1. A Known Unknown: Why Even Discuss Quantitative Hedonism?

The present note is by way of an appendix to two appendices. In her Platonic Ethics, Old and New, Julia Annas presents an appendix entitled ‘Hedonism in the Protagoras’ (Annas Reference Annas1999: 167–71); in his Plato on Pleasure and the Good Life, Daniel Russell presents an ‘Epilogue: Pleasure and Happiness in Plato's Protagoras’ (Russell Reference Russell2005: 239–48). Though Russell cites Annas's writings extensively in the course of his book, he does not make reference to her appendix in his epilogue. Nevertheless, there is considerable convergence between their views on some key matters regarding the discussion in the Protagoras of the doctrine that pleasure and the good are identical. They agree, in the first place, that the presence of this doctrine in the dialogue stands in need of some explanation. In this, they are more cautious and more judicious than, for instance, Nicholas White, who suggests that the quantitative version of hedonism in question possesses ‘naturalness’ for the dialogue's interlocutors (White Reference White2006: 49). Such supposed ‘naturalness’ is hard to credit, if for no other reason than that it is natural to think, as the characters Socrates and Protagoras agree, that some pleasures are bad and some pains are good (Prt. 351c3–4). If it is natural to think that some pleasures are bad and some pains are good, then quantitative hedonism is anything but a natural doctrine because it is in blatant conflict with something that it is natural to think.

There are some drastic ways to get around the embarrassment caused by this blatant conflict. One of the most drastic is to deny that Plato wrote the Protagoras (Gigon Reference Gigon1946), thus removing the need to justify what we find in it by reference to Plato's understanding—including what we find in other dialogues attributed to the same author—of the questions discussed. But whoever wrote the Protagoras displays a literary and philosophical acumen of a very high order, and, hence, it would still need to be explained why he or she (call her ‘Plato*’) introduces the unnatural doctrine that surfaces in the dialogue at 351b and is in play until at least 358a. Another fairly drastic approach is to say that the introduction of quantitative hedonism is ‘ludic’ or ‘ironic’. This is an ever-seductive option, but it always cries out for some account of the rules of the game and its players or for the prompt to ironising. As we proceed, we shall see some reason for making a very partial diagnosis of a short stretch of the text of the Protagoras in the direction of some playfulness in the offing. Yet, it is pretty clear that Plato or even Plato* is not presenting Socrates as subscribing to the hedonistic doctrine that Socrates offers to Protagoras, and so some have cast doubt on the soundness of the reasoning that underlies the ‘Socratic Paradox’ that only ignorance leads to wrongdoing (e.g., Taylor Reference Taylor1991: 180–81). In some measure encompassing these last points, the explanations that Annas and Russell give of the presence of the unnatural doctrine in the Protagoras turn not so much on what Socrates and Protagoras are represented as believing as on how the dialogue develops and hence on how the dialectical positions change. In short, Annas proposes that Protagoras is forced into ‘the potentially embarrassing position of having accepted a position in argument which he was unwilling to take on’ (Annas Reference Annas1999: 170), while Russell sees Protagoras accepting the position ‘as a friendly aid to his cause’ (Russell Reference Russell2005: 248).

Though there is a difference of emphasis in these accounts, Annas and Russell also agree that it would be extravagant to attribute the doctrine of hedonism to Plato or to that time-slice of him that could be called ‘Plato-writing-the-Protagoras’ (unless, of course, that is a time-slice of Plato*). As Russell puts it:

Granted, then, that hedonism is not a natural doctrine and that it is not attributable to Socrates, to Protagoras, nor yet to Plato, the question remains or arises as to why it is discussed at all in the Protagoras. If, that is, as Annas puts it, ‘Plato thought hedonism in this form worth formulating and discussing, and so introduced it into Socrates’ argument’ (Annas Reference Annas1999: 170), the question is: why? What makes it worth formulating and discussing? Is it not just an arbitrary and ill-founded opinion, in blatant conflict with what it is natural to think, that deserves no further reflection? And is there some formulation of it that is really worth discussing?

2. A Rude Interruption and an Identikit

In addition to the ingenious acccounts that Annas and Russell offer of the textual dynamics of the Protagoras, a supplementary way to answer these questions would be to imagine Plato to be responding to some spur to formulate and discuss the unnatural doctrine that pleasure and the good are identical, and specifically the version of that doctrine that we have already heard called ‘quantitative hedonism’. This is a risky business, not least because efforts to divine Plato's thought-processes on the basis of what we find in the dialogues are always risky. But risk can also be fun or instructive or even both.

Of Plato's three main critical examinations of versions of the view that pleasure and the good are the very same thing, two, the Gorgias and our target dialogue, may date to the years around 380 (e.g., Brandwood Reference Brandwood and Kraut1992: 112, but see also Denyer Reference Denyer2008: 175, and more generally on stylometry, Denyer Reference Denyer2001), while the third, the Philebus, is datable by common consent to a later period in Plato's literary career and may be set aside for present purposes.

