The Argument from RelativesFootnote ¹ concerns what I take to be the fundamental source of perplexity for Socrates and the primary philosophical challenge for the dialogue’s readers: the contention advanced by Critias that, unlike the other arts or sciences, temperance is an epistêmê, science, only of epistêmê itselfFootnote ² and of no other object. While at the previous stage of the conversation Socrates helped Critias articulate that claim, it is now clear that he did so merely for the sake of the argument. In truth, he says, the claim seems to him strange (atopon: 167c4) or, in the light of certain cases that serve as counterexamples, impossible (adynaton: 167c6). And he urges Critias to consider these examples with the expectation that, when Critias does so, he will come to the same conclusion (167c4–6). The Argument from Relatives consists precisely in this endeavour and has an explicitly stated goal: examine whether or not there can be a ‘science of science’ (167b1–2) and, on the basis of cases that are supposed to be analogous with epistêmê, bring Critias to admit that such a thing, i.e. a strictly reflexive form of science, appears strange or incoherent.

Philosophically, this argument is of the first importance. It contains pioneering work on relatives and relations and represents a major breakthrough in that regard. It raises questions about reflexivity and foreshadows logical conundrums bearing on self-predication. It may cause us to revisit traditional assumptions about the structure and behaviour of different categories of relatives, especially perceptual relatives and quantitative relatives. And it conveys valuable insights concerning the role of relatives in epistemic grounding. Historically, the Argument from Relatives represents a landmark in ancient philosophical thinking about these topics. Not only is it a breakthrough for Plato, but also its influence can be traced to Aristotle’s conception of relatives and his analysis of second-order perception and, further, to Stoicism and beyond. So far as the interpretation of Plato is concerned, the counterexamples constituting the main body of this argument point unmistakably to the so-called middle dialogues and the theory of Forms, while Socrates’ closing remarks reach further to the metaphysics and methods of the Sophist and the Statesman. Dialectically, the articulation of Socrates’ aporia underscores that the viability of Critias’ definition of temperance as a ‘science of science’ ultimately depends on whether or not this notion is credible or coherent. Since the Argument from Relatives aims to answer just that query, it is decisive for the development of the investigation.

As I said,Footnote ³ I believe that the Argument from Relatives has been misunderstood in various ways and has frequently been taken to undermine the point that it is supposed to make. I shall try to show that, on the contrary, it attains its principal objective, even though it does not purport to settle the issue in a definitive manner. At the outset, I wish to highlight one central assumption that I shall make and that is crucial for that purpose. Namely, both interlocutors operate with a constitutive view of relativity,Footnote ⁴ which begins with relatives rather than relations,Footnote ⁵ and which posits that every relative is constituted just by the relation to a correlative.Footnote ⁶ Or, a relation constitutes a relative if bearing that relation just is what it is to be the relative: being a brother of someone just is what it is to be a brother.Footnote ⁷

I submit that the counterexamples entertained by Socrates and Critias exhibit certain formal features that characterise, more generally, constitutive relativity.Footnote ⁸ First, reciprocity. Assuming that a relation constitutes a relative and that every relation has a converse, if X is relative to Y, then Y is relative to X. Sight is related to colour and colour is related to sight; double is related to half and half to double. Next, exclusivity. While on the standard interpretation of ancient relativity in terms of incomplete predicates exclusivity does not hold, on the constitutive interpretation it must. If a relative relates to a correlative, then it relates only to that correlative and no other. As we shall see, Socrates and Critias take for granted that, for example, sight relates only to colour, hearing only to sound, love only to what is beautiful, and the greater only to the smaller. Some of these constructions are prima facie more plausible than others, but there are ways in which we can make sense of all of them.Footnote ⁹ Besides, our interlocutors arguably presuppose that the pairs of relatives under discussion are existentially symmetrical and epistemically symmetrical, but these characteristics do not play any significant role in the argument.

The most prominent feature of constitutive relativity, however, is aliorelativity, and matters are complicated in that regard. On the constitutive view, a relative just is the relation to its correlative, and the latter must be something distinct from the relative itself. Reflexivity, let alone strict reflexivity, is extremely problematic and, on some views, cannot obtain on pain of incoherence. For constitution is not a reflexive relation: no item can be constituted just by its relation to itself. Rather, the constitutive relation is a grounding relation, a fundamental and unitary relation between a relative and its correlative. And, arguably, grounding relations are irreflexive. In principle, therefore, if the Argument from Relatives presupposes constitutive relativity, there are philosophical as well as dialectical reasons for rejecting strict reflexivity if not reflexivity tout court. Nonetheless, since the real purpose of the argument is controverted, we need to look closely at each of Socrates’ counterexamples in order to judge that issue.

The structure of the Argument from Relatives is as follows. The cases in question constitute three main groups that the interlocutors consider in turn: perceptual states, namely sight, hearing, and, generally, the senses (167c8–d10); certain psychological states irreducible to perception, i.e. desire, wish, love, fear, and belief (167e1–168b1); and what we may call quantitative relatives, namely greater and smaller, double and half, more and less, heavier and lighter, older and younger, and all other cases of that sort (168b2–d1). Then, Socrates shifts perspective and re-examines the perceptual cases of hearing and sound from a different angle (168d1–e2). Also, he briefly mentions the hypotheses of self-moving motion, self-heating heat, ‘and all other such cases’ (168e9–10). These may count as a fourth, separate group, but receive no further attention. After examining each of the above cases, Critias agrees with Socrates that none of them appears to make sense if it receives a strictly reflexive construction. Hence, Critias also agrees with Socrates’ tentative conclusion: assuming that the aforementioned relatives are relevantly analogous to epistêmê, and also that temperance is a form of epistêmê, it seems that strict reflexivity is implausible in some cases and entirely impossible in others (168e3–169a1).

Accordingly, sections 1 to 3 of this chapter discuss, respectively, the groups of perceptual relatives, psychological relatives irreducible to perception, and quantitative relatives. Section 4 is devoted to the re-examination of perceptual relatives and, specifically, of hearing and sight, in terms of powers orientated towards their respective proprietary objects or special sensibles. Section 5 discusses Socrates’ provisional conclusions and comments briefly on the cases of motion and heat. Section 6 is devoted to Socrates’ closing remarks.

1

This first group of analogues remains very close to his paradigm. Take the example of opsis, sight or seeing.Footnote ¹² Socrates hypothesises that there is a unique sort of sightFootnote ¹³ which, like the ‘science of science’, is reflexive: it is of sight and its privation, i.e. non-sight (167c9–10). The relation to its reflexive object is supposed to be exclusive and exhaustive. Even though Socrates does not explicitly state that the hypothesised sight is only of sight, he clearly implies it. For he says that the sight under consideration does not see what the other sights see (167c8–9), i.e. colour (167d1),Footnote ¹⁴ but itself and the other sights, i.e. sight simpliciter, as well as the privation of this latter, i.e. non-sights (167c9–10). Hence a contrast can be drawn between the putative second-order sight and all first-order sights, the object of the former and the proprietary object of the latter.Footnote ¹⁵ Following the paradigm of epistêmê, we may infer that the former can perceive only sight and its privation, whereas the latter can see only green, red, and yellow things.Footnote ¹⁶ If so, then the ‘sight of itself and the other sights’ is, so to speak, intransitive or intransparent in relation to the coloured things that constitute the objects of first-order sights: it perceives the other sights but not the green, red, and yellow objects that they see. Can there really be a sight with the above characteristics? Critias replies that he does not think so (167d3).

In accordance with a practice that he will follow all the way through, Socrates sketches the other members of the group in similar but more elliptical terms (167d4–5). He asks Critias whether he thinks that there could be a hearing that hears no sound whatsoever, but only hears the other hearings and non-hearings as well as itself. Comparably to the example of sight, the hearing in question is probably unique, strictly reflexive, intransparent (in the sense indicated above), and higher-order: it is exclusively directed towards hearing (itself and the other hearings, as well as the corresponding privation), but not towards the peculiar object of first-order hearing, namely phonê, sound (167d4). Comparably to the ‘sight of sight’, then, the ‘hearing of hearing’Footnote ¹⁷ hears only itself but nothing distinct from itself. In this it differs from every first-order hearing, which is always directed towards its own aliorelative object, sound. The ‘sight of sight’ is not of anything substantive, whereas the other sights are. Again, Critias denies that there can be such a sense (167d6).

The last case of this group is more difficult to figure out. On the basis of the two previous examples, Socrates now urges his interlocutor to consider ‘all the senses taken together’ (167d7),Footnote ¹⁸ i.e. examine the supposition that there may be a sense that perceives itself and other sensesFootnote ¹⁹ but none of their objects (167d8–9). We may assume that, in this example too, the sense under consideration is supposed to be strictly reflexive, govern the corresponding first-order senses, and have no access to their proprietary objects. Since it perceives only sense but no sensible, it cannot perceive what the other senses perceive. Some aspects of this example, however, call for further discussion.

