Today’s question: Can knowledge be defined as true belief with an account — and if not, why does the definition still feel so nearly right?
What I find difficult about reading Plato is the way Socrates tends to lead the witness. I know that is part of the Socratic method, but at certain points it feels rather straw-man-ish — the interlocutor agrees too quickly, and the ground gets staked out before the question is honestly explored. That said, I do agree with Plato and Socrates to a point: being able to identify the elements that make up a thing does not necessarily mean that you can identify the thing itself. Knowing the elements of a thing does not necessarily tell you everything you would need to know in order to say you truly know a given entity.
Take the wagon, which Socrates uses in this segment. Even with the description he provides — planks, axles, wheels, perhaps nails — that doesn’t tell you what a wagon is, or what it is for, or how it came to be. All of those, I would argue, are essential aspects of knowing the thing. So in a way the example works exactly as Socrates intends: it disproves enumeration-of-elements as a definition of knowledge. It helps us identify what knowledge isn’t, which is probably very useful in this context, and is, I think, his point.
What this puts on the table — though Socrates does not quite put it there himself — is something like an apophatic move in epistemology: an account of knowledge built out of what knowledge is not. Read this way, the dialogue is less about closing in on a positive definition than about clearing the ground around the question, ruling out the candidates that look closest to being right. It does mean, though, that anyone coming to the Theaetetus hoping for a definition of knowledge they can take home will leave hungry.
There is an aside that struck me before he reached the mathematical part of his dissection. The way Socrates describes the indivisible elements of a thing reminded me of prime numbers. There are many ways to make up six. Making up one is an entirely different prospect — unless you’re working in more exotic mathematics, the indivisibility is the whole point. And primes are only primary relative to an operation we have chosen — multiplication. Once you allow other operations, even one is constructible from something. So the indivisibility Socrates wants from his elements might be doing the same kind of work: looking primary only because we have not yet found the operation that decomposes them. There is a recent result in this same shape, due to Andrzej Odrzywołek: every elementary function can be obtained from a single two-argument primitive — eml(x, y) = exp(x) − log(y) — together with the constant 1 (arXiv:2603.21852). Once you allow that operation, “primary” becomes a designation you award rather than a property you find. I suspect this is a version of the same problem the dialogue runs into later, where every definition resolves into another definition — there is no place that is just primary.
The final move in today’s reading — identifying a thing by how it is distinct from everything else — is also interesting. I think this can lead you toward knowledge, but only to a point. It requires something else to exist in order for you to describe what you’re trying to describe. Which means, if that were the whole story (and I’m sure this comes up later), you would never be able to describe anything in isolation. Which is fair: context exists. But if the only route to a description runs through the absence of other things, I feel like we’re still missing the point.
So my reading of Plato’s — or Socrates’s — definitions is that they are useful in helping us identify what knowledge isn’t. Knowledge could be made up of some of these items, but they don’t actually bring us to a full understanding of what knowledge is.
Looking at his various descriptions — trying to define an army as made up of its soldiers, the composition of all the parts being the whole, or what have you — I understand this is part of what he is trying to disprove. But to his point, or perhaps to my reading of it, each of these individual items is itself made up of other items. An army is made up of soldiers; or, more concretely, of regiments, which are made up of battalions, which are made up of companies, which are themselves made up of individual soldiers. And the same is true of everything else in his examples. A wagon is made up of planks and axles and wheels, but all of those are themselves made of wood cut in different ways. So you would also need to explain wood, and you would need to be able to explain cut. These are further definitions that make up the definition of “wagon”.
This continues to be true the further down you go, until you arrive at definitions that are almost tautological. For example, describing one as a solitary representative of something, where “solitary” itself just means “one”. There may be a better example of a definition that is itself; I don’t think Plato was actually getting there.
And maybe some of why these specific examples break down is that our understanding of the world is so much broader now than it was when this was written. Even where Socrates is talking about a name being broken down into syllables and letters, today we could talk about phonemes, and about linguistic roots, and about why certain phrases evoke certain sensations or understandings universally — and we have a much better grip on all of that now than they did at the time. Letters were the supposed bedrock of his analysis — the elements beneath which only syllables could be known. But letters turn out to be analysable too: phonemes underlie them, and phonemes themselves resolve into distinctive features, voicing and place and manner of articulation. So the ground floor that Socrates pointed to as primary turned out to have a basement. And the relationship between sound and sense, which the dialogue treats as opaque, has structure of its own — sound symbolism, recurring morphemes, the strange near-universality of the bouba/kiki effect. The analytic move Socrates wants to make is still a real move; it is just that the elements he points at no longer hold up as elements. But none of that should take away from trying to understand what knowledge actually is.