  Given the impossibility of deducing PNC from anything else, one might expect Aristotle to explain the peculiar status of PNC by comparing it with other logical principles that might be rivals for the title of the firmest first principle, for example his version of the law of excluded middle—for any x and for any F, it is necessary either to assert F of x or to deny F of x. Instead, Aristotle defies others to find a prior principle (Metaph IV 4 1006a10–11). For modern philosophers, it is still an interesting question whether PNC is prior to other principles of logic, or, indeed, to the notions of truth, reference and identity. PNC assumes the notion of identity: It is impossible for (one and) the same thing to belong and not to belong to (one and) the same thing at (one and) the same time &amp;c. PNC is presupposed by Leibniz’s law, which states that if x and y are discernible (if one has a property that the other lacks), then x is not identical with y.