Ramon Vilà Vernis­

Plato in the cave: a Peircean reading of the myth


­­­­­­­­­­­­­­­­­Abstract: Plato is usually held to be one of the first spokesmen for dualism —first of all by himself—, though Peirce seems ready to dispute this point, at least on account of what Plato’s doctrine would look like if certain strands within it were developed as they purportedly should. The chosen stage for this constructive re-reading of Plato, and for his late mutation into a scientific (sic) philosopher, is the myth of the cave. As it is usually the case with this kind of heuristic exercises, the re-reading works both ways and science does not come out unperturbed of its dealings with dialectics.



         Burnyeat used to say: «There is always someone, somewhere, who is reading the Republic»,1 though he could have said it as well of one part of the dialogue only, the Book VII, where the famous myth of the cave is told. This myth is all that most people know about Plato, and even specialists devote to it much more time and ink than to any other part of his works. It is unlikely though that the author would have been flattered by this, since he denounced poetry in that same book as a dangerous distraction for the philosopher, and left only the door open for a purely pedagogic literature, closely inspired and censored by philosophy. Peirce however would have answered that it was all his fault, for making a too liberal use of his own exception: «There is no philosopher of any age who mixes poetry with philosophy with such effrontery as Plato» (EP-2, 38). And not only this: Plato’s habit of mixing poetry with philosophy, feeling with reason, is part of a broader tendency on his part to take exceptions that he shouldn’t take, or put in a more general way, of a certain tendency of his to exaggerate. Which is no minor fault for Peirce, but the very fountain of every mistake that Plato personally made, and also of those —more numerous still— he passed down to posterity.2 This critical assessment does not prevent Peirce, however, from showing a special indulgence to that past master of philosophy, since he discovers in him the remarkable peculiarity that the mistakes he makes are at the same time, though in another sense, great ideas. And as he grants him the dubious honor of having made worse mistakes than most philosophers, he also allows that he was more right than most of them; so much so that «in regard to the general conception of what the ultimate purpose and importance of science consists in, no philosopher who ever lived, ever brought that out more clearly than this early scientific philosopher» (EP-2, 37).

         The mere mention of Plato as a scientific philosopher will come as a surprise for many. But before we go into the deservedness or not of this title, it is important to see in what sense we can say that Plato generally exaggerates, and what relation can this most excusable tendency —at least seemingly so— bear with his mistakes, which not only include that of mixing poetry with reason, but also, in the brief but discouraging list offered by Peirce, that of favoring the discrete over the continuous, the actual over the potential, and, to cap it all, that of ascribing a practical value to science (EP-2, 37-38). This sense is much more specific than would be expected from the ordinary use of the term, since exaggeration is for Peirce the defining vice of dualism, we could even say, the usual wrapping in which dualism enters into our lives. We should not be surprised, thus, that the philosopher that presented himself as the «apostle of Dichotomy» plays a special part in the history of this vice (Ep-2, 38).

There is scarcely a better philosophical example than the myth of the cave to illustrate the tight relation that can be drawn between dualism and exaggeration. The scenery of the myth is quite explicit: the center of the stage is taken by an all-embracing threshold that divides the space in two and forces us to understand everything that appears to one side of it as opposed to something that appears to the other: outside versus inside, light versus dark, knowledge versus ignorance, virtue versus vice, freedom versus slavery, etc. Indeed, the same basic phenomenology is projected to every corner of the stage, so that every step that is taken on it turns out to be a mere repetition of the fundamental act of crossing the threshold. But despite its being the centerpiece of the set, the threshold is also something that you will vainly search onstage: everything is always to one side or the other of it, never in the threshold, to the point that it has no more consistence nor content than the very terms it divides.

