Is Plato’s Republic About Psychology or Politics? What Can Bayes’ Rule Tell Us?
HAT Plato’s Republic is not a literal work on political science, but a carefully crafted allegory for the internal governance of ones mind and soul seems to me beyond doubt. Several lines of evidence support this conclusion, beginning with dozens of explicit statements by Plato to the effect throughout the work (Annas, 1999; Uebersax, 2014a,b; Waterfield, 1993). Nevertheless I also know that before realizing this, I had, like most everyone else, uncritically accepted the received opinion that the Republic is Plato’s effort to describe a utopian society. So even though it may be wrong, the literal view of the Republic, widespread and deeply entrenched, can’t simply be brushed aside.
Recently it occurred to me that a strong argument for understanding the Republic as a psychological allegory can be made on the basis of formal probabilistic reasoning. Specifically, I refer to a principle called Bayes’ rule. This is a formula (named after Rev. Thomas Bayes, an 18th century mathematician) by which one can quantify the degree to which evidence supports a given conclusion. While Bayes’ rule is often considered something modern, it actually corresponds to how we naturally form inferences from empirical data. We will, in any case, omit details here. (Those interested in more background can find ample material on the web.) It is, however, assumed that the reader has at least a little knowledge of basic probability and associated notation.
First let us define the problem: we want to choose as more likely one of two hypothesis, H1 and H2, as follows:
H1: The Republic is a psychological allegory.
H2: The Republic is a literal work on political science.
We take H1 and H2 here to be mutually exclusive hypotheses: they cannot both be true. (If we like, we could add words like ‘mainly’, ‘mostly’, or ‘primarily’ to both hypotheses to make this more clearly so.)
Let E denote some empirical evidence. This can be any sort of evidence, but for present purposes we take it to be the entire text narrative of the Republic.
Our task is to choose whether H1 or H2 seems more likely after considering evidence E. In terms of probability theory, we wish to estimate the value of two conditional probabilities:
P(H1|E) = the probability that H1 is true, given E 
P(H2|E) = the probability that H2 is true, given E 
We may then decide in favor of H1 (allegorical meaning) if  is greater than , or in favor or H2 (literal meaning) if  is greater than .
As it happens we cannot directly estimate the values of  and . But this is where Bayes’ rule comes in. Bayes’ rule is an extremely simple formula that describes the relationship between a conditional probability and its converse — that is, between P(X|Y) and P(Y|X).
Again, we’ll skip the details here. All that matters is that a simple application of Bayes’ rule in the present case leads to the two following equations:
P(H1|E) = c × P(H1) × P(E|H1) 
P(H2|E) = c × P(H2) × P(E|H2) 
Thus, given some evidence E, we can decide whether H1 or H2 is more likely by evaluating and right sides of equations  and  and seeing which is larger.
The term c here is a constant, and as it appears in both  and  we can ignore it. Hence we need only know which product is larger: P(H1) × P(E|H1) or P(H2) × P(E|H2). If the former, we would opt for an allegorical reading of Republic; if the latter, a literal one.
Note that we’ve introduced two new categories of probabilities:
- P(H1) and P(H2) are the a priori or plausibility probabilities of our two hypotheses H1 and H2 — that is, these express how likely H1 and H2 are considered to be before considering evidence E. Here these reflect how likely we deem it a priori (i.e., before we consult the Republic) that Plato would have wanted to write a psychological allegory vs. a political treatise. For example, we might consider what we know about Plato’s personality and motives, the contents of his other dialogues, and so on.
- P(E|H1) and P(E|H2) are entailment probabilities. These express the degree to which H1 and H2 would, if true, lead to or entail the evidence E. In other words, how much sense does the evidence (i.e., the content of Republic) make under the alternative assumptions of allegorical vs. literal intentions by Plato.
Now comes the fun part. In truth, we have no way of attaching precise numerical values to any of the terms P(H1), P(H2), P(E|H1), and P(E|H2). Yet we can fairly easily make two judgements of comparative magnitude. Specifically, if one considers all the available background evidence besides what’s in the Republic, one can say whether this inclines more in the direction of supporting an allegorical or a literal meaning. Similarly, one can make a reasonably confident judgment about whether the details of Republic are more consistent with an allegorical vs. a literal reading. If these two comparative judgments line up in opposite directions, we cannot draw any firm conclusions. But if they line up the same way, we can.
For example if P(H1) > P(H2) and P(E|H1) > P(E|H2), then P(H1) × P(E|H1) > P(H2) × P(E|H2), and, from equations  and , we can assert that P(H1|E) > P(H2|E). That is, taking into account both background evidence and the text itself, we would judge it more likely Plato meant the Republic as an allegory. We address the two constituent pairwise comparisons, viz., between the two plausibility probabilities and the two entailment probabilities, below.