It is a standing mystery who if anyone other than an unruly youthful Plato himself (e.g., Reale Reference Reale2001: 20) lurks behind the figure of Callicles, the James Dean or Gordon Gekko proponent of a life of untrammelled desire satisfaction in the Gorgias. Though we are told of his deme (Grg. 495d3), the name of his lover (Grg. 481d5–6) and those of some of his other associates (Grg. 487e4–6), Callicles seems to have left no historical trace outside the Gorgias (Nails Reference Nails2002: 75). It may even be that there was a young man who may or may not have been called ‘Callicles’ and who burnt himself out with the excesses he proposes before making his mark in the city. For the very peculiar view that Plato attributes to Callicles is that pleasure can only be generated by filling a previous lack, so that to increase our pleasures we must increase our desires (Grg. 491e8–2a3). But this model of pleasure-generation is not mentioned in the Protagoras, and this gives us reason to think that whoever was the inspiration for Plato's invention of Callicles was not behind his introduction of the unnatural doctrine discussed in the passage Annas and Russell are concerned with.

Suppose, then, that around 380, Plato is applying his mind to, among other things, various ways in which pleasure might be associated with or opposed to the good. He has in hand two dialogues, one of which would become the Gorgias and the other the Protagoras as we know them. In view of the former, he has his sights on the idea that pleasure must arise out of the satisfaction of a preceding state akin to those of hunger or thirst. And in view of the latter, he has his sights on the idea—which I shall try to make a little more explicit below—that the measure of pleasure is the measure of the good. One thing that unifies these two ideas as targets of Plato's thinking is that each is linked to the idea that there can be a science or an art (technê) of the generation and selection of pleasures. This, in turn, lies close to the key concern common to the two dialogues, namely, the question of whether what Gorgias and Protagoras claim to teach (how to persuade and how to deliberate, respectively) is genuinely a science or an art.

Now I take a further imaginative risk. Though we know next to nothing for certain about the goings-on in the Academy or about Plato's compositional methods, it is not implausible to suppose that he discussed what he was up to with his closest associates and perhaps allowed pupils and other interested parties to be present at such discussions, primarily as an audience. Thus, we may imagine such a gathering in or around 380 in which Plato is setting out what he has attributed, is in the process of attributing, or will attribute to Socrates in the Gorgias about the relation between knowledge of the good and pleasure. Central to this is the notion that there can be no genuine science or art of pleasure but, at best, a sort of knack (empeiria) similar to that of a pastry cook who confects sweets without care for or knowledge about the health of those who eat them (Grg. 464e–5b).

Among Plato's associates there may have been his young nephew Speusippus, who would later inherit the headship of the Academy. If only to please his uncle, Speusippus hazards an explanation of why there can be no genuine science of the sort that Plato is considering. If we take what Aristotle later attributed to a later phase of Speusippus's career and read it back into this imagined conversation, it may be that Speusippus explained why there could be no technê of pleasure by saying that pleasure is indeterminate (aoriste: cf. EN, X, iii, 1173a17). If there can be no technê of what is indeterminate and if pleasure is indeterminate, then there can be no technê of pleasure. In any case, we find something similar in the Philebus (24e, 31a) so that, even if it was not Speusippus who talked this way (yet), something of the sort may have been making the rounds among Plato's associates.

At this point I fling myself headlong into purest speculation, cautioned only by the little that can be guessed about the practices in Plato's school. Let us suppose, then, that the exchange between Plato and Speusippus about there being no genuine science or art concerning pleasure was by way of discussion open to anybody interested in the question, not just to those with more or less specialized interests in ethics. At a certain point, someone in the audience might have lost patience with the negative turn the talk had taken and burst out with something like the following:

• (RI) If the good is what causes pleasure and the bad is what causes pain and if pleasures and pains can be relatively greater or smaller and more or less numerous and of greater or lesser intensity, then we can use the measure of pleasure and pain to arrive at a measure of good and bad.

(RI)—for ‘Rude Interruption’—is a loose and partially proleptic rendering of Protagoras 356a3–5. The interruption also gives a sense of a protest against a Platonic-Speusippean ban on a science of pleasure on the grounds of indeterminacy. For one man's modus tollens is another man's modus ponens: only what is determinate can be measured; therefore, if pleasure can be measured, it is not indeterminate. If there are at least some dimensions along which pleasures can be compared one with another and with pains, then these may be used to try to organize our lives in such a way as to make reasonable choices to avoid avoidable suffering. These dimensions may be expressed in terms of size, number, and intensity, and it may even be that there is some way to integrate these dimensions so as to arrive at an overall value for any given pleasure and, hence, to be able to estimate which pleasures are caused by or are measures of greater or lesser goods.

