ἀποροῦμεν] about which of the two we are to do.⁵⁷

The proper meaning of aporia, then, is puzzlement or an impasse in thought. And it is by metonymy that a certain logical situation that causes this puzzlement is also called ‘aporia’, where the term is used in what I have called its ‘logical-methodological’ meaning. Puzzlement in thought, thus produced, can indeed be a trigger and a driving force for philosophical enquiry. But what is especially interesting in this passage is what Aristotle identifies as the cause of this peculiar state of impasse: the perplexity in question arises from the presence of opposed arguments that are also equally compelling.

According to this passage, then, the presence of opposed arguments is essential for there to be a state of aporia. The rationale is presumably that a mere thesis and its opposite might not suffice to produce philosophical perplexity—that is, they might not put one in the position where it is difficult to decide which of the propositions to assent to. One of them might be capricious, for example, or openly absurd, and would not move anyone to endorse it. In contrast, if the thesis follows (or seems to follow) from premisses one is inclined to accept, it would not be so easy to dismiss it in favour of its rival, and vice versa. If, furthermore, both theses are equally plausible (or implausible), or if one does not have a definite opinion about either, the presence of a compelling argument for each proposition makes it evident that we are confronting a proper philosophical problem.

At this point a caveat is in order. There are certain aporiai where the presence of arguments is not necessary for there to be a problem. These sometimes appear in Aristotle’s cosmological, biological, and meteorological writings. Roughly speaking, in these cases the problem is associated with empirical facts, and arises because matters remote from or even inaccessible to perception are involved,⁵⁸ or because empirical facts that are difficult to explain are concerned.⁵⁹ Moreover, this use of ‘aporia’ need not imply the presence of conflicting theses (or conflicting explanations) either.⁶⁰ In these cases, ‘aporia’ designates the issue to be explained, the lack of a satisfactory explanation for it, or the lack of any explanation at all. Such aporiai are not the subject of this article’s enquiry, though, but the sort of difficulties that are more commonly found in the metaphysical, physical, and ethical works, and which Owen describes as ‘logical or philosophical puzzles’.⁶¹ I contend that the claims of Topics 6. 6 are valid for this kind of aporia.

If we take the passage in Topics 6. 6 seriously, then what produces the state of being at an impasse, which we call a philosophical ‘aporia’, is not just two conflicting philosophical theses. Rather, the text explicitly asserts that an aporia is caused by the presence of arguments for those conflicting theses and the fact that those arguments are equally compelling (ἡ τῶν ἐναντίων ἰσότης λογισμῶν). Hence, an aporia, in this derivative logical-methodological sense, involves the juxtaposition of conflicting arguments.

There are other passages which either concur with the passage from Topics 6. 6 or can be read in its light. For instance, this passage from Topics 1. 11, where Aristotle is defining dialectical problems, points in the same direction:

ἔστι δὲ προβλήματα καὶ ὧν ἐναντίοι εἰσὶ συλλογισμοί (ἀπορίαν γὰρ ἔχει πότερον οὕτως ἔχει ἢ οὐχ οὕτως, διὰ τὸ περὶ ἀμϕοτέρων εἶναι λόγους πιθανούς) … (104^b12–14)

Those matters with regard to which there are contrary arguments are also [dialectical] problems (for there is a difficulty about whether something is such-and-such or not, because there are persuasive arguments regarding both claims) …⁶²

The explanation in parentheses states again that the state of aporia (ἀπορίαν γὰρ ἔχει) arises from the presence of persuasive arguments supporting each of two conflicting theses. Just as in Topics 6. 6, the presence of arguments, far from being incidental, seems to be constitutive of an aporia in the logical-methodological sense, in so far as in both texts arguments (and their equally persuasive character) are pinpointed as the cause of the impasse between two propositions.⁶³

The definition of the cognate term aporēma in Topics 8. 11, although it is most likely not by Aristotle himself, is coherent with the reading I am putting forward.⁶⁴ It is claimed there that an ‘attack’ (epicheirēma) is a dialectical argument (162^a16), while an aporēma is a dialectical argument for the contradictory (162^a17–18): that is, to formulate an aporēma is to produce an argument for the contradictory of the conclusion of another argument. In other words, it is to produce an aporia in the logical-methodological sense.

It is therefore not just rival theses but rival arguments that fetter the mind, leaving it at an impasse,⁶⁵ so that it cannot move in either direction until the knot is untied:

ἔστι δὲ τοῖς εὐπορῆσαι βουλομένοις προὔργου τὸ διαπορῆσαι καλῶς· ἡ γὰρ ὕστερον εὐπορία λύσις τῶν πρότερον ἀπορουμένων ἐστί, λύειν δ᾿ οὐκ ἔστιν ἀγνοοῦντας τὸν δεσμόν, ἀλλ᾿ ἡ τῆς διανοίας ἀπορία δηλοῖ τοῦτο περὶ τοῦ πράγματος· ᾗ γὰρ ἀπορεῖ, ταύτῃ παραπλήσιον πέπονθε τοῖς δεδεμένοις· ἀδύνατον γὰρ ἀμϕοτέρως προελθεῖν εἰς τὸ πρόσθεν. (Metaph. Β 1, 995^a27–33)⁶⁶

For those who wish to make progress, it is useful to go through aporiai well. For subsequent progress consists in untying [lusis] what previously had been an occasion for aporia, and it is not possible to carry out this untying if one is ignorant of the knot. Aporia in thought makes this evident in the present case. For in so far as thought is in aporia, it is in a state similar to those who have been tied up: in both cases it is impossible to move forward.⁶⁷

The image of a knot (desmos) illustrates the binding character of arguments, which leaves the soul in a state of aporia or impasse, and the figure of ‘untying’ (lusis) is a fitting complement to this. ‘To go through the aporiai well’ (τὸ διαπορῆσαι καλῶς) clearly corresponds to ‘understanding the knot’ and thus being in a position to untie it and move forward, and I shall suggest that this alludes to essentially the same task described in the passage from Topics 1. 2. But before moving in that direction, let me strengthen the case a little further for the claim that logical-methodological aporiai involve arguments, by focusing on Aristotle’s comparison of ‘going through aporiai’ with the task of a judge:

ἔτι δὲ βέλτιον ἀνάγκη ἔχειν πρὸς τὸ κρῖναι τὸν ὥσπερ ἀντιδίκων καὶ τῶν ἀμϕισβητούντων λόγων ἀκηκοότα πάντων. (Metaph. Β 1, 995^b2–4)

Further, one is necessarily in a better position to judge once one has listened to all the contending arguments, as if they were opposing parties in court.

The situation of a person who faces an aporia is thus comparable to that of a judge in court, who listens to the arguments each litigant uses to construct their case, and who must make a decision based on an evaluation of their arguments.⁶⁸ This metaphor suggests that going through aporiai in search of the truth means ‘hearing’ the arguments (i.e. conflicting arguments) that support the theses in dispute, and thereby being in a better position to judge where the truth in fact lies.

The comparison with a forensic dispute in the following passage of De caelo also seems to point to the argumentative component in these impasses:

αἱ γὰρ τῶν ἐναντίων ἀποδείξεις ἀπορίαι περὶ τῶν ἐναντίων εἰσίν. ἅμα δὲ καὶ μᾶλλον ἂν εἴη πιστὰ τὰ μέλλοντα λεχθήσεσθαι προακηκοόσι τὰ τῶν ἀμϕισβητούντων λόγων δικαιώματα. (1. 10, 279^b6–9)⁶⁹

For the demonstrations of contrary theses are aporiai about those theses. At the same time, what is going to be said may be even more convincing to those who have previously heard the justifications of the claims in dispute.⁷⁰

‘Aporia’ is used here in its logical-methodological sense. Thus, Aristotle claims again that an aporia about a specific topic arises when two contrary theses on that topic are supplied with supporting arguments.⁷¹ Once again, what is called an ‘aporia’ is not merely the juxtaposition of contrary theses, but also of their respective arguments. In fact, the procedure for raising aporiai contributes to the persuasiveness of the overall exposition precisely because it brings those conflicting arguments into consideration. In this way, not only is there a full exploration of the philosophical problem being dealt with, but it also seems to do justice to the fact that, normally, philosophers do not just formulate theses: they also try to offer some argument for their truth.⁷² Now, the task of the philosopher, like that of the judge, is to analyse and evaluate those respective arguments and proofs in order to arrive at a verdict about the truth of the matter at hand. In other words, this evaluation of the arguments for conflicting claims, when performed well, leads to untying the knot. And I shall suggest that it is precisely this activity that constitutes diaporēsai₂: the task of analysing and evaluating—not formulating—arguments on both sides, in order to break the impasse.

The reading that it is arguments for conflicting theses that constitute an aporia in the logical-methodological sense also allows us to give an account of the oft-noted distinction between aporiai that express genuine philosophical problems and aporiai that seem to be mere artifices of the exposition, or even just the result of mistakes.⁷³

On the one hand, there may be cases where conflicting arguments do cause an impasse in thought but do not pose a genuine philosophical difficulty. Instead, they emerge from a methodological mistake or a mistake in argumentation. The reason that these are still puzzles is that there are arguments, however unsound or ill-conceived they may be, that support each thesis and may be, or in fact have been, compelling to some. The analysis of such arguments, which expose the source of the error, is no less important a task for the philosopher, since it contributes to the critical clarification of problems and pseudo-problems.