         In Plato’s text, such threshold is typically embodied by the light that should wait at the other side of it. «The glare will distress» the prisoner and make him «unable to see the realities of which in his former state he had seen the shadows», a state that will turn fast into pain when he is forced to look directly at the light; later, when he re-enters the cave his eyes become «full of darkness», leaving him literally disabled before his former companions a vulnerability that will have tragic consequences, as we now (Rep 515c-e, 516e). This treatment of light would be labeled «theatrical» by many a literary critic, and the same could be said of many of the elements (the chains, the conspiracy, the final crime) that Plato adds to the quite familiar bildungsroman he is evoking for his audience. And it must be said that philosophic commentators have also been unenthusiastic about this features of the tale: Annas, to name only one of the most respected, finds all those unexpected jumps from darkness to light and from light to darkness rather inconsistent with the more nuanced versions of the ascent of knowledge that can be found almost everywhere in Plato’s dialogues, including the two images (sun and line) that prepare the ground for the cave in the Republic. If you look at it from a distance, according to Annas, the myth of the cave reveals itself as a mere coup d’effet, an attempt to warm his audience to his philosophical agenda by overstating the misery of their present condition to ludicrous extremes, and by putting at the same time the overcoming of all those ills at hand-reach (Annas, 252-256 ff).

         However edifying the purpose of the tale, it is difficult not to end the detailed analysis of Annas without the conviction that the suppression of poetry from the field of philosophy though not from the republic, of course should be more conscientious than what Plato seemed to think. Literary exaggeration appears to be a much more dangerous virus for reasoned debate than any explicit objection, no matter how strong, because it undermines the very meaning of what is said until it endangers the very possibility of rational argumentation. To Popper’s mind, as we know, this lack of thoroughness looks rather as a cold calculation on Plato’s side: the mixing of reasoning and literature is for him the very essence of metaphysics, and this in turn a Trojan horse that always hides a drive to domination.3 Maybe in our day we won’t feel inclined to adopt such a suspicious stance, but the idea that metaphysical exaggeration has a something to do with our daily troubles is alive and well, and not only in Popper’s tradition: Bruno Latour too chooses the platonic cave to stage a charming parody of the manicheisms that continue to distort our self-understandings and frustrate our commerce with the world.4

         We have already seen that Peirce shared the aversion for any kind of mixing between poetry and philosophy, and he was certainly the first to warn against the dangers of the lack of theoretical rigor and sobriety. However, it is not so clear that he would put the blame for Plato’s exaggerations on poetry; in fact, judging from his definition of aesthetic goodness a theoretical excursion that Peirce himself recognizes as a departure from his most familiar ground the myth of the cave should seem to him as bad from a literary point of view as it did from a philosophic point of view (CP 1.383, 5.291). Plato’s characteristic tendency to exaggeration had a very different source for him, one that might seem odd at first, because it is placed at the very heart of the territory that everyone is trying so hard to protect from its contagion: the mirror of rational thought, i.e. mathematics. According to this, Plato was as dazzled by daylight as the prisoner in his tale, and if he went tumbling is only because he was nearer to the truth than anyone else. But let’s not get ahead of our story.

         In his history of philosophy, Russell insisted on the fascination that the first mathematical deductions may have produced among the Greek, on the feeling of omniscience that he who formulated them might have felt; according to Russell, we could see the birth of philosophy and the extraordinary explosion of theoretical models that it prompted as a direct expression of this mood (Russell, 38 ff.). Plato too gives a prominent role to mathematics in his myth of formation, a role that identifies it to a great extent with the light that marks the threshold of the cave and reveals everything onstage for what it really is.5 The metaphor is not far here from its more literal meaning: as Plato explains, mathematics teaches us to see objects differently of how we are used to see them, in a way that breaks with what we believed to be truest of them. When we consider something mathematically, we take its visible, tangible and generally sensible reality what we would rather take to be its reality tout court as a mere suggestion from which we can define an object purely from thought. Now from an object thus defined we can say that we have a perfect knowledge, or at least unrivaled by anything that we can know otherwise: we can go through every relation among the different features that we have attributed to it until nothing escapes our knowledge, nor awakes the slightest doubt in us. In Peirce’s words, about this object we are «virtually omniscient; that is to say, there is nothing but lack of time, of perseverance, and of activity of mind to prevent our making the requisite experiments to ascertain positively whether a given combination occurs or not» (CP 3.527).