The a priori plausibility evidence, in my opinion, strongly favors an allegorical reading of Republic. Perhaps the most telling argument is that Plato everywhere else shows an intense concern for the moral improvement of the individual. For Plato the stakes of moral salvation are infinitely high: nothing less than the fate of man’s immortal soul. It seems very implausible that Plato would suddenly drop his life’s work of teaching philosophia — a religious transformation of ones life based on personal holiness and the love of Wisdom and Virtue — in order to speculate about politics.
Further, a vast body of modern psychological literature has persuasively argued that (1) at some very fundamental levels, each one of us is a community of subselves; and (2) to manage these numerous competing and conflicting parts is one of the most difficult and important tasks we face as human beings (for reviews see Rowan, 1993 and Lester, 2010). We cannot suppose this basic fact of human psychology would have escaped the notice of the ancients. This insight, for example, is at the center of Philo’s vast psychological exegesis of the Old Testament (Uebersax, 2012). Said another way, to justify Plato’s singular reputation as the greatest philosopher of the Western tradition, we would expect him to have recognized and tried to address a reality so vital to our psychological and spiritual well-being.
Conversely, the background arguments supporting the literal reading are flimsy, or at least open to considerable question. The argument ‘from tradition’ — that Plato’s Republic has traditionally been understood to be about politics — is quite useless. One might as well argue that the Garden of Eden myth of Genesis was not meant as a moral allegory because generations of uncritical exegetes have taken it literally.
The Seventh Letter might potentially imply political interests of Plato, but this is offset by extremely strong doubts as to the letter’s authenticity. There remains Aristotle’s comments about the Republic in his Politics, which take a literal meaning by Plato for granted. However these highly polemical remarks seem far more concerned with advancing Aristotle’s own views than faithfully explaining Plato’s, and so must be discounted. Surveying all the background information, then, the only thing we can be sure of is Plato’s intense and abiding concern with personal morality and religion, and this favors the view that the Republic is a psychological allegory.
The second question is whether the details in the narrative of the Republic would be more likely if Plato meant the work as an allegory, or if he intended it as a literal work. Here the case is even clearer. As Waterfield (1993) especially has noted, if read at a literal level the Republic abounds in absurdities, incongruities, and gaps. We are not given anywhere near the level of detail that would be required to run a real city. Further, many details that Plato does supply are utterly outrageous — so absurd in fact, that they can seem almost calculated to tease literally-minded readers. If Plato intended to describe an actual city-state, we cannot believe he would have advocated such notions as infanticide, eugenics, communal wives, and intentional lying to citizens by rulers.
We can, however, make definite sense of these otherwise absurd suggestions if we read the Republic as a psychological allegory. For example, one may wish to abort negative or unproductive chains of thought soon after their conception; or, following similar lines of analogy, to encourage marriage and begetting of offspring by the more positive and virtuous elements of ones nature.
By the above, then, we have argued that (1) an allegorical understanding of Plato’s Republic is both more probable a priori than a literal interpretation, and (2) the content of the Republic is more consistent with psychological vs. literal intentions by Plato. By means of Bayes’ rule applied in connection with equations  and , these two comparative judgments allow us to conclude that, considering all available evidence, the Republic is more likely a psychological allegory than a literal political work.
The present is only a very brief treatment of the topic, intended more to introduce the leading principles than to arrive at final certainty. Much more work can go into identifying, evaluating, and comparing the plausibility and entailment probabilities. Herein we have taken the evidence E to be the complete text of the Republic. However the same sort of reasoning could be applied to individual passages; thus we could allow that some sections Plato wished to be taken literally, but in others, say that concerning the Noble Lie, he is writing allegorically.
I personally think that the deeper one delves into the Republic, the stronger the assurance that it is an allegory — but political philosophers may have other ideas, and probably aren’t likely to give up without a fight. In any case, the present supplies a framework in which the issue can be investigated impartially, scientifically, progressively, and in an edifying way.
Annas, J. Platonic Ethics, Old and New. Ithaca: Cornel University Press, 1999; Chapter 4, The Inner City, pp. 72−95.
Lester, David. A Multiple Self Theory of Personality. New York, 2010.
Rowan, John. Subpersonalities: The People Inside Us. London, 1990.
Uebersax, John. Psychological Allegorical Interpretation of the Bible. Paso Robles, CA, 2012.
Uebersax, John. The Republic: Plato’s Allegory for the Human Soul. 2014a. Online document. Satyagraha website.
Uebersax, John. Psychological Correspondences in Plato’s Republic. 2014b. Online document. Satyagraha website.
Waterfield, Robin. Republic. Oxford University Press, 1993.