Supposing something like the Rude Interruption to the consensus between Plato and his nephew, two questions arise: who might have said so brash a thing? And how should one respond to it?

Given what we have already said about how it is natural to think that some pleasures are bad and some pains good, it would seem that our rude interrupter is not one who takes much account of common opinion, for he (and it is most likely a he) asserts at least that, as such, all pleasures are good and all pains are bad. In the economy of the Protagoras, this would also be the voice of someone who says that pleasure and the good are the same thing (Prt. 354c) and that the word ‘pleasure’ can take the place of the word ‘good’ (Prt. 355c), two theses that constitute what we might call ‘qualitative hedonism’. It is only when there is superadded the idea of measuring in (RI) that we have full-blown quantitative hedonism.

As already also indicated, the introduction of the word for ‘indeterminate’ (aoristos) in this debate is due to Aristotle, for whom it is fairly common, appearing about a hundred times in his writings on all sorts of topics. Plato hardly knew the term, using it only three times in total and only in the Laws. So we may be nudged to rejig slightly the terms of our supposed debate to encompass such ideas as the ‘irrational’ (arrhetos) or the ‘incommensurable’ (asymmetros), terms that even if they are not very common in Plato were standard terms of art among the mathematicians in his circle for the relations between the diagonal and the sides of right triangle and between a curved line and a straight one. Even if Speusippus used ‘aoristos’, a mathematician might easily have heard ‘arrhetos’ or ‘asymmetros’, and got hot under the collar: by comparison with determining whether a given circle has the same area as a given square, the choice between two dishes, one roughage-based and healthy in the long run and the other dainty but destructive of one's digestion and one's figure, is, so to speak, a piece of cake. The dietician has knowledge that the pastry cook does not have, and practical choice lends itself to easier calculations than geometry does.

Among the mathematicians known to have been present in the Academy at the time in question some, such as Theaetetus and Theodorus, appear as characters in (later) Platonic dialogues. Others, such as Archytas, do not, though they may be alluded to or quoted without attribution or even being mentioned by name (in Archytas's case, nine times, but only in the Letters). Indeed, it may be that in his rundown of reasons that might be given for saying that pleasure is not a good at all in EN, VII, xi, Aristotle is alluding to Archytas's opinion that the temperate man avoids (bodily) pleasures (1152b16; cf. Huffman Reference Huffman, Caston and Graham2002). But it is not known whether any of those mentioned held or were prepared to express in open debate views about the nature of the good that were in conflict not only with the common opinion that some pleasures are bad and some pains are good, but also with the rather more refined antihedonism of Plato and Speusippus that became a hallmark doctrine of the Academy (Aulus Gellius [Reference Gellius and Bernardi-Perini1992], Noctes, IX, v, 4).

What looks likely, then, is that whoever piped up with (RI) was a mathematician not much acclimatized to the ethical debates of the Academy, that this person was nevertheless to be taken seriously and that he dissented, more or less knowingly, from the common opinion that some pleasures are bad and that some pains are good.

We do not have direct evidence of anyone in or around the Academy in Plato's day who held that pleasure can be measured in the three dimensions of size, number, and intensity indicated in (RI). But we do know from Aristotle of someone who argued (with perhaps greater efficacy than Aristotle gives him full credit for; see Weiss Reference Weiss1979 and Davies Reference Davies, Radice and Tiengo2015) that pleasure is good because (a) all creatures, both rational and irrational, gravitate to their own pleasures (EN, I, i and X, ii); that pleasure must be among the highest goods because (b) it is in reference to it that other goods are praised (EN, I, xii), and because (c) it is chosen for itself and not in view of anything else (EN, X, ii; cf. Plato, Resp., II, 357b7 and Arist., Metaph., XII, vii, 1072b17 and 24); that pleasure must be a good because (d) it increases the good of any good activity to which it is superadded (EN, II, iii and X, iv); and, contrary to a (later?) view of Speusippus, that pleasure is a good because (e) it is opposed to a known evil, namely, pain (EN, VII, xiii and X, ii).

The someone who proposed reasons (a)–(e) in favor of the goodness of pleasure or qualitative hedonism was the geometer and astronomer Eudoxus of Cnidus. If Eudoxus was born in 403, which falls within the chronological range generally admitted (Merlan Reference Merlan1960; Lasserre Reference Lasserre1966: 13–14, 151–56), and if we give credit to Diogenes Laertius who says that Eudoxus was ‘about 23’ when he made his first brief visit to Athens to hear ‘the Socratics’ (Vitæ [Reference Laertius and Reale2005], VIII, viii, 86), meaning most likely the mathematicians of the Academy, and specifically Archytas (Iamblichus [Reference Pistelli1975], In Nic. Arith., 10, 17), then we may tentatively place him in Plato's circle around the year 380.

