All Ravens Is Logically Equivalent

If the phrase “all ravens are black” (statement 1) is logically equivalent to the statement “everything non-black is a non-raven” (statement 2), with the latter seeming to be confirmed by “this apple is green”, then “all ravens are black” should be too. However, this does not seem to be the case—but why isn't it? In the next couple hundred words I hope to explain my theory that the two statements are not, in fact, as equivalent as one might assume from the phrase “logically equivalent”. First, let me say that logically equivalent is not the same as equivalent. Logically equivalent refers to the equivalence of truth values between expressions, while equivalent refers more or less to two or more things being identical. Sharing identical truth values does not necessarily make the expressions identical in-themselves/in form.

Statement 1 describes the relationship stated previously in terms of “ravens”, while statement 2 describes the same relationship in terms of “non-black”. To illustrate this point a little more clearly we can remove the terms and re-write the statements as follows: All As are Bs (statement 1) and All Bs are As (statement 2). (The explanation for the alteration of statement 2 is simplification: everything is equivalent to all, with this change we then have the statement “all non-black [things] are non-raven” which allows for the two statements to have a more identical appearance.) In the “new” statement 1, Bs are identified in terms of As, and in the following statement 2, As are identified in terms of