Introduction

Sextus Empiricus' primary interest in philosophical arguments is in their psychological effect. As a Pyrrhonist, he regards arguments, at least those pertaining to obscure or non-evident (ἄδηλα) matters, not as the means for achieving a (more) adequate philosophical understanding of the matters in question but, rather, as so much argumentative material to be weighed on one side of a balance scale – against competing arguments on the opposite side – in achieving the psychological equipollence of pro and contra considerations pertaining to a particular issue (ἰσοσθένεια). This equipollence is intended to be propaedeutic to suspension of judgment concerning the matter (ἐποχή). When such a procedure is extended to all obscure matters, the ultimate result should be tranquillity (ἀταραξία), which is the Pyrrhonian summum bonum. In the first book of the Hypotypōseis or Outlines of Pyrrhonism, Sextus explicitly states that, with respect to the investigation of nature or ‘doing physics’ (φυσιολογία) the Pyrrhonist aim is not to establish by reasoning and ‘with firm confidence’ any dogmas but, with respect to every matter transcending the immediate deliverance of the senses (that is, every non-evident or obscure matter), to oppose a conclusion established by argument to a contrary and ‘equal’ conclusion established by argument with an eye towards achieving tranquillity (PH 1.18). This approach lends itself to a rather quantitative or additive view of arguments, according to which the sum of many rather unimpressive arguments might well ‘count’ just as much as a single rather impressive argument. It can also yield what may appear to the contemporary philosopher to be a not very discriminating attitude on Sextus' part: any port in a storm, any argument for the sake of constructing a formal antinomy (ἔλεγχος). He is also quite willing to produce a jumble sale of arguments, with such arguments and their underlying assumptions drawn from diverse ‘dogmatic’ sources.

At the heart of Pyrrhonian praxis is the assumption that suspension of judgment, rather than ascertaining the truth, is the path to tranquillity. In the words of Myles Burnyeat,

It seems that the Pyrrhonian assumption was that suspension of judgments pertaining even to theoretical issues that seem most removed from mundane practical affairs (such as those involved in physics or the investigation of nature – φυσιολογία) is necessary for the attainment of ‘happiness’ (i.e. tranquillity: ἀταραξία). Thus, Burnyeat's claim about Sextus' attitude towards suspension of judgment concerning the existence of motion also applies to suspension of judgment concerning the existence of causation: ‘Sextus' concern is to ensure that the arguments against [causation] are no less, but also no more, effective than the arguments in favour of it’ (Burnyeat & Frede Reference Burnyeat and Frede1997: 108). It seems to me that, apart from the commitments involved in Pyrrhonian praxis, Sextus' arguments will not be seen in quite the way that he sees them. From a different historical and philosophical perspective, those arguments may strike us in a very different way: features of the arguments that perhaps would not have been thought to be of great significance by Sextus catch our attention. This, I submit, is what happens when we examine his discussions of aitia (variously translatable as ‘causes’, ‘reasons’, ‘explanations’).

The thesis that I attempt to develop in what follows is a multipartite one. First: Sextus derives rhetorical advantage, when developing his contra case with respect to the existence of aitia, from conceiving of cause and effect in terms of the Stoic category of ‘things that are relatively disposed’ (τὰ πρός τί πως ἔχοντα). As we shall soon see in more detail, this is the genus of what we might call external relations. Second: from Sextus' perspective, this argument is simply one part of an additive whole, the ultimate point of which is to develop a contra case with respect to the existence of causes and effects that is sufficiently strong to match the psychological effect of pro arguments – and, perhaps more importantly, our natural propensity to believe in the existence of causes and effects – and thus to produce equipollence of pro and contra considerations and suspension of judgment with respect to the existence of causes and effects. The ultimate goal, of course, in the case of the application of sceptical praxis to causation, as it is with respect to its application to any other issue – is the summum bonum of tranquillity (ἀταραξία). Third: from a different philosophical perspective, for example the contemporary one, the core of Sextus' contra argumentation concerning causation may seem to be not so much a convincing refutation of the existence of the causal relation but, rather, an anticipation of the empiricist reconceptualization of the causal relation that was a part of the anti-metaphysical, Way of Ideas programme of classical British empiricists such as John Locke and David Hume.

The structure of Sextus' discussion of causation in PH 3 and M 9

Sextus concludes the preceding section of Adversus Mathematicos 9, which has dealt with the gods and ‘the divine’ by claiming (M 9.194) that he has reached the point of suspension of judgment ‘with respect to active principles’ (περὶ τῶν δραστηρίων ἀρχῶν). It is clear that he thinks of divinities as pre-eminent instances of active causes; and he here announces that he will proceed to show in a ‘more sceptical’ (σκεπτικώτερον) discussion that the accounts of an ‘active cause’ and ‘the passive’ matter are both open to doubt. While it is far from clear to me what he means by ‘more sceptical’ discussion, one possibility is that he intends to emphasize that the following discussion will have wider and deeper sceptical implications concerning causation, in general – not just the sort of active causal principle represented by god or the deities. He begins this discussion at 9.195.

However, it is worth noting that parallel to this discussion of aitia in M9 is a much shorter discussion at Hypotypōseis3.17–29. In both places the pro arguments, in favour of the existence of causation, are given much less space than the contra arguments. The obvious explanation for this fact is Sextus' assumption that we have a much greater propensity to believe (in some sense of ‘believe’) in the existence of aitia (in some sense of ‘aitia’) than we do to deny the existence of ‘causes’ tout court. So, less argumentative material is needed on the pro side to achieve the balance of equipollence or ἰσοσθένεια with respect to the pro and contra positions concerning the existence of causation.