As already conceded, this is highly speculative and argues backward (abductively). Yet, though that view is not quite consensual opinion, the figure of Eudoxus can reasonably be invoked as at least in the background of the Philebus (Migliori, Reference Migliori2000: 30–31). And it is because Eudoxus comes to mind as someone who might have blurted out (RI) that it is worth suggesting Protagoras 356a3–5 as a crux to explain why Plato might have thought that the unnatural doctrine is, as we have heard Julia Annas saying, ‘worth formulating and discussing’ (Annas Reference Annas1999: 170). Supposing, then, someone brash enough to interrupt so rudely, whether this was Eudoxus or some Eudoxus*, I proceed to the second question posed earlier, namely, how to respond to (RI).

Let us take the two supposed interlocutors into whose conversation (RI) erupts: Speusippus and Plato. Though even younger than Eudoxus Speusippus might, with a certain disregard for the facts in the case, have thought him a bit of yokel who had recently arrived from the colonies and who had perhaps already shown himself rather inept in refined questions of metaphysics, such as the status of the Forms (thus, perhaps reporting later positions, Alexander of Aphrodisias [Reference Movia2007], In Metaph., 79, 3–83,30). So Speusippus permits himself to take no further account of the view that I have been attributing to Eudoxus. Plato, on the other hand, perhaps surer of himself and already well-disposed to the sharp young mathematician, is intrigued by the suggestion. His reaction is to play with the idea a bit and see whether it goes anywhere.

3. Weighing and Reckoning

Does the hypothesis that Protagoras 356a3–5 (i.e., RI) represents a Eudoxan view that Plato is putting to the test throw any light on the discussion in which it figures? One glimmer of insight it gives is that, in line with what Annas and Russell say, we do not have to take any of the options that have been advertised in the literature according to which the doctrine of quantitative hedonism is to be regarded as the belief of some one or more of the actors involved: not of Plato (nor Plato*), not of the characters Socrates and Protagoras, not of their historical counterparts, and not of the ‘many’ whose view is canvassed at 353c1–4e2. But this is rather negative. Nevertheless, the hypothesis of an external spur to formulating and discussing quantitive hedonism may cast at least some sidelights on several rather odd features of our text.

A first oddity lies in the implicit contrast that comes into view shortly after Protagoras has allowed that some pleasant things are not good and some painful things are not bad (351d5–6) and regards the ways in which various factors can be principles (archai: 352b6) guiding behavior. The factors picked out are knowledge, passion, pleasure, pain, love, and fear (352b7–c1), which, in the following exchange, are agreed by Socrates and Protagoras to fall into two categories: knowledge and the rest. Indeed, ‘the rest’ could also be extended to involuntary or compulsive movements such as fidgets and reflexes. For our discussants, knowledge and wisdom are naturally ruling in the soul: if knowledge is dragged about like a slave (352c2), then the soul is disorderly. If any of the rest governs our behavior, then we are not in control of ourselves.

The oddity that comes to light when we encounter (RI) a few pages later is that while Socrates and Protagoras converge on the idea that the knowledge and wisdom that ought to have the upper hand is knowledge of goods and evils (352c4), they implicitly count being actuated by any other of the factors mentioned (including pleasure and pain) as not involving knowledge at all. But if we take the dimensions mentioned in (RI) to be the terms of some sort of calculation, then Eudoxus's hedonism would be one in which it is not pleasure that is the principle of action, but rather knowledge of pleasures (and pains) resulting from an estimate of their size, number, and intensity. Indeed, even the more cautious qualitative hedonist might say that given the identity of pleasure with the good, knowledge of either is knowledge of the other.

Perhaps two further points follow from this. One might be that Plato (or Plato*) was so taken with the opposition between knowledge and the rest as factors of action that he is in difficulty doing justice to the view he wants to test. Suffice it to think of the ways that, in books VIII and IX of the Republic, the analogies between the factors structuring different souls and the constitutions structuring different states determine the terrifying conclusion that the well-ordered life of the ruler of the well-ordered state, in which knowledge (of the good) is hegemonic, will be 729 times more pleasurable (hedion: Resp. IX, 587e3) than that of the tyrant at the dissolution of society properly called thus in which fear dominates (see Adam [1902] Reference Adam1963: II, 360–61, nn. 23–28). This curiously presents an attempt to mathematize pleasure: the word ‘hedone’ and its cognates appear some sixty times between Resp., 561c1 and 591c6, and the model is intended to give a qualitative ordering so as to arrive at a quantitative hedonic value. One moral that might be drawn from the Republic story would be that being actuated by pleasure is not the best strategy for maximizing pleasure. And this is certainly something that Eudoxus could take on board: it is not by being ruled by pleasure that one lives well, but by exercising oneself in questions of geometry and astronomy as he did, thus earning himself a reputation for unusual termperance (EN, X, ii, 1172b15–8).