In the first place, it is not clear whether the expression ‘some sense’ (tis aisthêsis: 167d7–8) refers to one of the five senses,Footnote ²⁰ or one of the three remaining ones,Footnote ²¹ or a sixth sense perceiving the five senses.Footnote ²² This indeterminacy could be philosophically significant, for it could bear on the vexed question of how we perceive that we are perceiving. And while the interlocutors of the Charmides do not pursue the latter, the idea of a sense sensing itself cannot fail to evoke familiar puzzles in connection to that topic. For instance, is it through one of the five senses that we perceive that we are perceiving, or through some additional sense? Do we do this reflexively, i.e. without also perceiving the object of our first-order perception? Or do we perceive simultaneously both that we are perceiving and what we are perceiving? And what view of perception would be a better fit for each of these or other options? Regardless of Plato’s own intentions, the hypothesis of a higher-order sense directed towards itself is bound to make us think of such questions and look beyond the Argument from Relatives for possible answers.Footnote ²³ Nonetheless, in the absence of such evidence in the present context, I think that we should read Socrates’ reference to ‘some sense’ in a deflationary manner, namely as an invitation to Critias to apply the rules governing the examples of sight and hearing to each and every one of the five senses. Thus, Socrates points to new considerations that his interlocutor might want to entertain and then perhaps revise his attitude accordingly.Footnote ²⁴

Next, while Socrates identifies the objects of sight and hearing in concrete terms, as colour and sound, he refers to the objects of the ‘other senses’ in a more abstract manner, as ‘the things that the other senses perceive’.Footnote ²⁵ Since Socrates uses similar periphrastic expressions in order to refer to the objects of opinion and of knowledge, the difference between ‘substantive’ and ‘formal’ designations has been deemed significant: as has been suggested, each periphrastic formula serves as a place-holder for the ‘substantive’ description of the relevant object, while Socrates postpones the latter for some other occasion.Footnote ²⁶ However, it seems to me that this is an over-interpretation. Since Socrates tells Critias to consider ‘all the senses taken together’, he could hardly give a ‘substantive designation’ of the object. For there is no proprietary object of ‘all the senses taken together’, only of each sense taken separately and in relation to its own special sensible. Also, the difference between ‘substantive’ and ‘formal’ designations does not seem to matter philosophically when it concerns a specific sense. In fact, Socrates refers to the object of sight both as ‘colour’ (167d1) and as ‘what the other sights are of’ (167c8–9), and he substitutes the former for the latter without seeing any need to justify his move. Presumably, he would not object if the same practice were applied to each of the five senses.

Another noteworthy difference between this latter example and the previous ones is the hypothesis that the second-order sight and the second-order hearing under examination extend over their own privations, whereas corresponding second-order sense does not. In fact, from this point onwards, there will be no further mention of privative objects in the argument and one might wonder why. The reason is not, I believe, that privative objects are irrelevant to the logic of the argument.Footnote ²⁷ For since the purpose of the counterexamples is to test the plausibility or conceivability of the ‘science of science’, and since the latter is set over science as well as its privation, it would make sense to craft all the analogues accordingly. One possible explanation is that the examples of sight and hearing suffice to establish the terms in which the analogy with epistêmê is supposed to work and, therefore, Socrates sees no need to continue supplying all the details. Another reason may be dialectical. The explicit mention of privative objects works better in some cases than in others. While one might try to entertain the notion of a sight or a seeing that perceives itself as well as the incapacity to see or the absence of such an occurrent act, the idea that there may be, generally, a higher-order sense orientated towards sense and non-sense appears completely incoherent. Yet another possibility to consider is that, by omitting further reference to privative objects, Socrates intends to alert us to the fact that such objects can be especially problematic. In his final summary of the debate, some of his remarks will bear on this point (175c3–8).

A final comment concerns the question of whether the perceptual cases refer to sensory faculties or sensory activities or some combination of these two. Is Socrates asking whether there can be, for example, a faculty of sight whose sole object is itself and every other such capacity or the absence thereof ? Or is he asking whether there can be a seeing that perceives itself and other seeings as well as the non-occurrence of the latter? This issue has been debated in the literatureFootnote ²⁸ and, therefore, I shall merely outline some aspects of the discussion and indicate where I stand. Regarding the faculty reading, its defenders can point out that the terms opsis (sight), akoê (hearing), and aisthêsis usually refer to capacities rather than activities or occurrent acts. Also, since Socrates’ perceptual examples are supposed to be analogous to epistêmê, and since the latter is arguably conceived as a capacity or a disposition, it seems reasonable to infer that sight, hearing, and every other sense are supposed to be dispositions as well.Footnote ²⁹ Furthermore, as the possessor of reflexive science is able to discern what he himself and others know or do not know, so the person endowed with, for example, reflexive sight is capable of perceiving what he and others see or do not see. Again, the analogy between the ‘science of science’ and reflexive sight or reflexive hearing seems to focus on faculties rather than activities or occurrent acts.

However, the faculty reading has difficulty accounting, for instance, for Socrates’ use of the plural in the hypotheses of ‘a sight of itself and the other sights and non-sights’ (167c10)Footnote ³⁰ and a ‘hearing of itself and the other hearings’.Footnote ³¹ And even though the nouns ‘opsis’ and ‘aisthêsis’ are typically reserved for sensory faculties, arguably they can refer to sensory activities as well. On the other hand, the activity reading offers a prima facie plausible interpretation of these locutions: a seeing perceives itself and other tokens of the same type, and also registers the non-occurrence of such tokens. The higher-order sight hypothesised by Socrates is not a sense but a sensing. And its activity consists in perceiving itself and other such sensings. Nonetheless, the aforementioned arguments in support of the faculty reading tell against its rival, albeit not in a decisive manner. For example, the activity reading does not suit well the paradigm of epistêmê, for, on some views, the latter is primarily understood as a capacity and not as an activity. Also, the activity reading arguably accounts less successfully than the faculty reading for the cases of the second group. Attempts to combine the two readings vary and each has its own problems too. For instance, if one supposes that the higher-order sight under consideration is a faculty of both itself (i.e. the capacity to see) and a given seeing, one needs to confront the undesirable consequence that the terms ‘opsis’, ‘akoê’, and ‘aisthêsis’ would switch meanings within the context of a single example. A reflexive sight would ‘see’ both in the sense of being capable of perceiving the faculty of vision and in the sense of actually perceiving an activity of vision.

The above controversy highlights the fact that no reading on offer can fully account for all the elements of Plato’s text. This is all the more striking because Plato shows himself to be perfectly aware of the distinction between faculties and activities, capacities and occurrent acts, at many places in the corpus. To my mind, therefore, the fact that the perceptual cases of the Argument from Relatives, as well as the psychological relatives of the second group, are susceptible to a variety of different readings is deliberate on Plato’s part. The following consideration may weigh in favour of that suggestion. Methodologically, Socrates constructs his analogues so as to closely match the paradigm: ‘a science of itself and the other sciences and of non-science’ or, in shorthand, ‘a science of science’. Even though ‘epistêmê’, science, and ‘the epistêmai’, the sciences, are more likely to refer to faculties rather than activities, the interlocutors never specify the meaning of these terms. Likewise, even though it seems more natural to take ‘sight’, ‘hearing’, and, generally, ‘the senses’ to refer to faculties rather than activities, Socrates refrains from doing so. In both cases the motivation is philosophical. On the one hand, Critias intends the ‘science of science’ to be as general and abstract as possible: govern everything that is science and all the sciences, the capacity to know scientifically as well as every application of such knowledge, the absence of epistêmê as well as every individual manifestation of it. The all-comprising scope of the ‘science of science’ is terribly important for Critias, since, as we shall see, he conceives of temperance as a unique higher-order science on the basis of which the temperate rulers will discern experts from non-experts and will delegate and oversee the execution of works in the state. On the other hand, if Socrates is to show the strangeness or impossibility of such a science, he needs to cast his net as wide as possible. He needs to show that strictly reflexive relatives behave very oddly or even incoherently, whether they are senses or sensings, capacities or activities, dispositions or occurrent acts. Even so, the perceptual cases presented by Socrates appear calculated to generate further reflection on these matters. The ongoing debate between the defenders of the two rival readings and their variations attests to Plato’s success in that regard.