         It does not seem that mathematical illumination falls short of any other historical or religious revelation enjoyed by the human species. From this point of view, Plato’s exaggerations don’t seem so much a spicing for popular use or a subterfuge for political manipulation but a honest try at giving the real measure of what we’re talking about. The difference between the usual understanding of an object and the understanding made possible by mathematics is practically incommensurable, an instantaneous jump from nothing to everything in the most literal of senses. At this point we could be tempted to read all of Plato’s dialogues to the light of the myth of the cave, instead of doing the reverse, and conclude that the word “dialogue” is used with a certain irony here. We should not see them so much as open roads to knowledge but as barricades of words that make visible and tangible the breach that actually separates us from it not unreasonably, since they were the first university brochures. The distance between the dialectical master from his partners turns their alleged dialogue rather into a series of monologues, for both the enlightened and the unenlightened sides, because none of them is really seeing what the other sees in what is said. In the Republic, Socrates barely brings himself to feign some interest towards Trasymacchus’ position, though all his argument is built at least for his hearers and readers in response to his objection.

         But if mathematical revelation seems to offer a glimpse of another world, it also puts the novice’s faith immediately to test, because it doesn’t let him take a single step towards the new horizon it has just shown him a feature not altogether unusual among revelations.  As we’ve seen, the mathematician only attains this privileged perspective over his object when he previously defines it by himself, which certainly turns him into a theoretical superman, able to fly instantly through the most immense distances, to bend and submit without resistance anything that he might find in the world of his creation, and to anticipate with perfect exactness the result of all his actions; he can even make true the proverbial dream of eating the cake and keeping it, if he so wishes, since he has the almost divine power to extend or reduce his definition at will, so that «two propositions contradictory of one another may both be severally possible» (CP 3.527). But at last he has to acknowledge that mathematics are not really interested in reality, that is, not in «how things actually are, but how they might be supposed to be, if not in our universe, then in some other» (CP 5.40). Those are Peirce’s words, but could perfectly be Plato’s, since he also denounced the knowledge given by mathematics as simply «a dream».

         However, Plato believes he has seen enough of this dream to anticipate the path that will enable us to break the circle of definition and reach the really real: according to him, we should extend the investigation to every definable object, and explore it with the help of other thinkers until we have determined the relations that obtain among them all, so that we can climb back reversing the movement of mathematical reasoning toward their first principles. That is, we should get to define the model of models, the model of everything that can be defined by thought. Once we reach this point we are no longer limited, strictly speaking, by any definition, and thus we should have our feet firmly placed on reality itself, a reality of which we should also have a complete knowledge, this time, yes, the knowledge of a god.

         There has been much talk about the lack of clearness and concreteness of Plato’s notion of dialectic, the science that should take us supposedly out of the mathematical dream. There’s the famous definition by Robinson, according to which dialectics actually means «the ideal method, whatever that may be».6 And we may have there the most exact definition we can get: judging by the meager hints offered by Plato, the dialectical method consists in answering every relevant question and in overcoming every pertinent objection.7 Only this kind of totality which can have properly no limits, and thus admits of no definition can turn the dream of the mathematician into de vigil of the philosopher, or in other words, only it can grant any truth to the conclusions of dialectical enquiry; the path that leads to reality is the longest, and before the end there can be no proper knowledge. In this sense, Plato would probably agree with his modern interpreters that his images mislead as much as they lead, but unlike them he wouldn’t think that proceeding by arguments alone is much safer: as long as they remain partial, they won’t be able to do much more than suggest a path to truth; in a sense, an argument can be even more misleading than a myth, because it tempts us to take it as true by itself, and thus prematurely stop the dialectical journey.8 That’s also why Plato’s arguments are so strikingly bad at times, as many commentators many of them with an excess of zeal have warned us: we should not see those arguments as anything more than a sketch, a mere half-way stop for the dialectician, completely unimportant and devoid of truth by itself.