The other point regards the ambush that Socrates springs on the ‘many’ who want to use the phrase ‘be overcome by pleasure’ (352e1, 3a1, 5, c2, 4e6 and 5c2–6a1) to describe someone who indulges in the immediate pleasures of eating, drinking, and sex while knowing them to be wrong (353c5–6). We shall return in a little more detail to the point shortly, but what Socrates aims to show is that this description must be inadequate if what is known to be wrong (poneros) is that the indulgence is not the best way of getting pleasure in the long run. Again, this is a point that a quantitative hedonist ought to welcome: if we get right the size, number, and intensity of the pleasures that are available to us, then we will not be overly impressed with those that present themselves as immediately available. In this respect, Eudoxus can agree with Socrates that episodes of indulgence are, indeed, cases of ignorance or, at best, of knowledge that is not put to work (cf. EN, VII, viii, 1146b31–6).

If we think of (RI) as a Eudoxan suggestion of the dimensions along which pleasures may be measured, a second cluster of oddities that comes into focus centers on the way Socrates handles the notions of size, number, and intensity. For he appeals to some modes of measuring that do not quite fit the case. Perhaps here we have a hint that Plato himself is not quite sure how to take these alleged dimensions—and surely he was right not to be sure. We may have some inkling of what it is for one pleasure to be greater than another, of what it is for one number of pleasures to be larger than another, and of what it is for one pleasure to be more intense than another. But it must be admitted that these inklings are to some degree muddled. It is not clear, for instance, what differences there might between a great pleasure and an intense pleasure, or what relations might hold between a certain number of pleasures and a certain duration of a single pleasure. And even such numbers seem to have rather more complex relations to time than mere duration would suggest: two pieces of cake immediately may not double my pleasure, though one piece today and another tomorrow may have that arithmetical characteristic.

James Warren rightly describes Socrates's attempts to literalize the notion of measuring pleasure as ‘analogies’ or ‘metaphors’ and notes some of their shortcomings for furnishing a calculus of pleasures (Warren Reference Warren2014: 206–10). It might be worth going a little further to see why they cannot capture what (RI) seems to demand.

The first analogy that Socrates mobilizes is, in place of the size, number, and intensity invoked in (RI), to think of pleasures as having greater or lesser weight. Appealing both to common sense and to an image already deployed in the Euthyphro, he likens the weigher of pleasures to someone who is competent in the use of scales (Prt. 356b1–2), which is to say to someone who can arrive at a result that is not subject to further dispute (Euphr. 7c). The idea of using a measure of pleasure to put an end to dispute is all well and good, but can the analogy work?

A first point would be that, apart perhaps from a certain hippy jargon, it is hard to think of anyone praising a pleasure for being ‘heavy’—and, indeed, to say that a certain pleasure is ‘light’ would seem to be a commendation for those of a certain sensibility. Socrates then introduces two complications that further strain the analogy, one regarding the relation to time and the other the relation to pains.

The former of these complications seems to arise from a dialectic that Socrates plays out for Protagoras's benefit in two passages almost adjacent to the enunciation of (RI) at Protagoras 356a3–5. At Protagoras 355d5 Socrates imagines himself cross-examining someone A who is charged with having allowed himself to be overcome by pleasure. And at Protagoras 356a6, we seem to have another imagined interlocutor, B; rather than recognize differences in size, number, and intensity of pleasures, B says how great the difference is between immediate pleasures and pleasures and pains at a later time, and the former are to be privileged. What A and B have in common is that both take the difference between present pleasures and future pleasures and pains to be the main difference that makes a difference to our choices. A has been overcome by an immediate pleasure because he sees it as different from future pleasures and pains, which he simply ignores. B endorses the priority A gives to time. But Socrates counterattacks wondering whether present and future pleasures and pains differ when considered purely as (he: 356a8) pleasures and pains, and he clearly thinks they do not. If a future pleasure is as much a pleasure as a present one, then the fact of its being in the future should not make any difference to the use of the scales to ascertain its weight.

The incongruity that one might feel here is that the intial advantage of invoking the scales seemed to be that it could provide a procedure for satisfying (RI) without doing too much arithmetic: we just see to which side the scales incline and act accordingly. In this sense, the scales do not seem to be of much help factoring out the degrees of futurity. Though that was no doubt the intention in invoking them as a paradigm case of measuring to put an end to disagreement, the fact remains that A and B can still be misled into favoring immediate pleasures because time does seem to be a factor in our choices. For as common experience teaches, a choice between otherwise equal total amounts of pleasures and pains, over a certain period of time centerd on the present, in which the former are all in the future and the latter in the past or vice versa is not a matter of indifference (McTaggart Reference McTaggart1921–27: §701). Moreover, if one considers a pleasure in the far future less appealing, that may not be because it weighs less but rather because it is (now) less likely: to put it in a modern idiom, we discount on probabilities rather than on payoffs, and given the uncertainties of life, satisficing may be more rational—even the product of an art or a science—than trying to maximize.