On the other hand, and more interestingly, it can happen that conflicting arguments cause an impasse in thought because the nature of the problem itself is in fact puzzling. That is, there is a genuine philosophical problem or state of affairs that accounts for the existence of conflicting arguments, and these in turn produce an impasse in thought when one reflects on them. It seems, then, in this case that the logical-methodological sense of ‘aporia’ refers to the logical situation that causes the impasse or intellectual puzzlement, and the problematic state of affairs (the philosophical difficulty itself) is in turn what accounts for the presence of conflicting theses and arguments. But the presentation and close examination of these arguments do not just lead us to an impasse. They are also what is required for a thorough understanding of the precise nature of the philosophical problem at hand. Thus, the assessment of the arguments that constitute an aporia initiates our understanding of why this is a philosophical problem, where the problem lies precisely, and what its importance is. This close examination of the puzzle often sets the standard for a proper philosophical answer to the problem as well, in so far as the new proposal should be able to provide some kind of response to the argumentative impasse⁷⁴—that is, it should count as a resolution of the problem at hand (on this see especially Phys. 4. 4, 211^a7–11).

If my account of the argumentative structure of the aporiai is roughly correct, there is a plausible way of understanding what it is to diaporēsai₂: to analyse the aporia by assessing the various arguments for each thesis in order to comprehend the nature of the philosophical puzzle, as a preparatory task prior to resolving it.

This reading of the argumentative structure of aporiai also paves the way for a more precise account of the task of diaporēsai₁. Taking into account the three levels on which Aristotle speaks of an aporia, namely (i) the ‘existential’ or the intellectual puzzlement, (ii) the logical-methodological dispute, and (iii) the philosophical problem itself, diaporēsai₁ can then be understood as an argumentative procedure that yields (ii) the logical-methodological aporia, which in turn produces (i). Thus, to raise an aporia, which was the meaning of diaporēsai₁, would be to produce precisely the conflicting arguments that constitute the aporia (ii).⁷⁵

To this extent, then, diaporēsai₁ actually means ‘to produce arguments on both sides’ of a problem, and is certainly connected with the dialectical ability to argue for and against a thesis. However, this task is not carried out to resolve an aporia, but simply in order to raise one.

To conclude this section, let me emphasize that an analysis of the senses of diaporēsai, together with an understanding of the different levels of the concept of aporia, shows that in none of those senses can the activity called diaporēsai be identified with arguing about each conflicting thesis in order to refute one of them and leave the other one standing. In the next section I discuss the concept of resolution (lusis) of the aporia, the ideal result of diaporēsai₂, in order to formulate an alternative to the reading that it consists in the refutation of one of the conflicting theses. This alternative account will allow me to offer a more concrete interpretation of what the philosopher does as he ‘goes through the aporia’ and its dialectical roots.

5. The resolution (lusis) of the aporia

In the previous section I argued that Aristotle claims in several passages that the mental state of aporia is not caused by the mere presence of conflicting theses, but by the fact that these theses are supported (or refuted) by arguments which are equally compelling. Hence, what Aristotle calls an aporia at the logical-methodological level consists in conflicting arguments rather than just conflicting theses. It is impossible to examine Aristotle’s actual practice thoroughly here, but if we look at the cases presented in Metaphysics Β, for example, it becomes clear that not all of the arguments that constitute these difficulties are arguments for one thesis or the other. On the contrary, most often an aporia emerges because there are arguments against both theses, i.e. because there is a refutation of x and there is a refutation of the conflicting thesis as well.⁷⁶

Now, if aporiai arise owing to the presence of conflicting arguments (whether these are formulated by others or are raised by ourselves when we diaporēsai₁), and these are often refutations of each of the conflicting theses, then it is no longer plausible to think either that the ‘untying’ or resolution of an aporia ideally happens through a refutation of one of the conflicting theses, or that diaporēsai₂ consists in ‘producing arguments on both sides’ in order to find a refutation.

In addition, it should be noted that the passages in which Aristotle refers to diaporetic procedures concur: there is almost no mention of refutation (elenchos) in the context of resolving aporiai. The one exception is a passage from EE 1. 3, which is traditionally read as supporting the idea that (i) an aporia consists in the opposition of two theses, and hence (ii) the preferred method for resolving an aporia is to refute one of the theses in dispute, thereby proving the contrary one. I shall discuss this customary reading of the passage briefly and then propose an alternative to it.

The passage appears within the context of deciding whose opinions are to be considered and discussed in the subsequent investigation about the best life. After dismissing the opinions of children, lunatics, and the many, Aristotle implies that it is the opinions of the wise or other qualified opinions that should be examined, and adds:

ἐπεὶ δ᾿ εἰσὶν ἀπορίαι περὶ ἑκάστην πραγματείαν οἰκεῖαι, δῆλον ὅτι καὶ περὶ βίου τοῦ κρατίστου καὶ ζωῆς τῆς ἀρίστης εἰσίν. ταύτας οὖν καλῶς ἔχει τὰς δόξας ἐξετάζειν· οἱ γὰρ τῶν ἀμϕισβητούντων ἔλεγχοι τῶν ἐναντιουμένων αὐτοῖς λόγων ἀποδείξεις εἰσίν. (EE 1. 3, 1215^a3–7)⁷⁷

But since each enquiry has its own aporiai, so evidently will the one concerning the best and highest life. It is these opinions, then, that it is right to investigate; indeed, the refutations of those in dispute about a certain position are demonstrations of the opposing views.⁷⁸

The usual reading of this passage is that aporiai consist in a contradictory opposition between ‘our’ thesis (that is, Aristotle’s) and another thesis. Hence, the refutation of theses contradictory to ‘ours’ would be a resolution of the aporiai in ‘our’ favour. For the reasons explained throughout this paper, even if this reading were correct, the passage could not be taken to have a general prescriptive significance, methodologically speaking, or to express the essence of diaporetic procedure. Rather it would have to be seen as an exception regarding how an aporia is defined and how diaporetic procedure is depicted generally in the corpus.

I contend, however, that this common reading of the passage is not without difficulties. In the first place, Aristotle does not state here that an aporia consists in just two conflicting theses to be proved or refuted; he speaks of ‘opinions’, and it is not at all clear that the opinions which Aristotle refers to in line 1215^a6 are just theses. The context suggests that they are the qualified opinions alluded to in the previous lines,⁷⁹ so that it is probable that they, being not unreflective, are backed up by grounds of some sort, in contrast to what holds of the opinions of the many.

In the second place, the refutations mentioned in this passage do not refer to just theses either. What are refuted are ‘opponents’ (τῶν ἀμϕισβητούντων). This is a broader use of the term ‘refutation’, and it leaves considerable room concerning what is to be examined: it might not be just their theses, but also their arguments, which would fit with my previous point, that Aristotle does not merely have contradictory theses in view here, and there is no further basis within the passage for reading the ‘refutation’ of adversaries as being directed against their theses rather than their arguments. In fact, if anything, context favours the latter, since Aristotle has qualified opinions specifically in mind. The broader use of ‘refutation’ suggests, then, that an attack against an opponent’s argument would be closer to a resolution than a refutation, even if in the form of a counter-argument.⁸⁰ This might be taken as an instance of Aristotle’s methodological (and terminological) flexibility in dealing with aporiai. But however that may be, these lines from EE 1. 3 do not straightforwardly claim that an aporia consists in just two contradictory theses and can be resolved simply by refuting one of them.

Indeed, the drift of the passage suggests another reading. Aristotle speaks of refutations (in the plural) of those who disagree (τῶν ἀμϕισβητούντων), and these are proofs or demonstrations (again in the plural) of their conflicting views. One possible reading, as we have seen, is that Aristotle is claiming that ‘our’ refutations of the opposing views are proofs for ‘our’ own. But another possible reading is that, just as in De caelo 1. 10, 279^b6–9, the refutations that people in disagreement advance against each other are actually proofs for their own, contrary views (and not for ours). This would explain the plurals, since there would be at least two refutations, one for each conflicting view.⁸¹ But that is precisely what an aporia is, and is what Aristotle is telling us, here in the Eudemian Ethics, that we should examine. So understood, the passage would be an invitation to examine and study aporiai: after saying that there are aporiai about matters proper to practical philosophy, and that it is good to examine the opinions that lead to impasses (1215^a3–6), he finally explains how these impasses come about: because the opposing views are refuted, respectively, by those in dispute about them.

Leaving this passage aside, now let me underline more generally that in practice the simple refutation of one of the conflicting theses is not the way Aristotle typically puts an end to an aporia.⁸² On the contrary, they are usually a way of raising an aporia (see n. 76 above). When discussing aporiai, moreover, he almost never speaks about ‘refutation’ in that way—the one exception being the passage of EE 1. 3, on certain readings (which in my view are questionable). Most often, he speaks instead of a resolution as literally bringing an aporia to its end. This is not only the case within the idealized accounts of diaporetic procedure in Metaph. Β 1 (995^a29–30) and NE 7. 1, but it also finds confirmation in Aristotle’s concrete discussions of aporiai: he makes copious use of the Greek term lusis and its cognates in connection with the end of aporiai in the treatises.⁸³

The thesis I want to put forward is that the resolution that ideally puts an end to an aporia is akin to the resolution that Aristotle presents as part of dialectical training in the Topics and SE, as well as the resolutions of arguments carried out in the treatises I mentioned in Section 2(b)(ii), because all of them involve the critical analysis of arguments. This is a very broad thesis, but I shall offer support for it, as well as introducing some nuances. Let me be clear: I do not want to claim that there is anything like absolute uniformity in Aristotle’s treatment and resolution of aporiai. There are cases, indeed, where Aristotle seems to resolve an aporia by ignoring the arguments offered in raising it.⁸⁴ And in view of the passage of EE 1. 3 discussed above (at least on one possible reading) and Rhetoric 2. 25, it would seem that a counter-argument might also be admitted in some cases as a solution. Finally, I do not want to suggest that the resolution of aporiai always consists in pointing to an inferential mistake in the arguments that constitute them. In fact, resolution as a critical examination of arguments is not as uniform as might seem at first glance. It involves a great deal of creativity, especially when the problem arises not from an inferential mistake, but through a false premiss or a partial truth, or when the argument is resolved by adding new relevant information.

