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 allembracing 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 selfunderstandings 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.
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 A more esoteric formula would be: we always know something “as something”.
2 The first utterance of the dilemma or feality occurs in Peirce’s commentary to Berkeley, Ess I, 91.
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.
Bibliography:
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.