The second complication of the scales analogy suggests that both pleasures and pains should be put in the pans of the scales (Prt. 356b5–6). In this extension of the metaphor, pains have negative weight (uplift?). If we wish to be baroque about it, pleasures are like stones with the attendant pains being like helium balloons attached with bits of string. Even without stooping or rising to this level of parody, it might be supposed that we have here at least a symptom that Plato either has not quite taken on board (RI) or is sabotaging by literalizing it in a certain way by putting this complication into Socrates's mouth. In such a case, we might have reason for thinking what we earlier alluded to, namely, that there is something ‘ludic’ or ‘ironic’ in this passage or at least that it is not an entirely thought-out application of what Eudoxus(*) might have meant by (RI).

Though Socrates begins with the idea that pleasures can be measured against each other, the addition of pains into the weighing process must mean that what are being weighed are not pleasures but something more like potential courses of action that are associated with certain nets of pleasure and pain. And this reflects the perfectly unobjectionable locution that one ‘weighs one's options’. In this sense, what are being weighed are already results of calculations—rather than weighings—by which pains are subtracted from pleasures. Given that the commensurability of the various dimensions of pleasures is already problematic, the idea that the size, number, and intensity of pains can likewise be calculated within a single range to arrive at a sum to be subtracted from the value of the corresponding pleasures leaves quite unclear what the commensurating units in question might be. Indeed, it may even be that a guide to decision making does not require that pleasures and pains be directly commensurable one with another (see Richardson Reference Richardson1990).

Socrates then drops the idea of comparing weights and replaces it, swiftly and rather allusively, with that of reckoning quantities at a distance. Here he is picking up at least verbally the first of the factors set out in (RI): the ‘bigger’ or ‘greater’ (meizo) of Protagoras 356a3 recurs at c5. In this latter passage, he likens the size of a pleasure to the way that an object will look larger if it is close up than if it is far away. Conversely, the moon looks as though it is the size of a sixpence coin, though the one is very distant and the other is in my hand; the example is not Socrates's, but it serves our purpose because the text is very cramped. Likewise, the notion of the intensity of a pleasure seems to be modelled by the way that a shout from afar may sound fainter than even a whisper in your ear. Again, the concrete case is supplied because Socrates does not spell the analogy out though perhaps he should have. Along with other cues, these optical and acoustic effects enable us to work out how we are placed relative to the things in our environment: if a sixpenny piece subtended the same angle to my eyes irrespective of where it was placed relative to me, I would be quite at a loss to know how far away it is from me.

The analogies between the reckoning of the spatial extents of such things as the moon and the sixpence and the estimates of pleasures and pains may have a certain intuitive appeal, but, as in the case of the scales, Socrates's gestures at them bring to light some further oddities.

While in (RI) we have three measures of pleasures—size, number, and intensity—the spatial analogy can model only two of these—size and intensity—and then only by relying on implicit analogies with different sensory modalities. Oddly, Socrates supposes that he can extort from B assent to the idea that numerosity (ta polla) will appear to vary with distance (Prt. 365c7). Yet, it would seem that B has every right to say, for instance, that three buttons close up visibly have the same numerosity as three towers in the distance. As a good (proto-)Euclidean, Eudoxus(*) is likewise free to say that where space has three dimensions (up-down, back-forth, and left-right), what is at issue in choosing pleasures is always and only the future. Moreover, where the disposition of space seems homogeneous, differing levels of unpredictability in our circumstances may—for the reasons similar to those hinted at above about satisficing—mean that our strategies or priorities in choosing pleasures may vary from moment to moment. In times of great uncertainty about our future, such as war, immediate pleasures may reasonably be allowed to be more salient objects of choice than in periods of tranquillity.

The ‘intuitive appeal’ of the analogies of the scales and of reckoning quantities in space to which we have alluded may emerge in light of the contrast term that Socrates employs. If one is inept in the use of scales or unable to grasp that the moon is bigger than a sixpence, then one will be subject to the ‘power of appearance’ (tou phainomenou dynamis: Prt. 356d4). If one succumbs to the appearances of pleasures that seem big but are not, that seem numerous but are not, and that seem intense but are not, then one will bungle everything and not live a life of pleasure even if that is all one is aiming at. So far, so negative. What the use of the scales and the capacity to estimate quantities at a distance are supposed to exemplify is ‘the art of measuring’ (he metretike technê: first at Prt. 356d4 and then, in quick succession, at d8, e3 and 4, 7a1, b2 and 4, d7). The art of measuring, then, is a guard against the illusion (phantasma, 356d8) imposed by the power of appearance.