What is the dialectical value of the perceptual counterexamples discussed above? And what is their philosophical value? I think that they go some way towards justifying Socrates’ discomfort regarding the ‘science of science’ and towards highlighting its main focus. What appears odd about them is not merely that they are reflexive but that they are both reflexive and intransitive, i.e. their relation to themselves or every item of that type is intransparent. Self-sight is of itself and other sights but not of colour, self-hearing is of hearing but not of sound, and so on. While we normally think of the senses as a principal source of information about the world, the ‘sight of sight’, the ‘hearing of hearing’, etc. cannot fulfil that function. Generally, the hypothesis of a sense that can perceive no sensible object is hard to envisage.Footnote ³² And the same holds for the probable implication that the exercise of such a sense will not give access to any specific content. Moreover, the aforementioned cases prompt us to reflect on second-order perception,Footnote ³³ the psychological processes involved in perceptual awareness, and the nature of perception itself.Footnote ³⁴

It is important to acknowledge the legitimacy of raising these issues as well as the philosophical interest that they have in their own right. But it is also important, I think, to stress that Socrates does not appear concerned with such matters in the present context. On balance, T. G. Tuckey’s conclusion seems exactly right:

2

This second group of counterexamples consists of five cases that cover a fairly broad range of psychological phenomena. How to categorise them is controversial and also a matter of philosophical significance, since it bears on the purpose that they are intended to serve. To begin, I shall address this general issue and, moreover, I shall comment on what I believe to be a distinctive characteristic of these examples: they gain plausibility in the light of other relevant Platonic texts.

Despite claims to the contrary, I submit that the cases of desire, will or (rational) wish, love, fear, and belief belong together, and are intended to jointly bolster the point of the perceptual examples.Footnote ³⁶ Textually, nothing indicates that they should be divided into subcategories.Footnote ³⁷ Rather, Socrates treats them as a single group and demarcates them from both what precedes and what follows. He introduces the first member of the group, desire, with the word ‘alla’ (167e1), an adversative conjunction marking the transition from the previous phase of the argument to the present one. Then, after completing the examination of all five cases and drawing an interim conclusion, he flags the move to another group of examples, i.e. quantitative relatives, with the expression ‘phere dê’ (168b2) – an invitation to Critias to turn his attention to this new set of cases. Meanwhile, he uses connectivesFootnote ³⁸ in order to move from one example to another, thus underscoring that there are strong conceptual links between these five cases.

Structurally, Socrates takes care to construct these five examples according to the same pattern and to treat them alike. All of them are strictly reflexive. In every case the relation binding the postulated relative to its correlative is exclusive, exhaustive, and intransparent.Footnote ³⁹ And in every case Socrates refrains from mentioning a privative object, e.g. the absence of desire or of love. In these ways too, the examples currently under discussion appear to constitute the same group and have the same dialectical function. At the same time, we should note that there is continuity between Socrates’ treatment of the perceptual cases and his discussion of this second group. For every example of the two groups suggests a sharp contrast between a hypothetical capacity or activity, which is strictly reflexive and higher-order, and the corresponding conventional capacity or activity, which is first-order and aliorelative. Moreover, as in the former group, so in the latter, Socrates designates the proprietary objects of first-order capacities or activities in two different ways, one ‘substantive’, the other ‘formal’. On the one hand, parallel with sight and hearing whose objects are colour and sound, the characteristic objects of desire, will or rational wish, love, and fear are, respectively, some pleasure, something good, something beautiful, and something dreadful. On the other hand, comparably to the object of ‘all the senses in general’, i.e. whatever they perceive (167d8–9), Socrates indicates the characteristic object of opinion as whatever is opinable (168a3–4) and the characteristic object of knowledge as whatever can be learned (168a5).Footnote ⁴⁰

Philosophically, the five cases of this group taken together amplify the scope of the argument and lend cumulative force to it. The interpretation according to which these examples can in fact admit of reflexive constructions and therefore are intended to undermine Socrates’ ostensible purpose will be rejected, I hope, as soon as it becomes clear what sort of reflexivity is at stake. In fact, as I shall try to show, Socrates is not guilty of double-dealing and Plato does not have a hidden agenda in mind.Footnote ⁴¹ Like the perceptual analogues, the psychological analogues are meant to be taken at face value and can be defended within the limits of a dialectical argument. One of the aims of my analysis will be to highlight an important and largely neglected feature of the cases under consideration, namely that they are intensely intertextual. Part of Plato’s tactics in this passage is, I think, to direct the reader both to other passages of the Charmides and to other dialogues in order to corroborate the seemingly arbitrary claims that Socrates makes about the characteristic objects of desire, rational wish, love, fear, and also belief. Even though intertextuality is an integral aspect of Plato’s strategy in the Charmides,Footnote ⁴² its role seems exceptionally prominent in the passage that we are about to discuss. Let us look at it case by case.

The first counterexample is desire (epithymia). Critias is asked to consider a desire whose sole object is desire, not the proprietary object of desire, namely pleasure.Footnote ⁴³ The relation between the aforementioned desire and its object is constitutive: that desire just consists of its relation to itself or every desire, and this precludes its being related also to pleasure. If constitutive relativity is operative for the first-order desires as well,Footnote ⁴⁴ the converse holds true of these latter. Each of them is related to pleasure, and this precludes their being related also to themselves. Socrates’ language underlines the tentative nature of the argument’s premises: he invites Critias to relay what seems to him to be the case (167e1). Nonetheless, one might object that, as Socrates surely knows, desires can aim at things other than pleasure, such as honour, virtue, or the good.Footnote ⁴⁵ Pain too can be an object of desire, and the same holds for evil as well.Footnote ⁴⁶ Is this example designed, then, to undercut Socrates’ stated goal?

There is no compelling reason to accept this inference. For the aforementioned objection invites the retort that, strictly speaking, we only desire the pleasure of having honour, virtue, something good, or even something evil. Moreover, if Socrates assumes that relatives have a one-to-one relation to their respective correlatives (and there is strong evidence that he does), he can only pick one object for desire and no more. Given that ‘epithymia’ refers, generically, to desire and, specifically, to appetite, pleasure is a plausible choice as the special object of epithymia, or at any rate more suitable than, for example, honour or virtue. The chief philosophical point of the counterexample is also defensible. Although we may conceive of a desire for desire, e.g. for having desires or appetites about various things, it is very difficult to envisage a desire that would be only of desire and not of any desirable object. Desire is an intentional disposition or activity, and a desire that has no intentional object other than desire itself would risk having no content.

Readers familiar with Plato’s Socrates will recall that the claim under discussion is articulated and debated elsewhere. Notably, in the Protagoras, the desire for pleasure and the desire for the good coincide and constitute the basis of the argument purporting to show on hedonistic premises that weakness of will is impossible (Prot. 352e–357e). In the Gorgias, the assumption that pleasure is the ultimate object of desire is embedded in Callicles’ theoretical stance, which combines psychological hedonism, ethical naturalism, and political amoralism. One could pursue the parallel further, enquiring whether there might not be certain significant associations between the brutal ideology of Callicles and the sophisticated position defended by Critias and pointing to his historical counterpart.

The next example is boulêsis, will or rational wish. Critias must consider the possibility of a rational wish that would not be directed to the characteristic object of boulêsis, which, according to Socrates, is the good (agathon),Footnote ⁴⁷ but would only be a rational wish of itself and every other such item or, equivalently, a rational wish only of rational wish and of nothing else. This is constructed, then, as a strictly reflexive item to be contrasted with every first-order boulêsis, which is aliorelative. While the former consists solely of its relation to boulêsis itself, the latter is related to a proprietary object distinct from itself. And while the former governs every boulêsis, it has no access to the good that the boulêsis is of or for. In this case too, the common objection that boulêsis can be reflexive misfires. For the issue is not whether we can rationally wish to have rational wishes, but whether there can be a rational wish that has this as its sole object. And I think that Socrates and Critias are right to give, tentatively, a negative answer: it doesn’t seem so. One can rationally wish to have rational wishes for good things. But what would it mean to have a rational wish for rational wishing, period?

One might object that if rational wishing is a good thing, we should be able to wish for it. A defensible answer, it seems to me, could be that our wishing for rational wishing is a wish for it as a good – an aliorelative object. One might also point out that Socrates’ assertion that boulêsis is constitutively related to the good is arbitrary and ought to have been challenged. However, ‘boulêsis’ is usually related to deliberation and choice, and Plato’s Socrates repeatedly attaches this notion to the operations of reason. Since Critias is portrayed as an intellectualist with Socratic leanings, it is not surprising that he too assumes that, when we rationally wish for something, we wish for it as a good. The idea receives also external support from, for example, the Gorgias and the Laws. In the Gorgias, Socrates contends that a just man will never wishFootnote ⁴⁸ to do unjust things (460c); and he argues that, while power may protect a man against suffering injustice, boulêsis (509d3) suffices to protect him against doing unjust deeds (509c–511c). The legislators of Magnesia also presuppose the closest connection between reason and boulêsis. Prayer ought to be regulated so that the citizens will ask for their prayers to be answered only if they derive from one’s boulêsis, rational wish, and are in accordance with one’s rational judgement. And the same ought to hold for state prayer as well (Leg. 687e).