My thesis, in sum, is that ideally the resolution of aporiai requires a critical analysis of the arguments that constitute the problem, and hence that this critical task, which can lead to a proper resolution, is precisely ‘to go through an aporia on both sides’, i.e. diaporēsai₂. If my suggestion is correct, a lusis would be simultaneously the image of untying the knot that constitutes the aporia (Metaph. Β 1, 995^a30) and a technical concept that has its roots in the dialectical practice of resolving arguments, as developed in Topics 8. 10 and SE 16–33.⁸⁵

I shall explore this reading a little further and make some necessary qualifications.

In Topics 8 and SE Aristotle claims that a resolution must expose the cause due to which an argument is incorrect, and this clearly presupposes its critical analysis. By bringing forward the cause of the error, the argument is disarmed and its conclusion no longer binding. Does something similar happen, ideally, with aporiai? If I am correct, and aporiai at the logical-methodological level are constituted by conflicting arguments, then the idea seems promising: find the weak point in one (or both) arguments that ties thought down, and then expose this point (i.e. by resolving one or both arguments) in order to dissolve the difficulty in question, since if the argument for one (or both) theses has been shown not to be as solid as it seemed, our thought is no longer tied down by them. On this reading, a fairly concrete account can also be given of Aristotle’s claim about the need to understand the knot in order to resolve an aporia (Metaph. Β 1, 995^a29–30). If the knot is the reason why thought is fettered, and this image refers to the arguments that constitute the aporia, then it is plausible that understanding the knot means understanding how the arguments for (or against) both theses work to produce the impasse. Indeed, understanding this is the same as detecting (if there is such a thing) where the key to their resolution lies.

The ideal scenario occurs when there is a flaw in the arguments of the aporia which allows the philosopher to untie the difficulty. In practice, this often happens with aporiai. For instance, resolutions by the elimination of a false premiss can be found in NE 7. 4–9 (against various aporiai concerning lack of self-control, which I shall discuss further below); Phys. 3. 3, 202^a21 ff.; Metaph. Η 6, 1045^a14–33; GC 1. 10, 327^b6–10; Meteor. 1. 3, 340^a19 ff. I have also mentioned examples of resolutions of arguments by the elimination of a false premiss in Section 2(b)(ii), taken from Physics 6. 9, where Aristotle discusses Zeno’s paradoxes. Zeno’s arguments against movement can also be considered instances of aporiai of the kind I shall consider in the next paragraph. For resolutions based on the non-conclusive character of arguments (which are not very common) see Physics 1. 2–3 against Parmenides and Melissus, some of which I commented on earlier in Section 2(b)(ii). Just as with Zeno’s arguments, Parmenides’ and Melissus’ arguments can be counted as paradoxes, a special sort of aporia.

Indeed, further support for the suggestion that the lusis of aporiai is akin to the lusis of arguments comes from paradoxes, a special sort of aporia, where there is only one argument involved. In SE 33 Aristotle discusses this kind of impasse and says they are a ‘most incisive argument’,⁸⁶ one that we need to investigate further to decide which premiss to eliminate in order to resolve it (182^b33–7). This argument, which results in an aporia, is one that starts from opinions that are as generally accepted as possible, but then eliminates a thesis that is as plausible as possible.⁸⁷ One might also put it this way: given two conflicting theses, one of which is extremely plausible and the other utterly implausible, an argument is given only for the implausible one, the other being in no need of argument on account of its high plausibility, resulting in an impasse in thought. Hence, once again it is the presence of an argument that raises an aporia, not just the two conflicting theses.

This type of aporia is referred to and discussed several times in the philosophical treatises. One clear example is the Eleatic arguments against movement,⁸⁸ and another is the aporia relating to the lack of self-control in NE 7. 2. In the much-discussed passage of NE 7. 1, 1145^b2–7, Aristotle claims that after collecting commonly held opinions on the subject, one must raise difficulties concerning them (i.e. diaporēsai₁), and then finally resolve (luein) those difficulties while seeking to leave as many endoxa standing as possible. In this manner, he contends, these matters would have been sufficiently expounded. The passage does not describe a ‘method’ in the modern sense, but merely sufficient means for expounding a case, a manner to be pursued if possible and in different degrees according to the matter at hand.⁸⁹

What Aristotle actually does immediately after these remarks is explore several plausible and commonly held theses about the lack of self-control, and its relation to knowledge and the affections (7. 2, 1145^b8–20). He then promptly proceeds to raise problems or aporiai (1145^b21–1146^b5) that consist precisely in arguments from plausible (or apparently plausible) premisses which go against the various endoxa just enumerated. In order to resolve these aporiai, he claims, ‘we must now do away [ἀνελεῖν] with some of the assumptions involved, while leaving others undisturbed’ (1146^b6–7).⁹⁰ One cannot help noticing that to eliminate or to do away with a premiss is precisely one form of resolving arguments noted in Top. 8. 10, 160^b23–37, and SE 18, 176^b29–36 (cf. above, Section 2).

Finally, a passage of NE 7. 2 illustrates my point with particular clarity. In it Aristotle refers to the sophistic argument that mindlessness combined with lack of self-control is excellence:

ἔτι ὁ σοϕιστικὸς λόγος [ψευδόμενος] ἀπορία· διὰ γὰρ τὸ παράδοξα βούλεσθαι ἐλέγχειν, ἵνα δεινοὶ ὦσιν ὅταν ἐπιτύχωσιν, ὁ γενόμενος συλλογισμὸς ἀπορία γίνεται· δέδεται γὰρ ἡ διάνοια, ὅταν μένειν μὴ βούληται διὰ τὸ μὴ ἀρέσκειν τὸ συμπερανθέν, προϊέναι δὲ μὴ δύνηται διὰ τὸ λῦσαι μὴ ἔχειν τὸν λόγον. (NE 7. 2, 1146^a21–7)

Next, the argument the sophists offer is also an aporia. Because they want to refute people in paradoxical ways, so as to be clever (if they can get their way), the resulting argument turns into an aporia; for one’s thinking is tied down when it does not wish to stay where it is out of distaste for the conclusion, while unable to move forward from an inability to resolve the argument.

Many of the themes dealt with in this article appear in this passage: an argument becomes an aporia, the mind is ‘fettered’, unable to move forward, and finally there is a lack of resolution of an argument. The importance of this passage for my proposal is that all these elements are here conjoined: the binding force of the aporia emerges clearly from the argument; the argument is a refutation of a plausible thesis (resulting in distaste for the conclusion), and the resolution that sets thought free, by dissolving the aporia, is undoubtedly the resolution of that argument.

To conclude this section, I shall add two nuances to my proposal, and a caveat.

First, since an aporia consists in two arguments⁹¹ for (or against) conflicting theses, in order for there to be an aporia it is a necessary condition that these theses either actually contradict each other or appear to. In fact, a typical manner of dissolving a difficulty in Aristotle is to show that the conflicting theses are only apparently contradictory. An apparent aporia can rest on an imprecise formulation of the initial theses in dispute, so that they are both partially true and hence not really incompatible. This is a clear case of finding the true and the false in both parts of the aporia (cf. EE 7. 2, 1235^b13–18; Top. 1. 2, 101^a35–6).⁹²

While, strictly speaking, it is not a matter of aporiai, the same sort of lusis can also be seen in dialectical encounters in two clear ways. In the first place, the examination of different senses of a term is one of the tools (ὄργανα) of dialectic (Top. 1. 13, 105^a21–5; 1. 15), one that is especially useful in detecting fallacies (cf. 1. 18, 108^a26 ff.). In the second place, it is connected to the resolution of incorrect arguments that depend on homonymy and other apparent forms of contradiction such as those that involve secundum quid. Aristotle even claims that most incorrect arguments are due to such ambiguities of language (SE 1, 165^a4–6, and 16, 175^a6). The resolution of these fallacies is not mentioned in Top. 8. 10, but it is treated at some length in SE 19 and 25, and it basically consists in pointing out the diverse senses in which a term is understood, and (in the case of the secundum quid) adding the respect in which each proposition is to be understood.⁹³ Now, in the case of aporiai the ambiguity results in an apparent contradiction between two theses that do not really conflict. In both cases the task undertaken is a formal-critical one (identifying the key to untying an argument or aporia, respectively), but also involves a positive or philosophically creative moment. The latter is especially clear in the case of aporiai: distinctions of senses and disambiguations sometimes require the introduction of substantive philosophical doctrines.⁹⁴

The second important nuance in my proposal refers to the limits of dialectic. I want to stress that, even at an ideal level, the critical analysis presupposed by resolution is not necessarily a formal task, for the error may rest on a false starting point (one of the modes of resolution). It must be part of diaporēsai₂, then, to detect when a false premiss is explicitly or implicitly assumed in an aporia, a task for which mere dialectical training is clearly insufficient. Dialectical training may be useful for detecting what premiss the conclusion depends on (i.e. which false premiss is the cause of the conclusion). However, the identification of a premiss as false requires substantial philosophical knowledge about the subject matter under investigation, and this is not provided by dialectic as such.⁹⁵ To diaporēsai₂ is thus not just dialectical critique, but a critical analysis that is also philosophical, and so the resolution of an aporia is not merely a formal business, but a substantively philosophical one. It is both a critical and a creative task at the same time, since it is often the occasion and engine of new philosophical approaches to problems.⁹⁶

Finally, a caveat. There seem to be various degrees of resolution of aporiai, and there are also aporiai that appear to be unsolvable, or at least whose resolution is indefinitely deferred. This is noted by many commentators when analysing what actually happens when Aristotle deals with such impasses (as opposed to what would ideally happen).⁹⁷ As far as I can see, this is not a serious difficulty for my reading. In the first place, I am primarily concerned with how Aristotle conceives of the treatment of aporiai ideally. And in the second place, the fact that some logical-methodological aporiai are easier to resolve than others might be thought to depend on the difficulty of the philosophical problem that produces the impasse. It might be the case that conflicting arguments are particularly difficult to resolve precisely when the underlying issue constitutes a serious philosophical problem. In such cases, just as with the most incisive arguments in SE 33, we have to investigate further in order to find a resolution.