In running through the advantages of the art of measuring to ‘save our lives’ (356d3 and 7a6–7), Socrates emphasizes that it would allow us to choose those pleasures that really are greater, more numerous, and more intense, and he introduces the arithmetical-Pythagorean notions not only of excess and defect, but of the even and the odd (357a2–3) to indicate that, unlike the use of the scales, this type of measuring really calls for some expertise and calculation. But, once again, he makes misleading reference to the nearer and the farther (357b1). From the point of view of the art of measuring, this reference is something of a red herring, as we and Socrates have already hinted, and Eudoxus(*) was free to say, because the pleasurableness of a pleasure does not depend on when it is enjoyed. If pleasurableness coincides not only with goodness but also with choosableness, as (RI) would seem to assert, then the choice of a lesser pleasure is indeed a sign of ignorance.

But it might be thought that considerations of the nearer and the farther are functional to explaining how Socrates's first interlocutor A was overcome by an immediate pleasure: given that A was subject to the power of appearance, the pleasure he chose seemed greater because nearer; had A been in possession of the art of measuring, then he would not have chosen it and thus saved himself from having less pleasure than was, as a matter of fact, available to him. Even though, at Protagoras 356a8, Socrates has responded tartly to B’s defence of A’s choice, he seems, at 357b1, not to have got his own message and to continue thinking of nearness and farness as characteristics that make for or against the choosableness of a given pleasure. This, in turn, might be a sign that Plato is not attending fully to what has been presented to him at least implicitly in Eudoxus(*)’s rude interruption (RI), and still has an ear for the choosableness of pleasures on grounds other than size, number, and intensity—such as what that arch-quantifier Jeremy Bentham puzzlingly called the circumstance of ‘propinquity’ (Reference Bentham1823: IV, ii).

In short, the analogies or metaphors that are deployed to get a handle on (RI) seem hardly apt to cash out what someone, such as Eudoxus, might have in mind when talking about measuring the size, number, and intensity of pleasures.

4. No More than Part of an Art

At Protagoras 357b6–7, Socrates suddenly says that he and Protagoras will have to put off to another time the enquiry into what the art or science of measuring consists in. Though it is not attested in any Greek text prior to the Protagoras, the adjective for ‘measuring’ (‘metretikos’) was not a hard neologism to coin out of ‘metros’. Socrates uses it, as we have noted, eight times in the space/time of barely more than one Stephanus page, and then drops it. It does not appear again in the dialogue. Apart from what we have already alluded to regarding the Republic, the formula for the ‘art of measuring’ recurs also in the Statesman (at Pol. 283d1, 284e2, 285 a1 and c1 and 286d1) associated with the art of ruling, which, in line with the accord between Socrates and Protagoras at Protagoras, 352c4, is a matter of knowing about goods and evils rather than about pleasures and pains. Still, some concluding remarks may be in order about why this way of talking so quickly looks unpromising and why it perhaps looked unpromising to Plato himself when applying it to the notion of pleasure.

The use of scales is an art of measuring weights and does not call for much skill. Some part of geometry—something like a theory of perspective or trigonometry—is an art of measuring the sizes of objects at a distance as well as of measuring the distances at which objects of known size are placed. Some part of acoustics is an art of measuring the intensity of sounds at a distance, and knowledge of the relative speeds of light and sound in air can be used to provide a measure of distances, as in the case of colocating lightning and thunder. Arithmetic is an art of measuring relative numerosity and also such complex matters as excess and defect and the odd and the even. These are species of which metretike technê is the genus. Each species has its own modes and skills and, in some cases, units of measuring. You cannot weigh a distance or a height, and only when you have some relevants units can you give a number to a weight or a height. While weights ought to be in, for instance, pounds or kilos and heights in feet or meters, it makes no sense to say that a certain stone weighs three-and-a-half feet.

In its brief and metaphorical appearance in the Protagoras, the species of the art of measuring that would apply to pleasures is expressed as if one could simply carry across modes and units from the other species just mentioned. In the appeal to the scales, one pleasure is to be counted as ‘heavier’ than another if it is more pleasurable. But this should not be taken to allow that a pint of pure pleasure weighs a pound and a quarter, for example. Rather, the heavier stands to the lighter as the more pleasurable stands to the less pleasurable (or vice versa). Or again, the use of the scales stands to the measurement of weight as the use of something stands to the measurement of pleasure, and pounds and kilos are units of weight as something is a unit of pleasure.

