On one well-known telling, the history of Western philosophy began in ancient Greece, and specifically with Plato. One of the reasons behind this origin story is institutional: Plato founded the Academy, often regarded as the first known school in Europe where philosophy was taught. But another reason Plato is so often invoked as a founding figure for Western philosophy has to do with the nature and method of Platonic philosophy itself, with a particular way of doing philosophy first encapsulated in Plato's writings. In the Apology, Socrates – Plato's teacher and the central protagonist of many of his dialogues – defends the practice of philosophy as an unsparing examination of one's beliefs and those of others. Famously professing his commitment to the idea that ‘the unexamined life is not worth living’, Socrates describes the task of the philosopher as that of perpetually challenging his fellow citizens to think for themselves. We should be able to give reasons for the things we happen to believe, rather than merely accepting the givens of our culture. Accordingly, Plato's best-known dialogues consist, in large part, of Socrates taking apart his interlocutors’ arguments with merciless logical rigour.

On display in Plato's writings, in other words, are values that we continue to associate with philosophy today, such as a commitment to systematic critical inquiry, or the idea that our beliefs ought to be grounded in reasons, and therefore held to a higher standard of argumentative rigour. It can therefore come as a surprise to readers that Plato's writings contain, not just philosophical arguments, but a good number of myths. A myth is a specific kind of traditional tale, often featuring fantastical or otherwise supernatural elements, that has been passed down over generations within a culture, usually through oral transmission. Greek culture in Plato's time, for instance, had inherited a vast and well-known corpus of myths about the Olympian deities and human heroes. These traditional stories, in turn, often formed the subject matter of poetry and songs, sculpture, vase paintings, and the tragedies that were performed in the theatre.

Plato constructed his own myths by imitating or incorporating conventional elements of traditional myths, and integrating the resulting stories into his philosophical dialogues. In Book 3 of the Republic, for example, the character Socrates suggests telling a myth to the citizens of the ideal city, which he and his interlocutors have been sketching out over the course of a long discussion about the nature of justice. Socrates's myth tells the story of citizens who have been born out of the earth with gold, silver, bronze and iron mixed in their natures – a detail that appears to have been borrowed from traditional Greek myths, also preserved in the poetry of Hesiod, about the gold, silver, bronze and iron ages of mankind. Not all of Plato's myths borrow from Greek mythological tradition. In the Phaedrus, for instance, Socrates tells a myth featuring the Egyptian god Thoth (though even his interlocutor is quick to remark on how easily Socrates seems to make up stories from Egypt and anywhere else he pleases). Oftentimes, as seems to be the case in the myth about Thoth, Plato was happy to invent myths that happened to mention familiar deities or places from pre-existing mythological traditions but were otherwise entirely original. This is true, for example, of what is perhaps his most famous myth: the myth about the sunken island of Atlantis, which is told across two dialogues, the Timaeus and Critias.

For many readers, Plato's myths can provide some of the most memorable parts of the experience of reading his work. But when squared against Plato's reputation as the founding figure of Western philosophy as we know it, his myths begin to look problematic. If a central feature of philosophy, both as Plato conceived of it and as we tend to think of it now, is a readiness to put ideas under rational examination at a high level of rigour, Plato's myths have the curious effect of appearing to remove their claims from further critical scrutiny. The overtly supernatural elements of these stories – humans born out of the earth, deities wielding magic powers, creatures with two sets of arms, legs, and genitals – signal that they are not meant to conform to the rules of logic or the expectations of ordinary reality. Rather, like many traditional myths, Plato's myths tend to be ‘just-so’ stories, simply offering a narrative about the way things are or came to be – say, an account of what the afterlife is like, or how humankind first came together in political communities. When presented with such stories, it is usually beside the point to press, as one might with an argument, for additional clarification, facts, or reasons.

In the more argumentative parts of Plato's dialogues, consistency and coherence appear to be especially important values of philosophical inquiry; Socrates's interlocutors are constantly held to task for contradicting themselves. In Plato's myths, however, such concerns seem to fade quickly out of view, as the vivid and often elaborate stories come to take a life of their own. Across his dialogues, there are no fewer than four prominent myths about the afterlife, each offering a different account of what happens to the souls of individuals after death. More alarmingly, there are moments when Plato's myths seem to conflict, not just with his other myths, but with the actual arguments being advanced elsewhere in the dialogue in question. For instance, one of Plato's myths about the afterlife, the Myth of Er, has perennially attracted complaints from commentators that it appears to undermine the central argument of the Republic, the dialogue it concludes. Whereas the greater part of the Republic is dominated by the philosophical project of defending justice as valuable in and of itself, independent of any external rewards it might bring, a conspicuous portion of the Myth of Er is about how souls who had been just in their previous lives are rewarded in the afterlife, while those who had been unjust are severely punished.

In fact, it is by no means always clear how Plato's myths relate to the arguments around them. In this way they can be contrasted to famous philosophical thought experiments like Philippa Foot's trolley problem or Judith Jarvis Thomson's unconscious violinist. For the most past, Plato's myths are not obviously instrumental to the philosophical argument in the same way that thought experiments seem to be. They are also much more elaborate. Whereas thought experiments are often designed to be especially efficient mechanisms for testing our intuitions about particular questions, Plato's myths usually resemble traditional myths in containing extraneous flourishes of storytelling – a feature that the political theorist Danielle Allen has called ‘linguistic surplus’.