Next, Socrates presents the case of erôs, erotic love. Let us suppose, he tells Critias, that there is a sort of love that is of love alone, but not of what all other loves are about, namely kalon, beautiful.Footnote ⁴⁹ In accordance with the above pattern, the erôs hypothesised by Socrates is not of anything beautiful, but only of itself and ‘the other loves’ (167e8). On the other hand, each of ‘the other loves’ is of something beautiful, but not of love itself. While the ‘love of itself and the other loves’ is strictly reflexive, ‘the other loves’ are aliorelative.Footnote ⁵⁰ And while the former has no access to the characteristic object of erôs, i.e. kalon, it remains formally open whether the latter have any access to erôs itself.Footnote ⁵¹ Like the examples of fear and belief, the example of erôs too has been denounced as blatantly false and revelatory of Socrates’ or Plato’s real purpose. In the first place, why should Critias accept the arbitrary contention that erôs is characteristically of something kalon, and also why should we accept it? In the second place, it seems evident that there is such a thing as an erôs of itself. There are people who love being in love, never mind with whom. We all encounter such characters in literature, cinema, and, usually to one’s detriment, real life as well. Doesn’t this show that eros can be reflexive in just the sense required by the argument? And if so, should we not conclude that this example is chosen in order to falsify Socrates’ earlier claim that reflexivity is implausible or impossible?

There are grounds for resisting that conclusion. First, assuming that ‘kalon’ here has a predominantly aesthetic meaning, Socrates’ claim that erôs is characteristically directed towards something beautiful (or something perceived as beautiful) is borne out by the opening scene of the Charmides. There, the narrator portrays the beautiful Charmides as the object of erôs for almost everyone present. Not only is he preceded and followed by a throng of young erastai, lovers (154a5, c4), but also his beauty (kallos) appears to have erotic effects on the older men in the gymnasium, including Socrates himself. In the capacity of narrator, the latter tells us more about his own erotic susceptibility to the kaloi, beautiful youths (154b9). He declares himself ‘a blank ruler’ in respect of measuring their beauty, since every one of them appears to him beautiful (154c8–10).Footnote ⁵² He relays that he admired Charmides’ wonderful stature and beauty (154c1–2) and experienced the heat of erotic passion when he accidentally glanced into the youth’s cloak (155d3–e1). He was mesmerised by Charmides’ look (155c8–d1), was charmed by the beauty of the young man’s blush (158c5–6), and attempted to find the beauty of the youth’s soul (154e1–7), even though he managed to withstand his physical attractions.

For his own part, Critias is portrayed as overly susceptible to the beauty of his ward. In the opening scene, he describes him as ‘most beautiful’ (kallistos: 154a5), and asserts that the youth is ‘beautiful and good’ (kalos kai agathos: 154e4), philosophical, and ‘most poetic’ (154e8–155a1), as well as excelling in virtue (157d1–4). Generally, he appears captured by Charmides’ beauty and talks as if he were in love with him. Thus, the dramatic frame of the dialogue illustrates the close relation between erôs and kalon, whether the latter is physical or psychic, and also explains why Critias does not reject the contention that love is characteristically of something beautiful. Besides, in light of the refined aestheticism of fifth-century Athenians, it seems implausible for a man of Critias’ origins and sophistication to reject Socrates’ claim out of hand.

Both Socrates’ claim that erôs is of the kalon and the suggestion that an erôs directed exclusively to erôs and never to its characteristic object would be very strange can be re-examined and re-assessed in the light of different Platonic contexts. One such context is Socrates’ attempt to convey the nature of erôs in the Symposium. While his drinking companions propose different objects of erôs,Footnote ⁵³ he initially describes erôs as ‘a desire for beauty but never for ugliness’ (Symp. 201a). Subsequently, he modifies and elaborates his view in the context of Diotima’s speech. According to Diotima, erôs is really every desire for good things and for happiness, and it includes but is not exhausted by the desire for beautiful things alone (204d–205d). Since loving the good entails desiring to possess it forever (206a), it follows that the object of love is precisely this, to live forever in possession of the good and be immortal (205e): to reproduce and ‘give birth in beauty’ (206b),Footnote ⁵⁴ and thus subsist after death through one’s physical descendants or, better, one’s virtuous acts (208e–209e). Only when Diotima undertakes to initiate Socrates in ‘the rites of love’ (210a) does beauty re-emerge explicitly as the object of the lover’s devotion (209e–211d) so that, in the end, the lover comes to know ‘just what it is to be beautiful’ (211d). Diotima’s speech, therefore, supplies a metaphysical and ethical dimension to Socrates’ assertion in the Charmides, that erôs is of the kalon. And it also provides implicit support to the point of Socrates’ counterexample: those initiated to the ‘rites of love’ understand that eros is orientated outwards towards Beauty, not inwards towards itself. The myth of the Phaedrus too brings out that point, insofar as it depicts the lover’s longing to recollect the ‘radiant’ form of Beauty and his erotic pursuit of Beauty through its earthly images.Footnote ⁵⁵ Again, love is of beautiful things and, ultimately, of Beauty. It is not of itself.Footnote ⁵⁶

But could Socrates hold his ground vis-à-vis the objection that a lover’s love might have solely itself as its own object? Consider for a moment what it would be to be in love with love alone in the absence of any object. You will probably find it difficult if not impossible to envisage what this might be like. An object will always creep into the picture, even on the hypothesis that the lover has no attachment whatsoever to that particular object and would readily replace it with another. Even if the aim of love is merely to perpetuate the disposition or the experience of love, to achieve that aim the lover will always need to love someone or something. If this concession is made, Socrates’ point may stand.

The following case is phobos, fear. Switching the order that he has followed in the earlier examples of this group,Footnote ⁵⁷ Socrates asks his interlocutor whether he has ever thought of a fear fearing fear, i.e. itself and the other fears, but nothing fearsome (deinon).Footnote ⁵⁸ In this case too, the psychological state under consideration is higher-order, has a constitutive relation to its reflexive correlative, and governs its first-order counterparts but not their objects. Moreover, a contrast is implied between that hypothetical fear and every other fear. The former is of itself and the other fears but of nothing fearsome, whereas the latter is, characteristically, of something fearsome but presumably not of fear itself. Critias promptly concedes that he has never conceived of fear in these terms.Footnote ⁵⁹ It is not clear whether he finds Socrates’ hypothesis merely strange or unintelligible.

Like the case of erôs, the case of fear appears especially liable to criticism. While the implicit claim that fear is typically of fearsome things is unexceptional, one may point out that it is uninformative. More importantly, one may object that a fear of fear is perfectly conceivable and commonly experienced. A soldier may fear his fear rather than the enemy,Footnote ⁶⁰ and phobic passengers often fear their own fearful feelings rather than the possibility of an accident. It would seem that the example completely fails to suggest that reflexivity is problematic; if anything, it suggests the opposite.

Socrates need not be troubled by these objections. First of all, although the dialectical form of the argument prevents him from defending the contention that, characteristically, fear is of fearsome things distinct from the fear itself, two incidents that he relays as narrator illustrate the aliorelative nature of the emotion. When Socrates accidentally glanced into Charmides’ cloak and became ablaze, he remembered Cydias’ warning to someone infatuated with a handsome youth: ‘beware of approaching as a fawn approaches a lion and of being seized as his portion of flesh’ (155d6–e1). At the time, Socrates feared that he would be consumed by such a wild beast (155e1–2). His dread was not about fear itself but about something fearsome: the all-consuming power of sexual passion that had him in its grip. Later in the dialogue, Socrates refers to his own fear about a different object. In response to Critias’ accusation that he cares for dialectical victory rather than truth (166c3–6), Socrates declares that the only reason why he wishes to pursue the search is his fear that he might suppose he knows what he does not know (166c7–d2). In a way, his fear is self-referential, since it concerns his own ignorance. Nonetheless, it is not reflexive in the sense that the ‘fear of itself and the other fears’ is reflexive, but has an intentional object distinct from the fear itself.

The idea that fear is typically of fearsome things is presupposed or illustrated in many other Platonic passages. In the Laches, for instance, the interlocutors debate the nature of courage on the assumption that courage primarily has to do with fear of fearsome things (deina), such as the perils of war and of seafaring (Lach. 191d–e, 193a–c).Footnote ⁶¹ Nicias conceives of courage as a sort of general knowledge of what is to be dreaded and what is to be hoped for,Footnote ⁶² as opposed to the specific knowledge of fearsome or hopeful things in specific fields of expertise (194e–196e). In either of these cases, i.e. the expertise equivalent to courage or the expertise in the technai (arts or sciences), the things to be feared or hoped for are distinct from fear or hope itself.

