Plato’s Theaetetus really gets going when Socrates asks Theatetus to define knowledge (145e), and Theaetetus answers with a list: whatever you can learn from Theodorus (Theaetetus’s teacher), or (perhaps implicitly) another expert: disciplines such as geometry, and crafts such as cobbling. Socrates then thanks Theaetetus for his generosity: asked for one thing, he gave many. That is, he was asked for a definition that would distinguish knowledge from possible rivals, but instead he enumerated things we can know — asked about the intension of a term, he gave an answer about its extension (146d-e). Imagine, he continues, if someone asked you what clay is, and instead of saying “Earth mixed with water,” you said, “Oh the clay that potters use, the clay that brick-makers use, etc.” (147a). If they didn’t already know what clay was, wouldn’t that list leave them just as much in the dark as they were before?
So far, so good, Socrates — as Robert Brandom observes, “You do not convey to me the content of the concept gleeb by supplying me with an infallible gleebness tester which lights up when and only when exposed to gleeb things” (Articulating Reasons, 65). Knowing when to apply a term doesn’t guarantee that you understand it. Consider the confused soul who has become convinced that cats are a kind of dog. The odd thing about this persons’s situation is that she could be an infallible discriminator of cats from non-cats, without ever betraying her mistake — show her a cat, and she’ll unfailingly say “cat”; and show her a non-cat, she’ll say “non-cat.” Her confusion would only show up if you asked her to explain what a cat is, or perhaps if you asked her to discriminate dogs from non-dogs (more on what that signifies in a moment).
Next, however, Socrates doubles down hard — much too hard, I think — on the connection between possessing an explicit concept and appropriately using a term. If cobbling is “the knowledge of making shoes,” he reasons, “No one who is ignorant of ‘knowledge’ understands cobbling, nor any other art (σκυτικὴν ἄρα οὐ συνίησιν ὃς ἂν ἐπιστήμην ἀγνοῇ, οὐδέ τινα ἄλλην τέχνην)” (147b). That is, unless you explicitly possess the concept “knowledge” you can’t understand what it is cobblers do, nor (a fortiori) do it yourself. Now, this is plainly false — surely it’s the most ordinary thing in the world for the practitioners of some language-game (whether a craft, an intellectual discipline, or a natural language such as English) to understand scarcely any of the necessary conditions upon which their successful performance depends. Speakers of English don’t need to understand verb-paradigms, mathematicians don’t need to have a well-developed view about the ontology of abstract objects, and craftsmen don’t need to understand what it is they’re knowing when they know how to make things.
Socrates, in avoiding the Scylla Brandom names “regularism” (whose emphasis on success in deploying a term collapses the distinction between a perceiver and a differential responder, such as a parrot or a thermometer), steers himself into the Charybdis Brandom names “regulism,” the view that every successful use of a term requires possessing its explicit concept (Making It Explicit, 27-9). The way to avoid these false alternatives, Brandom insists, is to attend to the way we can possess concepts implicitly, by using them inferentially. Consider the example of the confused cat-discriminator from above: Socrates would say that she would only possess the concept “cat” if she could offer a definition sufficient to distinguish cats from other kinds of thing, perhaps from every other kind in the world. But, as I observed above, the more ordinary way of working out whether someone possesses a concept is by seeing both whether she knows when to apply it, and whether she can use it inferentially, for instance, by acknowledging that anything that is a cat cannot also be a dog, or by recognizing that a cat is an animal, is not a flavor, and so on. Just as there are degrees of competency in making such discriminations, so there are degrees to which one can possess a concept (depending on how fuzzy its boundaries are for its user) — but implicit, inferential use of concepts belongs every bit as much to the “space of reasons” as does the explicit articulation of a definition.