In sum, I do not want to claim that every aporia raised in the treatises finds a full-fledged resolution through a resolution of the arguments in it, but only that diaporetic procedure ideally and prima facie involves the critical analysis of arguments, a kind of analysis exercised in dialectical encounters. This analysis frequently leads to the resolution of one or more of the arguments that constitute the aporia at the logical-methodological level, and this has the effect in turn of dissolving the ‘intellectual puzzlement’ aporia, though in practice this sort of resolution is not always achieved or even attainable.

6. Conclusions

(a) The third use of Topics for philosophy: what is, then, ‘diaporēsai on both sides’?

In these pages I have emphasized, first, the difference between a refutation (elenchos), understood as an argument against a thesis, and a resolution (lusis), understood as a critical evaluation of an argument, and I have shown that Aristotle’s use of these terms in the philosophical treatises is consistent with these definitions. This supports the thesis that resolution, as a specific critical procedure, has a distinctive role in Aristotle’s scientific and philosophical investigations. I then turned to diaporetic procedures and the role of dialectic, taking as a starting point Aristotle’s claim in Topics 1. 2 about the utility of that treatise for these procedures. To clarify the specific dialectical abilities employed there, I stressed that aporiai at the logical-methodological level are constituted by two conflicting and equally compelling arguments. Accordingly, I proposed that to raise an aporia—one of the possible meanings of ‘diaporēsai’—would be to collect or formulate conflicting arguments, i.e. arguments for (or against) the conflicting theses. I called this ‘diaporēsai₁’. But there is another widely recognized use of ‘diaporēsai’, designating an activity that ideally ends in the resolution of an aporia, and this I called ‘diaporēsai₂’. The main thesis I have put forward is thus twofold. In the first place, the resolution of aporiai is akin to dialectical resolution in so far as it involves the critical analysis of arguments. As a result, in the second place, diaporēsai₂ is precisely the activity of critically analysing arguments that constitute the aporia.

If my suggestion is correct, then the dialectic involved in Aristotle’s treatment of aporiai is not just the ability to find arguments or refutations of conflicting theses, which is developed through playing the role of the questioner in the dialogue (this is involved in diaporēsai₁), but also the critical ability to disarm an argument developed when responding in dialogue (this corresponds to diaporēsai₂). The dialectician is appropriately prepared for dealing with aporiai, then, because her training involves learning both refutation and resolution (Top. 8. 14, 163^a36–^b1, 164^a16–^b7). Of course, the latter ability may not be enough to resolve an aporia: the formal training provided by dialectic in the critique of arguments must be supplemented by a philosophically robust knowledge of the puzzle’s subject matter, which allows one to detect falsehoods or partial truths in the starting points of arguments.

I return briefly now to the lines in Topics 1. 2 where Aristotle claims that the treatise is useful for philosophy because, as dialecticians, we will be able to ‘diaporēsai on both sides’ and hence be in a better position to see the true and the false.⁹⁸ I believe we are now in a position to claim that there are two possible answers to the question of what ‘diaporēsai on both sides’ means here. Although I am inclined to favour the second answer, I believe the first is also defensible.

The first is to assume that the sense of diaporēsai in Topics 1. 2 is diaporēsai₁, i.e. to properly raise an aporia by formulating (or collecting) the arguments on both sides. In this case, Aristotle is saying here that the Topics is useful for philosophy because the dialectical training for which it provides a ‘manual’ contributes to developing a skill—namely, that of arguing on both sides—that allows one to state a philosophical problem in the form of an aporia. Such a skill would have the advantage of allowing us to comprehend thoroughly the importance and implications of the problem in question. It is crucial to emphasize, however, that if it is read as ‘arguing on both sides’, the activity described in Topics 1. 2 as diaporēsai would not end in the resolution of the aporia, but rather in its statement or formulation. In that case, the ability to diaporēsai would make it easier to grasp the true and the false in the sense that it would prepare us for the subsequent search for a resolution, whose guidelines it would establish.

A second possible way of reading this passage, though, and the one I prefer, is to hold that the word should be construed instead as diaporēsai₂, i.e. an activity that ideally leads to the resolution of the aporia. If this is the case, then ‘going through aporiai’ in this passage would mean critically analysing the arguments that cause an impasse in thought and that constitute a philosophical puzzle in need of resolution, which would put an end to the impasse by ‘untying the knot’. The advantage of this reading is that it seems consistent with the logical-methodological structure of Aristotle’s philosophical aporiai. The ideal culmination of going through the aporia, so understood, would be to discern the true and the false, not in the immediate sense of demonstrating that one of the conflicting theses is true and the other false, but in the sense of being able to produce resolutions that reveal false starting points in arguments that lead to impasses, or that grasp the merely apparent contradiction in the initial theses being disputed and so recognize the extent to which they both involve partial truths.

(b) The critical use of dialectic expanded

If what I have maintained is even roughly correct, then an important result of this paper is that arguing for and against a thesis is not the only relevant skill involved in dealing with aporiai. Rather, there is another critical ability that is crucial to these procedures and is likewise obtained through dialectical training. This is the critical analysis of arguments in dialectical resolutions.

A further ramification of the thesis is a corresponding expansion of the critical use of dialectic in philosophy, from the critique of theses or propositions (as in peirastic argument, for example)⁹⁹ to the critique of arguments. This expansion of the critical dimension of the Aristotelian dialectic is not only significant but has also been largely overlooked in the literature, and I believe it is one of the main benefits to be gained from paying attention to the role of resolution in the treatises (with or without aporiai).

Finally, this also points to a possible philosophical use of the Sophistical Refutations.¹⁰⁰ Up until now, when searching for the usefulness of this treatise for philosophy, much emphasis has been placed on peirastic argument, as discussed in SE 8 and 11 (thanks especially to the works of Robert Bolton). But the Sophistical Refutations is a specific study of incorrect and deceptive arguments in dialogue and is also about the resolutions of those arguments. It is there, indeed, that the resolution is more extensively studied. After what I have argued for in these pages, it is worth asking whether this is largely where its usefulness for philosophical investigation lies.

Universidad Adolfo Ibáñez

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© Gabriela Rossi 2017

I am grateful to Alejandro Vigo for his unfailingly generous reading, discussion, and criticism of a very early draft of the main ideas included in this article. My thanks also to several audiences in Buenos Aires, and in particular to Gabriela Müller for her careful reading of the last draft and her helpful suggestions. I also cannot fail to mention Álvaro Sánchez-Ostiz and Erik Norvelle, for their invaluable help. I owe a special debt of gratitude to the anonymous readers: I have benefited greatly from all their comments and suggestions, and they have helped me improve this article in numerous points. Finally, I wish to add a special word of thanks to Victor Caston for his many helpful suggestions, and for his kind support as I drafted the final version of the manuscript. All remaining errors are, of course, my own responsibility.

¹ W. D. Ross claims that ‘the procedure throughout the Metaphysics never becomes deductive; it always remains aporematic’, and adds: ‘It may be noted that the method is substantially the same in nearly all Aristotle’s writings’ ( W. D. Ross, Aristotle’s Metaphysics, 2 vols. (Oxford, 1924; repr. 1975), i. 252). In the twentieth century, the dialectical nature of the diaporetic procedure was highlighted particularly by P. Aubenque, ‘Sur la notion aristotélicienne d’aporie’ [‘Aporie’], in S. Mansion (ed.), Aristote et les problèmes de méthode (Louvain, 1961), 3–19, and it has become a widely held opinion: cf. e.g. G. Ryle, ‘Dialectic in the Academy’ [‘Dialectic’], in R. Bambrough (ed.), New Essays on Plato and Aristotle (London, 1965), 39–68 at 66. T. Irwin, especially in ‘Le caractère aporétique de la Métaphysique d’Aristote’, Revue de Métaphysique et de Morale, 95 (1990), 221–48 at 221, praises the influence of Aubenque’s work on the aporetic nature of Aristotle’s metaphysics: ‘L’un des nombreux mérites du livre de Pierre Aubenque sur le problème de l’être chez Aristote est d’avoir mis l’accent sur les questions qui concernent les rapports entre la méthode d’Aristote et sa doctrine. Sur cette question, j’ai trouvé les vues d’Aubenque plus stimulantes que tout ce dont je puis avoir connaissance en anglais. A cette occasion, je voudrais discuter sa thèse selon laquelle l’argumentation d’Aristote dans sa métaphysique est essentiellement aporétique’; cf. also A. Madigan, Aristotle: Metaphysics Books Β and Κ 1–2 [Metaphysics] (Oxford, 1999), xvi–xix; C. Rossitto, Studi sulla dialettica in Aristotele [Studi] (Naples, 2000); and more recently A. Laks and M. Crubellier, ‘Introduction’, in A. Laks and M. Crubellier (eds.), Aristotle’s Metaphysics Beta [Beta] (Oxford, 2009), 1–23 at 3–4.

² I follow the Greek text of W. D. Ross, Aristotelis Topica et Sophistici elenchi [Topica] (Oxford, 1958), except where noted.

