Two modes of cognition

Geometry and the City-Man

There is a famous moment in Plato’s Meno where Socrates encounters an unschooled slave boy who, upon questioning, proves to know geometry. Socrates takes him through a series of questions, each of which the boy is able to answer, eventually reaching the correct conclusions regarding the figures and forms Socrates has laid out in the dirt. It is the boy’s capacity for thinking geometrically, for employing abstract definitions and rules, that interests Socrates. The boy clearly possesses such a capacity, but where does it come from? If it was not taught to him, how did he come to know it? And if he learned it, how did he know how to learn? These kinds of moments, which demonstrate our capacity for learning and reasoning, inspired Socrates to seek out the nature and origin of this capacity for conceptual thinking. As Socrates points out, the boy’s knowledge (and ours, who follow the argument) clearly transcends perceptual, image-based thinking. He is able to reason conceptually, abstractly, in terms of principles and rules, not things. This ability to think conceptually must be explored, Socrates urges, if we wish to understand the nature of our knowledge and of the world we hope to understand. The history of western philosophy is in large part a discourse on this capacity to think conceptually—on its origin, structure, function, and value.

In Book II of Plato’s Republic, there is a famous argument in which Socrates investigates the nature of civic justice by thinking of the city as a large person. Again, his interlocutors listen and respond to his questions, following his reasoning and generating conclusions alongside him. But curiously, Socrates seems uninterested in the capacity for thinking that he and his interlocutors exhibit. Perhaps this is because they have been schooled and should be able to follow an argument. Or perhaps it is due to the peculiar nature of the argument itself: it is not conceptual, it cannot be laid out explicitly in terms of concepts, principles, and rules. In fact, it violates conceptual thought, and flagrantly so, since it is based on the conflation of things. The argument is that we can identify justice in the city by thinking of the city as a large person, by actively conflating the one with the other. By thinking of the city as a large person, Socrates builds his argument, step by conflated step: As a large person, the city needs muscles. As a large person, the city needs a head. As a large person, the city needs courage to protect itself. And as a large person, the city needs each part of itself to work together for the good of the whole person/city. This is justice, he concludes, the many parts of the city functioning together obeying the ruler as the parts of a person function together obeying the head, the intellect.

Given his passionate curiosity concerning the nature of human cognition, it is striking that Socrates seems uninterested in the fact that his interlocutors can follow his conflated thinking, and that they can use it to generate knowledge and insight. This is clearly also a capacity, one that Socrates himself possesses and employs across his many conversations. But it is a capacity never taken up by Socrates as a philosophical topic, as an object of wonder and inquiry, in the way that conceptual thought is taken up. When he does acknowledge it, as when he considers the knowledge of the poets, Socrates rejects it. The poets, he argues, are unable to offer a sufficient account of their knowledge in conceptual terms, relying instead on a form of thinking that is conflated, mimetic, one kind of thing understood as another kind. Poetic thought disrupts the proper operation of concepts by mixing what should be kept separate. It is equally striking, I think, that historically philosophy has largely ignored this capacity as well—especially since, as Mark Johnson has recently argued,[1] philosophical history is steeped in metaphorical arguments that philosophers stubbornly refuse to acknowledge or take seriously as metaphorical. Instead, most philosophers have preferred to investigate the nature of conceptual thought, which they assert to be the highest, if not the only, form of genuine thought. In doing so, as Johnson has shown, philosophers deny the very resources and capacities with which they manifestly do their work. The argument of the city-man (like so many philosophical arguments involving metaphorical thought) is extremely effective, as is the argument from geometric principles. But it is metaphorical.

In addition to metaphorical thinking, Plato rejected (or marginalized) narrative, poetry, drama, and the visual arts, and all for the same reason, their mimetic character.^[2] In examining their structures, it was clear that these “pretenders” to cognition were not rooted in a principle governing thought but instead involved acts of comparison, likeness, or copying. They were essentially double, not singular, multivocal, not univocal, suggestive, not determinative. And they were concrete. True cognition, he argued, was always the result of an abstract principle providing its structure to thought, a principle that cognition carries out in its own activity, e.g., geometry. On such a view, conflation can only lead to error, as it continually mixes and undermines the distinguishing, separating efforts of conception. But, as the example above illustrates, these very forms of thought that Plato rejected play crucial roles in his own thinking, and it is hard to imagine his philosophy without the many narratives, analogies, metaphors, dramatic exchanges, and poetic tropes that populate his writings. And it is hard to imagine the history of philosophy without such tropes that are rooted, I claim, in the conflation of one thing as another.

 Copyright © Tim Adamson, 2026. All Rights Reserved. Please do not distribute without the author’s permission.

[1] The Aesthetics of Meaning and Thought, Ch. 2. See also Philosophy in the Flesh.

^[2] Republic, Book III, 392-395.