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Plato's Cave Allegory

Updated on December 22, 2014

The Cave Allegory

This text is to be found in the VIIth book of Plato's Republic. As usual, it is Socrates who delivers it. Unlike the speech on Eros of the Symposium, there is no attribution to anyone else in this case but the thinking seems to be rather Plato's and the dialogue in which the allegory is related is generally considered to be a Platonic work from the intermediate period - over which the influence of Socratic teachings has been waning and Plato's own philosophic system has begun to emerge more or less in full swing. Although Greek, the word "allegory" is a neologistic projection backwards - Plato does not have this word and calls the "allegory" of the cave an "icon:" this does not mean what the word "icon" means in English, of course; the meaning is rendered more or less by the word "allegory" but there is a catch: Consistently with Plato's mystical inclinations, his word, "icon," suggests that immediate apprehension is available at some point throughout the process of putting together archetype with its token.Significantly, this word contrasts sharply with "mimesis" (imitation). So, strangely when we first think about it, Plato's depiction by means of the cave narrative is not liable to be charged with the mortal sin of the artists who imitate things at a remove. The point must be that the cave narrative appeals directly to the mind and comprehends within itself the whole range of beings so that it, the "icon," is also like the "icon"-like mode of reflection or simulation that allows beings to reflect the Forms and so borrow what makes them be.

Mimetic reproduction, on the other hand, is mindless (the artists, Plato complained, cannot given a reasoned and sufficiently detailed account of what they do in the artistic creation process.) Of course, an image ("icon") that contains within it the imaging of things after their archetypes may itself be evaluated in the same fashion - by appealing to a yet more comprehensive image; this would lead to infinite regress which the Greeks considered a refutation of a theory. Plato addresses this issue directly in the dialogue Parmenides.

Using the word "allegory" conveys the point that the narrative is an illustrative explication of insights into the nature of things, which could be presented directly but at the price of using a more cumbersome and less easily comprehensible idiom. This is also missing, in all likelihood, from Plato's understanding of what his imaging of the relations between sensible and transcendental beings does. The dialogues of Plato are aimed at instructing those less capable of grasping more abstract teachings. At the same time, instruction itself is supposed to be carried out by means of pushing the student toward a more and more direct and ever clearer recollection of the Forms. The dialogue Meno is supposed to be showing how this works.So, the image of the cave is both about education, as Socrates intimates, and it is also an education - as it ought to be since correctness is the criterion of success for Plato, and correctness is attained through the process and the results of the process of matching things with their original standards. The listener to whom the cave narrative is presented is both being educated and becomes an instance of one who has been educated - or, as it is put in the narrative, one who turns around toward the light of knowledge.

We are liable to misunderstand Plato's overall philosophy if we take more creative modes of expression to be more fit in expressing what is otherwise claimed to be ineffable. Plato often has things to say about what is ineffable but his theory requires him to prefer, for the sake of precision, not pictures - or analogical illustrations - but increasingly more abstract modes of delivery. Mathematics is, then, better suited than creative or figurative presentations. The image of the cave is not mathematical or eidetic (concerned directly with how Forms are interconnected )- so, it is, after all, offered for popular consumption.

Socrates makes it clear from the beginning that the allegory is about "paideia", which is translated usually as "education". It should be kept in mind that the Greek meaning is considerably broader than ours and should be rather captured by a phrase like "formation or proper cultivation of the whole person". The education is supposed to be content-ful and not merely a matter of staccato serializations of information: we can understand this today too. But, additionally, the skills the educated person ought to have are also to accrue from training the mental capacities across the board. This is the view that became encapsulated, in the west at least, in the liberal arts and humanities point of view - in sharp distinction to vocational training which was to be understood as decidedly inferior in the strong sense that leaves what is potentially excellent about a human being in a state of brutish and uncultivated impoverishment.

The cave allegory is illustrative of many aspects of Plato's philosophic system and, if the system works as it should, this means that the allegory can be useful in shedding light on any aspect of Plato's philosophy: this is because the parts are all supposed to fit together (everything is related to everything else in nature and so it should be in the theory that gets it right!) (I am resuming use of the word "allegory," but under the caveats that follow from the discussion in the preceding paragraphs.)

