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. The kind of representation Brandom is particularly concerned with, which he attributes to Descartes, is based on isomorphism rather than resemblance. The kind of inference he is particularly concerned with is the material inference discussed by Sellars.
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 concretely uttered words are isomorphic to meanings of those words in any one of the contexts (speaker-centered, hearer-centered, community, dialogical, etc.) that could be distinguished in association with the utterance. The words do not resemble their meanings.
Plato is pessimistic about the potential of representation, as witnessed by the dialogues’ discussions of “imitation”, and the treatment of writing in Phaedrus. By contrast, inference 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.
Aristotle is 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. 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 also Aristotelian Propositions.)