         According to Plato’s myth, the mathematical illumination teaches us to see our ordinary experience as a cave; and as everyone has always reckoned, the cave is a metaphor of particularity, quite intuitively understood as a prison, a closed place, no doubt constricted and with a low ceiling too. He who finds himself trapped behind those almost unbreakable walls, the very provinciality of the portion of reality where he has to live, has access only to this or that particular “datum”; this word catches well his dependent position: trapped as he is in the particular world, things are quite literally given to him. Given by society, by education, by politics, but more generally by the very limitation and finiteness of his experience those are Plato’s fearsome jailers. But if that is the meaning we should ascribe to the cave, then the outside we are longing for cannot be anywhere else than the cave itself and in this we must admit that Plato’s metaphor is much less than intuitive because if the cave were excluded from it, we would find ourselves trapped in a fake outside, listening to canned-birdsongs and gazing at a gas-lit sun. All this could be no more than a poetic fiasco, if Plato didn’t repeat it time and again in his dialogues, to the point that it has developed into a full-blown philosophical topos: the problem of Plato’s “degrees of reality”. Quite expectably, this is also the point where Peirce and Plato part company, though maybe the terms of the parting will be less expected, since they seem more like the terms of a bar brawl than those of a philosophic discussion: to those who think that reality is the «pure distillate of Reason», Peirce can only hope that someone distracts them from their speculations with a good blow in «the small of the back»… maybe this way they will notice that some data are still missing from their ideal model.9 However, the violence of Peirce’s argument has more to do with irritation than with any real confrontation, since he is only asking from Plato that he brings his own principles to their last consequences, that is, that he doesn’t enclose the dialectical enquiry in the comfortable and readily accessible territory of men’s ideas. That is to say, he accuses Plato of giving in to the characteristic cave temptation of clinging to that which is more familiar, and of taking for more real that which is simply more available in this case, his own thought and that of his usual talking party.

         In his renowned paper of 1878 on The Fixation of Belief, Peirce had explained that the dogmatic method —of which Peirce was one of the first and most notorious champions— had to lead inevitably to the experimental method; only a partial and inconsistent application of its own “dialectical” premises could prevent it. But why did Plato fall into this mistake? As Peirce makes clear in his paper, the reason why a man does not inquire more into a question is always and everywhere the same: that there’s no need to —or at least so it seems to him. In fact, Plato too sees laziness in the astronomers that study the movements of the stars by looking at the stars instead of at a sheet of paper, as he takes it that they limit themselves to observing the movements of this or that rock they find in front of their noses when they look up, instead of studying every possible relation among bodies in movement, and the laws that govern their cycles and combinations; it is in this sense that Plato said, rightly enough, that nothing is really gained by practicing astronomy in this fashion (Rep 529-530c). But if someone had answered, as Peirce no doubt would have done, that the astronomer that looks at the sky must keep looking until his eyes go dry, and compare the results of his selfless observation with those of an unlimited number of observers, placed at an also unlimited number of observation posts, until they completed an integral table of the movements of the stars, both in space and in time, Plato would no doubt grant that such an unlimited community of astronomers —assuming that was only attainable— should learn exactly the same as his little party bended on the sheet of paper. His objection would be reduced to the less grandiose idea that there’s no need to go that far.