In the allegory, we are given a picture that is supposed first to amuse and then terrify us. Imagine, says Socrates... Plato writes in a sophisticated literary manner - rare for philosophers: the use of a verb like "imagine" here takes us from below, as it were: imagination is one of the lower places, below sense perception and knowledge. We will ascend as we sojourn through the story of the cave and when we leave its hapless dwellers behind.

In the cave itself, people are seated on the ground, chained to the spot so that their heads cannot move over the whole range and their bodies are also pinioned so that one cannot rise and attempt to turn around. They behold, and have beheld throughout their lives, shadows cast on the wall in front of them. This is all they know and it cannot even occur to them that shadows require - ontologically - originals which cast those shadows on an impenetrable medium like a wall. We could be cast in the same predicament. The prisoners of the narrative are unaware of the limits of their situation - and, a recurrent theme in Plato's dialogues - one may not figure out that he or she labors under limitations precisely because of suffering from those limitations in the first place. In that case, it seems that improvement is impossible: one would not detect what is missing, on account of the defects made inevitable by what is missing; and one would not listen to those who might know better because persuasion also presupposes minimally shared presuppositions. It is not clear why force would work - which seems to be suggested in the cave narrative, oddly. The resolution of the broader paradox of knowledge - in the Meno - becomes possible because, it is asserted, knowledge is recollection. The prisoners of the cave are presumed incapable of being stimulated by the shadows toward recalling, even if dimly, higher or more abstract (and more real) beings. This is a pessimistic twist that was missing from the Meno (assuming that the Meno is an earlier work than the Republic.)

One of Plato's Socratically inspired preoccupations is that one should strive to attain the correct definitions. Plato thinks of definitions as matching the concepts as they "really" are - this is his theory after all. The cave dwellers are so pathetic in their predicament that whatever they think "shadow" means fails badly to get it right what a "shadow" really is in its ontology (what kind of thing it is, which should be reflected in the definition.) For the cave dwellers, the shadow is a primary thing - they don't get it that it is a thing that has derived or parasitic existence as it depends entirely on the original whose shadow is cast when it is hit by light. The language of the cave dwellers must itself be woefully inadequate to "cut reality" into the right pieces - as Plato likes to put it sometimes, especially in some later dialogues. This view of language, which Plato has, seems rather wrong: one cannot correct language. Nevertheless, the point can be made that we are talking about theoretical definitions here. The theory about natural kinds (what things exist in reality and how they are arranged taxonomically within the nature of the whole), which the natives have, is woefully inadequate. As if we were talking about natives who think that the earth is the only planet that exists and that it is flat, and so on.

The predicament of the cave dwellers strikes us as rather grotesque: it seems unrealistic that one would live life chained like that. We may wonder if the analogy can work - considering the unrealistic character of the depicted predicament. Nevertheless, the relevant element, which will give us the analogy we need, is that something prevents the "prisoners" from getting more and more access to the totality of existent things - only shadows are taken as real by them! From being somewhat incredible - perhaps aesthetically functioning as grotesque - to being posited as an analogy, to being rather amusing, the story then is supposed to turn into a terrifying and eye-opening realization. It could be us! After all, the cave dwellers are not aware of their predicament either. If they were aware, they would not be hopelessly deceived; at least, they could be embarking on a struggle to liberate themselves, to stand erect and turn around toward the "more real" things - the puppets that are manipulated by some mysterious characters, and whose reflections on the wall furnish the totality of things believed to be real by the natives of the cave. They are deceived and they don't know it. It is possible, then, to be deceived (D) and not to know (-K). Logically, this is equivalent with "it is not true that if we are deceived, D, then we know it, K."

