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This is incorrect. "Arbitrary" has nothing to do with truth or falsity, possibility or impossibility. Like floating abstractions (see the recent discussion), arbitrary propositions have no connection to reality; they're mere concatenations of words that follow the syntactic rules of propositions. Assertions about truth and possibility (or their absence) are about knowledge. If a statement is not knowledge, it is a category mistake to even ask if the statement is true or possible; it is the same sort of error as asking if a concept has polkadots. So, before wondering if a statement is possible, you must first know that the statement is some kind of knowledge. Knowledge is the product of integrations of percepts. A statement that does not derive from percepts is not knowledge. Now, we have the notion of "the matrix" from science fiction (and earlier), but no percepts from which one might derive the possibility that such a thing is more than fiction. Without that, it is simply an error to ask if "the matrix" is possible. "But that's not satisfying!" Awww. Poor baby.