         The passage of the Republic where Plato advises to practice astronomy without actually looking up has become a hotspot of philosophic wonderment and perplexity, and some even doubt that Plato could be speaking in earnest. However, the radicalism of Peirce’s answer will raise no doubt more than one eyebrow. It is certainly quite reasonable to suggest that there’s no need to survey one by one every singular case in the domain of a science to get some knowledge; indeed, such a tour can teach us absolutely nothing unless it is paired with a simultaneous contemplation of the whole —that is precisely what it means to know something, or to conceive an idea. So then, if we need to contemplate things on the whole and not one by one to learn something —or what in Plato’s imagery would rather be to substitute the eyes of reason for the sensible ones— ¿why not do it from the beginning instead of waiting to the end of the journey? ¿Or maybe from some point halfway? In essence, the reason offered by Peirce is that we can’t be as sure as Plato was of what we see when we contemplate things “on the whole”: «It would be a great mistake to suppose that ideal experimentation can be performed without danger of error».10

         Not even in the sunny region of mathematics can one be sure to see well and not to need a second look. We shouldn’t get duped by the conveniences that we find in this field, and assume that we have emancipated ourselves of all the limitations of our knowledge, so painfully obvious in every other field; and we have good reason to be suspicious, because a closer analysis would show that the mathematician does nothing different —however he might do it in a more controlled and gracious way— than the inhabitant of the darkest corner of the cave. To stick to the ocular metaphor: we can only contemplate several things at a time at the price of reducing to some degree what we see of each of them—or what amounts to the same, at the price of substituting a model defined by ourselves in their place.11 This is as true of the eyes we have in our face as of any other duplication of them that we may project to another cognitive level. Thus, the extreme case of mathematics has only made us aware of the real nature of a problem shared by every form of cognition, from the most crude and muddled to the most sophisticated and formal: you can’t escape the model to get to the really real. And thus considered, it doesn’t seem that Plato’s strategy of reserving our gaze for the great vistas can be of much help; we’d rather think that it will only shut us more tightly in our prison —a prison, it should also be noted, that looks more like the dollhouse of generality than the cave of particularity. But it is not Peirce’s idea to simply reverse the formula, and reveal that we are trapped in generality —or in “signs”, as is more fashionable to say of lately—, when Plato thought us trapped in particularity; rather, his idea is to question every exaggerated opposition between particularity and generality in the domain of knowledge. The absolutely particular is as inaccessible to us as the absolutely general, or rather both are —in a sense that will become clear later— different names for one and the same “real reality”.

         However, and much as Plato’s methods as an astronomer make him a strange guest among the fathers of this science, Peirce thinks that his fundamental intuition is still correct, and goes even further than most of those who have called themselves champions of the experimental method. Just before the curtain goes up on the great scenario of the myth, Plato offers a very enlightening explanation of how we are to interpret it, an indication that bears implicit all that Peirce would want to mark in red in his dialogues. Plato offers only one clue to tell apart the method of mathematics —and with it every other inferior method of knowledge— from the method of dialectics: the former relies on what is at the beginning of the research, the latter only in what is at the end. That is all that Plato can offer by way of explanation, before plunging back into the misty world of myth; and it must be said that Peirce wouldn’t have much to add to that explanation. What he would probably say is that the spatial metaphor of the cave only complicates and to a great extent betrays that very idea. If we should be interested not in the coordinates of the starting and ending points —inside or outside, up or down…— but in how we understand the path —if we “come from” or if we “go to”— ¿why not settle for a simple temporal image, and say that knowledge must rely not in what’s before but in what’s after, not in the first principle but in the final opinion?12

         The idea of entrusting oneself to the future rather than to the past, to what one will know rather to what one has known, has a very clear purpose —the same that Hernán Cortés had in mind when he ordered his men to burn the boats behind them. The requirement to cut with the past includes every guarantee, support or “foundation” that could give a sense of safety to the knower, since that would only be the ironic safety of the bars in the cage. Nothing can get us “out” of an experience limited to this or that datum… unless it is the next datum, and the next, and so on. And this is a movement that must push us beyond the circle of human opinions and formal problems, and lead us in search of the next datum to the most rocky paths of research, the most uncomfortable and opaque to the gaze of the researcher. Peirce is only using his club to encourage Plato to cover this part of the journey too; because the only way out of the cave of particularity —to stick to the formula most cherished by Plato— is to completely explore the relations of each and every particular with the rest of particulars. Plato speaks at times as if the dialectician should distance himself in some way of particulars, when in fact and according to his own description of dialectics, he should go out of his way to meet them, expose himself to them as much as he can. That is exactly what Plato does —via Socrates— when he exposes himself almost obsessively to the objections and questions of his disciples, and that is what Peirce asks him to go on doing with the objections that are in themselves and by definition all other particulars, however they might not be enrolled in the Academy.