In symbols: (D & - K) <=> - (D -> K)

This is what should terrify us. Deception in and by itself does not afford us epistemic opportunities. This is consistent with a broad point Plato never tires of making. The world of sensory experience - the Heracleitian flux - does not make available, in and by itself, any properly effective means for attaining knowledge. Even to detect the deceptions cast by the vanishing things of sensory experience requires that one has ALREADY been aware of the true things, the standards. If deceived, then I must be deceived relative to the truth. The truth - or "more true" state of affairs - in the case of the cave prisoners comprises, as a first step, the realization that there are beings (the puppets) which are the originals of the shadows. The shadows themselves have borrowed being, as it were: their reality depends on that of their originals. But the originals too - the puppets - are themselves vitiated because of the same predicament: their being too is reflective or borrowed - a simulacrum which is anything, has being, only to a lesser degree than its original. The turnaround of the soul (periagoge psyches, in Greek) toward the more real things is only the first step. Only then one realizes that he has been deceived for so long - and the deception could have lasted indefinitely.

Venting his spleen about Socrates' infamous sentencing to death by a massive jury of the "people", Plato takes the opportunity to castigate the "common" masses again. If one were to tell the truth to the prisoners, they would "lay hands on him" and even put him to death for spreading spurious, alarmist, ideological dubious and radical notions. As it happened with Socrates in democratic Athens. We can already see that there even political-philosophic implications to all this.

Plato's Ontology

The cave allegory illustrates Plato's ontology - his taxonomy of the kinds of things that exist within the totality of all existent things. Of course, his epistemology and political theory can also be elicited: he was striving to build a holistic system thinking that the nature of reality is such that anything that is understood fully fits within the hole in such a way that everything should also be understood fully in the process...

In a broad sense, Plato is a Dualist. He accepts both material and non- material entities. He is Realist about both kinds: Realism here means the view that something exists independently of anyone thinking it or observing it. The main source of the oddity of this position is that real (mind-independent), existent things do not have to be in spacetime or in the physical universe.

The way Plato's Socrates speaks about these things might have been peculiar in his own language. Take the verb "to be" and see how we derive the noun "the being" or "the beings" in plural. Plato treats being-ness as a property or attribute. As such, being-ness must be the broadest or universal attribute. Whatever other attributes beings have, they must surely have the attribute being-ness! We will need to revisit this.

This raises a parallel problem about the metaphysical status of nothingness - a problem for Greek Metaphysics since Parmenides at least. Investigating this begins to raise alarms also about taking beingness to be a property. Either nothing is a property - with nothingness the matching concept or Form - or it is not. Either way we run into problems. On the one hand, nothingness may not be a property but the absence of any properties. Down this path, we find some of the odd solutions to the problem of evil (Augustine and Dionysius), denying that evil exists insofar as evil is a negation (of good): as such, evil cannot have the property of being-real or existing-really either. (Notice an anomaly: in the preceding comments, why does it seem that both I am and I am not attributing properties to what is supposed to be a "non-existent?") In the other direction, nothing may be a property - and, Plato thinks. it should be if we can declare a proposition like "there is nothing here" as true - but then, in Plato's theory, it would have to be self-predicated: "nothingness is nothing" would have to be true! We have run into trouble again.

The uneasiness about treating "nothingness" as a property is in evidence in Plato's work: the issue parallels the equally problematic handling of "beingness" as a property. There is no Form of Being as such in Plato (unless the Form of the Good is supposed to be that, which is debatable.) Yet, Socrates in the Republic speaks of things having this property of being to a lesser or greater extent. The Forms, of course, all have this property since they "really are" (ta ontos onta.) We need to keep in mind that "real" and "realness" are interchangeable with "being" in the sense of "existent" and "beingness." The Greek words in the text probably sound as awkward as in the English - but it might be the case that Socrates' interlocutors have become habituated to this way of speaking.

The error in treating "being" and "nothing" as attributes can be argued as a classic example in confusing apparent grammar with logical grammar. On the surface grammatical reading of the sentence "there is nothing outside" it seems that the proposition expressed is the same as "there is something that is outside and it nothings" but it is immediately obvious that this is the wrong reading. Standard contemporary logic fixes the logical grammar as that which is apparent in the sentence "there is not anything outside." A similar case is often made about existence as a property. "There is something that exists" is pleonastic and "there is something that doesn't exist" is contradictory. This is supposed to show that there is a gross misunderstanding involved in taking existence to be a property. Nevertheless, this subject is more complicated once non-standard logical languages are taken into account. There are alternative formal languages that permit treatment of existence as a property. And, unlike the case of nothingness, linguistic intuitions support the view that existence can be a property of entities - although perhaps not of concepts. Incidentally, a property of a property is a second-order property. A lot of what Plato says points to the direction of second-order properties. For instance, to say that all Forms have the property of existence - assuming we are treating existence itself as n-order property - is to attribute to properties the second-order property of existence. Second-order logic is beset by certain formal deficiencies but it is not clear what impact this should have on the metaphysical claims. Another related point is that, it seems, Plato does not "see" any distinction between first- and second-order properties.