The courageous man knows ‘which ones of these things’ are harmful and fearsome and which ones not (196a). Likewise, doctors know what is to be feared in disease (195b), farmers in farming (195b), seers in the premonitory signs (195e–196a), etc. Not once do the interlocutors of the Laches air the possibility that fear may be also or only of itself. Similar observations apply also to the Republic, since in that dialogue too fear is always treated as an aliorelative whose correlative is distinct from fear itself. ‘What is fearsome’ includes death and Hades (386a–387b), the decimation of one’s family and the deprivation of one’s possessions (387b–388c), pains and pleasures, and desires (388c ff., 429c–d). Correspondingly, Socrates suggests that the city is courageous by virtue of the superlative ability of the trained guardian-soldiers to thoroughly absorb the laws, just like a dye (430a), and ‘to preserve through everything the correct and law-inculcated belief about what is to be feared and what is not’ (430b).

Does the suggestion that fear is typically not reflexive but aliorelative have philosophical merit? I suggest that it does, metaphysically and conceptually as well as psychologically. On the constitutive view, fear must be constituted by its relation to something else, since, if there were a fear solely of fear, that fear would be self-constituting and not grounded in anything. Moreover, there is plausibility to the suggestion that people cannot fear fear without there being some content to the first-order fear. While it is unquestionable that there is such a thing as a fear of fear, it seems virtually impossible to defend the idea that the latter is only of fear and of nothing else. As in the case of a ‘love of itself’, so in the case of a ‘fear of itself’, it seems that one would eventually have to refer to some object, i.e. what the fear that one fears is about.Footnote ⁶³ This appears to be a fact of proper grammar and a feature of human psychology. Those who wish to deny it bear the onus of proof.

The final and most challenging case of this group is doxa, belief or opinion.Footnote ⁶⁴ Conceptually, it lies closest to the paradigm of epistêmê and serves as a springboard from which Socrates reaches a set of interim conclusions.Footnote ⁶⁵ Can there be, Socrates asks, an opinion that is only of other opinionsFootnote ⁶⁶ and of itself but not of ‘what other opinions opine’ (168a3–4), i.e. not of anything opinable? Like all preceding hypotheses, this hypothesis entails that the item to be entertained is strictly reflexive and, by virtue of strict reflexivity, governs the other opinions insofar as they are opinions but cannot access or govern their proprietary object. The latter is designated in a formal manner that carries no commitment regarding the particular content of an opinion but nonetheless underscores its aliorelativity: first-order opinions are of whatever it is that they opine,Footnote ⁶⁷ whereas the opinion under consideration is constructed as an opinion of opinion, namely an opinion orientated only towards opinion itself.

As in the other examples, so in the present one Socrates does not state that the hypothesised item is only of itself. However, in the case of opinion, as in all other cases, he makes this explicit by contrasting the reflexive item in question with its first-order counterparts: the opinion serving as a counterexample is directed towards itself (X is directed towards each and every X), whereas all other opinions are directed towards opinable things. Conversely, for reasons indicated above, we are to infer that the first-order opinions are only of opinables. They are not of themselves as types or instances of opinion.Footnote ⁶⁸ If Critias could defend the notion of a strictly reflexive opinion, he would gain considerable support for his contention that temperance is a strictly reflexive form of epistêmê.

Does the argument go through for opinion? Many contend that it does not, for it is evident that we can opine about opinion. This is what Socrates and Critias are currently doing, and this is what epistemology is about. More than any other example, then, belief or opinion would seem to undercut Socrates’ stated goal, especially because it is the closest analogue to knowledge. If, as the interlocutors agree, there can be no opinion of other opinions and of itself, it seems probable that there also cannot be knowledge of other knowledges and of itself (168a3–a9). If, on the other hand, one accepts the evident truth that opinion can be of opinion, then one should also probably accept that knowledge can be of knowledge. Nonetheless, this objection too derives from a misunderstanding. Socrates constructs his counterexample so as to challenge, precisely, the idea of an opinion that is only of opinion but, most emphatically, of no content.Footnote ⁶⁹ He does not question in the least the possibility of second-order opinions or the coherence of epistemological endeavours.Footnote ⁷⁰ Critias understands him correctly and, therefore, emphatically denies that there can be such an opinion: ‘Of course not’, he says.Footnote ⁷¹

Earlier in the Charmides, Socrates’ sketch of the ‘best method of enquiry’ (158e6–159a4) provides an opportunity to compare and contrast the latter sort of belief with reflective beliefs about oneself. There is nothing strange about the suggestion that Charmides should attend to his own sense of himself and tell Socrates what he takes temperance to be ‘according to [his] own opinion’ (159a10). Likewise, there is nothing strange about the beliefs that the youth expresses in turn, namely that temperance is doing things quietly and decorously (159b2–5) or that temperance is aidôs, a sense of shame (160e4–5). Both these beliefs are self-referential insofar as they concern qualities that Charmides registers in himself. And both are substantive: they are about temperance as well as about Charmides, and say something about a character that Charmides may or may not truly possess. But neither of them is reflexive in the sense specified above. Neither of them is about belief, but rather about the sort of thing that beliefs characteristically are about. My point is this: the target of the counterexample under discussion is not reflexivity or self-referentiality in a broad sense. In fact, ‘the best method’ makes it clear that the latter can be unexceptional, and the same presumably holds for most kinds of higher-order belief. Socrates aims only at the hypothetical notion of a belief reflexive in such a way as to have no content. If this is correct, he is merely stating the obvious not only about belief, but about epistêmê as well.

It seems worth pressing the point that, consistently with the Charmides, Plato standardly treats belief as an aliorelative in other dialogues. In the Meno, knowledge and belief have the same object and that object is distinct from either of these capacities. Socrates uses a well-known example in order to suggest that, at least in some cases, knowledge and belief are equally reliable guides to action: whether one knew the road to Larissa or had true belief about the road to Larissa, one would be in a position to lead people correctly to that town (Men. 97a–b).Footnote ⁷² As in the Charmides, so in Republic V knowledge and belief have distinct objects. But although in the Argument from Relatives Socrates appears to leave the door open for the so-called two worlds of the Republic, the world of epistêmê and that of doxa,Footnote ⁷³ he is not in a position to do the metaphysical work to explain the respective objects of these two faculties. However, he does this work in the Republic. In the argument aiming to convince the lovers of sights and sounds that they have only belief and not knowledge (Rep. V 475a–480a), he distinguishes belief from both knowledge and ignorance and identifies their respective objects: while knowledge is of what-is and ignorance is of what-is-not, belief is of what-is-and-is-not (476d–478e). As it turns out, the empirical particulars instantiating a given Form are cases of what-is-and-is-not and, on account of that fact, they are the proprietary object of belief (478e–480a). For all the controversies surrounding this argument, one thing remains uncontested: knowledge and belief are related to their respective objects in an aliorelative manner. What-is is distinct from the knowledge that knows it, and what-is-and-is-not is distinct from the opinion that opines it.

At this point, we should pause with Socrates to assess where matters stand.

Speaking in the first-person plural,Footnote ⁷⁴ Socrates points out that their assumption that there is a science directed only towards science and not towards any mathêma, scientific object or field, is now under severe strain. Clearly, he thinks that the cases examined so far, taken together, provide reasonable grounds for concluding that, even if the aforementioned science is possible, it is entirely atypical.Footnote ⁷⁵ None of the psychological analogues proved to be relevantly similar to it. Rather, these analogues jointly constitute cumulative evidence for Socrates’ intuition that a ‘science of science’ seems strange or even absurd (atopon: 168a10).Footnote ⁷⁶ However, Socrates shows himself fully aware of the fact that such evidence is inconclusive. And therefore he proposes that they press on.

3

Socrates now returns to the paradigm of epistêmê to discuss it specifically from the perspective of science as a dynamis, power or capacity: a power or capacity to be of something (tinos), i.e. of its proper correlative, whatever this may be. ‘Dynamis’ in this context need not be theoretically loaded or indicate relations of some specific type.Footnote ⁷⁸ Socrates employs this term merely to underscore the assumption that this third group of analogues, i.e. comparative quantities such as the greater and the smaller or the more and the less, are relative to their own correlative objects, just as epistêmê is. If the quantitative relatives of this group can be strictly reflexive, the same probably holds for epistêmê as well. If, on the other hand, they do not tolerate strict reflexivity, it is likely that epistêmê does not tolerate it either.Footnote ⁷⁹

Again, Socrates develops fully the first example of this group and goes more quickly through the others. He supposes that there is a greater (meizon) whose power to be greater than something smaller (168b5–9) is directed towards itself and other items like itself (168b10–11),Footnote ⁸⁰ but is not greater than the correlative object that every other greater is greater than (168b11), i.e. something smaller (elatton). And he infers that, in such a case, the higher-order greater would have to be both greater and smaller than itself, since it both consists in the power to be greater than something smaller and is determined by hypothesis to be its own correlative, i.e. smaller than itself. Critias considers this a necessary inference and assents to it (168c3).Footnote ⁸¹

Also, Critias agrees (168c8) that similar inferences would have to be drawn for other quantitative relatives, if they too received reflexive constructions. Socrates presents these constructions in an elliptical manner, and the reasoning he suggests is the following: since the double (diplasion) must be always of half (hêmiseos),Footnote ⁸² the hypothesis that there is a double ‘of both the other doubles and itself’ (168c4–5) entails that the former would be both double and half. Since what-is-more (pleon) must beFootnote ⁸³ of what-is-less (elatton), a reflexive construction of what-is-more would entail that it would be both more-than-itself (pleon hautou) and less-than-itself (168c9). Since the heavier (baryteron) must be of the lighter (kouphoteron), something heavier than itself (and whatever else is heavier) would have to be both heavier and lighter (168c9–10). Since whatever is older (presbyteron) is necessarily of (i.e. necessarily older than) something younger (neôteron), the supposition that there is something older than ‘the other olders and itself’Footnote ⁸⁴ entails that the latter is both older and younger (168c10). And, as Socrates contends (168c10–d1), the same holds for every other example of that kind.