Both the Hypotypōseis and Adversus Mathematicos contain an argument that is presented as the final, capstone argument of the relatively brief pro sections in the discussions of causation of the respective works. The argument is dialectical in the sense that it assumes an opponent who denies the existence of aitia and then attempts to refute this opponent's negative claim by reductio. Crucially, the argument equivocates on two substantive terms often translated as ‘cause’ (or ‘reason’, or ‘explanation’). It employs both the feminine abstract noun αἰτία and the neuter adjective αἴτιον (plural, αἴτια) used substantively. Exactly what this linguistic distinction amounts to – indeed, whether it has any semantic force at all – seems to depend on the particular Greek writer and is, in many contexts, not clear.Footnote ¹ In what follows, it seems most natural to translate forms of the noun αἰτία as ‘reason’ and to translate the substantive neuter (τὸ) αἴτιον as ‘cause’. The argument as it appears at PH 3.19 goes as follows:

Sextus' argument is a destructive dilemma, which depends on its proponent's finding an opponent who is willing ‘dogmatically’ to deny the existence of any aition. The argument is repeated in virtually the same terms at M 9.204, again as capstone of the pro arguments with respect to the existence of causation. Here the dilemma presented to the opponent is between denying the existence of any cause (αἴτιον) either ‘without a reason’ (χωρὶς αἰτίας) or doing so ‘with some reason’ (μετά τινος αἰτίας). Sextus expands on the first horn of the dilemma: if an opponent seizes this horn, he is, again, not credible (ἄπιστος) because of ‘its being no more appropriate for him to conclude what he does [viz. that no cause exists] than its opposite’. But if he seizes the second horn, denying the existence of any cause with some reason, ‘he is refuted’ (περιτρέπεται) because, ‘in saying that no cause (αἴτιον) exists, he is putting forth the existence of some cause (τι αἴτιον)’.

This argumentFootnote ² is in the style of a ‘Dialectician’ or Megarian such as Stilpo or Diodorus Cronus. A necessary condition of its validity is the assumption that any reason (αἰτία) that one might have for denying or asserting the existence of a cause (αἴτιον) is itself a cause of the assertion that one makes: that is, reasons for asserting something must themselves be (a species) of causes. That Sextus himself is clearly making this assumption is indicated by a logical gloss on the argument that he sets forth at M 9.205–6, which is formulated entirely in terms of the substantive αἴτιον. The argument has three premises: if some cause exists, then a cause exists; if it is not the case that some cause exists, then a cause exists; either some cause does exist or some cause does not exist. The conclusion, that a cause exists, follows by disjunctive syllogism. The first and third premises are logical tautologies. In effect, the argument that we have just been examining is intended to support the second premise. Sextus summarizes that argument by his claim that ‘a cause's existing follows from a cause's not existing, again, since one who says that no cause (αἴτιον) exists says that no cause exists moved by some reason (ὑπό τινος αἰτίας)’. Of course, this claim is arguably false. Even if one stipulates that a reason for our making some claim is a cause of our making it and (more controversially) that if we do not have some reason for our making a claim, then there was no cause of our making the claim, there is still the following problem. My asserting, without a reason, that no cause exists, may not supply any grounds for the hearer to believe my claim. But it does not entail the falsity of my claim. In other words, my supposedly causeless assertion of the non-existence of causes is not equivalent to and does not entail the conditional that is the second premise of the argument, ‘if a cause does not exist, then a cause exists’ – which is indeed logically equivalent to ‘a cause exists’.Footnote ³

In the short Hypotypōseis passage, the remainder of the pro argumentation is of two closely related ‘commonsensical’ kinds. The observed existence of nature (φύσις) in the Aristotelian sense – as characterized by increase, decrease, generation, destruction, and ‘process, in general’ (καθόλου κίνησις) – must be accounted for by ‘some kind of causation’ (κατά τινα αἰτίαν). ‘Moreover, if causation did not exist, then everything would come to be from everything, as chance would have it: for example, horses might happen to be born from flies and elephants from ants’ (PH 3.18). The pro causation section of M 9 expands upon the same theme that nature/change/regularity implies causation. The fundamental point of such arguments is not difficult or particularly technical: the regularities discernible in our everyday experience of the world around us imply some sort of causal structuring of that world (or of our experience of it).

But, as is not infrequently the case with respect to Sextus' text, additional argumentative bulk does not yield greater philosophical cogency. I doubt that Sextus would go so far as to maintain that the denial of the existence of causation represents what the Stoics termed a ‘common notion’ (κοινὴ ἔννοια). Consequently, it is not surprising that, in addition to devoting considerably more argumentative space to the contra position concerning the existence of aitia, he also employs much more technical argumentation. Jonathan Barnes comments that he finds much of the contra-causation discussion of M 9 to be ‘rude and mechanical’ (Barnes Reference Barnes1983: 176), and I would not disagree. Most of the arguments contra causation have a distinctly rigid and formulaic character. The result is a sort of artificiality that divorces the arguments from what we take to be ‘real world’ cases of causation. Sextus' penchant for such arguments perhaps derives from his expressed preference for general arguments as more ‘artful’ than arguments dealing with particular cases.Footnote ⁴ However, despite the potential tediousness of the exercise, there may be some value in setting out the basic, ‘bare-bones’ structure of argumentation in the long contra-causation passage in M 9. I therefore beg the reader's indulgence with the promise that I shall eventually return to what seem to me to be the philosophical issues of most substantive interest in this material.

Starting at M 9.210, Sextus produces a number of ‘arguments from the elimination of cases’ against the existence of causes. In older terminology, these are destructive dilemmas; more properly, some of them assume the form of ‘destructive tetralemmas’, others ‘destructive trilemmas’, and so on.