One crucial point is to be made next: Plato understands class-inclusion (whether a thing we can call "a" has a property F) to be a matter of degree. Even though classical mathematics has a sharp theory of sets (either what is referred to by "a" is or is not in the set F), our ordinary linguistic conventions seem to work rather with degrees of inclusion: "he is sort of handsome" or "she is tallish." Only the abstract concepts themselves (which Plato takes to be real) are included (self-predicated) to 100% (or let's say to degree 1 with the values ranging between 0 and 1.) So, only Beauty is beautiful to the fullest degree. Let's spell this out. Self-predication means that property X itself has property X. Of course, there is a problem here: X should be a second-order property when predicated of a property X: so we should say X' is predicated of X where, in our example, X' refers to the second-order property "beautiful" and X refers to the first-order property "beuatiful." Compare: "Jill is beautiful and being beautiful is itself beautiful." Plato, however, sees no difference between different orders of properties; moreover, Plato actually treats the substantivized Forms as entities which he names in the same way we name individuals. So, "a, the Form of Beauty, is beautiful" is a first-order attribution of the property "beauty" to the individual entity, the Form of Beauty.

We need names first and the meanings of the names are their referents. For instance, if someone is to be tracked by "a", we say ref(a) = *** where "***" stands in for the entity named by "a". Plato names concepts like Beauty. We know this from another dialogue, the Cratylus. So, let's say that ref(b) =Beauty. The thing named by "b" is in the class Beauty to the degree 1. Nothing else is included to the degree 1. We will be explaining this.

Some "really" gorgeous entity, call it "t" might be in the class Beauty to degree 0.8888. A famous Platonic conceit in this respect, showing the partial influence of Heracleitus, is that the thing referred to by "t" is radically unstable as a sensible, perceptible, physical thing: its matching of the standard Beauty fluctuates all the time. From 0.8888, it might even rise to 0.91 let's say, if the entity works out but it can fall and keep falling because of the ravages wrought by environmental factors, aging, disease, lack of exercise, wrong makeup, etc.... Yet, Plato thinks, we could not have learned the concept Beauty based on this in-flux morass made available through the senses. Besides, take the proposition made by the sentence "t is beautiful." If it is true, something must be responsible for this: a truthmaker must be "causing" the proposition to be true. (It doesn't seem that we are working with the "eternal" propsitions of classical extensional logic.) The truthmaker, though, must have what it takes to engender participation in the standard to some extent. Thus, the possibility that "t is beautiful" is true depends ultimately on the unconqualified truth of the proposition "Beauty is beautiful."

Interestingly, although Plato does not note this, the degree 0.5 is the one of maximum vagueness about whether the property is or is not possessed by the item: it is possessed to the same degree that it is not possessed! Below 0.5 we can say it is true that the negation of the proposition becomes truer and truer by degrees. A consequence of all this is that the law of non-contradiction does not apply (something Aristotle missed about his dear Plato - although he remarked ruefully about it with respect to Democritus and Protagoras.)

Plato's talk of degrees of reality reminds us that he takes Being-ness, like Beauty, to be a property that is also predicable by degrees. We addressed this seminal issue above but let us remind ourselves. This sounds counterintuitive perhaps. We might think that either something exists or it does not; it cannot "sort of exist" or "sort of not exist." The Greeks, however, since the times of Homer were accustomed in talking of lesser existence. As we would say, "anemic existence." Another element to notice is that "real" and "existent" are apparently treated interchangeably. In Greek: to on (plural: ta onta) = being(s), existent(s). But when Socrates wants to say emphatically "really (i.e. maximally) existent" he says "to ontos on": literally, and atrociously in English (maybe also monstrous in his language initially), "the beingly being" or "really real" (the latter sounds fine in English, suddenly...)