These counterexamples make a stronger point than the previous ones. For while the latter show strict reflexivity to be extremely odd, they fall short of establishing, even provisionally, that it amounts to nonsense. And while they offer cumulative evidence against the plausibility of strictly reflexive perceptual and other psychological notions, several of those cases invite us to entertain inclusively reflexive notions, such as a love which is both of itself and of what is beautiful, or a fear which is both of itself and of what is fearsome. The comparative relatives constituting this third group are, on the contrary, irreflexive in every way. Socrates and Critias stress that the greater is related to the smaller by necessity (168b9, c1, c3), the double is necessarily of the half (168c6–7), and the same applies to every other such relative (168c10–d1). Although they do not clarify further the kind of necessity involved in these relations, it is probably logical or conceptual necessity. But if it is logically necessary that the power of every such comparative quantity be directed to its characteristic object, and if the latter is invariably aliorelative, the supposition that the power of a comparative quantity will be directed towards itself will entail inconsistency or contradiction.

The implication concerning epistêmê is this: if epistêmê behaves, logically or conceptually, in a way comparable to the way that quantitative relatives behave, then, in all probability, Critias’ definition of temperance as a ‘science of science’ ought to be dropped. Socrates’ next move will be to apply the notion of dynamis, power, to the perceptual cases of hearing and sight and examine these cases again from a new angle.

4

Socrates begins by articulating a principle that he derives from examining the hypothesis that quantitative relatives might be reflexive. Namely, if a relative has a power such as to be of something, i.e. of a certain ousia,Footnote ⁸⁶ and if it has that power directed towards itself, it must also possess the aforementioned ousia – in other words, it must also be its own characteristic object. A greater has the power of being greater than a smaller, and so, if it is directed towards itself, it must also possess that special nature, i.e. it must also be smaller. A double has the power of being double of half and, therefore, if it is directed towards itself, it must also be half. In such cases the relative both has the power to be of a certain ousia and possesses that ousia. In the preceding stage of the argument, the application of that principle to comparative quantities appeared to result in logical impossibilities. In the present passage, Socrates undertakes to show that, when the aforementioned principle is applied to the perceptual examples of hearing and sight,Footnote ⁸⁷ these latter do not fare well either.

First, a brief comment on ‘ousia’ – a term that can mean ‘being’, ‘special nature’, and also ‘that which is one’s own’. Like ‘dynamis’, ‘ousia’ can be a metaphysically loaded term: it can refer to a metaphysical essence captured by a definition. But ‘ousia’ need not to be used in a metaphysical sense and, in the present case, it is not. The context strongly suggests that ‘ousia’ here refers to the special nature of a relative’s proprietary correlative. Thus, the term underscores the one-to-one constitutive relation that, as the interlocutors evidently suppose all along, holds between a relative and what that relative is of: the former is a relative just in virtue of its power to be directed towards its own correlative ousia and no other. Relatives like the greater and the double are clear illustrations of that sort of relation, and perceptual relatives too, as Socrates will now argue, behave in a comparable manner.

Characteristically, hearing is of sound and sight of colour. But let us suppose that there is a hearing of itself and a sight of itself.Footnote ⁸⁸ In the former case, since hearing is directed to itself, hearing itself must have the ousia that it is characteristically related to, namely sound. Regardless of whether hearing is reflexive or aliorelative, it can hear only sound. Hence, to hear itself, hearing must be sonorous. Likewise, in the case of sight, supposing that there is a sight that sees itself, it must have the ousia that sight is characteristically related to, namely colour. Irrespective of whether sight is directed to itself or to something else, it can only see colour. Therefore, if sight is to see itself, it must be coloured. In these examples, then, the distinction between hearing and sound, sight and colour, or, generally, sense and sensible collapses entirely. Prima facie this implication seems unacceptable, even though later on Socrates will intimate that it may be palatable to some people (168e9–169a1).

It is instructive to compare Socrates’ earlier treatment of perceptual relatives with the argument under discussion. For we find that, on these two occasions, he follows different dialectical strategies. In the former passage (167c8–d10), he suggests that the hypothetical cases of reflexive sight and reflexive hearing appear strange on account of the fact that each of them is directed only towards itself (and the other sights or hearings) and not towards the characteristic object of that sense, i.e. colour or sound. Therefore, the strangeness of these cases chiefly results from the intransparency of the relation between the postulated reflexive sense and the characteristic object of the other sights or hearings that it governs. A sight that sees only sight but no coloured object seems incredible mainly because it sees nothing visible. And a hearing that hears only itself and every hearing but no sound appears odd mainly because it hears nothing audible.

Contrast Socrates’ tactics in the latter passage (168d1–e2). Here, reflexive hearing and reflexive sight are shown to be strange not because they don’t perceive sound or colour, but because they must. To repeat the reasoning, since hearing hears only sound and sight sees only colour, if either of them is directed to itself, it itself must possess sound or colour.Footnote ⁸⁹ But the idea that hearing hears itself by virtue of being sonorous and sight sees itself by virtue of being coloured strikes one as paradoxical or absurd. These two tracks of argument undermine the notion of a ‘science of science’ in different ways. According to the first, as it is strange to suppose that there is a sight that sees sight but no colour and a hearing that hears hearing but no sound, so it seems strange to suppose that there is a science or knowledge that knows only knowledge but no discipline. According to the second, the notions of a sonorous hearing and of a coloured sight are extremely odd, and we are prompted to question whether the same holds for the notion of an epistêmê that is simultaneously a mathêma (168a7). As for Socrates, he is poised to draw some tentative conclusions.

5

Socrates urges Critias to ‘see’ (168e3) where the argument has led them. I take it that he uses that form of the verb horan, ‘to see’, not in order to indicate that perception or knowledge or both are reflexive after all (as some scholars maintain), but in an ordinary sense in order to exhort his interlocutor to focus his attention on the inferences to follow.Footnote ⁹² A fair assessment of the latter requires that we take into consideration the following features: the dialectical nature of the argument; its exact purpose and target; and the fact that Socrates ascribes different degrees of credence to different groups of counterexamples. Furthermore, something needs to be said about the reflexive cases of motion and heat as well as the final allusion to those who might remain unconvinced by the argument.

First, then, let us get clear about the sort of warrant that we are entitled to look for. The Argument from Relatives is dialectical and proceeds through analogy and induction. Thus, to judge whether it is successful and whether its conclusion is legitimate, we should not ask whether the premises of the argument demonstrate the conclusion, but whether the former have Critias’ consent and convincingly, albeit not decisively, support the conclusion. I submit that the correct answer is affirmative on both these counts.Footnote ⁹³

As noted, Socrates consistently uses the language of belief both to express the puzzle that motivates the Argument from Relatives and to conduct the latter. At the outset, he tells Critias that, if he is willing to consider cases analogous to epistêmê, he too will believe, as Socrates himself believes,Footnote ⁹⁴ that ‘a science of itself and the other sciences and non-science’ (167b10–c2) is impossible. Thus, he clarifies what the analogues are expected to achieve: provide sufficient grounds for belief, not demonstrative knowledge. Accordingly, after presenting each counterexample of the first two groups, he asks Critias what seems to him to be the case, or what he would say might be the case, or what he imagines to be the case (167d1, 6, 8, e1, 7, 10). Likewise, although he treats the comparative quantities of the third group in a more assertive mode, nonetheless he highlights the dialectical standing of the premises by drawing attention to the fact that they have been secured through agreement (e.g. 168b5, c2). He follows the same practice when he revisits the perceptual relatives of hearing and sight (168d3). For instance, he makes clear that the principle that whatever has its own power directed towards itself also must possess the corresponding ousia (168d1–3) will be treated as a premise only if Critias endorses it (168d3–4). Finally, in the passage cited above, he invites Critias to contemplate the conclusions that seem to both of them (168e4)Footnote ⁹⁵ to have been reached. And he remarks that these latter may incite disbelief in some people,Footnote ⁹⁶ though not necessarily in everyone.