The trouble, of course, is that we (in the broadest sense, including presumably Eudoxus*) are quite in the dark about what the ‘something’ to be used and the ‘something’ to be numbered might be when it comes to measuring pleasures. That is, given that (RI) is couched in terms of sizes, numbers, and intensities and that we do not know what counterparts of these to measure when it comes to pleasures, the promise of there being a technê for ending dispute and for giving (numerical) values to pleasures is just that: a promise.

After all, there are obstacles that look insurmountable to fulfilling a promise of even outlining an art of measuring pleasures. Too many kinds of things seem to answer to the conclusions of lines of reasoning like the arguments (a)–(e) that Aristotle attributes to Eudoxus, and some of the kinds of things that answer to one or another of (a)–(e) seem quite different from—and even incompatible with—some of those that answer to one or another of the other arguments. For instance, there are important differences between the anaplerotic pleasures that Callicles insists on and many other sorts of bodily pleasures, not to mention the differences between the large class of bodily pleasures that, as Aristotle observes, have appropriated the surname (kleronomos) of pleasure (EN, VII, xiii, 1153b33–5) and those that a temperate hedonist like Eudoxus cultivates in his preferred activities of geometry and astronomy. If only on these grounds, Elizabeth Anscombe was surely right to say that the concept of pleasure ‘reduced Aristotle to sheer babble . . . because, for good reasons, he wanted to make it out both identical with and different from the pleasurable activity’ (Anscombe Reference Anscombe1958: 27). And if the emphasis here falls on ‘for good reasons’ in both directions, we may have at least some measure of the polysemy in play, even if we do not have the instruments for keeping it under control.

Since the time of Eudoxus and Aristotle, there has been no shortage of proposals for characterizing, classifying, and hierarchizing at best some rather haphazard samples of the very different kinds of things that are pleasures. Apart from those just alluded to, we have yet to see strong reasons for privileging, for instance, Epicurus's distinctions of the natural and the necessary, and of the katastematic and the kinetic, however we should reconstruct them (see Nikolsky Reference Nikolsky2001), relative to Mill's distinctions of the qualities of the higher and the lower, however we should reconstruct them (see Donner Reference Donner and Skorupski1998), or vice versa.

In the more recent philosophical literature, we find, for instance, Fred Feldman citing a passage of Brentano in which the idea is mooted and mocked of someone's claiming that his pleasure in listening to a Beethoven symphony is 127 times greater than that of smoking a good cigar (Feldman Reference Feldman2004: 45). Feldman's partial dismantling of Brentano's mockery presupposes that there is some unit of ‘“size”’ (49, scare quotes his) that make such pleasures ‘in principle measurable’ (ibid.). Feldman calls this a ‘hedon’ (introduced on p. 25) but does not explain quite how to conceive of hedons, which seem to have some characteristics, such as countability and perhaps linear additivity, of what others have called ‘utiles’.

In parallel, it may be enough to attend to the subtitles of books such as those by Yale psychologist Paul Bloom, How Pleasure Works: The New Science of Why We Like What We Like (Bloom Reference Bloom2010), and by Johns Hopkins neuroscientist David J. Linden, Pleasure: How Our Brains Make Junk Food, Exercise, Marijuana, Generosity & Gambling Feel So Good (Linden Reference Linden2011), to get a sense of how narrating certain sorts of empirical findings may be ‘a case of trying to play a conceptual salmon with a cricket-bat or an ace of spades’ (Ryle Reference Ryle1954: 60—recalled also by Miss Anscombe immediately after the remark about Aristotelian babble).

Absent even a minimally plausible taxonomy of the categories in play, there will remain something ridiculous about expecting to find some measure—especially some numerical expression of proportion—common to these very different kinds of things.

All the same, it is hard to get away from the thought that in being overcome by an immediate pleasure and hence subject to the power of appearances and to an illusion, Socrates's imagined interlocutor A (at Prt. 355d5) was lacking some knowledge that, if it had had the upper hand, would have enabled A to make a better choice. That is, if some subject—perhaps Eudoxus himself—were to explain why, in suitably similar circumstances to A’s, he did not succumb to the pleasure that overcame A by saying that, in line with (RI), he had reckoned the size, number, and intensity of some alternative to what overcame A and had chosen a course causing pleasures that were bigger, more numerous, or more intense (in some proportioning of those dimensions), would we not say that Eudoxus was actuated by knowledge that A lacked? Even if this knowledge was not a full-blown art of measuring, because the dimensions mentioned are mere placeholders for the something that should be measured when measuring pleasures, Eudoxus's effort to subtract himself from the power of appearances and illusion does seem to represent a line of thought that, as Julia Annas says, is ‘worth formulating and discussing’ (as previously cited, Annas 1999: 170). But in the nearly 2,500 years since the Protagoras was written, we have not yet seen a formulation that is not ‘sheer babble’, and that is really worth discussing.