How should Plato's readers reconcile the apparent tension between his myths and his reputation as the founder of a critical tradition of philosophy? For Karl Popper – one of the most famous, and most controversial, of Plato's twentieth-century critics – the problem was serious enough that he felt it undermined any philosophical tradition that traced its roots to Plato. Popper drew an influential distinction between a liberal or ‘open’ society, which promotes a culture of free criticism, and a ‘closed’ society, which relies on the deceptive power of myths to freeze out change. The foundation myth told in Book 3 of Plato's Republic, about citizens being born with metals mixed in their natures, was a paradigmatic example of a myth that sustained closed societies. The political use that Plato made of this myth was, for Popper, a betrayal of the open ideal of criticism essential to philosophy, and his example, in turn, would reverberate, to fateful consequences, throughout the history of Western thinking. In fact, the myth in question offended Popper so much that he compared it to the race-based Nazi ideology of his own time.

One way of diffusing the tension that Plato's myths can introduce to our evaluation of his work is to downplay their role, and to see them as at best incidental to his philosophical accomplishment. We could argue, for instance, that Plato's myths are just a sort of rhetorical ornament to the real philosophical substance of his texts. Influentially, Lucretius defended poetry as a ‘honeyed cup’ that makes it easier for the bitter medicine of philosophy to go down. Plato's myths might serve a similar function: presenting difficult, hard-to-swallow philosophical ideas in a more vivid, easily manageable form. On this interpretation, a reader might get hooked onto a dialogue like the Republic or Phaedrus by the memorable myths in these texts, but get reeled into working through the intricate and demanding arguments that make up the rest of the work.

A more extreme variant of this line of reading draws a distinction between two types of audiences for which Plato might have been writing. According to this controversial view, the dense, difficult arguments in Plato's dialogues are intended for an educated and attentive philosophical readership, while the myths were written for a less capable, non-philosophical audience. His texts may have different intended takeaways for each of these two audiences, and so it doesn't necessarily pose a problem if the myths and the arguments appear to make different points. In the case of the Republic, for instance, sophisticated, critical readers can follow the argument that justice has intrinsic value regardless of what external rewards just acts might bring. Meanwhile, less able readers can fall back on the simpler message of the concluding Myth of Er: that they should strive to lead just lives, and so avoid punishment in the afterlife. The lesson the myth teaches is not quite right, but it is good enough – and the best that Plato can do for an uncritical reader who prefers stories to proofs.

Both these approaches to Plato's myths have the advantage of preserving our customary understanding of the essence of philosophy, and of Plato's status as the thinker who first shaped that understanding. Whether the myths function as a honeyed cup aiding the intake of philosophical ideas, or as a crude rhetoric for persuading the unphilosophical, they are ultimately subservient to the argumentative core of Plato's work. But such readings tend to miss the mark when it comes to accounting for the intricacy of the myths themselves. Interpretations that treat Plato's myths as rhetorical embellishments to the main arguments run into trouble whenever they come up against moments when a myth's details appear to contradict the argument they were supposed to be supporting. It is also simply not true that the myths convey messages that a supposedly unphilosophical reader can reliably digest more easily than a proper argument. Indeed, Plato's myths are so elaborately constructed that it can often be difficult to make out what the lesson of a particular myth is supposed to be.

I believe there is a more satisfying way of making sense of Plato's myths, but it is one that may require us to revise our standing ideas about the nature of philosophy and its relationship to myth. Rather than minimize the significance of the myths to his philosophy, this approach suggests that Plato may have constructed them deliberately as a form of philosophical discourse in their own right.

We might take, for example, the Myth of Er, which has so divided readers of the Republic. This myth about the afterlife is presented by Socrates as the dream vision of an eponymous warrior, Er, who comes back from death in order to tell the story of what he had seen in Hades, as though he had merely slept through the experience. As it happens, this narrative framing – an awakening from a slumber that takes place in a subterranean realm – is a feature that the Myth of Er shares with two other myths that appear earlier in the dialogue. In each of these earlier myths, the story about dreaming and waking is used to introduce a revised conception of individual nature, following a discrete phase of the educational curriculum of the city described in the Republic. Taking seriously the literary continuity between these three myths suggests a way of reading the Myth of Er as the extension of an iterative effort to overhaul how to think about the natures of individuals after they have undergone transformative educational experiences.

At stake in the sequence of myths culminating in the Myth of Er is an inquiry into the idea of individual nature, a thick concept that carries especially fraught normative implications. This is a distinctly philosophical project that Plato, as I read him, undertakes using a series of interconnected myths, which he placed at important junctures in the arguments of the Republic. What the medium of myth allows him to do at these points is to deploy the conventions of a traditional literary genre to tell a just-so story about a concept – one's own nature – that is already foundational to the way individuals understand themselves and relate to the world. And in so doing, he reshapes the very contours of the imaginative framework in which the rest of the argument operates.

Plato's practice of writing myths into his dialogues, I believe, stemmed from an insight that it takes more than arguments and criticism to engage philosophically with the imaginative frameworks structuring our worldviews. It is from this expansive standpoint that we can better appreciate their significance. Perhaps there is no need after all to feel that there is anything strange about a philosopher writing myths. Plato left us an idea of what philosophy ought to look like – one important component of which was highly rigorous, self-critical argument. But Plato's myths stood alongside this vision from the very first. If the full richness of his texts now seems surprising or contradictory, it is perhaps not because of a failure on his part, but because our own view of what philosophy can consist in has grown narrower than his.