Chapter 4 Pyrrhonism and the Law of Non-Contradiction Diego E. Machuca The question of whether the Pyrrhonist1 adheres to certain logical principles, criteria of justification, and inference rules is of central importance for the study of Pyrrhonism. Its significance lies in that, whereas the Pyrrhonist describes his philosophical stance and argues against the Dogmatists by means of what may be considered a rational discourse, adherence to any such principles, criteria, and rules does not seem compatible with the radical character of his skepticism. Hence, if the Pyrrhonist does endorse them, one must conclude that he is inconsistent in his outlook. Despite its import, the question under consideration has not received, in the vast literature on Pyrrhonism of the past three decades, all the attention it deserves. In the present paper, I do not propose to provide a full examination of the Pyrrhonist's attitude towards rationality, but to focus on the question of whether he endorses the law of non-contradiction (hereafter LNC).2 However, I will also briefly tackle the question of the Pyrrhonist's outlook on both the canons of rational justification at work in the so-called Five Modes of Agrippa and the logical rules of inference. In addition, given that the LNC is deemed a fundamental principle of rationality, determining the Pyrrhonist's attitude towards it will allow us to understand his general attitude towards rationality. In Section 1, I briefly present and analyze the LNC by distinguishing its three most common formulations. This provides the necessary framework for examining 1I will employ interchangeably the terms "Pyrrhonist" and "Skeptic" (with a capital "S") to refer to the philosopher whose outlook is described and defended in Sextus Empiricus' surviving writings. I will say nothing about the outlooks adopted by Pyrrho, Timon, or Aenesidemus. Also, following Sextus, I use the term "Dogmatist" (δoγματικóς) to designate anyone who makes positive or negative assertions about how things really are on the basis of what he considers to be evidence and rational arguments. 2I should note that, when using the language of adherence, endorsement, or espousal, I refer to commitment to logical principles and epistemological criteria. By contrast, when speaking of observance, I will not necessarily presuppose any such commitment: the observance of, say, a rule may consist in simple obedience without strong adherence. D.E. Machuca (B) Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Academia Nacional de Ciencias de Buenos Aires, Av. Alvear 1711, 1014 Buenos Aires, Argentina e-mail: diegomachuca@conicet.gov.ar 51D.E. Machuca (ed.), Pyrrhonism in Ancient, Modern, and Contemporary Philosophy, The New Synthese Historical Library 70, DOI 10.1007/978-94-007-1991-0_4, C© Springer Science+Business Media B.V. 2011 52 D.E. Machuca the Skeptic's alleged commitment to that law. In Section 2, I lay out the reasons why he is supposed to endorse those three formulations of the LNC in much the same way as the Dogmatist, and examine the passages of Sextus Empiricus' extant corpus that seem to show unequivocally that such is the case. These passages appear to make it clear that adherence to the LNC rests at very the basis of the Pyrrhonist's skepticism, since suspension of judgment (ε'πoχή) seems to depend on commitment to that law. In Section 3, by contrast, I analyze a number of passages which can be taken as conclusive evidence that the Pyrrhonist is not actually committed to the three versions of the LNC presented in Section 1, but suspends judgment about their truth. I also speculate on some of the reasons for such a lack of commitment. In Section 4, I argue that the Skeptic's ε'πoχή regarding the LNC does not imply that he does not observe, motivated by psychological and practical reasons, certain qualified versions of this law when thinking, speaking, and acting. In doing so, I consider some objections that could be directed against the Skeptic's suspending judgment about the truth of the LNC. I also contend that the reason he makes use of what may be called the "dogmatic" versions of the LNC has to do with the therapeutic and dialectical side of his philosophy: since he tries to cure the rashness and conceit of the Dogmatists by argument, he needs to use those versions of the LNC in his argumentation because they are endorsed by the majority of his dogmatic patients. Although others have arrived at a conclusion about the Pyrrhonist's observance of the LNC which is similar to mine in certain respects, they have neither carried out a thorough analysis of this subject nor provided the necessary textual support for the interpretation just sketched. In Section 5, I argue that neither the uncommitted observance of a psychological version of the LNC nor the dialectical use of this law are isolated cases in the Pyrrhonist's philosophy, for something very similar happens both in the case of his ε'πoχή and in the case of his use of the Modes of Agrippa and the logical rules of inference. Finally, in Section 6, after summarizing the results of the previous analyses, I briefly address the question of whether the Pyrrhonist is an anti-rationalist. Although in examining the issues addressed in this paper I sometimes go beyond what is explicitly said in Sextus' surviving writings, my conclusions are in keeping with the Pyrrhonian way of thought, since I draw on what I take to be its conceptual and argumentative resources. 1 Three Versions of the LNC Three different versions of the LNC have been distinguished by scholars by examining Aristotle's discussion of this law in Metaphysics .3 These versions may be formulated as follows4: 3On Aristotle's discussion of the LNC, see Lukasiewicz (1971), Cassin and Narcy (1989), Wedin (1999, 2000, 2003, 2004a, 2004b), and Gottlieb (2007). 4The following taxonomy is based on Lukasiewicz (1971, pp. 487–8), and Gottlieb (2007, section 1). I must emphasize that, by offering the taxonomy, my sole purpose is to provide a useful and adequate tool for analyzing the Pyrrhonist's attitude towards the LNC. 4 Pyrrhonism and the Law of Non-Contradiction 53 Ontological version: it is impossible for the same attribute to belong and not to belong to the same thing at the same time and in the same respect (Met.  3 1005b19–20; cf.  4 1007b17–18, 6 1011b17–18, 21–22). In other words: it is impossible for x both to be F and not to be F at the same time and in the same respect. Logical version: it is impossible for contradictory propositions to be true at the same time and in the same respect (cf. Met.  6 1011b13–17, 20–21; 8 1012b2–3). This version is sometimes called "semantic" or "propositional." The symbolic form is: ¬ (p & ¬p). Doxastic version: it is impossible for two beliefs or opinions whose contents are expressed by contradictory propositions to exist simultaneously in one mind (cf. Met.  3 1005b23– 26, 1005b29–31). Some remarks about these three versions of the LNC are in order. First, the ontological version tells us how things in the world can and cannot be, that is, what forms reality can and cannot take. This obvious remark will be important when examining the Pyrrhonist's attitude towards the LNC. Second, the logical version is commonly construed as depending on the ontological version. Indeed, given that a proposition affirms or denies that an object possesses a given attribute, the reason two contradictory propositions cannot be true simultaneously is that objects in the world cannot hold contradictory attributes at the same time. Third, the doxastic version may be interpreted either descriptively or normatively. That is to say, it may be interpreted as the empirical claim that it is in fact impossible to hold contradictory beliefs, or as the normative claim that one ought not to hold such beliefs because it is not rational to do so (cf. Gottlieb 2007, section 1). In its normative sense, the doxastic formulation seems to rest on the logical formulation, since the reason it is irrational to hold contradictory beliefs at the same time seems to be that the contradictory propositions which express them cannot be true simultaneously. Understood descriptively, the doxastic version makes an assertion about the nature of the mind, since it affirms that we are unable to believe contradictory propositions at the same time. Finally, although someone might argue that the doxastic version rests on the ontological version (cf. Met.  3 1005b 26–32), it is clear that the doxastic version construed descriptively would still hold even if one proved the falsity of the ontological version. Indeed, it could be the case that, even if it were possible that contradictory attributes belong to the same thing at the same time and in the same respect, we would still not be able to conceive of such a state of affairs and, hence, to believe that the thing in question really has contradictory attributes. This brief presentation of the three most common formulations of the LNC proves to be necessary for the examination of the Pyrrhonist's outlook on that law. It must be noted that Sextus speaks of τὰ ε'ναντία (contraries) or τὰ α'ντικείμενα (opposites), not αι'α'ντιφάσεις (contradictories). However, in Hellenistic (e.g. Stoic) jargon, τò α'ντικείμενoν often refers to the contradictory, and not generically to the opposite. Also, in Metaphysics  Aristotle sometimes speaks of contraries rather than contradictories. We must bear in mind that the LNC governs both contradictory and contrary opposites, since neither contradictories nor contraries can both be true because they are inconsistent. In order to refer to both contradictories and contraries, I will often talk about "opposites." 54 D.E. Machuca 2 The Pyrrhonist's (Alleged) Commitment to the LNC At first glance, it seems obvious that the Pyrrhonist accepts the LNC in propria persona for at least three reasons. The first is that it is Sextus' observance of the LNC which makes it possible for us to understand the meaning of what he expounds in his writings. To begin with, if he did not observe that law, we would not be able to comprehend his account of the distinctive character of the Pyrrhonian philosophy in the first book of the υ

