In the context of modern philosophy, Brandom has developed an important contrast between representationalism and inferentialism. Representationalism says that representation comes before inference in the order of explanation, and inferentialism says that inference comes first.
Plato was very pessimistic about the potential of representation, as witnessed by the dialogues’ discussions of “imitation”, and the treatment of writing in Phaedrus. By contrast, inference or reasoning is presented as the main way to truth in the dialogues. Inference — and not representation — is what is primarily appealed to in the validation or invalidation of assertions. (See also Dialogue; Platonic Truth.)
Aristotle was less pessimistic about representation, but even more concerned with inference. He was the great originator of the world’s first developed logic, which was in fact centered on inference rather than truth values. While taking pioneering steps toward formalization, he also devoted much attention to definition, meanings of terms, and their distinctions and ambiguities in concrete usage (see Aristotelian Semantics; Aristotelian Demonstration). Aristotle distinguishes between inference based on the fact, which is a kind of formal inference, and inference based on the meaning, which is the material inference of Sellars and Brandom, also known to medieval logicians. Further, Aristotle’s elementary criteria for truth and falsity depend on material inference (see Aristotelian Propositions).
The kind of representation Brandom is particularly concerned with, which he attributes to Descartes, is based on isomorphism rather than resemblance. As an aside, I tend to think there was a notion of isomorphism in the ancient world, though it is a little hard to separate from resemblance. Euclid talked about similar triangles, which are technically an example of both. Aristotle would certainly say that resemblance is “said in many ways”, one of which could be isomorphism. I think given the opportunity he would say, for instance, that individual concretely uttered words are at some level isomorphic to whatever meanings those words turn out to have in some context. The words do not resemble their meanings. (See also Historiography, Inferentialism; Inferentialism vs Mentalism;.)