³ Unless otherwise noted, translations of the Topics are based on R. Smith, Aristotle: Topics I and VIII [Topics] (Oxford, 1997), with modifications.

⁴ E. Kapp, Greek Foundations of Traditional Logic (New York, 1942), 12–13 (cf. 61), was the first to underline this important point; cf. also O. Primavesi, Die aristotelische Topik [Topik] (Munich, 1996), 49 ff.

⁵ Some authors believe that these are two different uses of dialectic (cf. J. Brunschwig, Aristote: Topiques I–IV [Topiques I–IV] (Paris, 1967), 116 n. 1, and more recently ‘Dialectique et philosophie chez Aristote, à nouveau’, in N. Cordero (ed.), Ontologie et dialogue: hommage à Pierre Aubenque (Paris, 2000), 107–30 at 120–1; Smith, Topics, ad 101^a36–^b4). Others maintain that they are two aspects of a single use (cf. Primavesi, Topik, 52 ff.; E. Berti, ‘Aristote et la méthode dialectique du Parménide de Platon’ [‘Méthode’], Revue Internationale de Philosophie, 34 (1980), 341–58 at 345). Still others argue that they are identical ( C. Rossitto, ‘La dialettica e il suo ruolo nella Metafisica di Aristotele’, Rivista di Filosofia Neo-Scolastica, 85 (1993), 370–424 at 381–3 and n. 36). It is true that in [ii] Aristotle makes explicit reference to the principles or first truths, while in [i] there is no mention of such principles. For my purposes here, there is no need to settle this matter. It is sufficient that we can safely establish that in both [i] and [ii] Aristotle alludes to a philosophical use of the Topics.

⁶ Although it has an independent title, SE is usually considered to be the last book of the Topics (cf. L. A. Dorion, Les Réfutations sophistiques [Réfutations] (Paris, 1995), 24–5). However, even if it is to be considered an independent treatise, it is clear that SE is part of the same project as the Topics and is a natural extension of the study of dialectic, since it analyses fallacious arguments and general errors that can occur within that dialogical framework.

⁸ This does not mean that he can (or should) reject any question leading to his refutation solely on the ground that it would entail his defeat in dialogue. A proper objection must be put forward against the rejected question, or else one will be considered captious (Top. 8. 8, 160^b2–3: τὸ γὰρ ἄνευ ἐνστάσεως ἢ οὔσης ἢ δοκούσης κωλύειν τὸν λόγον δυσκολαίνειν ἐστίν). Whoever acts in this way goes against the rules of dialectic (cf. 160^b12) and engages instead in a merely competitive exchange (cf. Top. 8. 11, 161^a23–4).

⁹ For the two tasks and skills involved see also Top. 8. 14, 164^a16–^b7; SE 34, 183^b10–12. In all passages, resolution (lusis) is consistently listed among the tasks that fall to the respondent.

¹⁰ In studies specifically devoted to SE, on the other hand, these two procedures are often clearly distinguished: cf. esp. Dorion, Réfutations, 19–20. As Dorion points out, the idea that lusis and elenchos are synonyms (or that the former is a species of the second) goes back to ps.-Alexander’s commentary on the SE.

¹¹ ἔλεγχος δὲ συλλογισμὸς μετ ᾿ ἀντιϕάσεως τοῦ συμπεράσματος. Unless otherwise noted, translations of SE are my own. On the conditions for a genuine contradiction see SE 5, 167^a23–7.

¹² The expression ψευδὴς συλλογισμός alludes to the incorrectness of an argument, hence it can mean that either (1) the conclusion of the argument is false, or (2) there is a mistake in the argument, with the result that the conclusion does not really follow from the premisses (see SE 18, 176^b29–36). In Top. 8. 12, 162^b3–5, for instance, ψευδὴς λόγος is used with the second meaning; in Top. 8. 10, 160^b23 ff., it is used with the first.

¹³ There seems to be an exception in Rhet. 2. 25, where Aristotle discusses rhetorical lusis and includes counter-argument (ἀντισυλλογίζεσθαι) as one of its forms (1402^a31–4), the other being objection (ἔνστασις). To offer a counter-argument is to build an enthymeme with a conclusion contrary to the enthymeme of the rival orator (cf. 2. 26, 1403^a25–8). J. Sprute, Die Enthymemtheorie der aristotelischen Rhetorik (Göttingen, 1982), 129, and E. Ryan, Aristotle’s Theory of Rhetorical Argumentation (Montreal, 1984), 139–49, claim that this form of rhetorical resolution is the same sort of argument that Aristotle calls ‘refutative enthymeme’ (ἐλεγκτικὸν ἐνθύμημα) in Rhet. 2. 22, 1396^b25–7, 1397^a2–3. If they are right, and a refutative argument is one form of rhetorical resolution, then this is an exception to the otherwise rather consistent terminological use of lusis and elenchos by Aristotle. Still, it is worth noticing that, parallel to what occurs in SE, resolutions in the Rhetoric are presented in chapter 2. 25 just after the study of apparent enthymemes in 2. 24, so that—as in SE and elsewhere—they are reactions against arguments (more precisely, against enthymemes). I shall not deal here in any further detail with rhetorical resolutions and refutations.

¹⁴ The translation is based on W. A. Pickard-Cambridge, Aristotle: Sophistical Refutations, in J. Barnes (ed.), The Complete Works of Aristotle (Princeton, 1984), with major modifications.

¹⁵ I am being deliberately vague here in referring to a ‘mistake regarding premisses’, since in other passages Aristotle does not speak of apparently acceptable premisses but of false premisses (Top. 8. 10, 160^b23–7; cf. Phys. 1. 2, 185^a9–10, discussed below). As for apparently plausible premisses (ϕαινόμενα ἔνδοξα), Aristotle explains in Top. 1. 1, 100^b26–101^a1, that not everything that at first appears acceptable actually is so, though in eristic arguments this sort of mistake ‘is usually obvious at once to those capable of even modest discernment’. This should probably be understood in terms of the mechanics of a real dialogue. As a dialectical encounter develops, what first appeared to be acceptable, and was thus granted as a premiss by the respondent, turns out in the end to have been a trick, making it evident that one has been refuted by having accepted it. As Smith comments: ‘To be caught by the trick, I must first concede this premiss, which I might do because it has a certain superficial plausibility; on reflection (or after seeing what follows from it), I realize that I do not believe it after all, even though at first I thought I did’ (Smith, Topics, 48).

¹⁶ Probably building on the Stoic tradition, Alexander of Aphrodisias (In Top. 40–1 Wallies) and other commentators after him interpreted these as material and formal errors, respectively. The problem with this reading, as Ebbesen puts it, is that ‘to speak of formally invalid arguments does not make much sense unless it is quite clear what a valid argument would be like’, given that Aristotle does not speak in SE of syllogistic figures ( S. Ebbesen, Commentators and Commentaries on Aristotle’s Sophistici elenchi, i. The Greek Tradition [Commentators] (Leiden, 1981), 97). In any case, the relation between these two general kinds of incorrectness—interpreted in this fashion or some other—and the thirteen incorrect arguments and illicit moves presented in SE 4–5 is anything but clear (cf. Ebbesen, Commentators, 95–9, and for a thorough discussion see Dorion, Réfutations, 69–91). The thesis to be defended in this paper, fortunately, does not hinge on a resolution of this problem.

¹⁷ Cf. Pr. An. 2. 2–4; Post. An. 1. 32, 88^a20–3; Top. 8. 11, 162^a9–11; 8. 12, 162^b11–15.

¹⁸ In SE 24, 179^b18–20, Aristotle insists that merely showing that an argument has concluded something false is not itself a resolution, unless one also shows the point on account of which this takes place, i.e. that wherein the error lies. Here again the treatment of the rhetorical resolution in Rhet. 2. 25 is an exception: a counter-argument is one of the possible forms of resolution admitted in rhetoric (cf. above, n. 13).

¹⁹ Another possible sense is involved in διελόντα at 176^b36.

²⁰ Aristotle assimilates the Fallacy of the Consequent to the Fallacy of Accident on several occasions (SE 6, 168^b27–31; 7, 169^b6–7; 8, 170^a4–5), and the reason seems to be precisely that both exploit accidental identities: cf. J. D. G. Evans, ‘The Codification of False Refutations in Aristotle’s De sophisticis elenchis’, Proceedings of the Cambridge Philological Society, 21 (1975), 542–52 at 548.

²¹ Cf. SE 16, 175^a9–12, 175^a20–2; 18, 177^a6–8.

²² Brunschwig,‘Dialectique’, 125–6, argues against the reading that takes this to be an application of dialectical method in the spirit of Top. 1. 2, 101^a36–^b4, but he acknowledges that the argument has the form of a refutation. His resistance to seeing it as an application of dialectic in Metaphysics Γ is ultimately rooted in more general reservations against the possibility of finding dialectical arguments, in a strict sense, in Aristotle’s writings (cf. ‘Dialectique’, 107–14). For general reservations about the presence of dialectical arguments see also Primavesi, Topik, 36–49 and 53–8, and Rossi, ‘Desanudando argumentos’, 80–6 and 96–7, where I have also attempted to show that these reservations do not apply to resolutions.

²³ These are DA 1. 2, 405^b1–5 (where Aristotle mentions Hippo’s refutation of those who claim that the soul is blood); Phys. 4. 6, 213^a22–5 (how Anaxagoras would refute people’s wrong opinion about void); Pol. 7. 11, 1330^b32–5 (the facts refute those who claim that cities with pretentions to valour should not have walls); Pol. 5. 8, 1307^b40–1308^a2 (a reference to claims refuted by the facts, ὑπὸ τῶν ἔργων); and EE 1. 3, 1215^a3–7, which I discuss below. There are also a couple of passages where Aristotle refers to sophistical refutations in passing: Metaph. Ζ 6, 1032^a7; Θ 8, 1049^b33. Finally, Metaph. Β 2, 998^a2–4, mentions Protagoras’ refutation of the geometers’ claim that the circumference of a circle touches the tangent at a point, though it is not entirely clear whether this refutation is understood as being directed against the geometrical thesis or against an argument.