ώνειoι 'Υπoτυπώσεις (PH). Indeed, it is clear that Sextus relies upon our giving definite meanings to his explanations of the way in which we must interpret the Pyrrhonian stance. For instance, at the beginning of PH he cautions that, with respect to none of the things that will be said in that work does he affirm that it is certainly just as he says it is, but that he merely reports the way things appear to him at the moment (PH I 4). Similarly, in a number of passages, he points out that Skeptics use the verb "be" in the sense of "appear" (PH I 135, 198, also Adversus Mathematicos [AM] XI 18–20).5 Also, an important portion of the first book of PH is devoted to making clear the sense of the Skeptical φωναί, i.e., the various expressions used by the Pyrrhonist for describing his experience and outlook. Sextus carefully explains the sense in which each φωνή must be interpreted so as to avoid ascribing dogmatic views to the Pyrrhonist: the Skeptical φωναί are not assertions about non-evident matters, but only reports of the Pyrrhonist's appearances (φαινóμενα) or affections (πάθη)6 (PH I 187–208). These passages show that it is crucial for Sextus that his readers correctly understand the phenomenological character of the Pyrrhonian discourse if they do not want to form an inaccurate picture of the Pyrrhonian outlook.7 It is also worth noting that, in some texts, he points out that certain objections directed against Skepticism are the product of misinterpreting what Pyrrhonists actually say (PH I 19, 200, 208). In those texts, Sextus explicitly urges us to attribute specific meanings to the terms and expressions used by the Pyrrhonist so as not to misunderstand his outlook. One could argue that he 5Although elsewhere I do not follow the common practice of using the title Adversus Mathematicos VII–XI to refer to the five extant books of Adversus Dogmaticos, I here do so to maintain consistency with the other essays in this volume. 6A πάθoς is a state or condition someone or something is in as a result of being affected by an agent. Although in ordinary English the word "affection" does not have this meaning, it has become in the specialist literature a technical term to render the Greek πάθoς. 7Rachel Barney (1992) rejects a wholly phenomenological (i.e., non-epistemic or non-judgmental) interpretation of the Pyrrhonist's discourse on the grounds that it cannot account for his consideration of arguments (see also Bailey 2002, pp. 221–9). Myles Burnyeat (1997) advances a similar objection but as a problem for the Pyrrhonist, since he adopts a non-epistemic interpretation of Pyrrhonism. Although I cannot discuss this issue here, I think that one flaw in the argument of these interpreters is that they fail to distinguish between believing/judging that p and having an inclination to believe/judge that p (see Machuca 2005, pp. 219–20; 2006, p. 134). For other interpretations which reject a wholly non-epistemic understanding of Sextan Pyrrhonism, see Frede (1997a, b) and Brennan (1999). 4 Pyrrhonism and the Law of Non-Contradiction 55 would, at least implicitly, agree with Aristotle in that, without the LNC, it is impossible to have a meaningful conversation or to make oneself understood, thereby being forced to accept that law. Aristotle maintains that, as soon as the person who rejects the LNC utters a word in order to signify something, he shows that he is committed to it (see Met.  4 1006a21–31; cf. 7 1012a21–24, 8 1012b5–8). In the case of Sextus, it seems that as soon as he utters a phrase reporting any one of his appearances or affections, he shows that he consciously or unconsciously espouses the LNC in its different dimensions.8 In addition, the polemical discussion of both the three parts into which postAristotelian philosophy was commonly divided (PH II–III, AM VII–XI) and of the six μαθήματα or liberal arts (AM I–VI) requires observance of the LNC so as to be able to comprehend the sense and scope of both the doctrines discussed and the arguments directed against them. This is most clearly seen in the passages in which Sextus tells us how to interpret the arguments the Pyrrhonist directs against the dogmatic theories. On some occasions he explicitly points out that, when he advances arguments yielding negative conclusions, his intention is not to induce us to give our assent to them. Rather, he wants to show that those arguments appear to be equal in force to the opposite arguments, so that we will have to suspend judgment about the truth of the theses that the conflicting arguments purport to establish.9 Also, in the final chapter of PH, Sextus explains that the Pyrrhonist propounds arguments which differ in their persuasiveness because, out of a philanthropic interest, he wants to cure by argument the rashness and the conceit of the Dogmatists. Hence, just as physicians employ remedies different in power to cure the different degrees of the disease that afflicts his patients, so too the Pyrrhonist employs arguments different in persuasive power to cure the different degrees of conceit and rashness that afflict his dogmatic patients (PH III 280–1).10 In these passages, Sextus explains the intention of the arguments he puts forward and it seems plain that it makes a difference to him whether we interpret those arguments the way he asks us to or the opposite way or both ways at the same time. Sextus therefore seems to rely consciously or unconsciously on the LNC in order both that his negative arguments are not construed dogmatically and that his argumentative therapy is clearly understood, since without that law we would be unable to draw distinctions, which in turn would make rational discussion impossible.11 8I say "unconsciously" because it is possible for a person either to adhere to the LNC without being aware of the fact that it is a precondition for meaningful language or to deny the LNC without realizing this fact. 9See PH II 79, 103, II 130, 133, 187, 192, III 29; AM VII 444, VIII 159–60, 298, 476–7, IX 206–7. 10On this passage, see Machuca (2006, pp. 150–3; 2009, pp. 102–9). 11It could be argued that the fact that, in composing his writings, Sextus seems to rely on the LNC does not entail that the Pyrrhonist portrayed in those writings does. However, given that Sextus is describing his own outlook and is therefore a Pyrrhonist, one may claim that that fact shows that, when communicating his stance and discussing with others, the Pyrrhonist seems to be consciously or unconsciously committed to the LNC. 56 D.E. Machuca The second reason for maintaining that the Pyrrhonist adheres to the LNC is that belief in this law is in the origin of the road that leads to Skepticism: as the various views on a given topic cannot all be accepted or held together because of being conflicting or incompatible, it is necessary to carry out an investigation intended to make it possible to choose among them. If this is not in fact possible, then one must suspend judgment about which of the conflicting views, if any, is correct. For instance, given that (i) honey appears sweet to some people and bitter to others (PH I 211, 213, II 63), (ii) it cannot be both at the same time and in the same respect, and (iii) it is not possible for the Skeptic to decide whether it is sweet or bitter, then (iv) he must suspend judgment about how honey really is. In a word, belief in the LNC in its ontological dimension appears to be what makes it possible for the protoSkeptic to become a full-fledged Skeptic: the former begun to philosophize in order to determine which appearances are true and which false (see PH I 12, 26) because opposite attributes cannot hold of one and the same thing at the same time and in the same respect. Given this apparent commitment to the ontological version of the LNC, it also seems clear that the proto-Skeptic thinks that it is impossible for opposite propositions to be true simultaneously and, hence, that it is not rational to hold opposite beliefs at the same time. One could also argue that part of the reason the proto-Skeptic suspends his judgment is that he believes that it is not in fact possible for opposite beliefs to exist at the same time in his mind. Finally, the third reason for attributing to the Pyrrhonist a commitment to the LNC is that this law appears to continue to govern the full-fledged Skeptic's thinking. Indeed, he continues to suspend judgment about all the non-evident matters he has investigated because he can assent neither to any one of the positions in conflict because they appear equipollent, nor to all of them because they are incompatible. With regard to the last two reasons for claiming that the Skeptic endorses the LNC, there are quite a few passages from Sextus' oeuvre which seem to support them explicitly. In the exposition of the Second Mode of Aenesidemus, Sextus observes that we cannot determine what things are by nature, but only report how they appear in relation to each of the differences among humans. The reason is that We will believe (πιστεύσoμεν) either all humans or some of them. If all, we will be attempting the impossible and accepting the opposites (καὶ α'δυνάτoις ε'πιχει ήσoμεν καὶ τὰ α'ντικείμενα πα αδεξóμεθα). But if some, let them say to whom it is necessary to assent. For the Platonist will say to Plato, the Epicurean to Epicurus, and the others analogously. Thus, since they quarrel in an undecidable way (α'νεπικ ίτως στασιάζoντες), they will lead us again to suspension of judgment. (PH I 88)12 This text presents two alternative roads which, in his search for truth, the Skeptic finds blocked: assent to all the positions in conflict and assent to one of them (cf. PH III 33–6). It is precisely because both roads are blocked that he is led to take a third, namely, suspension of judgment. In this passage, we seem to find a reference to the doxastic version of the LNC, since Sextus says that it is impossible to believe 12The translations of the passages from Sextus' works are my own, but I have consulted Annas and Barnes (2000), Bett (1997), Bury (1933–49), Mates (1996), Pellegrin (1997), and Spinelli (1995). 4 Pyrrhonism and the Law of Non-Contradiction 57 all humans because they have opposite opinions. Similarly, in the ethical section of the third book of PH, he tells us: If, then, the things which move by nature move everyone in the same way, whereas we are not all moved in the same way with respect to the so-called goods, nothing is good by nature. The reason is that it is not possible to believe (πιστεύειν) either all the positions expounded above, on account of the conflict [among them], or any one of them. (PH III 182; see also AM VIII 333a) The reason the latter alternative is ruled out is that the person who says that one must trust one of the positions in conflict is a party to the disagreement, and hence cannot be taken as an impartial judge. He will therefore have to be judged along with the others, but given that there is no agreed upon demonstration or criterion, we end up suspending judgment (PH III 182). As for the former alternative – namely, to believe in all the conflicting positions – it seems to be ruled out because it violates the doxastic dimension of the LNC. Indeed, as in the previous quoted passage, Sextus refers to the impossibility of believing in all the positions in conflict. Given both this impossibility and the impossibility of believing in any one of those positions, ε'πoχή is the attitude the Skeptic is compelled to adopt. In the chapter of PH III devoted to a discussion of time, Sextus mentions the various positions about the nature and substance of time that have been adopted and remarks that "either all these positions are true, or all are false, or some are true and some false" (PH III 138). He then rules out each of these alternatives and concludes that "we will not be able to affirm anything about time" (PH III 140), i.e., we will have to suspend judgment. Now, the reason for rejecting the first alternative is that most of the positions reviewed conflict (PH III 138). Sextus seems to endorse the logical or semantic version of the LNC when he says that the positions which make conflicting assertions about time "cannot all be true" (PH III 138). Finally, in the course of his discussion in AM XI of whether there is anything good or bad by nature, Sextus remarks: If, therefore, everything which appears good to someone is altogether good, then since pleasure appears good to Epicurus, bad to a Cynic, and indifferent to the Stoic, pleasure will be simultaneously good and bad and indifferent. But the same thing cannot be by nature contrary things (τὰ ε'ναντία) – simultaneously good and bad and indifferent. (AM XI 74) To all appearances, in this passage Sextus is espousing the ontological version of the LNC, since he excludes the possibility that the same thing may have contrary attributes at the same time. The quotations could easily be multiplied, since in several other passages Sextus says that it is absurd (α' τoπoς) or impossible (α'δύνατoς, α'μήχανoς) for conflicting things to be equally real or true or credible (AM VIII 18, 25, 119), or for the same thing to be simultaneously true and false or real and unreal or existent and nonexistent or credible and incredible or evident and non-evident (e.g., PH I 61, III 113–4, 129; AM I 200; VII 67, VIII 36, 46, 52, 344). But the texts that have been examined