  In response, one could point out: (a) Definitions like (1) or (2) are “mini-theories”—mini-theories are quite common in philosophy—and it is not at all obvious that they are vacuous merely because they are modeled on common usage. (b) There are correspondence theories that go beyond these definitions. (c) The complaint implies that definitions like (1) and/or (2) are generally accepted and are, moreover, so shallow that they are compatible with any deeper theory of truth.  This makes it rather difficult to explain why some thinkers emphatically reject all correspondence formulations. (d) The objection implies that the correspondence of S’s belief with a fact could be said to consist in, e.g., the belief’s coherence with S’s overall belief system. This is wildly implausible, even on the most shallow understanding of “correspondence” and “fact”.