         Among the crucial evidence presented against Plato’s dialectics it is frequently cited its contradictory character: sometimes he refers to it as a collective process of dialogue and analysis, sometimes —especially towards the final stages of the progress in knowledge— it seems to be about an intuitive and immediate access to truth, an essentially private “vision” (Annas, 282-283). But in the context in which Plato speaks of such visions, “seeing” seems more adequately read as a metaphor for “understanding”; certainly not a very fortunate metaphor, since it is not likely that the idea of a vision will encourage us to imagine an integral analysis that not only requires an unlimited dialogue, but also an unlimited exploration of reality in its every detail. But beyond the fortune of Plato’s images, there doesn’t seem to be any contradiction in his notion of dialectics, nor any mystic. At least, there doesn’t need to be if we choose to understand, with Peirce, that his method is none other than the scientific method —and that his dialectic “inversion” of deduction can be nothing else, as anyone after Aristotle would have protested, than induction. It is not likely, however, that a reading like this will sound very convincing for a Platonist, who will no doubt think that Peirce is only projecting onto Plato the scientific notions of his day. To be fair, though, it should be said that this point works also, at least to the same degree, the other way around: the experimental method as conceived by Peirce —and his conception differs more than it may seem to the notions of his day— is the same as Plato’s dialectics, only brought to its last consequences.

         According to what was said before of dialectics, and against what one would think when consulting the index of the Collected Papers, for Peirce there’s scarcely anything to say of the experimental method —and a good deal of what is said only adds to the confusion. Science too is «the ideal method, whatever that may be». In particular, every certainty or confidence that the scientist might draw from his instruments, his procedures or the peculiar objects of his research does nothing but adulterate the purpose of his efforts. Plato chose wonderfully well the image of the cave to point out that the prison of the knower is the very idea of a guarantee; and awfully bad, at the same time, since with that he seemed to suggest that the real is something that is somewhere else —or made of another stuff, or…—, which turns the promised way out into a new and exasperating way in. If it is not to suggest more than it is intended to suggest, Plato’s spatial image should be reworked in purely temporal terms, and the same should be said of the famous “degrees of reality” of which the myth seemed to be the map. «Rightly analyzed», according to Peirce, Plato’s philosophy is not dyadic but triadic, and the degrees he distinguishes in reality should be read as potency, act and end.

         The analysis offered by Peirce to prove a statement so contrary to the literality of Plato’s texts cannot be more concise and allusive. In particular, it starts from a point that seems quite contrary to his interests: from the well-known critique that Plato —driven by his dualistic frame of mind— ignores the external causes in Aristotle’s table, that is, the efficient and the final. To which Peirce answers with a characteristic barrage of truncated arguments, more akin to what would shortly be known as “flow of conscience”; with a little reconstruction, it would be something like: Aristotle is not right when he says that Plato denies the external causes, for he doesn’t really deny the final cause, though Aristotle’s thesis is saved even beyond what he could have thought by the fact that Plato does deny the second of internal causes, which suggests rather that it is Aristotle and not Plato who’s being dualistic here —as is shown by his scheme of causes being purely built out of dualities (EP-1, 37-38). So then, both philosophers say what they don’t think and think what they don’t say, and the objection raised against Plato points now to Aristotle.