are sufficient evidence for the Pyrrhonist's apparent commitment to the LNC in its ontological, logical, and doxastic dimensions and for the claim that the attainment 58 D.E. Machuca and maintenance of his ε'πoχή rest upon such a commitment. In the next two sections, I will try to determine whether this is really the case. This is all the more important because most interpreters believe that Skeptics are indeed committed to the LNC.13 3 The Pyrrhonist's Suspension of Judgment About the LNC The previous analysis has left us with the impression that there is conclusive evidence that conscious or unconscious acceptance of the ontological, logical, and doxastic versions of the LNC is a necessary condition for the communication, the emergence, and the maintenance of Pyrrhonism as well as for the Pyrrhonist's discussion of the dogmatic theories. If this is the case, then this law represents a limit to his suspension of judgment, i.e., his ε'πoχή πε ὶ πάντων does not encompass the truth of the LNC. Close consideration of the conceptual resources of the Pyrrhonian outlook and careful examination of a number of texts from Sextus' writings show, however, that such a conclusion is hasty. It is beyond doubt that the proto-Skeptic is committed to the LNC. However, his commitment to this law does not tell us anything about the scope of the Pyrrhonian ε'πoχή, since he is still nothing but a Dogmatist. The fact that he suspends judgment and hence becomes a full-fledged Skeptic because he can assent neither to all the conflicting positions on a given topic nor to any one of them does not tell us anything about the Pyrrhonian ε'πoχή either. For it is possible that, after suspending judgment, the full-fledged Skeptic realizes that he cannot actually exclude the possibility that opposites might hold of one and the same thing simultaneously, and hence that opposite propositions may be true at the same time. Similarly, he may also realize that he cannot discount the possibility that it might be rational and feasible to hold opposite beliefs at the same time. Now, is there any textual evidence that the Pyrrhonist does not exclude such possibilities? Several texts of Sextus' writings clearly show that the Pyrrhonist considers the thesis that opposite attributes exist in the same object at the same time and in the same respect as one of the alternatives to take into account when confronted with a conflict of appearances, and hence that he does not take for granted that only one of the conflicting appearances corresponds to how the object really is. By the same token, those texts show that the Pyrrhonist does not rule out the possibility that opposite propositions may be true simultaneously and the possibility that it may be rational to hold opposite beliefs at the same time. The reason the Pyrrhonist does not discount such possibilities is that the existence of a conflict of appearances is compatible with three alternatives among which he cannot decide. 13See Rossitto (1981), Maia Neto (1995, p. xv), Harte and Lane (1999, p. 165 with n. 13), Polito (2004, p. 52), Long (2006, p. 54 n. 30), Trowbridge (2006, p. 262 n. 4). Cf. Frede (1996, pp. 6, 12–3 with nn. 47, 19). 4 Pyrrhonism and the Law of Non-Contradiction 59 The first alternative is that no more than one of the conflicting appearances corresponds to how the object really is. This alternative is in fact the outlook ascribed to the Skeptic by some interpreters when explaining why Skepticism is not the same as what we usually understand as relativism.14 They claim that, whereas the Skeptic supposes that x is really either A or B, but cannot decide which one it is, the relativist affirms that x is in itself neither A nor B, but that it is one or the other relative to a given person in certain circumstances. As we will see in what follows, it is a mistake to think that the Skeptic assumes that only one of the conflicting appearances is true. The second alternative which the Skeptic takes into account is that contrary attributes corresponding to conflicting appearances do subsist in the same object, which is the position Sextus ascribes to Heraclitus and Protagoras. It is important to examine the passages of PH in which he presents their views because therein he makes it clear that the Skeptic is not committed to the LNC.15 In the chapter of PH I in which Sextus distinguishes Heracliteanism from Skepticism, he points out that the difference between the two philosophies is clear because Heraclitus "makes dogmatic assertions about many non-evident matters" (PH I 210), whereas Skeptics do not. Sextus is, however, forced to expand on their differences because Aenesidemus and his followers used to say that the Skeptical way of thought is a road towards the philosophy of Heraclitus, because [the fact] that contraries appear with respect to the same thing leads to [the claim] that contraries are real with respect to the same thing (π oηγειται τoυ τα'ναντία πε ὶ τò αυ'τò υ'πά χειν τò τα'ναντία πε ὶ τò αυ'τò φαίνεσθαι), and Skeptics say that contraries appear with respect to the same thing, while Heracliteans go from this also to [the claim] that they exist [with respect to the same thing]. We declare against them that it is not a dogma of the Skeptics that contraries appear with respect to the same thing, but a fact (π αγμα) which manifests itself (υ'πoπίπτoν) not only to the Skeptics, but also to the other philosophers and to all men. (PH I 210) Sextus then explains: The Skeptical way of thought not only does not ever help to the knowledge of the philosophy of Heraclitus, but is an obstacle to it, since the Skeptic denounces all the things about which Heraclitus dogmatizes as being said rashly, thereby opposing the conflagration, opposing [the claim] that contraries exist with respect to the same thing, and with respect to each dogma of Heraclitus ridiculing the dogmatic rashness and, as I said before, uttering "I do not apprehend" and "I determine nothing," which is in conflict with the Heracliteans. (PH I 212) This chapter of PH is crucial for the vexed question of the so-called Heracliteanism of Aenesidemus. Although this is an intriguing issue, it is beyond the scope of this paper.16 The important point for my present purposes concerns both the 14See Annas and Barnes (1985, pp. 97–8), Bénatouïl (1997, pp. 232–3), Pellegrin (1997, pp. 552–3). Cf. Bett (1994, p. 149). 15Scholars have not noticed the importance of these passages for understanding the Pyrrhonist's attitude towards the LNC. 16For discussion of this issue, see Brochard (2002, pp. 284–301), Hankinson (1998, pp. 129–31), Bett (2000, pp. 223–32), and especially Polito (2004), Pérez-Jean (2005), Bonazzi (2007), and Schofield (2007). 60 D.E. Machuca reason Sextus opposes the Aenesideman interpretation of the relation between Heracliteanism and Skepticism and the attitude he adopts towards Heraclitus' claim that contraries hold of one and the same thing (cf. Met.  3, 1005b24–25). Sextus rejects this claim because it is an assertion about a non-evident matter. Indeed, the Skeptic notices the fact that contraries appear to hold of one and the same thing, but given that from this fact by itself one cannot draw the conclusion that contraries do hold of one and the same thing or any other conclusion that goes beyond the realm of appearances, he is forced to suspend judgment. Thus, the Skeptic opposes the Heraclitean view, not because he considers it to be false, but only because he thinks that Heracliteans affirm it without sufficient evidence in its favor and without realizing that there are other possible views which appear to be as plausible as theirs. In other words, the Skeptic suspends judgment about whether Heraclitus' position is true. This is clearly seen in the fact that, to each of the Heraclitean dogmas, the Skeptic applies the phrases oυ' καταλαμβάνω and oυ'δὲν o' ίζω, which express the attitude of suspension of judgment (see PH I 201 and 197, respectively). The chapter under consideration thus makes it clear that the Skeptic does not adhere to the LNC in its ontological dimension, since he does not know whether Heraclitus' position is true or false. It also makes it clear that he is not committed to the logical dimension either, since he would refrain from affirming that contrary propositions cannot be true at the same time. If this is so, then it is plain as well that the Skeptic withholds his assent about whether or not it is rational to hold contrary beliefs at the same time. Just as with Heraclitus, Sextus devotes a chapter of PH to discussing the differences between Skepticism and Protagoras' position (PH I 216–9). There Sextus expounds the elements of the Protagorean stance which determine that there is a fundamental difference between it and Pyrrhonism: [Protagoras] declares, indeed, that matter is in flux and that, given that it is in flux, additions continuously take place in lieu of the effluxions, and that the senses are rearranged and altered on account of the ages and the other constitutions of the bodies. He also says that the reasons (τoὺς λóγoυς) of all things subsist (υ'πoκεισθαι) in matter, so that matter, insofar as it is itself concerned, can be all the things that appear to all (πάντα ει'ναι o'σα πασι φαίνεται). Men grasp different things at different times, depending on their different conditions: someone in a natural state apprehends (καταλαμβάνειν) those things in matter which can appear to those in a natural state, someone in an unnatural state apprehends what can appear in an unnatural state. And further, depending on age, and according to whether we are sleeping or waking, and by virtue of each sort of condition, the same account holds. Therefore, according to him, man becomes the criterion of the things that are, for all things that appear to men also exist, and the things that appear to no men do not exist. We see, then, that he dogmatizes about matter being in flux and about the reasons of all things that appear subsisting in it, things which are non-evident and about which we suspend judgment. (PH I 217–9) For my present purposes, it does not matter whether this account of Protagoras' position is historically accurate, or whether it is entirely compatible with that found at AM VII 60–4 in the course of the discussion of the criterion of truth. What does matter is Sextus' attitude towards the position he ascribes to Protagoras in the quoted passage. Like the Heraclitean and the Skeptic, Protagoras notices the conflict of 4 Pyrrhonism and the Law of Non-Contradiction 61 appearances, since he points out that things appear differently to people by virtue of the various states in which they find themselves. Like the Heraclitean but unlike the Skeptic, Protagoras goes beyond the realm of τὰ φαινóμενα, since he maintains that there is correspondence between what appears to a person by virtue of the state in which he finds himself and what is present in matter. That is to say, Protagoras takes τὰ φαινóμενα as an epistemic criterion, since anything that appears corresponds to an objective feature of reality, which is why Sextus uses the verb καταλαμβάνειν. Now, the beginning of the passage seems to suggest that the same thing possesses different attributes or properties only successively; that is to say, during its permanent change, each thing adopts different attributes or properties in parallel with the alterations experienced by the individuals which apprehend them. The rest of the passage, however, shows that, according to the Protagorean position, opposites coexist simultaneously in the same thing. Indeed, given that the individual man is the criterion of truth, everything that appears to anyone is real, and it is clear that things appear differently to different men at the same time by virtue of the different