Consider the following modeling of some of the familiar items we have met in the allegory of the cave. We need a lexicon of symbols - and one is provided.

ref(s) = shadow-of-puppet-tree; ref(p) = puppet-tree; ref(t) = natural tree; ref(c) = concept-treeness (what all trees as such must have in common, what makes all trees similar to each other so that they are correctly assessed to be trees)

Now, we have: ref(s) is in the class Beingness to a small degree only. Plato would be interested even in numerical precision given the influence he shows from the Pythagorean school and his paramount theoretical view that understands truth as a matter of correct matching of referent with standard (for instance, matching of the referent of t with the concept Beauty as a standard: this matching is then given to us as degree of inclusion in the class Beauty.) The referent of "p", ref(p) is in Beingness to a higher degree than ref(s). The puppet is more real than its shadow. This coninues, of course, ascending to the tree (relative to which the pupper of the tree is lower in beingness) and, finally, to the concept treeness. Finally, we have the item (the concept treeness)) which is in the class Treeness to degree 1. Is this also in the class Beingness to degree 1? This is not clear. It seems that only the concept Beingness (existence) is in the class Beingness to degree 1. Yet again, don't all concepts exist or are real imperturbably? It seems not! It is the coordination of abstract concepts effected by the GOOD that does the job. So, even in the transcendental universe of the concepts or Platonic Forms, there can be derivative being - and this is reflected by the matching or parallel derivations down here below. In the end, Beingness and Goodness have to be the same form - and we get the impression that they are. In the cave allegory, the visible reflection of the Good is the Sun. [We could amend by having a plurality of Suns, although Plato, of course, had no idea of this. This by itself does not damage the theory: after all, there are many dogs running around...]

What seems wrong in the logic of this ontological view is this: existence, like nothingness or non-existence, are not logical predicates. The surface grammar of a language can mislead us about this but attention is needed because the underlying logical grammar is by no means guaranteed to dovetail the surface grammar. If we are asked for examples of this, we can hardly do better than using as examples "existent" and "nothing." "Pegasus does not exist" does not mean that there is something named "pegasus" which has the property of non-existence. It means - if it means anything at all - that there is no such thing that is named "pegasus." This is the orthodox view today about how the underlying logical grammar of existence works. There are complexities around this but, clearly, this view is critical of Plato's treatment of existence or reality in his ontology.

