It seems to me that if a deflationist answers the question "when can you correctly say "snow is white"" with the answer "when snow is, in fact, white", then the deflationist is a correspondencist. If he says "when you have good enough evidence that snow is white", he is an epistemicist. Deflationism on its own is surely just a shallow concern with the word "truth". Of course asserting "it is true that P" is the same as asserting P, but that is not an interesting fact.

Is deflationism historically a response to some obsolete idea about "truth" as an immaterial substance that adheres to true propositions, by virtue of which they are true? Neither of the other two theories assert such an idea.