Thus, at 210ff. we have the following argument: if cause (aition) exists, either (i) the corporeal is the cause of the corporeal, or (ii) the incorporeal is the cause of the incorporeal, or (iii) the corporeal is the cause of the incorporeal, or (iv) the incorporeal is the cause of the corporeal. None of the four alternatives is possible; hence it is not the case that cause exists. With respect to (i): ‘the corporeal will never be the cause of the corporeal since both have the same nature. And if one is said to be the cause of the other inasmuch as it is corporeal (εἰ τὸ ἕτερον αἴτιον λέγεται παρόσον ἐστὶ σῶμα), the other one, being corporeal, will also certainly be a cause (πάντως καὶ τὸ λοιπὸν σῶμα καθεστὼς αἴτιον γενήσεται).’ Elaboration of this consequence follows: ‘since both are equally causes, there is nothing that is acted on or is passive (τὸ πάσχον); and without something that is acted on, there will be nothing that acts (τὸ ποιοῦν)’. With respect to (ii) the same argument holds. Also emphasized is the following point: ‘if both partake of the same nature, why should this one be said to be the cause of that one rather than that one of this one?’ With respect to (iii) and (iv): ‘that which acts must touch (θιγεῖν) the matter that is acted on so that it may act, and the matter that is acted on must be touched so that it may be acted on; but the incorporeal is not of such a nature as to either touch or be touched’.

Another tetralemma occurs at 227–31. That which is moving (τὸ κινούμενον) is not the aition of that which is moving; nor is the stationary (τὸ μένον) of the stationary; nor is that which is moving the aition of the stationary or vice versa. The arguments for the four premises are developed in ways very similar to the ones employed to support the premises of the preceding argument.

At 232–6 we find a trilemma. ‘If anything is the aition of anything, then either (i) the simultaneous (τὸ ἅμα) is the cause of the simultaneous, or (ii) the earlier (τὸ πρότερον) of the later (τὸ ὕστερον), or (iii) the later of the earlier.’ (i) is not the case because of ‘both being instantiated together, and this one's being no more productive of that one than that one of this one – since each one is the same with respect to existence’. (ii) is not the case because,

And (iii) is simply ‘completely absurd’ (ἀτοπώτατον).

At 236 there begins an actual dilemma. ‘If there exists some cause, either (i) it is a cause independently (αὐτοτελῶς) and using only its own power or (ii) it needs for this [in order to be a cause] the assistance of passive matter, so that the effect is understood to occur as a result of the conjunction of both.’ But in the case of (ii), ‘if one is conceived as relative to the other, and of these one is active and the other passive, there will be one conception; but they will be denominated by two names, the active and the passive. And on account of this, the efficacious (δραστήριος) power will not reside more in [the relatum said to be the ‘cause’] than in the one said to be passive.’ The reason for this consequence is that the power that is efficacious for bringing about the effect (a necessary condition of the effect) will not reside in one relatum any more than in the other one.

Another dilemma follows at 246–51. ‘If a cause exists, either (i) it has one efficacious power (τὴν δραστήριον δύναμιν) or (ii) it has many.’ (i) is not the case since, ‘if it had one [efficacious power], then it ought to affect everything alike and not differently’. But the sun, for example, has different powers since it causally affects different things differently. But (ii) is not the case ‘since then [a cause] ought to actualize all of [its powers] in all cases (ἐπεὶ ἐχρῆν πάσας ἐπὶ πάντων ἐνεργεῖν)’ of its causal action; but it obviously does not do so. The dogmatists' usual reply to this last claim is that the effects that come to be through a given cause vary because of differences of (the kind of) things affected, difference of the distances involved, and suchlike. But those who make this response grant, almost without dispute, that ‘that which acts is not different from that which is acted on (τὸ μὴ ἕτερον εἶναι τοῦ πάσχοντος τὸ ποιοῦν)’. In effect, the opponents are admitting that the ‘conjunction of both (ἡ δὲ ἀμφοτέρων συνέλευσις)’ active element and passive element produces the effect. Thus, singling out the active element as cause – as opposed to the conjunction of the active and passive element – is absurd.

Still another dilemma begins at M 9.252. ‘If there exists a cause of something, either (i) it exists as separate from the passive matter or (ii) it exists along with it (ἤτοι κεχώρισται τῆς πασχούσης ὕλης ἢ σύνεστιν αύτῇ).’ (i) is not the case, because, in that circumstance, ‘since the matter with respect to which it is said to be a cause is not present, the matter is not affected, because that which acts is not co-present with it’. In the case of (ii), ‘if the one were to join/couple with (συνδυάζοι) the other, the one said to be the cause either (a) itself acts only, and is not acted on, or (b) both acts and, at the same time, is acted on’. If (b), ‘each will be that which acts and that which is acted on. For in so far as [the cause] itself acts, the matter will be what is acted on. But in so far as the matter acts, [the cause?] itself will be what is acted on. Thus, that which acts (τὸ ποιοῦν) will be no more active than what is acted on (τὸ πάσχον), and that which is acted on will be no more passive than what acts, which is absurd.’ But … if (a), then either (1) it acts, only at the place of contact (κατὰ ψιλὴν ψαῦσιν) – that is, at the surface (κατ' ἐπιφάνειαν) – or (2) it acts by distribution/permeation (κατὰ διάδοσιν). If (1), ‘it will not be able to act since surface is incorporeal, and the incorporeal is not naturally able to act or to be acted on’. But if (2) were the case the cause would either (1′) ‘go through solid bodies or (2′) go through certain intelligible but imperceptible pores’. It is not the case that (1′) because ‘body is not able to go through body’. But neither is it the case that (2′), since this reduces to case (1) above.

Although the reader may be benumbed by now, Sextus is far from finished in having his way with him or her. Starting at about M 9.258, there occurs a sequence of what I term arguments ‘by reduction’. By this I mean that the issue of the existence of aitia is ‘reduced’ to the issue of the existence of something else Φ, where the existence of Φ (or of Φs) is asserted to be a necessary condition of the existence of aitia. Sparing the reader the details, I note that the first arguments of this sort, extending from M 9.258 to 266, concern the existence of touching or contact (ἁφή). Sextus' assertion is that the existence of contact is a necessary condition of the existence of what acts (τὸ ποιοῦν) and of what is acted on (τὸ πάσχον). So he proceeds to argue from the non-existence of contact to the non-existence of the active and the passive, the existence of which he seems to hold to be a necessary condition of the existence of causation.