states in which they find themselves (cf. Met.  4 1007b20–25; 5 1009a5–15). For instance, if a certain portion of honey appears at the same time sweet to a healthy person but bitter to a sick person, then one must infer that both appearances are equally true, i.e., that the same portion of honey is both sweet and bitter. Thus, in the quoted passage Sextus ascribes to Protagoras a position similar to that which he ascribes to Heraclitus. Just as in the case of the Heraclitean theory, Sextus does not oppose the Protagorean theory because he considers it to be false, but only because he takes it to be one view about the conflict of appearances which appears as plausible as the others. He explicitly points out at the end of the quoted passage that the Skeptic suspends judgment about that theory. Therefore, given that the Skeptic neither affirms nor denies the truth of the Protagorean position, we must conclude that he does not embrace the ontological, logical, or normative doxastic versions of the LNC. In addition, since the Skeptic is aware that Heraclitus and Protagoras affirm that contraries subsist in one and the same thing at the same time, he must also be aware that, to all appearances, there are people who are in fact able to hold contrary beliefs at the same time. Both thinkers believe, e.g., that honey is sweet and bitter simultaneously, and given that, unlike Aristotle (see Met.  3 1005b23–26 in relation to Heraclitus), the Skeptic has no a priori reason for questioning the sincerity of what they claim to believe, he cannot adhere to the descriptive doxastic version of the LNC either. The third possible view about the conflict of appearances which the Skeptic takes into consideration is that, e.g., honey is in itself neither sweet nor bitter, but appears to be one way or the other only by virtue of the diversity of species, individuals, or senses that perceive it or by virtue of any other factor. This kind of position is attributed to Democritus in the chapter of PH in which are expounded the differences between his philosophy and Skepticism. Sextus indicates that the two philosophies have been thought to be similar because Democritus' theory seems to make use of the same material as we do. For from the fact that honey appears sweet to some but bitter to others, they declare that Democritus concludes that the same thing is neither sweet nor bitter, but utters the expression "not more" (oυ' μαλλoν), which is 62 D.E. Machuca Skeptical. The Skeptics and the followers of Democritus, however, employ the expression "not more" differently, since the latter apply the expression to the fact that neither of the alternatives is the case (ει'ναι), whereas we apply it to the fact of ignoring whether one of the things that appear is both or neither (α'γνoειν πóτε oν α'μφóτε α oυ'θέτε óν τι 'εστι των φαινoμένων). Hence with respect to this we differ. But the distinction becomes most evident when Democritus says "in reality atoms and void," since he says "in reality" instead of "in truth." And I regard it as superfluous to say that, when he says atoms and void exist, he has differed from us, even though he starts from the anomaly of the things that appear (της α'νωμαλίας των φαινoμένων). (PH I 213–4) The alleged similarity between the Democritean and the Skeptical philosophies is based on two elements: both start from the conflict of appearances and both use the expression oυ' μαλλoν. However, from the anomaly of the things which appear Democritus takes a road that leads him to a dogmatic thesis, which he expresses by way of that expression. Indeed, Democritus uses oυ' μαλλoν in its usual sense, namely, to indicate that neither of the conflicting appearances corresponds to what the object is like in itself. By contrast, the Skeptic employs oυ' μαλλoν to convey his ignorance about whether both appearances are true or neither is – that is to say, the Skeptical oυ' μαλλoν is a way of expressing the state of ε'πoχή. Taking also into account what Sextus says about the expression oυ' μαλλoν at PH I 188–91, one should say that this expression expresses the Skeptic's ignorance about whether (i) only one of the conflicting appearances is true, or (ii) both are true, or (iii) neither is true. Hence, Sextus makes it clear that the Democritean position is one possible account of the conflict of appearances which goes beyond what the Skeptic has been able to establish, since he has noticed and described such a conflict but has not been capable of determining what things are really like. In sum, the chapter devoted to explaining the differences between Democritus and the Skeptic, too, shows that the latter is not committed to the LNC in its ontological, logical, and normative doxastic dimensions.17 The reason the Pyrrhonist suspends judgment about which of the three alternatives is true is that they strike him as equipollent or equally persuasive. Both philosophers and ordinary people, Sextus tells us at PH I 210–1, notice the conflict of appearances. Most of them adopt a dogmatic position in the face of this conflict, i.e., they make assertions which go beyond that which appears. By contrast, the Pyrrhonist cannot determine which one of the three alternatives is correct because, up to now at least, he has not found a criterion which would allow him to resolve the 17In several passages, Sextus jointly mentions the three alternative positions that have been examined and explicitly remarks that the Skeptic is unable to choose among them, which is of course to be understood in the sense that he suspends judgment about which one corresponds to the way things really are (see PH II 53; AM VII 369, VIII 213–4, 354–5). These passages and those examined in the main body of the text show that Sextus time and again makes it clear that the Skeptic is aware of the various positions the Dogmatists have adopted in the face of the disagreement among appearances, and that he does not incline to any one of those positions. The reason is simply that they are parties to a second-order disagreement he has not been able to resolve. Hence, once again, the Skeptic does not rule out the possibility that the ontological, logical, and doxastic versions of the LNC may be false. 4 Pyrrhonism and the Law of Non-Contradiction 63 dispute among them. This is why he limits himself to describing the various ways in which things appear to him. The mere existence of an as yet unresolved conflict among appearances points to no specific state of affairs, i.e., it does not establish that only one of the conflicting appearances is true, or that all are true, or that none is true. Thus, the Pyrrhonist refrains from endorsing any of these views because none of them follows from the mere fact that contraries appear to hold of one and the same thing. He cannot take a stand on the first-order conflict of appearances because he cannot settle the second-order disagreement among the three dogmatic positions that have been examined. We must therefore consider the Pyrrhonist's adoption of ε'πoχή as a fourth alternative attitude one may adopt in the face of a conflict of appearances. Besides his inability to choose among the three dogmatic positions just referred to because they are, so to speak, underdetermined by the mere conflict of appearances, there are deeper reasons for the Pyrrhonist's suspending judgment about the truth of the different versions of the LNC. The first that comes to mind is the disagreement about the truth of that law. Indeed, those who affirm that only one of the conflicting appearances can be true embrace the LNC. By contrast, those who affirm that all the conflicting appearances are true reject that law. The Pyrrhonist considers this disagreement to be as yet irresolvable because any attempt to justify one of the sides in dispute can be attacked by strong arguments. Against those who deny the LNC, the Pyrrhonist would make use of the Aristotelian arguments found in Metaphysics . And against the attempt to justify endorsement of the LNC, he would take Aristotle's claim that the endeavor to demonstrate everything, including the LNC, leads to an infinite regress (Met.  3 1006a8–9) as a recognition that the attempt to justify that law by inferring it from other premises is caught in the Agrippan mode deriving from regress ad infinitum (PH I 166). Unlike Aristotle, he would not regard this as a reason for accepting the LNC as a first principle which as such does not require a proof. Rather, he would argue that the mode deriving from regress ad infinitum represents a problem for the justification of the LNC. Similarly, to the Aristotelian claims that the LNC does not depend on anything else to be known (Met.  3 1005b11–17) and that it cannot be apprehended by demonstration (Met.  6 1011a8–13), the Pyrrhonist would respond by pointing out that they amount to an arbitrary assumption, that is, that they are caught in the Agrippan mode deriving from hypothesis (PH I 168). This shows once again that it does not seem possible to justify commitment to the LNC. Finally, Aristotle maintains that the LNC is the highest or ultimate principle of all demonstrations (Met.  3 1005b32– 33), which implies that every proof of the LNC which is not refutative, but intends to establish it directly, necessarily presupposes it. The factual impossibility of offering a direct demonstration of the LNC without making use of it would not be taken by the Pyrrhonist as evidence that it is a first principle which we must endorse. Rather, he would emphasize that this fact shows that it is not possible to demonstrate directly the LNC without begging the question, and that this, too, represents a problem for anyone trying to justify endorsement of that law.18 It is worth emphasizing that the 18For the Pyrrhonist's use of the charge of petitio principii, see e.g. PH I 59 and II 36. 64 D.E. Machuca Pyrrhonist does not deny the truth of the LNC, but only observes that, given that its justification appears to be aporetic, we end up in suspension of judgment.19 4 The Pyrrhonist's Non-Dogmatic Observance of the LNC As already noted, in Metaphysics  Aristotle argues that, as soon as those who reject the LNC say something meaningful, they show by this very act that they are committed to this law (see Met.  4 1006a21–31; cf. 7 1012a21–24, 8 1012b5–8). Indeed, if a word or a proposition could have opposite meanings at the same time and in the same respect, then what it intends to convey would be unclear; and if this happened with every word or proposition, then communication would be impossible. Hence, even those who deny the truth of the LNC presuppose it in order to make clear what they mean by such a denial – otherwise their words would be understood both the way they intend them and the opposite way. One could maintain that this argument may also be effectively used against the person who suspends judgment about the truth of the LNC, since once the Pyrrhonist utters a meaningful word either when expounding his own outlook or when discussing a dogmatic theory, he shows that it is not possible for any and every word or proposition to have opposite meanings.20 I think that the Pyrrhonist would respond that this argument does not prove that reality is such that opposite attributes cannot belong to the same thing at the same time and in the same respect, but at most that people cannot help observing the LNC when uttering words they take to be meaningful. Thus, Aristotle's maneuver at most shows that people observe, not the ontological version of this law, but what might be regarded as a variant of the doxastic version. The Pyrrhonist would explain his observance of the LNC when communicating his philosophical stance and arguing against the Dogmatists by saying that, as a matter of fact, he has been unable to communicate his thought and discuss with others without his observing that law. 19The ancient Pyrrhonist would also have had strong grounds for suspending judgment about the truth of the LNC as an all-embracing principle if he had witnessed the development of so-called paraconsistent logic since the second half of the twentieth century. First, he would have pointed out that there is a disagreement between the champions of traditional logic who endorse the LNC, on the one hand, and, on the other, the defenders of dialetheism who maintain that there are some true contradictions – as is shown by classic logical paradoxes such as those of the Liar and the Barber – thereby accepting that sometimes p and ¬p may be true at the same time and in the same respect. Second, the Pyrrhonist would have observed that at least so far that disagreement appears unresolvable, so that he is constrained to suspend judgment about the status of the LNC as a fundamental logical principle. (The term "dialetheism" was coined by Graham Priest and Richard Routley in 1981. For a basic presentation of this logical theory, see Priest (2004), also Horn (2006, section 4). On paraconsistent logic in general, see Priest and Tanaka (2007).) 