         But where did Peirce get this idea, that Plato does not reject at all, nay, that Plato understands even better than Aristotle —without ever even mentioning it— what the latter defined as the final cause? Well, from a place that could seem quite unfitting too at first sight: from the identification of ideas with numbers of Plato’s later days. Indeed, it would seem that the old Plato, tired of his ill-conceived effort to break the circle of definitions and sail out finally to the real, had ended by shrinking the extension of dialectics until it coincided again with the domain that he had defined in better years as mere dreamland. But it immediately gets clear that Peirce has chosen not to read in this way the latter turn in Plato’s doctrine: the dangerous idea that «ideas are numbers», according with the formula used by Aristotle to summarize it (Met I, vi), is paired with a progressive recognition of the intimate relation among ideas. However truncated, Plato’s dialectical progress has been driving him apart from his initial preference for the discrete, until he recognized ideas as a net of relations —and thus as something of a continuum, as Peirce would have seen it. The reasoning, as Peirce also recognized, might be incomplete, but it was sufficiently shaped to conclude that Plato did not take —though he might have done sometimes— the object of mathematics to be that of dialectics, but that he rather conceived his legitimate object in the image of how mathematics conceives its own.

         If this is right, then Plato didn’t think that numbers offer us the only real reality, nor a more real reality, nor even —properly speaking— a reality different from that we usually know through experience. What numbers offer us is an incomparable window to see what it could be to really know an object. This is all that Plato would mean by suggesting that the ultimate reality, the reality really known, should take the shape of a number. Since what is a number, and what makes it different from “sensible” things? A number is nothing more in itself than its relations with other numbers. There’s no opaque and unintelligible “something” that the number is and that we could later relate to other opaque and unintelligible “somethings” that would be the other numbers. Five is two plus three, and one plus four, and…: it is no more the former than it is the latter, nor it is anything apart or beyond those relations. Plato would be saying, then, that the heavy substantiality of the thing is nothing but an “optical” effect derived of our limited perspective on things, of our incapacity of exhaustively surveying the relations of a thing with the surrounding totality. If we did, the thing would at last dissolve before our eyes in a matrix of relations: at that moment, and not before, we could really say that we have come out of the cave.

         Summing up, to say that things are numbers is the nearest we can get to saying that reality is in itself relation; we could even say that the true walls of the cave are the mere limits of things, which have no more content nor reality that our own ignorance. In this sense too, we could say that we know nothing until we know everything, and as we announced before, that particularity and generality ultimately converge.13 That is why Peirce concludes, against everything that Plato himself held by mouth or by hand, that Plato’s philosophy is not truly dyadic but triadic: to say that reality is constituted in the last analysis by one and two would be like saying, in a numerical language, that reality is precisely not number —as is shown by Peirce’s own analysis of the “conception” proper to both numbers. And this certainly isn’t what Plato would have said, if he only knew what he was saying.

         Maybe some people will be put off but this way of speculating over what Plato would have said or not in case he had thought differently than he actually thought. But it could be noted that Peirce’s lack of concern for the particulars of what Plato said chimes well with Plato’s own lack of concern with this lesser matters. The radically systematic approach of both Peirce and Plato to the dialectic endeavor —the only approach that, for both thinkers, can really protect us from dogmatism— leads in both authors to an exasperating tendency to revise and question their own past doctrines, and to a hands-on approach to those of others.

         In connection to what has just been said, it is worth noting that in 1910 Peirce was still in the mood to add a sentence to his 1878 paper (CP 5.383). At the end of his account of the dogmatic method, Peirce qualified the almost entirely negative vision he had given of it by noting that in spite of all «this method is far more intellectual and respectable from the point of view of reason than either of the others which we have noticed». Thirty years later, he added: «Indeed, as long as no better method can be applied, it ought to be followed, since it is then the expression of instinct which must be the ultimate cause of belief in all cases». With these words, Peirce was giving out to the dogmatic method the government of our lives in all their practical sides, since it is obvious that it will be impossible to apply a «better method» to those —science, or dialectics, being the only better method in store. We need only consider that a practical issue could be quite reasonably defined as that which by its very nature cannot wait to the end of the dialectical itinerary —which means exactly the same as, to the end of times— to get solved. Such a definition makes it clear why the Greek idea that science could have any practical relevance whatsoever sounded immediately absurd to Peirce’s ears.