Beginning at M 9.266, Sextus concentrates on the concept of what is affected or acted on (τὸ πάσχον). He suggests that preceding arguments have rendered dubitable the active or acting cause (τὸ ποιοῦν αἴτιον), both considered by itself and considered along with what is affected by it. But, he says, he will now call into question the account given of the passive or what is affected (τὸ πάσχον), ‘taken by itself’. He proposes (at 277) that something's being affected must be a matter either of addition (πρόσθεσις), or of subtraction (ἀφαίρεσις), or of alteration and change (ἑτεροίωσις καὶ μεταβολή) and proceeds to call into question the existence of each of these. In the remainder of the section with which I am concerned (to M 9.330), subtraction is dealt with in a disproportionately long and somewhat digressive discussion extending from 280 to 320. Addition is treated from 321 to 327. Finally, alteration and change are apparently (and quite summarily) disposed of in just a few lines of text at 328 by being reduced to transposition (μετάθεσις), which is said to be merely the taking away (ἄρσις) of one thing and the addition (πρόσθεσις) of something else.Footnote ⁵

Sextus concludes the long section of M 9 pertaining to the concepts of aition and of the passive/what is acted on (τὸ πάσχον) with an artful if perhaps somewhat strained transition to the next general topic of M 9, on ‘the whole and the part’. Subtraction seems to presuppose as a necessary condition the ideas of whole and part. And he has argued that the non-existence of subtraction (along with that of addition) implies the non-existence of τὸ πάσχον, which in turn implies the non-existence of any aition (and the non-existence of what is affected by it). So, if doubt can be cast on the coherence of the idea of part and whole, yet more trouble can be caused for the concept of causation.

At the end of the section on aitia and the active and passive – in his summary treatment of change, for example – even Sextus himself gives evidence of having tired of his topic. As I hope that the preceding discussion has substantiated, Sextus' argumentation is exceedingly schematic and abstract–‘mechanical’, according to the characterization by Barnes. While most of his general arguments are clearly valid with respect to their form (the conclusions of the respective arguments logically follow from their premises), it is frequently difficult to assess their soundness (whether the premises are in fact true) because of the abstract and technical character of the premises. But Sextus is also not above invoking the occasional paralogism, which he must surely recognize as such. A choice example occurs at M 9.302–6 in his long discussion of subtraction (ἀφαίρεσις). If subtraction exists, it must be possible to subtract the lesser from the greater. So the concept of the lesser's being included (ἐμπεριέχεσθαι) in the greater must be a coherent notion. Suppose, then, that 5 (the lesser) is included in 6 (the greater). Analogously, 4 would be included in 5, 3 in 4, 2 in 3, and 1 in 2. By an unstated transitivity premise, 4 and 3 and 2 and 1 (as well as 5) would be included in 6. By yet another unstated premise – an extremely implausible premise and the one that allows him to reach his desired conclusion – their sum, 15 would then be included in 6. So, in conclusion, it turns out that the greater is included in the lesser, which is impossible. Sextus opines that, if this were not bad enough, there is an obvious generalization of this argument with the conclusion that indefinitely great numbers are included in any finite number.

The occasional clever clinker of an argument such as this will not, I think, be a source of much embarrassment for Sextus. As I stated earlier, Sextus gives evidence of being most interested in the psychological effect of (mountains of) arguments rather than in exploring the details of individual arguments. If a given reader perhaps smiles at the occasional argument, surely there will be other arguments in the great heap that will give pause – that will contribute some degree to the doubt that will eventually, according to the Pyrrhonian faith, yield equipollence with respect to one's convictions concerning the existence and non-existence of causation. According to the same Pyrrhonian faith, repeated experience of achieving such equipollence with respect to other non-evident matters eventually yields suspension of judgment with respect to all non-evident matters. And, then, can the summum bonum of tranquillity be far from reach?

The relativity of aitia

If one considers Sextus' discussion of causation from a perspective not influenced by any prior commitment to Pyrrhonian praxis, the idea of the relative nature of causation is particularly salient. Early in the contra-causation passage of M 9 Sextus invokes the relativity of aition and a Stoic example of causation. Something is the (corporeal) cause of something else (an incorporeal ‘sayable’ or ‘property’) to a third something (corporeal); for example, the lancet is the cause of cutting to the flesh (M 9.207; cf. M 9.211). At M 9.208 Sextus gives a very short argument: relatives (τὰ πρός τι) are only conceived (ἐπινοεῖται) and do not exist (ὑπάρχει) – as, he claims, he has established in his discussion of demonstrations. Consequently, an aition, as a kind of relative, is only conceived and does not actually exist. When one turns to the relevant passage in Adversus Dogmaticos 2 (M 8) pertaining to relatives, one finds Sextus arguing that the dogmatists agree concerning their definition: ‘what is relative is what is conceived (νοούμενον) as being relative to something else’. They do not define ‘the relative’ as ‘what exists (ὑπάρχον) as relative to something else’ (M 8.454). He elaborates on the point by claiming that (according to good Stoic principles) nothing that exists can undergo ‘any change or alteration’ (ἀλλαγήν τινα καὶ ἑτεροίωσιν) without being affected. But ‘what is relative is changed without being affected and when no alteration occurs in it’ (M 8.455–6). From the examples that follow, it is clear that Sextus has in mind what may be called external relations. A thing can be equal to and then cease to be equal to something else without itself being affected (e.g. because of an enlargement or diminution of the other thing); and it can be below and then come to be above something else without undergoing any intrinsic change. Indeed, any sort of change with respect to a relation in which something stands becomes what has, in modern philosophy, been termed a ‘Cambridge change’ of that thing. Sextus emphasizes the relational status of an aition in M 9:

Sextus' doctrine, particularly in M 8, appears to involve a conflation of two classes of relations distinguished by the Stoics. In a passage from his commentary on Aristotle's Categories, Simplicius argues that the Stoics distinguished between the genus of things that are relative (τὰ πρός τι) and the genus of things that are ‘relatively disposed’ (τὰ πρός τί πως ἔχοντα). The former genus includes ‘those things that, while they are disposed according to their own proper character, are somehow directed to something else’; the latter includes ‘those things that naturally obtain and then do not obtain without any internal change or alteration and which look toward what is external’.Footnote ⁶ Examples of relatives simpliciter given in the passage are knowledge, sensation and (slightly later in the passage) the sweet and the bitter. The point is made that what is sweet or bitter could not change with respect to its sweetness/bitterness without the change of some internal differentia (διαφορά) or power (δύναμις). (Apparently Simplicius has in mind a change in the object of perception, in what is perceived as sweet/bitter by some ‘fixed’ perceiver, although he elsewhere seems willing to allow that the subject of perception is what undergoes ‘internal change’.)

Examples given of ‘things that are relatively disposed’ are a son (and father) and the person standing on the right (and person standing on the left). A son can cease to be a son and the person on the right can cease to be the person on the right without undergoing any intrinsic, internal change or alteration – that is by undergoing only a Cambridge change.

Whether wilfully and disingenuously or not, Sextus appears to identify ‘what is relative’ (τὰ πρός τι) with the latter Stoic category described by Simplicius, that is, with ‘what is relatively disposed’ (τὰ πρός τί πως ἔχοντα). Indeed, at M 8.455 he gives as apparent examples of things that are not relative what is black and white and what is sweet and bitter, on the grounds that the change from one property to its contrary cannot occur without some internal alteration in the subject of the properties. Sextus proceeds to characterize quite explicitly what is relative simpliciter (τὰ πρός τι) as what is susceptible to change apart from any ‘internal’ (read: real) change: ‘But what is relative is changed apart from affect and when no alteration comes to be in it.’Footnote ⁷ This (mis)identification of the relative with the ‘relatively disposed’ makes it easier for him, in M 9, to argue for the non-existence of aitia as a species of relatives – of τὰ πρός τι.Footnote ⁸

From a strictly logical perspective, Sextus could have concluded his contra argumentation pertaining to causation at M 9.209. His argument can be paraphrased as follows: no relation simpliciter (identified with a Stoic τὸ πρός τί πως ἔχον or external relation) exists. This is so because such a relation holds or fails to hold apart from any ‘real’ alteration or affection in its relata; and only what is susceptible to such alteration/affection really exists. Sextus concludes therefore, that (a) relatives do not exist.Footnote ⁹ From (a) and the additional premise that (b) aitia are relatives, it follows that aitia do not exist. Note that this is a ‘technical’ or ‘theoretical’ argument in the following sense. It depends both on a particular (Stoic) conception of existence and on a particular conception of relations. Only corporeal entities, which are susceptible to ‘internal’ affections/alterations – and, perhaps what is ‘immediately dependent’ upon such bodies and their changes – really exist. Since every relation is identified as external (that is, as what is ‘relatively disposed’, in Stoic terminology), none is ‘immediately dependent’ on the ‘internal’ affections or alterations of its relata.Footnote ¹⁰

But, to reiterate my earlier claim, Sextus seems to be not as much interested in the soundness (or validity) of individual arguments – that is, in the formal, semantic properties of arguments according to either an ancient or a contemporary account of ‘formal, semantic properties’ – as he is in the cumulative psychological effect of a great heap of arguments. As we saw in the preceding section, the heap that he produces from M 9.210 to 330 is a characteristically promiscuous one. I believe that the attempt to impose any very simple, general interpretative schema on the heap that I described in that section would be a Procrustean task. Consequently, I shall hypothesize only that some of Sextus' arguments can be illuminated by invocation of his idea that cause and effect are to be treated, in effect, as ‘things that are relatively disposed’: τὰ πρός τί πως ἔχοντα. These arguments point up the difficulties that such a conception raises with respect to various beliefs and expectations we (and other assorted ‘dogmatists’) have concerning the nature of causation.

Causal relations: dyadic or triadic?

The conception of aition that is suggested by its classification as a ‘relative thing’ (in the τὰ πρός τί πως ἔχοντα sense) is often that of one term in a dyadic relation: there is the ‘cause’ (αἴτιον) and there is its ‘effect’ (ἀποτέλεσμα). The second term of the relation is sometimes connoted by the word ἀποτέλεσμα in Sextus' arguments.Footnote ¹¹ More frequently, it is merely implied by his use of the ‘cause of …’ locution: the noun αἴτιον followed by a noun (or some other nominative construction) in the genitive case. Yet, many of the arguments also appeal to the idea – which I suppose to be grounded in some commonsensical assumptions – that the causal relation is triadic. There is (1) the aition conceived as ‘causal agent’ (τὸ ποιοῦν); there is (2) something passive (τὸ πάσχον) on which the causal agent acts; and there is (3) the ‘effect’ as a tertium quid that results from this action. The triadic model is reflected in some of the more technical ancient conceptions of causation, such as the Stoic analysis of a body-producing-a-lekton-as-applied-to-some-other-body.

Jonathan Barnes has analysed what he takes to be the forms of Sextus' causal claims. According to his analysis, underlying the simple dyadic form is a ‘more explicit, sentence, “The fire is cause of melting for the wax”; and that appears to be triadic in form, C(x,y,φ)’ (Barnes Reference Barnes1983: 175). But, according to Barnes,

In effect, the introduction of ‘event causation’ into the analysis reintroduces a dyadic schema of causation: one event (e.g. that the fire is hot or the fire's being/becoming hot) is the cause of a subsequent event (e.g. that the wax melts or the wax's melting). This sort of dyadic analysis of causation in terms of cause-event and effect-event certainly facilitates the later, classical Empiricist analysis of causation as an external relation between the (idea of) cause and the (idea of) effect. Whether it represents, as Barnes believes, the ‘underlying truth’ of a notion of causation that is assumed either by Sextus or by his dogmatic opponents is another matter about which I myself am uncertain. However, it seems to me that Sextus does not clearly and explicitly distinguish dyadic and triadic paradigms of causation and, indeed, has little motivation to seek philosophical clarification with respect to such a non-evident (ἄδηλον) matter. Rather, he switches freely but tacitly between the two paradigms in many of his contra arguments concerning causation.