20It is worth noting that it is only a total denial of the LNC (i.e., the claim that all contradictory predicates equally apply and do not apply) that seems to lead to a breakdown of meaningful language. It may be argued that the acceptance of some contradictions is compatible with meaningful language. But the important point here is that the Pyrrhonist's linguistic practice seems to show that he does not endorse a total denial of the LNC and, hence, that in at least some cases he accepts the truth of this law. 4 Pyrrhonism and the Law of Non-Contradiction 65 His apparent endorsement of the LNC should therefore be interpreted as his following something that imposes itself upon him. That is to say, out of psychological constraint, he thinks and speaks in accordance with the LNC, even though he can conceive of and express the possibility that this law may not correspond to the way things really are, that is, even though he cannot rule out the possibility that things may have opposite properties or qualities at the same time and in the same respect. Hence, of the three versions of the LNC presented at the outset, the doxastic version seems to be that which better describes the Pyrrhonist's observance of that law. It is clear, however, that he cannot endorse this version of the LNC because he does not affirm that it is irrational or unfeasible for anyone to hold contrary beliefs at the same time. Indeed, with respect to the normative doxastic version of the LNC, given that he cannot rule out the possibility that contraries may subsist in the same thing at the same time and hence that contrary propositions may be true simultaneously, he cannot affirm that it is irrational to hold contrary beliefs at the same time. As for the descriptive doxastic version, I argued in the previous section that it appears to him that certain people, such as Heraclitus and Protagoras, in fact hold contrary beliefs simultaneously. Therefore, the Pyrrhonist does not embrace a view about what humans in general should or can believe, i.e., he does not dogmatize about the nature of the human mind and the way it should or does function. In sum, although the Pyrrhonist is not committed to the truth of the LNC, in certain circumstances he feels psychologically constrained to think in conformity with this law and to assent to it in the sense of simply acquiescing in or yielding to it in a way similar to that in which he assents to the appearances or affections which are forced upon him (see PH I 13, 19, 29, 193). It seems we can formulate what we may call a "psychological" version of the LNC which the Pyrrhonist finds himself constrained to observe21: Psychological version: up to now I have, as a matter of fact, been unable to assent to two or more conflicting appearances at the same time.22 The reason I have expressly introduced subjective and temporal qualifications is that these kinds of restrictions are constantly used by Sextus in his account of the sense in which the Skeptical φωναί must be interpreted (PH I 187–208). Such qualifications manifest the Pyrrhonist's distinctive caution that makes him limit the range of his claims to his personal experience. He makes no normative claim, but a merely descriptive one. It is worth noting that his observance of the psychological version of the LNC would make it possible to reply to the following objection: the Pyrrhonist's adoption of ε'πoχή after considering the second-order disagreement about the truth of the LNC depends upon endorsement of this law. For the reason he suspends judgment is that he can assent neither to one of the second-order positions in conflict 21Cf. McPherran (1987, pp. 315, 317–8) and Nussbaum (1994, p. 308). Spinelli (1995, p. 244) also seems to think that the Pyrrhonist suspends judgment about the truth of the LNC. 22This formulation encompasses both dogmatic assent to epistemic appearances and non-dogmatic assent to non-epistemic appearances. For a fine discussion of the distinction between two types of assent in both Pyrrhonism and Academic skepticism, see Frede (1997b). 66 D.E. Machuca because they appear to be equally persuasive, nor to all of them because they are incompatible. In other words, in this case the Pyrrhonist's appearance expressed in the proposition "It appears to me that not (p and ¬p)" must be epistemic. He would reply to this objection by saying that his reason for suspending judgment in the face of such a second-order disagreement between equipollent positions is rather that, in point of fact, he finds himself psychologically unable to give his assent to all the rival positions simultaneously. It is therefore not a matter of dogmatic commitment to the LNC. Concerning the Pyrrhonist's observance of the psychological version of the LNC, it is also important to remember something Sextus says when explaining the Pyrrhonist's criterion of action. He tells us that τὰ φαινóμενα are such a criterion (PH I 21–2) and induce the Pyrrhonist's assent involuntarily (PH I 19). This criterion is fourfold, one of its parts being the "guidance of nature," which is that guidance by virtue of which the Pyrrhonist is naturally capable of perceiving and thinking (PH I 24). One may reasonably suppose that this natural capability of thinking includes the observance of the psychological version of the LNC, to which he assents involuntarily and non-dogmatically, i.e., without making any assertion about its epistemic credentials (cf. McPherran 1987, p. 318). This lack of dogmatic commitment is explicitly made clear by Sextus when he points out that the Pyrrhonist follows the appearances without holding opinions (α'δoξάστως) – i.e., without believing or disbelieving that things are as they appear to him to be – and for the sole reason that he cannot remain utterly inactive (PH I 23–4). As already noted, the Skeptic communicates in conformity with the LNC, which must be accounted for by his observing a linguistic version of this law. He would explain this as a convention that allows him both to make himself understood and to understand others, which does not presuppose any view about the real nature of things or about the nature of our mind.23 This non-dogmatic version of the LNC could be formulated thus: Linguistic version: in order for me to have meaningful or intelligible communication within my linguistic community, I have so far been unable as a speaker to assign opposite meanings to every word at the same time and in the same respect, and as a hearer to interpret every word as having opposite meanings at the same time and in the same respect. Observance of this linguistic version of the LNC on the part of the Skeptic does not represent a dogmatic commitment simply because he interprets it as an empirical claim which merely expresses a linguistic convention that makes communication possible among the members of his group. It is clear that this version of the LNC also exerts some kind of psychological constraint on the Skeptic. Against those who reject the LNC, Aristotle also argues that, by choosing one course of action over another, they show that they believe that things are one way rather than another (Met.  4 1008b12–27). For instance, a person does not jump 23Cf. Stough (1984, pp. 156–7). For a critical analysis of the Skeptic's general attitude towards language, see Cauchy (1986), Caujolle-Zaslawsky (1986), and Corti (2009). 4 Pyrrhonism and the Law of Non-Contradiction 67 out of a plane without wearing a parachute if he does not want to die. The reason seems to be twofold: (i) it is not the case that jumping out of a plane without wearing a parachute is and is not a cause of death, and (ii) a person cannot both believe and not believe that jumping out of a plane without wearing a parachute causes death. Thus, even though the refusal to say something on the part of those who deny, or suspend judgment about, the truth of the LNC prevents them from betraying their actual endorsement of this law, they cannot avoid that their actions do reveal their conscious or unconscious commitment to it. This argument does not seem to represent a serious difficulty to the Pyrrhonist, since his criterion of action seems to be complex enough to allow him to choose among different courses of action. The Pyrrhonist prefers one course of action to another, not because he believes that things are really one way rather than another, but simply because some appearances strike him as persuasive from a merely psychological point of view, so that he is not at the same time persuaded and unpersuaded by those appearances in such circumstances.24 In other words, he acts one way rather than another because certain appearances strike him one way rather than another. It is precisely because he does not find conflicting appearances equally persuasive psychologically speaking that he can make decisions and act upon them. When conflicting appearances strike him with the same psychological force, he refrains from acting in accordance with either of them. From an external viewpoint, the Pyrrhonist's actions can be interpreted as though he was committed to the ontological and doxastic versions of the LNC, but this by itself is not sufficient evidence to ascribe such a commitment to him. It would also be necessary to prove that action is not possible in the absence of beliefs about how things really are.25 In relation to the previous remarks, it must be noted that there is also a practical reason for the Skeptic's non-dogmatic observance of the LNC. In the chapter of AM XI which examines whether it is possible to live happily if one believes that there are things good or bad by nature, Sextus points out: If, then, someone should assume that everything which is in any way pursued by anyone is by nature good, and everything which is avoided is by nature to be avoided, he will have a life which is unlivable, being compelled simultaneously to pursue and avoid the same thing – to pursue it insofar as it has been supposed by some a thing to be chosen, but to avoid it insofar as it has been deemed by others a thing to be avoided. (AM XI 15) Similarly, in a later chapter in which he discusses whether there is a τέχνη relating to life, Sextus argues: The skill which is claimed to relate to life, and thanks to which they suppose that one is happy, is not a single skill but many and discordant, such as the one according to Epicurus, and the one according to the Stoics, and the one of the Peripatetics. Either, then, one must follow all alike or only one or none. And to follow them all is something impracticable 24On this non-epistemic kind of persuasiveness, particularly in relation to arguments, see Machuca (2009, pp. 116–23). 