²⁴ And, of course, leaving aside non-argumentative meanings of the term; cf. H. Bonitz, Index Aristotelicus [Index] (Berlin, 1961), 438^b42–439^a11; 440^a52–^b1.

²⁵ In EE 2. 8, 1224^b2–11 (esp. 1224^b6), Aristotle resolves an argument which concludes that those who are driven by desire act under force and involuntarily, by appealing to the disambiguation of ‘acting under force’. In NE 5. 9, 1136^b23 ff., he shows that an argument for the possibility of committing injustice against oneself can be resolved by resorting to the definition of ‘committing injustice’; cf. also 5. 11, 1138^a26–8. In NE 6. 13, 1144^b32–4, he gives a resolution of a dialectical argument that someone might offer to prove that virtues can exist in isolation from each other. In NE 7. 12, 1153^a27–9, and the following discussion he claims that arguments to the effect that the temperate man avoids pleasure, the prudent man pursues freedom from pain, and animals and children pursue pleasure can all be answered by the same resolution. In GA 1. 18, 722^a1 ff. (discussed below), he gives the resolution of an argument that supports pangenesis. Several passages in Physics 1 (1. 2, 185^a8–9, 185^a14–17; 1. 3, 186^a4–7, 186^a22–4) concern the resolution of Parmenides’ and Melissus’ arguments. In Phys. 4. 7, 214^b9–11, Aristotle mentions the resolution of arguments that prove the existence of vacuum. In Phys. 6. 9, 239^b9–11, in referring to Zeno’s four arguments, which are resolved in the same chapter, Aristotle even recalls the methodological principle of SE, according to which deceptive arguments that derive from the same kind of error should be resolved in the same way (cf. SE 177^b31–2). With reference to the same arguments cf. also Phys. 6. 9, 239^b20–6. In Phys. 8. 2, 252^b7, he introduces his discussion of arguments against the eternity of movement with the claim that they are easy to resolve. In Phys. 8. 8, 263^a11–18, there is a reference to the resolution of Zeno’s arguments, and in 263^a21 ff. he offers a new resolution of the same difficulties. The use of the term lusis in connection with arguments also appears in EE 1. 6, 1217^a13–14; 7. 12, 1245^b13–14; NE 7. 2, 1146^a24–7; 7. 13, 1153^b4–7 (which mentions a resolution of Speusippus’ and criticizes it); Metaph. Γ 7, 1012^a18–20; Ζ 6, 1032^a6–8; Ν 2, 1089^a3–4; Phys. 8. 8, 262^b28; De sensu 445^b17–21. Bonitz, Index, 439^a18, adds Pol. 7. 6, 1340^b41.

²⁶ Cf. the first sixteen passages mentioned in the previous note.

²⁷ Phys. 1. 3, 186^a22–4: καὶ πρὸς Παρμενίδην δὲ ὁ αὐτὸς τρόπος τῶν λόγων, καὶ εἴ τινες ἄλλοι εἰσὶν ἴδιοι· καὶ ἡ λύσις τῇ μὲν ὅτι ψευδὴς τῇ δὲ ὅτι οὐ συμπεραίνεται.

²⁸ The discussion of Melissus’ argument is not very methodically organized, but in lines 186^a10–13 Melissus’ argument is identified (and resolved) as a non-deductive Fallacy of the Consequent (παρὰ τὸ ἑπόμενον), of the kind studied in SE 5 and 28, and lines 186^a13–16 can be read as claiming that a premiss in his argument (sc. that in all cases there is a beginning) is false.

²⁹ R. Bolton, ‘Dialectic, Peirastic and Scientific Method in Aristotle’s Sophistical Refutations’ [‘Peirastic’], Logical Analysis and History of Philosophy, 15 (2013), 26785 at 281–4, has recently argued that peirastic arguments are involved at this stage of the resolution, and although I believe he is probably right, I think it is important to stress that they are used as a means for resolution.

³⁰ I am especially indebted to the Editor for helping me clarify my point here.

³¹ 722^a2: τά τε γὰρ εἰρημένα λύειν οὐ χαλεπόν.

³² Later in GA 1. 18, after this resolution, Aristotle offers a series of reductiones ad absurdum of the pangenesis thesis, but they do not seem to be part of the resolution just discussed.

³³ Phys. 6. 9, 239^b5: Ζήνων δὲ παραλογίζεται; cf. 240^a2.

³⁴ For Zeno’s first argument see 239^b13–14 (referring back to 6. 2, 233^a21–31).

³⁵ My own examination of the remaining passages cited in n. 25 confirms this hypothesis: those resolutions are all aimed against arguments, although they do not always work in terms of detecting (one or both of) the two main argumentative errors discussed in Topics 1. 1 and SE 2. It is also important to remember that there is a lot more material for resolutions in the second part of SE (esp. chapters 19–30), where Aristotle provides the preferred resolutions for each of the thirteen sorts of eristic argument presented in SE 4–5. It is a matter for further enquiry if, and to what extent, those resolutions are actually employed by Aristotle in the treatises. Just to mention a couple of promising examples: there is the discussion of Melissus’ argument in Physics 1. 3 as a non-deductive argument παρὰ τὸ ἑπόμενον (see n. 28); and in Physics 1. 8 the resolution of the aporia about the impossibility of generation seems to be tackled partly using the distinction between what is said simply (ἁπλῶς) and in some respect (πῇ, cf. SE 25).

⁷ In this section I develop several claims made in my ‘Desanudando argumentos: las aplicaciones filosóficas de la dialéctica según las Refutaciones sofísticas’, Méthexis, 19 (2006), 79–109.

³⁶ For different accounts of this semantic oscillation see Bonitz, Index, 187^b, s.v.; Aubenque, ‘Aporie’, 8–11; Madigan, Metaphysics, xxi-xxii. My own division of meanings is close to Madigan’s, with the difference that he distinguishes a third, intermediate meaning of diaporēsai. Bonitz distinguishes two senses of diaporein, one of which does not differ from aporein, being in a state of aporia or impasse in thought (cf. Metaph. Α 9, 991^a9; Κ 1, 1059^b21–3; Μ 5, 1079^b12; Phys. 2. 8, 199^a22). Bonitz’s second and more proper sense of diaporein is διέρχεσθαι τὰς ἀπορίας, and it involves the two senses of the term (connected to the two stages of the procedure) that I distinguish here. F. Pironet, ‘Aristote: ἀπορία, εὐπορία et les mots étymologiquement apparentés’ [‘Aporia’], in A. Motte and C. Rutten (eds.), Aporia dans la philosophie grecque des origines à Aristote (Louvain-la-Neuve, 2001), 151–98 at 186, finds two senses of diaporein in the Organon and Physics which are essentially the same as Bonitz’s, and also brings together the two activities I shall distinguish under the same (second) sense. Whether or not the two activities I differentiate are referred to by the term diaporein under different senses or with the same sense, the relevant point for my purposes is that Aristotle uses the term to designate two activities that, as I shall try to show, involve different argumentative means and capacities.

³⁷ Cf. Metaph. Β 1, 995^a24–33; NE 7. 1, 1145^b2–6; for the distinction of these three steps in diaporetic procedure see Aubenque, ‘Aporie’, 4 and passim, and J. Barnes, ‘Aristotle and the Methods of Ethics’, Revue Internationale de Philosophie, 34 (1980), 490–511 at 491–3. I am inclined to understand the description of these steps as not being prescriptive in nature (cf. below, n. 89).

³⁸ Madigan, Metaphysics, xxi, offers the following examples of this use of diaporein: Metaph. Γ 5, 1009^a22–3; Μ 9, 1085^a25; EE 1. 5, 1216^a11; 7. 12, 1245^a27–9, to which we can add (not exhaustively) Post. An. 2. 3, 90^a36–8; 2. 4, 91^a12; GC 1. 5, 321^b11.

³⁹ Madigan, Metaphysics, xxi, offers the following examples of this use of diaporein: Metaph. Κ 1, 1059^a19; Μ 9, 1086^a19, 1086^a34; Bonitz, Index, s.v., adds Phys. 4. 10, 217^b30; Post. An. 1. 1, 71^a31, 33; GC 1. 10, 327^b10; Pol. 3. 2, 1281^b22, 1282^a24, 1275^a21; to which we can add Metaph. Μ 5, 1079^b21; Meteor. 1. 3, 340^a19; 1. 6, 342^b25–7; DA 1. 2, 403^b20–4 (this list is not meant to be exhaustive).

⁴⁰ I quote the translation of W. E. Dooley and A. Madigan, Alexander of Aphrodisias: On Aristotle’s Metaphysics 2 and 3 (Ithaca, NY, 1992). Cf. also Alex. Aphr. In Metaph. 236. 26–9 Hayduck, and In Top. 28. 26–29. 2 Wallies.