A nice example occurs in his discussion of causation at M 9.213–17. It is the first of the contra arguments that I briefly discussed in the preceding section; and like so many of his other contra arguments, it is cast in what I earlier termed an ‘abstract and schematic’ form. Although this feature of the argument makes the soundness of the argument difficult to assess, it probably represents a good rhetorical strategy on Sextus' part. His goal of undermining the notion of causation would not be well served by appeal to concrete cases where we are actually predisposed to believe that causation obviously is present. Also like many of his other arguments in this section, the argument is in the form of a destructive dilemma (here, in fact, a ‘tetralemma’): if causation exists, then either A or B … or H. But not-A and not-B … and not-H. Therefore, causation does not exist. The actual argument is as follows: if causation exists, then either (i) the corporeal is the aition of the corporeal, or (ii) the incorporeal is the aition of the incorporeal, or (iii) the corporeal is the aition of the incorporeal, or (iv) the incorporeal is the aition of the corporeal. But none of (i), (ii), (iii) and (iv) is the case. Therefore, causation does not exist.

The paradigm of causation that is formally employed in the argument is the ‘straightforward’ dyadic-relation (A-as-cause-of-B) one. But the details of the argument, such as they are, are not so simple. Sextus' argument that the corporeal is not the cause of the corporeal seems particularly problematic:

While the argument begins by assuming the conception of causation as the ‘simple’ dyadic relation between cause and effect, an additional complication soon appears. The fundamental idea is that an aition is something that ‘acts’ to produce its effect. But then, by what seems to be a principle generally accepted by the ‘dogmatists’, there must be some corresponding ‘passive element’. Sextus concludes that there cannot be such a passive element in the purported case of the corporeal-as-aition-of-the-corporeal and, hence, that such a form of causation cannot exist. But why not?

Although his exposition is, to say the least, condensed, Sextus may have had something like the following line of thought in mind. Let us suppose that we have an instance of body as aition of body. How are we to analyse this supposed phenomenon? One consequence of a relational analysis of causation is that for the relation (causation) to obtain, both relata must in some sense be ‘co-present’, just as, for something ‘to be on the right’, there must be two relata that are ‘co-present’, something on the right relative to something on its left. In the case we are considering, a body-qua-corporeal is supposedly the aition of a (distinct) body-qua-corporeal. Sextus appears to conclude that either of the corporeal relata of the supposed causal relation – so long as those relata are ‘co-present’ as relata must be – could equally well be said to be the cause, in virtue of its corporeality, of the corporeality of the other. If this conclusion is warranted and if Sextus were to assume the anti-symmetry of the causal relation, this would be sufficient to obtain his conclusion, ‘if, therefore, the corporeal is the aition of the corporeal, there is no aition’.

However, he rather complicates the argument by arguing that, since there is no basis (in terms of its corporeality) for distinguishing one relatum of the causal relation as aition, there is nothing that can be τὸ πάσχον (the passive element) and, hence, that there can be no causation. Is τὸ πάσχον the ἀποτέλεσμα or effect (as in the dyadic-relation paradigm in which the argument is originally formulated), or is it that which is ‘affected’ by the cause in such a way that the ‘effect’ is produced in it (as in the triadic-relation paradigm)? The issue is not clarified when Sextus claims that the impossibility of the incorporeal's being the aition of the incorporeal follows by the same argument: In brief, ‘if both participate in the same nature, why should this one be said to be the aition of that rather than that of this’ (M 9.215)? But, when he turns to his argument that the incorporeal cannot be the aition of the corporeal nor the corporeal the aition of the incorporeal, it is clear that he is appealing to the triadic-relation paradigm:

The idea of a cause ‘touching’ its effect (ἀποτέλεσμα) would not seem to make much sense in terms of the dyadic-relation paradigm. But, it does seem to make sense to be concerned with whether something qua aition can ‘make contact’ with something (τὸ πάσχον) so as to act on it and thus produce some effect (ἀποτέλεσμα) ‘in’ or with respect to that πάσχον thing, as in the triadic-relation paradigm. Indeed, it is precisely such a concern that leads to the classical Cartesian problem in the history of modern philosophy of how (or whether) causal interaction can occur between (corporeal) res extensae and (incorporeal) res cogitantes.

Beyond its illustration of a certain rhetorical opportunism on Sextus' part, in terms of his shifting between the dyadic-relation and triadic-relation paradigms, this argument also introduces a general, recurring strategy in the contra arguments pertaining to causation. The relational conception of causation requires the co-presence, in some sense, of cause and effect. But our conception of the anti-symmetry of cause and effect, which is grounded in the idea of the aition as the actualization of an active potency, proves inconsistent with the co-presence of the causal relata. This strategy is illustrated in an argument developed by Sextus at M 9.232–6, again a destructive dilemma (here, a trilemma):Footnote ¹²

Sextus argues that the simultaneous cannot be the aition of the simultaneous since both ‘coexist’ (συνυπάρχειν); therefore, there is no reason to say that one is capable of originating the other (τόδε τοῦδε γεννητικὸν ὑπάρχειν) rather than vice versa, ‘since each has equal reality’ (ἴσην ὕπαρξιν) (M 9.233). But, the argument proceeds, ‘the former will not be productive of what comes to be later’ because an aition cannot be an aition in the absence of its effect (ἀποτέλεσμα), nor can the effect be an effect in the absence of its aition. Sextus emphasizes that this conclusion is due to the fact that cause and effect are relatives and ‘it is necessary that relatives coexist with one another (συνυπάρχειν ἀλλήλοις), and not that one precedes and the other follows’ (M 9.234). Of course, this argument would equally apply to the remaining case: the possibility that the latter should be the aition of the former. But Sextus here stresses that it is ‘most absurd’, from the perspective of common sense and experience, that ‘what does not yet exist should be the aition of what already exists’ (M 9.235).