Corollaries of the Cave Allegory

  1. The sensory data we collect through our bodily sense faculties or organs represents a pale reflection or, to vary the metaphor, a simulacrum (idolon) of reality. Knowledge is not possible on the basis of empirical information. To know that p means that p is true and there is, in principle, an available full account as to how and why p is true. "Alcibiades is beautiful" as an empirically based proposition cannot be fully supported by an account because what makes Alcibiades beautiful is only participation in, or reflection of, to a degree of the transcendental Form Beauty. Plato takes this account to be causal: this partaking of the Form causes the subject to be beautiful - ephemerally, briefly, unreliably, fleetingly... The proposition expressed by the sentence "Alcibiades is beautiful" is not true absolutely or to the degree 1 - from the [0, 1] spectrum as a subset of the real numbers. If we take as "true" only what has the value 1, then the proposition "Alcibiades is beautiful" is not even true in the way that counts - it is not true so that it can be rightly assertable. One way to have this is by saying that only 1 is designated as a value (only propositions that take the value 1 are correctly assrtable). A modal approach, instead, would take the proposition "Alcibiades is beautiful" not to be rightly assertable because it is not necessarily true - it is not true across all conceivable contexts, including temporal contexts. In this way, Plato concedes to Heracleitus that sensory experience exposes us to an incorrigible fluidity but then denies to Heracleitus the claim that knowledge, if at all possible, can be discovered empirically. Thus, Plato has always been and remains the paragon of Rationalists (minus his transcendental metaphysics, usually) and the target of the Empiricists.
  2. Most disciplines of human learning, like the deluded musings of the cave dwellers, are doomed to systematic error. It is harrowing especially that the deluded scholars of the cave have considerable sophistication in technical and apparent methodological instrumentalities and a misleadingly eloquent vocabulary. Over so long a time, they might have developed all sorts of detailed analyses of the shadows, with abstruse terminological distinctions. They are also known to dispute vigorously about the subjects they discuss. All this makes a grotesque impression on the reader - and it is meant to do so. On the other hand, if the cave dwellers were able to do math, they would not be deluded or deceived about that! We are to infer that they couldn't study math - although it is not clear if the cave metaphor readily supports that. The inferior disciplines in which they can linger may well include empirically based accounts - their empirical realm circumscribed, of course, by the shadowy surroundings in which they dwell. The study of philosophy, if at all possible, would lead some exceptionally rare individual in the case - one like Socrates - to the realization that the cave is removed from the real and the true.
  3. The artists fair dismally. If reality, and the truth of the statements made about things, depend on the narrowing of the distance from the transcendental Forms, then the artist appears as the imitator of imitations and is, thus, once more removed from reality than even the artisan is. This, of course, accords with Plato's deep suspicion of the artist as a person who cannot give an analysis even of what he or she does - and, hence, is removed from what matters, acting on mere inspiration. Needless to say, there is a special view of art at work in this - art being understood as thoroughly representational. The influence artists can and do exercise in a society troubled Plato mightily, as every reader of the Republic knows. This influence is far-reaching in a society in which low-brow gratifications rule and where artists become admired celbrities. In the cave, artists can exist and can have the same kind of influence we know them as having in our society. If, however, one were to prove the deficits of the cave by raising to the contemplation of mathematics and philosophy - such a person would not be persuasive but rather deemed undesirable, dangerous, or perhaps an eccentric or lunatic. It is significant that it makes better sense to think that this ascent to the higher disciplines may not even be possible within the cave. But the same is not true of the lower disciplines - and of the arts.
  4. A parallel point is that the cave dwellers may actually be satisfied in their daily pursuits - although a deep sense of uneasiness, nihilistic cynicism, lack of lasting satisfaction may well be endemic in the cave since the more permanent and ultimately satisfying mental pursuits are missing. Bodily desires like those associated with food and sex are readily satisfiable in the cave. Higher mental pleasures cannot be reached - expect that few might be studying patterns emerging in the sequences of shadows and such matters: those few would then possibly emerge as agitators and come to a grim fate as the one Socrates met in democratic Athens.
  5. Although the cave dwellers are chained in the story, this confinement is one that the narrator, Plato indicates through this metaphor. They do not see themselves as impeded in any way. If we take our contemporary view of political liberty - understood as the absence of impediments to what they might want to pursue up to the point only at which their liberty curtails equal liberty for all others - then, shockingly, the cave dwellers can be political free in the sense in which a liberal political system defines the concept. Indeed, the political system Plato has in mind for the deepest recesses of the cave is democracy - albeit the egalitarian-participatory variety. If I have a presumptive right to free options as to how to pursue my life, the cave dwellers do have that. The key is that it never occurs to them that they are limited by ignorance or lower appetites. Their wishes can only be congruent with their limited understanding of the world. Whatever they may wish, then, is in principle accessible to them. So, shockingly, the regime of the cave may well be a liberal regime with civil rights. The alternative is to mandate substantive education and the concomitant training of character that entails. Liberal systems most emphatically reject this superimposition of standards as preconditions for the granting of freedom in the politically relevant sense. Anyone who becomes truly liberated from the cave, by obtaining knowledge, has a better understanding of how the cave itself works. Tragically, even though his persuasive resources increase, he will find it still impossible to persuade the dwellers of the cave. It would be like persuading the average person that math or philosophy is the source of far greater pleasures than sweet things or that Plato's books are better than inebriating popular tales that give vent to mere animal instinct. There is not escaping the realization that Plato's political philosophy, entwined with his overall philosophic system, is Aristocratic Radicalism - of a poignantly elitist variety.

© 2014 Odysseus Makridis

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