Next, assuming that the premises of the Argument from Relatives bear, specifically, on strictly reflexive relatives and not every kind of reflexive or reflective psychological capacity and/or activity, the same should hold also for its conclusion. On the reading that I defend, the latter does not prejudice issues such as the possibility of higher-order perception and the legitimacy of higher-order belief. Even if Socrates indirectly problematises these higher-order functions, he certainly does not end up precluding them. As I argued, his counterexamples only aim to suggest that as there cannot be a perception only of itself and of no perceptible or an opinion only of opinion and devoid of content, so there cannot be an epistêmê, knowledge, only of knowledge and of no discipline. The conclusions he draws concern just that point. Furthermore, it is important to register that Socrates’ concluding inferences ascribe different degrees of credibility to the counterexamples. He appears to think that some of them offer stronger grounds than others for rejecting the assumption that a ‘science of science’ is possible.

We should bear these observations in mind while we evaluate, together with Critias, the conclusions that Socrates draws for us. On the basis of the different sorts of cases examined above,Footnote ⁹⁷ he infers that, on the one hand, the examples of the third group, namely quantitative relatives of ‘magnitudes and multitudes and the like’ (168e5–6), appear entirely impossible (168e4),Footnote ⁹⁸ while, on the other, the examples of the first and the second groupFootnote ⁹⁹ cause grave doubts as to whether or not ‘they ever have their own power directed towards themselves’ (168e5). While this phrase does not specify whether such doubts concern reflexivity in general or strict reflexivity alone, I propose that we read it consistently with the premises of the argument and take disbelief to concern just cases that receive a strictly reflexive construction: not whether, for example, love ever has its power directed towards itself but whether love ever has its power directed only towards itself. The philosophical disadvantages of the alternative option are considerable, as I hope to have shown.

Up to this point Socrates’ conclusions are defensible. Even his fiercest critics ought to admit that the hypothesis of a sense perceiving itself and no sensible, or generally of a psychological capacity directed towards itself and nothing else, beggars belief. If one does not want to dismiss it out of hand, one has to do conceptual work in order to explain and uphold it. As for comparative relatives involving quantitative measurement, Socrates puts his finger on a genuine logical puzzle and indicates how to avoid it. If the cases he has examined are relevantly analogous to epistêmê, they support (but do not demonstrate) his original claim that the conception of a ‘science of itself and the other sciences and of the absence of science’ is strange (167c4) and, in the light of certain cases, the sort of reflexivity that it exhibits seems impossible (167c4–6).

One may reasonably object that this is a big ‘if’, for it is not prima facie plausible to assume that knowledge is analogous to items as different as, for example, sight, love, and double, even though it may be relevantly analogous to belief. Socrates could respond, however, that his examples are so constructed as to mark out a single feature that constitutes the primary object of this argument: a certain sort of reflexivity, the capacity of a relative to have a one-to-one constitutive relation to itself. Since the analogy with epistêmê focuses on precisely that feature, it is arguably legitimate. And although the conclusions drawn on the basis of such analogues do not necessarily apply to epistêmê, they highlight a truth that the interlocutors of the Charmides and its readers ought to take to heart: reflexivity is not a straightforward phenomenon, and one form of it can be extremely problematic or lead to absurdities. In defending reflective, higher-order knowledge, one should be fully aware of the complexities of that task.

In the sequel of our passage, Socrates concentrates his attention on a subset of the cases where reflexivity arouses disbelief, namely the perceptual examples of hearing and sight. Also, he mentions inadvertently the examples of ‘a motion moving itself and a heat burning itself, and again all other such cases’ (168e9–10) and adds, in the way of an afterthought, that while some people will find such cases unbelievable, others might not (168e10–169a1). Admittedly, there is much here to puzzle us. The latter remark is cryptic, it is not immediately obvious why he singles out hearing and sight again, and the reference to motion and heat appears unmotivated and out of place. I take up these problems in reverse order.

Motion, heat, and ‘all other such cases’ (168e9–10) can be taken to constitute a fourth, separate group. For they do not have any obvious connection with perception or other psychological phenomena or, of course, with quantitative relatives. They are naturally associated with the domain of nature,Footnote ¹⁰⁰ not of psychology. These cases too have commonly been taken to suggest the opposite of what the argument purports to show.Footnote ¹⁰¹ In fact, the objection runs, Plato does conceive of the soul as a self-mover (Phdr. 245c–e) or as self-moving motion (Leg. 894e–896a);Footnote ¹⁰² or, the prologue of the Charmides, in particular the arousal that Socrates experienced when he accidentally glanced into Charmides’ cloak (155d3–4) and his ‘rekindling’ back to his senses (156d2–3), is an illustration of self-moving motion and self-kindling heat.Footnote ¹⁰³ However, first, in describing his arousal due to Charmides’ charms, Socrates does not talk about a motion moving itself, but about something that caused a motion in him. Also, when he relays that, after running the risk of falling prey to Charmides’ charms, he eventually was ‘kindled back to life’ (156d2–3) and regained his self-confidence, he alludes to a heat reviving him, not a heat reviving itself.Footnote ¹⁰⁴ The same holds for his successful effort to regain control of himself: if it is a motion, it is not orientated towards itself but towards a distinct goal. Hence, no conclusions can be drawn regarding the cases of motion and heat in our passage, either on the basis of the opening scene of the dialogue or on the basis of what Plato writes about self-movers in other works.

I propose that, elliptical as these cases may be, they have exactly the same form as all the others and serve exactly the same purpose. They too have no context and are constructed in such a way as to exhibit the property that constitutes the main target of the Argument from Relatives: each of them is of itself and of nothing else. Like the examples of the first two groups, a self-moving motion and a self-heating heat may prima facie seem odd. Nonetheless, the fact that Socrates mentions them towards the end of the argument and lumps them together with hearing and sight (in that order) seems to me significant. For his allusion to those who perhaps do not find reflexivity incredible (169a1) concerns, first of all, these four examples. The reason lies, I think, in the argument that Socrates advanced earlier in respect of hearing and sight (168d1–e1): if hearing is to hear itself, it must be sonorous, and if sight is to see itself, it must be coloured. As suggested, this argument has a forward-looking function insofar as it points to the issue of second-order perception and prompts us to examine reflexivity from that angle, as Aristotle did. Perhaps Socrates suggests that we may do something similar with motion and heat. Even though, taken in abstracto in accordance with the paradigm, the notions of a motion moving itself and a heating burning itself might appear strange, they can make sense if they are appropriately modified and embedded in some specific philosophical context. The argument about the self-moving soul in the Phaedrus, the importance of self-moving motion in Laws X, and the doctrine of universal conflagration and eternal recurrence in Stoicism illustrate different ways in which that goal could be achieved.

Where does the Argument from Relatives leave the interlocutors? Judging by his reactions, Critias now realises that his conception of temperance as a ‘science of itself and the other sciences and the lack of science’ is threatened. He has good reason to wonder whether he made the right move when he contended that temperance differs from all the other sciences and arts in that temperance alone is an epistêmê only of epistêmê and its privation and of nothing else. For his own part, Socrates ended up qualifying his earlier belief that ‘a science of itself’ is impossible (167c6) – a belief tightly intertwined with his staunch commitment to the technê analogy. The examination of different groups of analogues has led him to the tentative conclusion that some relatives are more susceptible to receiving a reflexive construction than others, and that the perceptual cases and the cases of motion and heat are worth re-examining in that regard.

For all its merits, however, the Argument from Relatives is inconclusive. In his final comments, Socrates suggests that its inconclusiveness is a matter of method, outlines what he takes to be the proper way of investigating reflexivity, confesses his inability to undertake such a project, and delegates it to someone else.

6

While the main body of the Argument from Relatives can be interpreted without importing elements from the metaphysics and epistemology of the Republic and beyond, the above passage has an explicitly forward-looking outlook. Socrates outlines a philosophical enterprise to be undertaken at some future time, which will involve the use of diairesis, division,Footnote ¹⁰⁹ – a hallmark of the so-called late Platonic dialogues, in particular the Sophist and the Statesman. He seems convinced that such an investigation could conclusively settle the issue under debate, but nonetheless believes himself unable to carry it through.Footnote ¹¹⁰ Therefore, he expresses his hope that ‘some great man’Footnote ¹¹¹ will take it on. And he sets out the questions that the ‘great man’ would have to answer in a familiar aporetic form. Does no being have its own power directed only towards itself, or do some beings have that power (169a3–5)? And if the latter is the case, does the epistêmê that Socrates and Critias agreed to be identical with temperance belong to their class (169a5–7)? To address these questions, the ‘great man’ would have to systematically divide into classes the-things-that-are (169a3). Since Socrates has no expertise in that method, he cannot pursue this agenda in any thorough manner. Nonetheless, as we see, he ventures to trace the main axis of the division and indicate the direction that the latter should take.