⁴¹ Among those who understand that diaporēsai in Topics 1. 2 essentially means arguing for (or against) conflicting theses, see e.g. Alex. Aphr. In Top. 28. 23–9 Wallies; Ryle, ‘Dialectic’, 66; Brunschwig, Topiques I–IV, 116, a reading he develops further in ‘Dialectique’, 119–22; Primavesi, Topik, 52–3. Among those who also hold that an aporia consists in conflicting theses see Aubenque, ‘Aporie’, and among those who add that the resolution of the puzzle consists in a refutation of one of them see M. Guéroult, ‘Logique, argumentation, et histoire de la philosophie chez Aristote’, Logique & Analyse, 6 (1963), 431–49, on aporiai: ‘dans une disjonction simple ou complexe, la preuve de l’impossibilité ou de la fausseté de tous les termes en balancement, sauf un, équivaut presque, quant à la certitude, à la preuve directe de la vérité du terme subsistant’ (446); Berti, ‘Méthode’, 342–3, agrees with Guéroult: ‘la méthode en question … consiste à chercher à réfuter les opinions des autres philosophes déduisant d’elles de véritables contradictions, et à montrer de cette façon la vérité des opinions qui leur sont opposées’ (343); cf. also E. Berti, ‘L’uso “scientifico” della dialettica in Aristotele’, Giornale di Metafisica, ns 17 (1995), 169–90, where the passage from Topics 1. 2 is also interpreted in this way, concluding that there is a close connection between diaporēsai and elenchein based also on EE 1. 3, 1215^a3–7; in the same vein, Rossitto, Studi, claims consistently that the way out of the aporia is an elenchos; more recently M. Zingano, ‘Aristotle and the Problems of Method in Ethics’, Oxford Studies in Ancient Philosophy, 32 (2007), 297–330 at 305–6, commenting on EE 1. 3, 1215^a3–7 (about which more below), identifies the context of that passage as clearly dialectical and understands that the way of dealing with aporiai proposed there is to refute one thesis, thereby obtaining a demonstration of the one that conflicts with it.

⁴² On the other hand, if we do not know the truth-value of the premisses in (P₁) from which A follows (or of the premisses in (P₂) from which not-A does), then the procedure in itself seems to be of little help for discerning the true and the false.

⁴³ Actually, this reading of the procedure described in Topics 1. 2 requires that the conflicting theses constitute a genuine exclusive and complete disjunction, since otherwise it would be impossible to infer the truth of one from the falsity of the other.

⁴⁴ Cf. Berti, ‘Méthode’, 343–5; R. Smith, ‘Dialectic and Method in Aristotle’, in M. Sim (ed.), From Puzzles to Principles? Essays on Aristotle’s Dialectic (Lanham, Md., and Oxford, 1999), 39–55 at 51.

⁴⁵ The reason, obviously, is that a true proposition can also be deduced from a false starting point (cf. Top. 8. 11, 162^a9–11; Pr. An. 2. 2, 53^b4–10; 2. 4, 57^a36–^b17).

⁴⁶ Cf. Primavesi, Topik, 52; Smith, Topics, ad 163^a36–^b16, and especially Brunschwig ‘Dialectique’, 119–22, and Aristote: Topiques V–VIII [Topiques V–VIII] (Paris, 2007), 302, who proposes—more than a mere connection—to read Top. 1. 2, 101^a34–6, in the light of this passage in Top. 8. 14.

⁴⁷ 163^a36–^b1: πρὸς ἅπασάν τε θέσιν, καὶ ὅτι οὕτως καὶ ὅτι οὐχ οὕτως, τὸ ἐπιχείρημα σκεπτέον, cf. 163^b6–8.

⁴⁸ Smith, Topics, 154–5, suggests a very interesting connection between this natural gift with respect to truth and the ‘natural virtue’ Aristotle discusses in NE 6. 13, i.e. the right disposition to feel pleasure and pain but without ϕρόνησις; if the analogy holds, those naturally gifted with respect to truth would be capable of detecting the truth without ἐπιστήμη, i.e. without being able to produce a demonstration for it. In the same vein, Brunschwig, Topiques V–VIII, 302, points to the ethical dimension of this natural gift.

⁴⁹ Brunschwig, Topiques V–VIII, 302 (my translation).

⁵⁰ I consider this sort of resolution in sect. 5.

⁵¹ This is nevertheless implicitly assumed by authors who defend this reading. For instance, Alexander of Aphrodisias, In Top. 28. 26–9 Wallies, in commenting on this passage, claims that it is about finding out more easily on which side of the contradiction the truth lies (ἐν ποτέρῳ αὐτῶν μέρει τῆς ἀντιϕάσεως τὸ ἀληθές ἐστιν).

⁵² At the same time, this reading does not in any way preclude the possibility that the true and the false are, respectively, in just one or the other of the two theses.

⁵³ For concrete examples see n. 92.

⁵⁴ For concrete examples see n. 76. I shall return to this issue in the next section.

⁵⁵ My account here builds on, but does not always coincide with, Aubenque, ‘Aporie’, 6–7, and Madigan, Metaphysics, xx. I also agree on a number of points in the detailed discussion of Pironet, ‘Aporia’, 151–60, who likewise emphasizes the importance of the passages in Top. 6. 6 and 1. 11 for understanding the methodological meaning of ‘aporia’.

⁵⁶ For this use see Meteor. 4. 7, 383^b20–1; DA 2. 11, 422^b19 ff.; Phys. 2. 8, 198^b16.

⁵⁷ My translation.

⁵⁸ Cf. e.g. Meteor. 2. 3, 357^b26–30; De caelo 2. 12, 292^a10–18; 2. 14, 297^a25–^b17.

⁵⁹ Cf. e.g. Meteor. 2. 2, 355^b20–32; 2. 5, 362^a11–13; HA 6. 37, 580^b14 ff.; GA 3. 10, 759^a8 ff.

⁶⁰ Cf. e.g. Meteor. 2. 5, 362^a11–13; GA 3. 10, 759^a8 ff.; 4. 4, 770^b28–771^a17; HA 6. 37, 580^b14 ff.

⁶¹ See G. E. L. Owen, ‘Tithenai ta Phainomena’, in S. Mansion (ed.), Aristote et les problèmes de méthode (Louvain, 1961), 83–103 at 87.

⁶² My translation.

⁶³ The vocabulary in both passages points to the causal role of arguments: in Top. 6. 6 the equality between contrary arguments is able to produce (ποιητικόν) aporia; and in Top. 1. 11 the state of aporia comes about because of (διὰ τὸ … εἶναι) persuasive arguments.

⁶⁴ The lines 162^a15–18 are included in the text by W. D. Ross, Topica, but Alexander does not comment on them and both Smith, Topics, 144, and Brunschwig, Topiques V–VIII, 293—following Strache–Wallies, Tricot, and Smith—consider them to be spurious for good reasons. Nonetheless, the definition of the aporēma as a species of epicheirēma seems to me to capture the essence of the structure of Aristotelian aporiai at the logical-methodological level.

⁶⁵ Commenting on Metaph. Β 1, 995^a27–33 (quoted immediately below), A. Laks agrees that what binds thought are arguments rather than just theses: ‘The state envisaged here [i.e. the binding] results less from the sheer disjunction … than from its sharpening by stating the arguments of the parties, which corresponds to the fetters: thought is really stuck, as a prisoner is’ (A. Laks, ‘Aporia Zero (Metaphysics Β 1, 995a24–995b4)’ [‘Aporia Zero’], in Laks and Crubellier (eds.), Beta, 25–46 at 43). He does not pursue this reading any further, however.

⁶⁶ I follow the Greek text of W. Jaeger, Aristotelis Metaphysica (Oxford, 1957).

⁶⁷ The translations of Metaphysics Β 1 are based on Laks’s translation in ‘Aporia Zero’. For thought caught in a state of immobility owing to an aporia cf. also NE 7. 2, 1146^a24–7.

⁶⁸ Even when this might be the weaker or less preferred reason given by Aristotle in favour of following the procedure of aporiai (cf. Laks, ‘Aporia Zero’, 41), the claim—for my argument—that an aporia entails a contraposition of arguments still holds.

⁶⁹ I follow the Greek text of P. Moraux, Aristote: Du ciel (Paris, 1965).

⁷⁰ My translation.

⁷¹ Here ‘demonstrations’ (ἀποδείξεις) clearly lacks a strict epistemological sense.

⁷² In some cases the exposition of aporiai coincides with the discussion of earlier philosophers’ doctrines: cf. Metaph. Β 1, 995^a24–7; DA 1. 2, 403^b20–4; there is also a clear example in Phys. 4. 6, 213^a19–22, where Aristotle proposes to review the arguments of his predecessors for and against the existence of void.

⁷³ In Metaph. Γ 6, 1011^a3 ff., Aristotle himself alludes to an impasse in thought that some fall into (ἀποροῦσι) which does not stem from a genuine problem but from a methodological mistake.

⁷⁴ I do not want to suggest that aporiai receive a definite answer in every case.

⁷⁵ There are many examples in the treatises where Aristotle raises aporiai by himself formulating arguments for or against conflicting theses (some of these are quoted in n. 38).

⁷⁶ Madigan, Metaphysics, xviii: ‘almost four fifths of the arguments in Β are refutative’; cf. Laks and Crubellier, ‘Introduction’, 8. Aporiai constituted by two refutations can also be found in Phys. 3. 3, 202^a21 ff.; 3. 4, 203^b30–2 and ff.; 4. 10, 218^a8–30; GA 2. 1, 733^b23–734^b4 (not exhaustive); in Meteor. 1. 3, 340^a19–^b3, there is an aporia which consists of two mutually exclusive theses only one of which is refuted, while the other, far from being viewed as demonstrated, seems to be taken as quite implausible and hence does not even need to be refuted in order to raise a difficulty.

⁷⁷ I follow the Greek text of R. Walzer and J. Mingay, Aristotelis Ethica Eudemia (Oxford, 1991), except where noted.

⁷⁸ The translation is from M. Woods, Aristotle: Eudemian Ethics, Books I, II, and VIII [Eudemian Ethics] (Oxford, 1982), modified.