[1] M.F. Burnyeat, «Plato as Educator of 19th-century Britain», in Philosophers on Education, ed. Amélie Oskenberg Rorty, Routledge, London, 1998.

2 CP 2.191. See also. 1.662, 2.148, 5.525, 6.445. In fact, all this references only reinforce the idea that exaggeration can function as a proxy for dualism and nominalism —Peirce’s choice term for disavowal.

3 Chapter 9 of The Open Society and its Enemies beautifully links a preference for “bigness” to metaphysic assumptions, authoritarian tendencies and an aestheticist outlook.

4 Latour, 23 ss. Behind the inconsistencies we suspect also the drive to domination, though the oppressors of this tale resemble much the liberatior of Popper’s.

5 The image of the line assingns the first of the two segments that constitute the intelligible world to mathematics and like disciplines; the second corresponds to dialectics. The exact correlation of this indications with the metaphoric universe of the myth of the cave can make for as long a discussion as one wants it to be, but it seems clear that the first contact with light is of a mathematical nature, and so is the initial process of recovery from dazzlement through observing shadows and reflections.

6 Robinson goes on to say: «In so far as it was thus merely an honorific title, Plato applied it at every stage of his life to whatever seemed to him at the moment the most hopeful procedure» (Robinson, Plato’s Earlier Dialectic, citado en Annas, 276). From Robinson’s modern outlook, it is the specialization of the method that gives authority to the results; one would think that for Plato —and for Peirce also— it is just the other way around.

7 Rep 510bss, 532d-535a (especially 534b-e); see also Fedr 276e-277c.

8 «To be sure, the dialectic exploration of reality, which is achieved in argumentational logos, is the ultimate aim of the philosopher» (Szlezak, 98), though while in faciendo, argumentational logos finds a good support in myths to find its way and persevere in it.

9 CP 5.92. The explicit reference is to hegel, but we can easily extend it to Plato as a first-row dogmatic. Moreover, it is a locus communis in history of philosophy that Hegel found his philosophical model in Plato, and particularly in his purest dialectical exercise, the Parmenides.

10 The contradiction with the previous quotation on the virtual omniscience of the mathematician is only apparent, since Peirce immediately adds that «by the exercise of care and industry this danger may be reduced indefinitely» (CP 3.528). See also CP 7.186; 1. 130; 3.529.

[1]1 A more esoteric formula would be: we always know something “as something”.

[1]2 The first utterance of the dilemma or feality occurs in Peirce’s commentary to Berkeley, Ess I, 91.

[1]3 In the «final opinion», the general should coincide with the particular, the sign with its object, or to put it more generally, firstness should coincide with secondness. It is clear that we are not talking here of an “opinion” in any usual sense of the term; in a way, we come closer to what is meant here if we think of death in Heidegger’s conceptual scenario, though a remark like this calls for misunderstanding at least as much as it helps to prevent it.







Annas, Julia. An Introduction to Plato’s Republic. New York: Oxford University Press, 1981.

­­­­­­­­­­­­­­­­­­­­­­­Latour Bruno, Politiques de la nature. Paris: La Découverte, 2004.

Peirce, Charles S. Collected Papers of Charles Sanders Peirce. Charles Hartshorne, Paul Weiss and Arthur W. Burks, eds. Cambridge, Mass.: Harvard University Press, 1931-1958.

Peirce, Charles S. The Essential Peirce, Vols. I-II. Peirce Edition Project, ed. Bloomington: Indiana University Press, 1998.

Popper, Karl. The Open Society and its Enemies. London: Routledge, 2006.

Russell, Bertrand. History of Western Philosophy. London: Routledge, 2004.

Szlezak, Thomas. Reading Plato. New York: Routledge, 1999.