Socrates seems to presuppose that, initially, the ‘great man’ will divide the things-that-are (ta onta: cf. 169a3) into two classes, beings per se and relative beings.Footnote ¹¹² He suggests that the ‘great man’ will subdivide the class of relatives into two classes: beings that have their power directed towards themselves (reflexive beings), and others that have their power directed towards something distinct from themselves (aliorelatives) (169a3–5). He will thus discover whether some beings are reflexive or none is. At this point, the outline traced by Socrates has a gap: while the ‘great man’ is supposed to settle the question whether there can be an epistêmê which is only of epistêmê and no other object, we are now told that, if he finds out that there are beings directed towards themselves, he will be in a position to decide ‘whether or not they include the science that we claim to be temperance’ (169a6–7). But the issue is not whether this latter science is a relative, but whether it is a relative strictly or exclusively of itself (169a5–6). There is no compelling reason to infer that Socrates lifts without warning the proviso that Critias so copiously built into his conception of temperance, namely that it is a science only of science and its privation.Footnote ¹¹³ Rather, Socrates’ faux pas seems to me intended to illustrate that he is not an expert in the method of division, and also invite the careful reader to correct him. Namely, assuming that the class of reflexive beings does have members (169a5–6), one should follow again the right line of the stemma and subdivide it into a class of relatives directed towards themselves as well as some other object (inclusively reflexive relatives) and relatives that are directed only towards themselves and no other object (strictly or exclusively reflexive relatives). This subdivision is necessary in order to judge whether or not epistêmê belongs to the class of strictly reflexive relatives. If the answer is affirmative, Critias will be vindicated, whereas, if it is negative, the ‘great man’ can examine whether epistêmê may belong to the class on the left side of the divisional tree, i.e. the class of relative beings that are of themselves and of some other object as well.

A further comment concerns the nature of the project outlined by Socrates as well as the qualifications of the person who would be able to accomplish it. Unlike the main body of the Argument from Relatives, which according to my analysis can be read without importing ontological commitments, the sketch of the above division clearly bears on ontology. For Socrates assigns to some ‘great man’ the task of dividing ta onta, the-things-that-are, into classes and subclasses with the purpose of discovering something essential about their nature (pephyken: 169a4).Footnote ¹¹⁴ These divisions, therefore, will not be just conceptual and semantic, but will apply to realities. The many divisions in the Sophist and the Statesman develop and illustrate that view. A division effected correctly cuts nature properly at its joints. Its aim is not to project some conceptual pattern onto the world, but to accurately reflect the structure of reality.

We may want to compare the details of Socrates’ sketch with the features of division discussed and illustrated in late Platonic works. The ‘great man’s’ division of the class of relatives into the subclasses of reflexive relatives and aliorelatives (169a3–5) is arguably consistent with the Eleatic stranger’s instruction that ‘it is safer to proceed by cutting through the middle, for in that way one is more likely to come across genuine classes; this’, he says, ‘makes all the difference in how one conducts investigations’ (Plt. 262b). Also, Socrates’ sketch indicates some concern for drawing the divisions systematically and in the correct order, preferably keeping to one side of the stemma and advancing step by step until the nature of epistêmê is discovered and the division is complete. It is obvious that the ‘great man’ will proceed dialectically, not eristically. For a characteristic feature of dialectical divisions, which marks them off with regard to eristic divisions is, precisely, that the former go systematically through the intermediate steps whereas the latter do not (Phlb. 16d–17a, 19a–b). Furthermore, the final move that the ‘great man’ is supposed to make, i.e. deciding whether or not the epistêmê equivalent to temperance belongs to the class of reflexive beings and classifying it accordingly, points to both the taxonomical and the epistemological value of the method of division. Perhaps its fullest illustration occurs in the Sophist: a string of divisions in combination with a long metaphysical detour are drawn by the Eleatic stranger in the hope of capturing the elusive Sophist and of defining him by reference to the divisional tree.

Finally, I should like to say something about the identity of the ‘great man’ and his expertise. Despite contentions to the contrary, there is no reason to believe that the ‘great man’ is Socrates: he explicitly says that he is not. The ‘great man’ could be taken as an anonymous hint at Plato’s future role. Namely, Plato may be indicating that the sort of problem posed by relatives in the Charmides needs a metaphysical answer that Socrates could not provide but Platonic doctrine can make available.Footnote ¹¹⁵ Evidently, Socrates wishes to underscore that an expert in the method of division will be a person of supreme intellectual ability.Footnote ¹¹⁶ Whoever the ‘great man’ may be, he will be able to perform the very demanding mission assigned to him so as to give satisfaction in every respect (169a1–3). Indeed, one might think that the expertise of such a person is almost superhuman. For, in the Phaedrus, Socrates confesses that he is ‘a lover of divisions and collections’ (Phdr. 266b) eager to follow anyone capable of drawing them correctly as if he were a god (266b). Moreover, he says that he has always called such people dialecticians, although he is not entirely sure that this is the right name to use (266b–c). And he attributes to these latter the expertise ‘to divide everything according to its kinds and to grasp each single thing firmly by means of one form’ (273e).Footnote ¹¹⁷

The Parmenides may also be relevant here. In concluding his criticisms against the theory of Forms, Parmenides remarks: ‘only a very gifted man can come to know that for each thing there is some Form, namely, a Being itself by itself. And only an even more remarkable prodigy will make that discovery and will be able to instruct some other person who has sifted all these problems thoroughly and critically for himself’ (Prm. 135b–c). Like Socrates in our passage, Parmenides asserts that only a miraculous expert would be able to pursue the project that he himself merely outlines: prove the existence of Forms and instruct a few other people. Dialecticians alone have the ability to carry out that task, whereas people who, on account of the problems raised in the early part of the Parmenides, deny the existence of Forms and do not try to determine the class to which each thing belongs ‘destroy dialectical reasoning altogether’ (135b–c). Whether or not Parmenides has in mind some sort of collection and division,Footnote ¹¹⁸ he appears to wish for an expert similar to Socrates’ ‘great man’: a dialectician with prodigious skill in the method of division and an understanding of reality that far surpasses one’s own.

In the same spirit, and in line with his intimations regarding the ‘great man’ in the Charmides, Socrates wonders in the Sophist whether the Eleatic stranger might not be some god (Soph. 216a–b). As it turns out, the stranger shows himself an expert in drawing divisions and in investigating his subject through different or complementary divisional paths. Also, he demonstrates his consummate expertise in the Statesman, where he also airs a new thought: while divisions serve to define the nature of the item under investigation (in this case, the statesman), the ultimate reason why we should systematically apply that method is that such practice can make us ‘better dialecticians in relation to all subjects’ (285d) and, perhaps, true experts in dialectic (253d)Footnote ¹¹⁹ and, therefore, godlike. The ‘great man’ of the Charmides could be taken to foreshadow that ideal.

At the end of the Argument from Relatives, however, there does not seem to be an obvious way forward, since Socrates believes himself incapable of dividing being and no ‘great man’ is at hand. Given the inconclusiveness of the Argument from Relatives, he declares that he cannot tell whether a ‘science of science’ is possible (169a8–b1). Nor can he assert without further proof that, if such a science were possible, it would be equivalent to temperance unless he answered to his own satisfaction the second leg of the aporia, namely whether or not the science in question would be beneficial (169b1–3). This latter move comes as a surprise, since it detaches the issue of benefit from the issue of possibility, whereas in the initial formulation of the aporia the former was dependent upon the latter (167b1–4). Now he appears ready to grant, if only for the sake of the argument, that Critianic temperance is credible or possible and proceed to investigate whether it is good for us.Footnote ¹²⁰ At the outset, he indicates his own position regarding the issue that will soon be under scrutiny: ‘I have the intuition’, he says, ‘that temperance is something beneficial and good’ (169b4–5). Pointing back to the view of Zalmoxis according to which temperance is the cause of everything good for man, Socrates now expresses a weaker formulation of that view on his own account. The verb that he uses seems significant: ‘manteuesthai’, ‘to have an intuition’ or, literally, to prophesise, appears to intimate that Socrates considers temperance good and beneficial because of a presentiment deriving from some sort of manteia, prophetic power. If so, Socrates is presupposing that what he intuits is true, even if he cannot explain why it is true.Footnote ¹²¹ And assuming his presentiment has a divine source, he will honour it: perhaps he will accept that temperance is a ‘science of science’, but only if the argument shows that it is beneficial for mankind.Footnote ¹²² Thus, the issue of benefit moves to centre-stage and becomes the topic of a superbly crafted argument that will take us to the end of the investigation.