25This is not the place to address the vexed question of whether the Pyrrhonist can live his Skepticism. For discussion of this issue, see esp. Burnyeat (1997), also Bailey (2002, chapter 11) and Comesaña's paper in this volume. 68 D.E. Machuca owing to the conflict [among them]; for what this one commands as a thing to be chosen, that one forbids as a thing to be avoided, and it is not possible to pursue and avoid the same thing simultaneously. (AM XI 173–4) The end of this passage clearly formulates what can be interpreted as a practical version of the LNC: Practical version: it is impossible to pursue and avoid the same thing at the same time and in the same respect, i.e., it is impossible to perform and not to perform a given action at the same time and in the same respect. This practical formulation of the LNC places a constraint on the epistemic or nonepistemic appearances we can accept as guides for action: it is not feasible to follow at the same time any two contrary epistemic or non-epistemic appearances when making practical decisions simply because we cannot act according to both. Now, the Pyrrhonist would clearly regard this formulation of the LNC as dogmatic, since it makes a universal claim about what kind of actions cannot be performed, which seems to presuppose the ontological version. Indeed, the reason one cannot eat simultaneously a piece of sweet and bitter honey is that it seems not to be possible for the same piece of honey to be sweet and bitter at the same time, and the reason one cannot simultaneously walk and stay still is that things seem to be by nature such that contrary actions cannot be performed at the same time. The Pyrrhonist would be more comfortable with the following qualified practical version of the LNC: Qualified practical version: up till now I have, as a matter of fact, been unable to pursue and avoid the same thing at the same time and in the same respect, i.e., to perform and not to perform the same action at the same time and in the same respect. The Pyrrhonist would point out that, even though he suspends judgment about the dogmatic versions of the LNC, he is still subject to the practical constraint in question because this seems to be independent of the truth of those versions. Indeed, his qualified practical formulation of the LNC is an empirical claim which does not necessarily presuppose the dogmatic assertion that the structure of reality is such that one cannot perform opposite actions at the same time and in the same respect. In keeping with his characteristic caution, the Pyrrhonist would say that, in stating the qualified practical version of the LNC, he is just reporting what has happened to him, without at the same time affirming that this version is universally true. It is crucial to note that the Pyrrhonist would not present the versions of the LNC observed by him as versions of the law or principle of non-contradiction. The reason is simply that he does not assert that those versions are objectively and universally true, but merely presents them as descriptive reports of his own experiences. The nature and status of these phenomenological reports is the same as that of the Skeptical φωναί. Hence, I speak of the Pyrrhonist's observance of certain versions of the LNC only as a matter of convenience. Now, my account of these non-dogmatic reports might give rise to a worry about whether the Pyrrhonist can make modal claims, namely, claims about possibility and necessity. The reason is that there cannot be an appearance of a possibility or a necessity and the Pyrrhonist cannot say that such claims are descriptive reports of some of his πάθη. For instance, he can 4 Pyrrhonism and the Law of Non-Contradiction 69 say "I feel cold," but not "It is impossible for me to feel cold and warm at the same time and in the same respect"; or "This argument non-epistemically appears sound to me," but not "It is impossible that this argument non-epistemically appear both sound and unsound to me at the same time and in the same respect." Likewise, he can say "As a matter of fact, I have used the LNC in communication," but not "It has so far been impossible for me to communicate without using the LNC"; or "I have not performed opposite actions," not "It has thus far been impossible for me to perform opposite actions." The same holds in the case of claims about necessity, since it seems the Pyrrhonist can say "Up till now I have not assented to two conflicting appearances at the same time," but not "Up till now I have been psychologically constrained not to assent to two conflicting appearances at the same time." Similarly, it seems he can say "I suspend judgment," but not "It is necessary that I suspend judgment" or "I am compelled to suspend judgment," something which, as we will see in the next section, Sextus repeatedly says in his exposition of the Ten and the Five Modes. It is clear that the Skeptic cannot make modal claims about what is and is not objectively possible or necessary, since these would be dogmatic assertions about what is non-evident – and one may assume that, when Sextus does make such claims, he is merely arguing dialectically. But the Skeptic can make descriptive reports of both certain spontaneous reactions he has had and his past failed attempts. For instance, knowing about Heraclitus' and Progatoras' views, the Pyrrhonist might have unsuccessfully tried to, e.g., communicate with another person by ascribing opposite meanings to everything he and his interlocutor say. He might as well have tried to simultaneously assent to conflicting appearances but failed, or might have tried to also feel warm while he was feeling cold but still felt only cold. Likewise, he might have tried not to suspend judgment after the consideration of a disagreement among apparently equipollent arguments, but as a matter of fact still suspended judgment despite his attempt. Hence, when formulating the versions of the LNC observed by the Pyrrhonist in terms of a de facto inability or constraint to do something, I obviously do not mean to refer to an objective impossibility or necessity. Those versions are rather records of the Pyrrhonist's past experiences. Now, if the Pyrrhonist suspends judgment about whether opposite attributes can coexist in the same thing at the same time, about whether opposite propositions can be true simultaneously, about whether opposite beliefs should or may be held at the same time, and about whether it is objectively possible to perform opposite actions simultaneously, how are we to explain the passages which seem to show unequivocally that he is committed to the dogmatic versions of the LNC? That is to say, why does Sextus claim in those passages that it is absurd or impossible to violate the LNC in its ontological, logical, doxastic, and unqualified practical versions? One possible answer is of course that he is just being inconsistent. Another possible answer consists in interpreting those passages in the light of the ad hominem argumentation characteristic of Pyrrhonism.26 Even though the Pyrrhonist does not 26Cf. McPherran (1987, p. 318; 1990, p. 140 n. 7). 70 D.E. Machuca accept the dogmatic versions of the LNC in propria persona, this does not in any way prevent him from employing them in the argumentative therapy by means of which he expects to cure his dogmatic patients (see PH III 280–1). The reason is simply that, since most of the Dogmatists are committed to the ontological, logical, doxastic, and unqualified practical formulations of the LNC, using these formulations in the therapeutic arguments intended to induce ε'πoχή is the best way to cure the conceit and rashness that afflict the Dogmatists. In Section 2, I presented three reasons for affirming that the Pyrrhonist is committed to the LNC. It is now time to determine whether the attitude towards this law that I have ascribed to him can explain away the evidence on which those reasons were based. With regard to the first of them, the Pyrrhonist would grant that conscious or unconscious observance of the linguistic version of the LNC reveals itself as a necessary condition for meaningful communication within his linguistic community. But he would also point out that this does not by itself imply that the ontological and logical versions of the LNC are true, nor that it is irrational or impossible for anyone to hold contrary beliefs at the same time. As regards the second reason, he would observe that, when he approached philosophy and during the philosophical journey that led him to Skepticism, he was committed to the dogmatic versions of the LNC, but that once he became a full-fledged Pyrrhonist, he abandoned that commitment. As for the third reason for maintaining that the Skeptic espouses the dogmatic versions of the LNC, he would make two remarks. First, he would say that his suspension of judgment does not actually rule out the possibility that contrary properties may belong to the same thing at the same time and in the same respect, since this is one of the alternatives he takes into account when dealing with the conflict of appearances. Second, he would observe that, when in his arguments against the Dogmatists he makes use of the ontological, logical, doxastic, and unqualified practical versions of the LNC, he does so only dialectically, because they are accepted by the Dogmatists against whom he is arguing.27 5  Eπoχή, Agrippa's Modes, and Rules of Inference The view that the Skeptic is not committed to the dogmatic formulations of the LNC and that he makes use of them solely for dialectical purposes is, as I will show in what follows, in keeping with his attitude towards ε'πoχή and with his use of 27It could be argued that my interpretation of the Skeptic's observance of certain versions of the LNC is obvious as an extension of what Sextus says about the Skeptic's following the appearances, since the Skeptic's use of this law is just the law itself prefaced by "It seems to me that." This objection, however, overlooks two facts. First, there is still fierce disagreement about whether all of the Pyrrhonist's appearance-statements are non-epistemic (see n. 7), and hence we cannot simply take for granted that he is not committed to the truth of the LNC. Second, most scholars who have referred to the Pyrrhonist's attitude towards the LNC have assumed such a commitment without exploring the question in any depth (see n. 13). 