The gist of the argument is that, while the status of an aition as a relative requires the ‘co-presence’ of its effect, this co-presence undermines the anti-symmetry between the ‘action’ of the aition and ‘passion’ of the effect that is demanded by our understanding of the causal relation. The theme is continued in a passage, beginning at M 9.237, which immediately follows the one we have been discussing. This passage, too, develops a destructive dilemma: ‘If there is any aition, either it will self-sufficiently be a cause, making use only of its proper power; or it needs the aid of the affected matter, so that the effect is understood to be due to the common coming-together of both’ (M 9.237). Sextus argues that neither alternative is possible. If the aition were to act ‘self-sufficiently’ (αὐτοτελῶς), then the cause ought always to be producing its effect, a consequence that, Sextus assumes, contradicts our actual experience of causal efficacy. But if an aition were to be conceived as something the action of which is relative – as in the second alternative – the consequence would be worse. In that case, there would be one, single conception (ἔννοια) of the active and passive relata, but they would be designated by two names. Sextus claims that, because of this fact, the ‘efficacious power’ (ἡ δραστήριος δύναμις) would not reside in what is called the aition any more than it would in what is called the passive relatum: for both are equally sine quibus non for the causal action. In other words, causal anti-symmetry, or the anisotropic character of causal action, would be lost. The inability to distinguish the active and passive relata, in the sense that both are necessary conditions of the causal effect is, I believe, significant for Sextus in precisely the way indicated by R. J. Hankinson:

Causation in classical British empiricism: a relation between ideas

This elusive idea of ‘causal action’ is a paradigmatic instance of an ἄδηλον matter, something that transcends our direct and immediate experience. As such, of course, it is an object to which Sextus' sceptical method can be appropriately applied. Although the ultimate philosophical motivation is obviously different from that of Sextus, the development of an ‘empiricist’ conception of causation associated with the Way of Ideas tradition reprises some of the themes of Sextus' contra arguments pertaining to causation. In particular, scepticism concerning what Sextus calls the δραστήριος δύναμις, the ‘efficacious power’ of causation, characterizes the Way of Ideas analysis. What experience, in the form of our ideas, gives us is only the ideas comprising a particular cause, the ideas comprising its particular effect, and a radically external relation between the two (collections of) ideas – in other words, something along the lines of the Stoic conception of things (ideas, in this case) that are relatively disposed, τὰ πρός τί πως ἔχοντα. In the words of John Locke's An Essay Concerning the Human Understanding, we have,

The fact that the relata of the causal relation are (collections of) ideas, and that these ideas are ultimately resolvable into atomic, simple ideas, lends support to Locke's conception of the causal relation as a dyadic external relation. Simple ideas are what they are; and their relations to other simple ideas in no way impinge on that internal nature or character. Thus, an idea (simple or complex) A can stand in or fail to stand in a ‘causal’ relation to idea (simple or complex) B without any change in the ‘content’, so to speak, of either A or B. To cite one of Locke's examples, ‘the finding, that in that Substance which we call Wax, Fluidity, which is a simple Idea, that was not in it before is constantly produced by a certain degree of Heat, we call the simple Idea of Heat, in relation to Fluidity in Wax, the Cause of it, and Fluidity the Effect’ (Locke Reference Locke and Nidditch1975: II, xxvi, §1). So, Locke's Way of Ideas analysis of causation understands it to be, in Stoic terminology, a kind of relative disposition: cause and effect are related in the manner of ‘things that naturally obtain and then do not obtain without any internal change or alteration and which look toward what is external’,Footnote ¹³ in just the way that ‘what is on the left’ is related to ‘what is on the right’.

David Hume also conceives of causation as a dyadic external relation. In Part III of the first book of A Treatise of Human Nature, Hume divides his seven philosophical relations into two classes. One class (containing the relations of resemblance, proportion in quantity and number, degree in any quality, and contrariety) contains relations that are internal in the sense of depending entirely on the (ideas of) the relata: a change in either of the relata yields a change in the relation and, as Hume puts it, ‘the relation is invariable, as long as our idea [of the relata] remains the same’ (Hume Reference Hume and Nidditch1978: book I, part iii, 1). The second class (containing the relations of identity, relations of time and place, and causation) is the class of external relations: in the case of these relations, the relation can vary (or be present or absent) quite independently of any change in (the ideas of) the relata. A consequence inferred by Hume is that it is impossible for reason, by acts of intuition or deduction, to establish the existence or non-existence of the causal relation. His assumption is that, with respect to our experience of relations, the simple ideas of which our conscious experience is ultimately composed are simple ideas of the relata of the relation. So, in the case of an external relation, such as causation or the separation of two objects by a certain spatial distance – in which the presence or absence of the relation cannot be inferred from our ideas of the relata – there is no intuition or demonstration of the relation itself that can be analysed in terms of simple ideas. Rather, in the case of the causal relation, our faculty of imagination or sensibility gives rise to our experience of (a) the contiguity in space and time of (idea of) cause and of effect, (b) the immediate temporal succession of (idea of) effect after (idea of) cause, and (c) the ‘constant conjunction’ in our experience of (idea of) cause and (idea of) effect.