⁷⁹ Walzer and Mingay, following Dodds’s suggestion that there is a lacuna in the text just before the claim in line 3, reconstruct lines 1–2 in this way: εἰκῇ γὰρ λέγουσι σχεδὸν περὶ ἁπάντων, καὶ μάλιστα περὶ 〈ταύτης· ἀλλὰ τὰς τῶν σοϕῶν ταύτης γε πέρι〉 {ἐπισκεπτέον} μόνας· (‘they [viz. the many] speak in an unreflective way on almost every topic, most of all when they speak about this; only the opinions of the wise—on this subject at least—should be examined’). Even if mention of ‘the wise’ might be bold to assume, the passage seems in fact to draw an opposition between qualified and unqualified opinions, such that only the former are worthy of philosophical scrutiny and discussion. I take it that the emphatic ταύτας in line 1215^a5 refers to these qualified opinions (whether they belong to the wise or not, we can presume these opinions are not unreflective, since they are different from the opinions of the many). For his part, Woods, Eudemian Ethics, ad 1215^a5–6, accepts Walzer and Mingay’s conjecture and maintains that the opinions which produce aporiai, and which should be examined, are indeed the opinions of the wise.

⁸⁰ This form of resolution that resorts to a counter-argument could be compared with the one in Rhet. 2. 25; cf. above, n. 13.

⁸¹ Admittedly, these plurals could be due to the presence of ἀπορίαι in lines 1215^a3–4. But they could also refer to the opinions of the wise (δόξας, which appears closer, immediately before our passage in line 1215^a6), which are precisely the ones to be considered in the investigation, as the whole passage emphasizes.

⁸² Refutations can appear as a component of a resolution, however. I have already discussed this possible role of the elenchos within resolutions that proceed through the elimination of a false premiss: see above, sect. 2.

⁸³ See e.g. Metaph. Η 6, 1045^a14–33, esp. 1045^a22; Κ 6, 1062^b20; Λ 10, 1075^a25–33; Μ 9, 1085^a26–9; Phys. 1. 8, 191^a23–4, ^b34; 4. 3, 210^b22–4; 4. 5, 212^b23; 4. 7, 214^b5–11; 8. 2–3, esp. 253^a31; 8. 10, 267^a17; GC 1. 5, esp. 321^b11–12; 1. 10, 327^b9–10; NE 7. 2, esp. 1146^a21–7 and 1146^b7–8; EE 7. 2, 1235^b14; DA 2. 11, esp. 422^b27–8; GA 2. 1, esp. 734^b4; MA 4, 700^a4; Meteor. 2. 2, 354^b21–3; De caelo 2. 5, 288^a8–9; 2. 14, 297^a25–^b17, esp. 297^a30–1; 4. 2, 309^b8–10; Pol. 3. 2, 1281^b21–4; 1282^a23–4, 32–3; Post. An. 1. 1, 71^a29–34. (This list is not intended to be exhaustive.)

⁸⁴ Cf. G. Matthews, ‘The Normalization of Perplexity in Aristotle’ [‘Normalization’], in Sim (ed.), From Puzzles to Principles?, 125–36 at 132–3, with examples.

⁸⁵ Laks, ‘Aporia Zero’, 40, suggests in passing that, for there to be a resolution of an aporia, there must be a flaw somewhere in the arguments for each conflicting thesis. Although he does not spell this out, his claim does in fact entail that lusis as applied to aporiai has essentially the same meaning as in the dialectical treatises— that is, it is a way to resolve arguments.

⁸⁶ ἔστι δὲ δριμὺς λόγος ὅστις ἀπορεῖν ποιεῖ μάλιστα, 182^b32.

⁸⁷ ἔστι δὲ συλλογιστικὸς μὲν λόγος δριμύτατος ἂν ἐξ ὅτι μάλιστα δοκούντων ὅτι μάλιστα ἔνδοξον ἀναιρῇ, 182^b37–8.

⁸⁸ In Phys. 1. 8, 191^a23–4, 191^b30, Aristotle calls Parmenides’ argument against generation and corruption an aporia, and he refers to it as ‘an extraordinary difficulty’ (θαυμαστὴ ἀπορία) in GC 1. 3, 317^b18–19. Aristotle’s critique of Melissus in Phys. 1. 2 is also consistent with this sense of aporia: our philosopher declares that Melissus’ argument against movement, being rudimentary (and hence not compelling), entails no aporia (185^a11). As I have shown above in sect. 2, Aristotle refers consistently to his discussion against the Eleatic arguments as a lusis, which is at the same time the resolution of those arguments and of the aporia they cause.

⁸⁹ In a similar vein, in Phys. 4. 4, 211^a7–11, he just describes how we should try (πειρᾶσθαι) to conduct the investigation so as to expound (δεικνύναι) each case in the best manner. And I think we should also read Metaphysics Β 1 in this manner (cf. Laks, ‘Aporia Zero’, 46). Aristotle makes no claims there about safely reaching the truth through an application of diaporetic procedure, which in contrast is a typical feature of modern ‘methods of discovery’. For a clear example of what Aristotle’s method is not, see R. Descartes, Regulae ad directionem ingenii, in Œuvres de Descartes, ed. C. Adam and P. Tannery, vol. x (Paris, 1908), 371–2: ‘Per methodum autem intelligo regulas certas et faciles, quas quicumque exacte servaverit, nihil unquam falsum pro vero supponet, et nullo mentis conatu inutiliter consumpto, sed gradatim semper augendo scientiam, perveniet ad veram cognitionem eorum omnium quorum erit capax’ (‘By “a method” I mean reliable rules which are easy to apply, and such that everyone who follows them exactly will never take what is false to be true or fruitlessly expend mental efforts, but will gradually and constantly increase his knowledge till he arrives at a true understanding of everything within his capacity’ (trans. D. Murdoch (modified), in The Philosophical Writings of Descartes, vol. i, trans. J. Cottingham, R. Stoothoff, and D. Murdoch (Cambridge, 1985)). Descartes, inspired by mathematics, paradigmatically strives in his early method to find not just a general method of discovery, but also a method that guarantees the absence of error. The method of discovery is intended to be, at the same time, a guarantee of the truth of the results obtained through its own application in every field of knowledge, and this accounts for the inflexible and exact character of its rules. In Aristotle’s descriptions of the diaporetic procedure there is no attempt to guarantee that anyone who follows it will never mistake what is false for truth, nor that one will find truth, but only that one will be in a better position to see the truth in a particular matter (cf. Top. 1. 2, 101^a35–6). This is a much more modest promise, one that leaves room for considerable methodological flexibility, and certainly one that will be appealing to those who are able to tell the true from the false in the first place. Thus, in general terms, Aristotle leaves considerable methodological room for the arbitrium of the expert in each particular field. This is not necessarily a methodological flaw. On the contrary, it does justice to the extremely difficult nature of philosophical investigation into principles, whose complexity cannot be reduced to exhaustive rules, and is such that only some individuals (who are naturally gifted, well trained, and well informed) can perform it competently. This is partly connected to the limitations of dialectic in philosophical investigations, which I shall say more about later in this section.

⁹⁰ αἱ μὲν οὖν ἀπορίαι τοιαῦταί τινες συμβαίνουσιν, τούτων δὲ τὰ μὲν ἀνελεῖν δεῖ τὰ δὲ καταλιπεῖν. Translations of the Nicomachean Ethics are based on S. Broadie and C. Rowe, Aristotle: Nicomachean Ethics (Oxford, 2002). As for the Greek of this work, I follow the edition of I. Bywater, Aristotelis Ethica Nicomachea (Oxford, 1894).

⁹¹ Except paradoxes, as we have just seen, where a single argument is sufficient to produce the impasse.

⁹² To mention just a few examples of this pervasive practice, cf. Phys. 3. 2, 203^b30–2, with 206^a12–14; Phys. 6. 2, 233^a21–34; GA 2. 1, esp. 734^b4–5. Another conspicuous example is the resolution of the Socratic aporia concerning lack of self-control in NE 7. 3.

⁹³ A good example of a resolution of an aporia that resorts to this kind of distinction between what is said without qualification (ἁπλῶς) and what is said in some respect (πῇ) is Aristotle’s discussion of Parmenides’ argument against generation in Phys. 1. 8; cf. also the resolution of Meno’s paradox in Post. An. 1. 1, 71^a29–^b8.

⁹⁴ The resolution of the arguments of Parmenides against movement in Phys. 1. 2–3 is, again, a clear example: Aristotle introduces his doctrine of the many senses of ‘being’ in order to resolve Parmenides’ puzzle.

⁹⁵ Cf. Metaph. Γ 3, 1005^b8–10; Top. 6. 4, 141^b13–14; this is also stressed by Primavesi, Topik, 53.

⁹⁶ I believe this is not just the case in Aristotle. Another illustration of the philosophically creative dimension of the resolution of aporiai understood as conflicting arguments is found in Kant’s discussion of antinomies in the Critique of Pure Reason, to mention a conspicuous example.

⁹⁷ Cf. Aubenque, ‘Aporie’, 12 ff.; Matthews, ‘Normalization’, 131–6; Laks, ‘Aporia Zero’, 40 and 46.

⁹⁸ The capacity of detecting the true and the false is certainly not provided by the dialectical exercise itself. As I have claimed above, it will rest on substantive philosophical knowledge, which cannot be obtained from the sort of training that dialectic provides.

⁹⁹ Notably defended by R. Bolton: see ‘The Epistemological Basis of Aristotelian Dialectic’, in Sim (ed.), From Puzzles to Principles?, 57–105, and ‘Peirastic’.

¹⁰⁰ Cf. SE 16, and for a more extensive defence of the philosophical utility of SE see Rossi, ‘Desanudando argumentos’, 99–101, 106–7.