4 Pyrrhonism and the Law of Non-Contradiction 71 the Agrippan modes and the rules of inference. If this is indeed the case, then the interpretation of the Pyrrhonist's observance of the LNC which I have proposed will gain further support. With regard to the state of ε'πoχή, the Pyrrhonist does not take it to be the conclusion of an argument he considers to be sound, i.e., he does not claim that, given certain true premises and certain argument schemes or inference rules, every rational person must draw a certain conclusion, namely, that he must suspend judgment. Such a claim would be problematic for the Pyrrhonist because it implies the existence of proof or demonstration (α'πóδειξις), but Sextus explicitly points out that the Pyrrhonist suspends judgment about its existence (see PH II 134, 192; AM VIII 328; cf. PH I 60).28 This is the reason he makes it clear that ε'πoχή is rather a state psychologically imposed upon him, i.e., it is the psychological effect of being confronted with claims, arguments, or theories which appear equipollent or equally persuasive to him. Indeed, Sextus observes that the Skeptical way of thought is called "'suspensive' because of the affection that comes about in the inquirer after the investigation" (PH I 7). To the extent that it is a πάθoς, suspension of judgment is something that imposes itself upon the Pyrrhonist and, hence, something he accepts involuntarily, in much the same way in which he accepts such πάθη as the feelings of hunger and thirst, and those of coldness and heat (PH I 13, 19). Hence, ε'πoχή is a state that supervenes on him as a result of his own psychological constitution by virtue of which he cannot avoid withholding his assent whenever conflicting epistemic appearances strike him as equipollent.29 It is also worth noting that, in his exposition of the Ten and the Five Modes of ε'πoχή, Sextus usually says that because of what has been argued it is necessary (δει, α'νάγκη, α'ναγκαιoν) to suspend judgment or that we are compelled (α'ναγκάζεσθαι) to do so (PH I 61, 78, 89, 121, 128, 129, 163, 170, 175, 177). Although one could construe this necessity as rational, it is also possible to interpret it as merely psychological, i.e., as independent of whether the adoption of ε'πoχή is a conclusion that validly and necessarily follows from a valid inference. There is therefore a clear distinction between logical necessity and psychological constraint. The way in which the latter works independently of any rational requirement may perhaps be seen more clearly in the following case. Suppose that a person believes that it is rationally required to refrain from assenting to any one of the conflicting positions on a given topic when they appear to be epistemically 28This is why I find unacceptable Thérèse Pentzopoulou-Valalas' claim that the Skeptic has "une foi profonde en l'efficacité de l'argumentation ainsi qu'en la force du syllogisme en tant que moyen d'apodicticité" (1994, 240). 29This interpretation of the relation between ε'πoχή and the arguments which induce it is generally accepted by scholars. See McPherran (1987, pp. 318–20; 1990, p. 140 n. 6), Barnes (1990, pp. 2610–1), Hankinson (1994, p. 49 n. 15), Pellegrin (1997, pp. 546–7), Annas (1998, 196), Palmer (2000, p. 372 n. 22), Striker (2004, p. 16), Grgić (2006, p. 142). See Annas and Barnes (1985, 49) and Barnes (2000, p. xxi) for the claim that the texts suggest that the relation may also be interpreted as a requirement of rationality. For the view that the relation must be understood this way, see Perin (2006, pp. 358–9 with n. 32). For the rejection of the psychological interpretation, see also Lammenranta (2008, pp. 15–9). 72 D.E. Machuca equipollent. One could argue that, if that person attempted to ground his belief, he would be caught in the web woven by the Agrippan modes of reciprocity, infinite regress, and hypothesis. It might well be the case that, despite his inability to provide a proof capable of establishing that it is logically necessary to refrain from assenting to any one of the theses in conflict when they appear equally credible, the person in question still finds himself psychologically compelled to suspend judgment. That is to say, even though he cannot provide a rational justification for his withholding of assent, this does not prevent him from ending up suspending judgment all the same. I think that that is the situation in which the Pyrrhonist finds himself and that he would say something like this: "Up till now this set of arguments have in fact been able to induce the state of ε'πoχή in me and others, but I do not know whether those arguments are sound and, hence, whether ε'πoχή is a conclusion that logically and necessarily follows from them." One could say that the Skeptic's suspensive attitude is rational only in the sense that ε'πoχή is a reaction triggered after the careful consideration of arguments pro and con a given thesis, but not in the sense that he is committed to ε'πoχή as the necessary conclusion of an argument or set of arguments he deems sound. If this interpretation is correct, then the factor which explains the Pyrrhonist's suspension of judgment is the same as that which accounts for his observance of the psychological version of the LNC. In this regard, it is also important to note that, just as the Skeptic does not maintain that everyone observes that version of the LNC, so too does he refrain from affirming that the kind of psychological constraint that compels him to suspend judgment affects every person who considers the Skeptical arguments. For just as it is a fact that there are people who claim to believe that contraries subsist in the same thing at the same time and in the same respect, so too is it a fact that most people continue to embrace dogmatic theories or assertions even after having been subjected to the Skeptical argumentative treatment. In the case of ε'πoχή, Sextus also distinguishes between the psychological and the ontological spheres and makes it clear that he does not believe that this state of mind has an ontological foundation. For he says that the φωνή "I suspend judgment" makes it clear that "objects appear to us equal in respect of credibility and incredibility. Whether they are equal, we do not affirm: we say what appears to us about them, when they manifest themselves to us" (PH I 196). Similarly, when explaining the notion of α'φασία, which is a form of referring to ε'πoχή, Sextus observes that "it is clear that we do not use 'non-assertion' to mean that objects are in their nature such as to move us necessarily to non-assertion, but rather to make it clear that now, when we utter it, we feel in this way with regard to these matters under investigation" (PH I 193). Thus, the Skeptic does not affirm that ε'πoχή has an ontological foundation but only indicates that it is the result of the way things appear to him or the way he is affected. This is in perfect accord with his attitude towards the LNC, since he does not adhere to the ontological version of this law but merely observes a psychological version of it. If we consider the ad hominem character of the Skeptical argumentation, it is possible to argue that, in the passages in which Sextus does make ε'πoχή the conclusion of an argument or an inference (PH I 36, 99, 123, 135, 140, 144), what he is 4 Pyrrhonism and the Law of Non-Contradiction 73 actually saying is that, given the rational principles followed by the Dogmatists in their reasoning, they are obliged to suspend judgment. That is to say, given certain principles, one must refrain from making any assertions about what has so far been a matter of an undecidable dispute. If this is correct, then once again the interpretation of the Pyrrhonist's qualified observance of the LNC that has been proposed is in perfect accord with the attitude he adopts towards ε'πoχή. As regards the Pyrrhonist's use of the Five Modes of Agrippa – namely, disagreement, relativity, infinite regress, reciprocity, and hypothesis (PH I 164–77) – some interpreters have rightly pointed out that he is not committed to the conception of rational justification underlying the latter three modes. Rather, the Agrippan modes are parasitic on the Dogmatists' own theories of rational justification, so that they are essentially ad hominem arguments.30 However, I think this is not all that can be said about the Pyrrhonist's attitude towards the Five Modes, since it may also be argued that there is a way in which he assents to them. Indeed, one may suppose that his philosophical and cultural milieu has influenced him in such a way that the conception of rational justification at work in the Agrippan modes still exerts some kind of psychological force on him. As noted earlier, the proto-Skeptic was a Dogmatist who was committed to certain logical principles and criteria of justification. It is likely that this past commitment still exerts an influence on the full-fledged Skeptic in such a way that in his daily life he spontaneously finds unacceptable a piece of reasoning which is circular or a chain of justification which does not come to an end or a claim made arbitrarily without any backing up. Of course, this kind of assent is not to be interpreted as dogmatic, but as a part of the Pyrrhonist's natural capacity to think and, hence, as a part of his general psychological or non-epistemic assent or yielding to the appearances. Thus, the Pyrrhonist's attitude towards the Agrippan modes is in perfect accord with his attitude towards the LNC, since he is not committed to them, but rather non-dogmatically assents to them and also uses them for dialectical purposes. It remains to consider the Pyrrhonist's use of rules of inference in his arguments. It might be thought that, even though the use of ad hominem arguments permits the Pyrrhonist to avoid endorsing both their premises and conclusions and the Dogmatists' criteria of justification, it does not save him from endorsing the inference rules used in those arguments. This endorsement would be precisely what allows him to undermine the Dogmatists' theories by showing them that, given that they themselves put forward these theories, they must accept conclusions which are at odds with their most important tenets. This interpretation, however, overlooks the full extent of the dialectical character of the Pyrrhonist's argumentation. The reason is that, in his ad hominem arguments, not only the premises but also the inference rules are taken from the dogmatic theories. One could object that it is hard to believe that in his daily life the Pyrrhonist's thinking does not follow certain rules of inference. The reply to this objection consists in distinguishing, once again, 30See Williams (1988), Bailey (2002, chapter 10), Striker (2004, p. 16), Machuca (2007, pp. 156–7). 74 D.E. Machuca between logical validity and psychological constraint: even though the Pyrrhonist suspends judgment about what the Dogmatists call "logic," his thinking involuntarily follows certain rules of inference which have been inculcated in him by the education he received and his interaction with others, and which have turned out (and still turn out) to work in practical contexts. In this regard, one could argue that the Pyrrhonist's natural capability of thinking also includes the use of such rules. In a word, the Pyrrhonist's use of rules of inference such as modus ponens and modus tollens is to be explained in part as a dialectical maneuver and in part as a psychological constraint in much the same way as his use of the various versions of the LNC. 6 Conclusion Let me sum up what has been argued in the previous sections. First, I have tried to show that, despite what one might tend to think, the Skeptic's observance of the LNC does not represent a commitment to the ontological, logical, doxastic, and unqualified practical versions of this law. Rather, it is based upon (i) a kind of psychological constraint on him, (ii) a linguistic convention shared by the group to which he belongs, and (iii) a practical unfeasibility. This is why I have argued that, when the Skeptic makes use of the dogmatic versions of the LNC, he does so simply as a dialectical maneuver in order to persuade his dogmatic patients and induce them to suspend judgment. Finally, I have contended that such an observance and such a maneuver are perfectly in keeping with those we find both in the case of the Skeptic's adoption of ε'πoχή and in the case of his use of the Modes of Agrippa and certain rules of inference. To conclude, I would like to briefly address the following question: is the Pyrrhonist's refusal to endorse the dogmatic formulations of the LNC, the inference rules employed in his arguments, and the conception of justification underlying the Agrippan modes a clear proof of his anti-rationalism? It depends on how one defines this position. If by anti-rationalism one understands the lack of commitment to the laws of logic, the rules of inference, and the criteria of justification for our beliefs, then the Pyrrhonist is an anti-rationalist. If, on the other hand, by anti-rationalism one understands the firm rejection or denial of such laws, rules, and criteria, then he is certainly not an anti-rationalist. As far as I can see, it is this latter sense which one has usually in mind when speaking of anti-rationalism and, hence, when saying that the Pyrrhonist adopts this position.31 The reason one cannot portray the Pyrrhonist as an anti-rationalist in this strong sense is that he does not reject rationality, but only suspends judgment about whether the logical laws, inference rules, and standards of justification endorsed by the Dogmatists are well-founded or groundless. This does not prevent the Pyrrhonist from making a use of reason which has a merely instrumental or practical function and which allows him to conduct his life within the 31See Striker (2001, pp. 120, 122, 124–5). Cf. Striker (1996, p. 113; 2010, pp. 204–6). 