Hume, of course, has some difficulty in locating what he takes to be an essential constituent of the conception of causation: what he terms the ‘necessary connexion’ between cause and effect. The problem is that, according to Hume, the ‘content’ of the idea of anything that might serve as a cause is entirely distinct from the content of the idea of anything that might be an effect:

And, ‘had ideas no more union in the fancy than objects seem to have to the understanding, we cou'd never draw any inference from causes to effects’ (Hume Reference Hume and Nidditch1978: I, iii, 6). The propensity of the faculty of ‘fancy’ or imagination – apparently produced from our experience of the ‘constant conjunction’ of the idea of a particular cause and the idea of a particular effect – to pass from the idea or impression of one to the idea of the other grounds Hume's psychologistic account of the necessary connection between cause and effect. ‘Reason can never satisfy us that the existence of any one object does ever imply that of another; so that when we pass from the impression of one to the idea of belief of another, we are not determin'd by reason, but by custom or a principle of association’ (Hume Reference Hume and Nidditch1978: I, iii, 7). So, although as a philosophical relation, causation implies contiguity, succession and constant conjunction, ‘'tis only so far as it is a natural relation, and produces an union among our ideas, that we are able to reason upon it, or draw any inference from it’ (Hume Reference Hume and Nidditch1978: I, iii, 6).

Conclusion

I may seem, in my discussion of the analysis of causation in the Way of Ideas tradition of the seventeenth and eighteenth centuries, to have moved far from the ninth book of Sextus' Adversus Mathematicos. From the perspective of his own philosophical programme, Sextus' contra arguments concerning causation are but one piece of his attempt to achieve ἀντίθεσις, ἰσοσθένενα, and ἐποχή (i.e. ‘contrariety’, ‘equal force’ and ‘suspension of judgment’) with respect to the non-evident matter of causation. One significant type of contra argument elaborates on the claim that the relation between cause and effect is an external relation or, in Stoic terminology, a relation between τὰ πρός τί πως ἔχοντα (‘things that are relatively disposed’). Many arguments of this type proceed to what is, in effect, the conclusion that such a conception of the causal relation leaves no place for the notion of a specifically causal agency. This is the δραστήριος δύναμις, the ‘causal efficacy’ or potency that is responsible, inter alia, for the anti-symmetry or anisotropy of the causal relation. My motivation in discussing Locke and Hume has been to point out that their strategy, too, was to analyse the causal relation as an external relation, an analysis which is grounded in their idealistic epistemology.

The result has usually been interpreted, both by scholars of classical modern philosophy and by subsequent philosophers, as yielding a conception of causation that is less ambitious and ‘thinner’ than earlier conceptions. Indeed, Barnes (Reference Barnes1983) advocates resolving at least some of Sextus' contra-causation argumentation by treating causal claims as the assertion of atemporal relations between two sentences or propositions.

In other words, if we (or the dogmatists or Sextus) take the ‘linguistic turn’ with respect to the analysis of our cause-talk, we can rescue causation from the problematic consequences of regarding it as the (meta)physical ‘cement of the universe’Footnote ¹⁴ holding together the events/states of affairs (or, alternatively, the objects and their properties and relations) that constitute that universe. According to Barnes' response to Sextus,

Of course, Barnes conceives of his response to Sextus (‘causation itself is unreal’) not really as eliminating causation tout court, but as yielding a more philosophically supportable and less metaphysically robust conception of causation. However, one perhaps might – if one were Sextus – be inclined to read Barnes' conclusion that ‘causation itself is unreal’ as an admission of the success of at least the contra part of Sextus' case.

Similarly, at least according to a minority view, Hume's analysis subverts – in the best sceptical tradition – the very concept of causation, irrespective of what Hume's actual intention might have been.Footnote ¹⁵ That causation should be analysed as a relation is a fairly obvious philosophical move. Perhaps the most significant contribution of Sextus' discussion of causation is to introduce into Western philosophical discourse the idea that causation is an external relation, a relation between τὰ πρός τί πως ἔχοντα (‘things relatively disposed’). How one makes use of this philosophical move will depend upon one's ultimate philosophical commitments. For Sextus, it grounds one class of contra arguments that undermine our confidence in the very existence of the causal relation. For a philosopher such as Locke or Hume – or perhaps Barnes – it leads to a more philosophically adequate and perhaps thinner notion of causation. In the particular cases of Locke and Hume, it grounds a modest empiricist analysis of causation, one that could be presented as performing the worthy service of stripping away obscurantist metaphysical accretions that had been attached to the notion by (scholastic and other) dogmatists. Causation, for the empiricists, becomes an external, dyadic relation between ideas, a relation the presence or absence of which can be established only by experience.

To conclude, it is worth noting that Sextus himself anticipates later anti-metaphysical, empiricist conceptions of causation. In his discussion of ‘signs’ (σημεῖα) beginning at PH 2.100, he rehearses a (Stoic) distinction between signs that are ‘suggestive’, ‘commemorative’ or ‘recollective’ (ὑπομνηστικά) and those that are ‘indicative’ (ἐνδεικτικά). An indicative sign ‘signifies that of which it is the sign by its own particular nature and constitution’ (ἀλλ' ἐκ τῆς ἰδίας φύσεως καὶ κατασκευῇς σημαίνει τὸ οὗ ἐστι σημεῖον) (PH 2.101). Sextus, of course, claims that Pyrrhonists argue against indicative signs as an invention of the dogmatists (PH 2.102). Recollective signs however, are based upon the mental association of one (type of) phenomenon with another, as in the case of smoke and fire (PH 2.100). Recollective signs, Sextus says, are utilized in everyday experience or life (ὑπὸ τοῦ βίου). Consequently, ‘we not only do not fight against everyday experience, but we support it by undogmatic assent, while opposing the private inventions of the dogmatists’.Footnote ¹⁶ While it may be the case that not all instances of the relation between recollective signs and what they are signs of are plausibly construed as causal relations, it seems that some might be so construed. And in those cases we would seem to have a modest, empirical Pyrrhonian account of the causal relation not unlike that of Locke or Hume.Footnote ¹⁷