4 Pyrrhonism and the Law of Non-Contradiction 75 limits of τὰ φαινóμενα (see PH I 17).32 This use of reason is not normative insofar as the Pyrrhonist is not committed to what the Dogmatists regard as the canons of rationality. The fact that people find themselves following certain canons (or even the purported fact that people are built to follow them) does not entail by itself that these canons are epistemically justified.33 Now, given that the Pyrrhonist is neither a rationalist nor an anti-rationalist, it is more accurate to characterize him as an "a-rationalist" – taking this term in the sense of someone who is not a champion of rationality, without thereby being its opponent. On the other hand, it could be argued that rationality consists not only in the acceptance of the LNC, the rules of inference, and the conception of justification underlying the Agrippan modes, but also in withholding one's assent whenever one does not have, when confronted with conflicting positions on a given topic, enough evidence for preferring any one of them to the others. If this is so, then one should recognize the rationality of the Pyrrhonist's ε'πoχή on this point. This is not to say, of course, that he suspends judgment because he thinks that it is rational to do so, but only that from the point of view of non-Pyrrhonists his attitude should not be condemned so rashly. Acknowledgments I presented an abridged version of this paper at the journée d'étude "Certitude et Méthode" organized by the École Pratique des Hautes Études à la Sorbonne in May 2008. I am grateful to Carlos Lévy for the invitation to participate in that event. Another short version was delivered at the international conference "Ancient Pyrrhonism and its Influence on Modern and Contemporary Philosophy," held in Buenos Aires in August 2008. I would like to thank the participants for his criticisms and suggestions, particularly Juan Comesaña, Lorenzo Corti, Plínio Junqueira Smith, and Markus Lammenranta. A revised version of the paper was read at a meeting of the B Club, University of Cambridge, in October 2009. I thank the audience for useful remarks. I am also indebted to Mark McPherran, Katja Vogt, and especially Luca Castagnoli for their comments on previous versions of this essay. Finally, I am grateful to Dale Chock for correcting some infelicities of my English. References Annas, J. 1998. Doing without objective values: Ancient and modern strategies. In Companions to ancient thought IV: Ethics, ed. S. Everson, 193–220. Cambridge: Cambridge University Press. Annas, J., and J. Barnes. 1985. The modes of scepticism. Cambridge: Cambridge University Press. Annas, J., and J. Barnes. 2000. Sextus Empiricus: Outlines of scepticism. 2nd edition. Cambridge: Cambridge University Press. Bailey, A. 2002. Sextus Empiricus and Pyrrhonean scepticism. Oxford: Clarendon Press. Barnes, J. 1990. Pyrrhonism, belief and causation: Observations on the scepticism of Sextus Empiricus. In Aufstieg und Niedergang der römischen Welt II 36.4, ed. W. Haase, 2608–2695. Berlin and New York: de Gruyter. 32On this use of reason, see Machuca (2009, pp. 119–20). 33Both the view that ε'πoχή is the rational result of the consideration of certain arguments and the underestimation of the actual scope of the Pyrrhonist's dialectical use of dogmatic logic and epistemology have led Pentzopoulou-Valalas (1994) to regard him as a "(crypto-)rationalist." Casey Perin (2006, pp. 358–9) and Katja Vogt (in her contribution to this volume) also claim that the Pyrrhonist is committed to certain canons of rationality. 76 D.E. Machuca Barnes, J. 2000. Introduction. In Annas, J., and J. Barnes 2000, xi–xxxi. Barney, R. 1992. Appearances and impressions. Phronesis 37: 283–313. Bénatouïl, T. 1997. Le scepticisme. Paris: Flammarion. Bett, R. 1994. Sextus's Against the Ethicists: Scepticism, relativism or both? Apeiron 27: 123–161. Bett, R. 1997. Sextus Empiricus: Against the ethicists. Oxford: Clarendon Press. Bett, R. 2000. Pyrrho: His antecedents and his legacy. Oxford: Oxford University Press. Bonazzi, M. 2007. Enesidemo ed Eraclito. Rhizai 4: 329–338. Brennan, T. 1999. Ethics and epistemology in Sextus Empiricus. New York and London: Garland Publishing. Brochard, V. 2002. Les Sceptiques grecs. 4th edition. Paris: Le livre de poche. Burnyeat, M. 1997. Can the sceptic live his scepticism? In ed. M. Burnyeat and M. Frede, 25–57. Burnyeat, M., and M. Frede, eds. 1997. The original sceptics: A controversy. Indianapolis, IN: Hackett. Bury, R.G. 1933–1949. Sextus Empiricus. vol. 4. Cambridge, MA: Harvard University Press. Cassin, B., and Narcy, M. 1989. La décision du sens: Le livre gamma de la Métaphysique d'Aristote. Paris: Vrin. Caujolle-Zaslawsky, F. 1986. Le problème de l'expression et de la communication dans le scepticisme grec. In Philosophie du langage et grammaire dans l'antiquité. Cahiers de Philosophie Ancienne 5, 311–324. Bruxelles: Ousia. Cauchy, V. 1986. Critique de la théorie su signe et langage chez Sextus Empiricus. In Philosophie du langage et grammaire dans l′antiquité. Cahiers de Philosophie Ancienne 5, 325–338. Bruxelles: Ousia. Corti, L. 2009. Scepticisme et langage. Paris: Vrin. Frede, D. 1996. How sceptical were the academic sceptics? In Scepticism in the history of philosophy: A panamerican dialogue, ed. R.H. Popkin, 1–25. Dordrecht/Boston, MA/London: Kluwer. Frede, M. 1997a. The sceptic's beliefs. In ed. M. Burnyeat and M. Frede, 1–24. Frede, M. 1997b. The sceptic's two kinds of assent and the question of the possibility of knowledge. In ed. M. Burnyeat and M. Frede, 127–151. Gottlieb, P. 2007. Aristotle on non-contradiction. The Stanford encyclopedia of philosophy, ed. E. Zalta http://www.science.uva.nl/~seop/entries/aristotle-noncontradiction/. Accessed 28 June 2008. Grgić, F. 2006. Sextus Empiricus on the goal of skepticism. Ancient Philosophy 26: 141–160. Hankinson, R. 1994. Values, objectivity and dialectic; The sceptical attack on ethics: Its methods, aims, and success. Phronesis 39: 45–68. Hankinson, R.J. 1998. The sceptics. 2nd edition. London/New York: Routledge. Harte, V., and Lane, M. 1999. Pyrrhonism and Protagoreanism: Catching Sextus out? Logical Analysis and the History of Philosophy 2: 157–172. Horn, L. 2006. Contradiction. The Stanford encyclopedia of philosophy, ed. E. Zalta. http://plato. stanford.edu/entries/contradiction/. Accessed 25 July 2008. Lammenranta, M. 2008. The Pyrrhonian problematic. In The Oxford handbook of Skepticism, ed. J. Greco, 9–33. New York: Oxford University Press. Long, A.A. 2006. Aristotle and the history of Greek scepticism. In From Epicurus to Epictetus: Studies in Hellenistic and Roman philosophy, ed. A.A. Long, 43–69. Oxford: Oxford University Press. Lukasiewicz, J. 1971. Aristotle on the law of contradiction. The Review of Metaphysics 24: 485–509. Machuca, D. 2005. Review of Bailey 2002. Ancient Philosophy 25: 212–222. Machuca, D. 2006. The Pyrrhonist's α'τα αξία and φιλανθ ωπία. Ancient Philosophy 26: 111–139. Machuca, D. 2007. Review of Sinnott-Armstrong 2004. International Journal of Philosophical Studies 15: 154–159. Machuca, D. 2009. Argumentative Persuasiveness in ancient Pyrrhonism. Méthexis 22: 101–126. 4 Pyrrhonism and the Law of Non-Contradiction 77 Maia Neto, J. 1995. The christianization of Pyrrhonism: Scepticism and faith in Pascal, Kierkegaard, and Shestov. Dordrecht: Kluwer. Mates, B. 1996. The skeptic way: Sextus Empiricus's Outlines of Pyrrhonism. New York: Oxford University Press. McPherran, M. 1987. Skeptical homeopathy and self-refutation. Phronesis 32: 290–328. McPherran, M. 1990. Pyrrhonism's arguments against value. Philosophical Studies 60: 127–142. Nussbaum, M. 1994. Skeptic purgatives: Disturbance and the life without belief. In The therapy of desire: Theory and practice in Hellenistic Ethics, ed. M. Nussbaum, 280–315. Princeton, NJ: Princeton University Press. Palmer, J. 2000. Skeptical investigation. Ancient Philosophy 20: 351–375. Pellegrin, P. 1997. Sextus Empiricus: Esquisses pyrrhoniennes. Paris: Seuil. Pentzopoulou-Valalas, T. 1994. Le rationalisme des sceptiques grecs. In Ainsi parlaient les anciens, eds. J. Lagrée and D. Delattre, 239–251. Paris: Presses Universitaires de Lille. Pérez-Jean, B. 2005. Dogmatisme et scepticisme: L'héraclitisme d'Énésidème. Lille: Septentrion. Perin, C. 2006. Pyrrhonian scepticism and the search for truth. Oxford Studies in Ancient Philosophy 30: 337–360. Polito, R.H. 2004. The sceptical road: Aenesidemus' appropriation of Heraclitus. Leiden and Boston: Brill. Priest, G. 2004. Dialetheism. In The Stanford encyclopedia of philosophy, ed. E. Zalta. http://plato. stanford.edu/entries/dialetheism/. Accessed 26 June 2008. Priest, G., and Tanaka, K. 2007. Paraconsistent logic. In The Stanford encyclopedia of philosophy, ed. E. Zalta. http://plato.stanford.edu/entries/logic-paraconsistent/. Accessed 28 Aug 2008. Rossitto, C. 1981. Sull'uso della contraddizione in Sesto Empirico. In Lo scetticismo antico, ed. G. Giannantoni, 547–562. Napoli: Bibliopolis. Schofield, M. 2007. Aenesidemus: Pyrrhonist and "Heraclitean." In Pyrrhonists, patricians, platonizers: Hellenistic philosophy in the period 155–186 BC, eds. A.M. Ioppolo and D. Sedley, 269–338. Napoli: Bibliopolis. Sinnott-Armstrong, W. ed. 2004. Pyrrhonian skepticism. New York: Oxford University Press. Spinelli, E. 1995. Sesto Empirico: Contro gli etici. Napoli: Bibliopolis. Stough, C. 1984. Sextus Empiricus on non-assertion. Phronesis 29: 137–164. Striker, G. 1996. Sceptical strategies. In her Essays on Hellenistic epistemology and ethics, 92–115. Cambridge: Cambridge University Press. Striker, G. 2001. Scepticism as a kind of philosophy. Archiv für Geschichte der Philosophie 83: 113–129. Striker, G. 2004. Historical reflections on classical Pyrrhonism and neo-Pyrrhonism. In W. SinnottArmstrong, 2004, 13–24. Striker, G. 2010. Academics versus Pyrrhonists, reconsidered. In The Cambridge companion to ancient scepticism, ed. R. Bett, 195–207. Cambridge: Cambridge University Press. Trowbridge, J. 2006. Skepticism as a way of life: Sextus Empiricus and Zhuangzi. Journal of Chinese Philosophy 33: 249–265. Wedin, M. 1999. The scope of non-contradiction: A note on Aristotle's "Elenctic" proof in Metaphysics G 4. Apeiron 32: 231–242. Wedin, M. 2000. Some logical problems in Metaphysics gamma. Oxford Studies in Ancient Philosophy 19: 113–162. Wedin, M. 2003. A curious turn in Metaphysics gamma: Protagoras and strong denial of the principle of non-contradiction. Archiv für Geschichte der Philosophie 85: 107–130. Wedin, M. 2004a. On the use and abuse of non-contradiction: Aristotle's critique of Protagoras and Heraclitus in Metaphysics gamma 5. Oxford Studies in Ancient Philosophy 26: 213–239. Wedin, M. 2004b. Aristotle on the firmness of the principle of non-contradiction. Phronesis 49: 225–263. Williams, M. 1988. Scepticism without theory. Review of Metaphysics 41: 547–588.