In explaining where the PNC fits in our study of metaphysics, Aristotle makes clear that general 'principles of reasoning' or, axioms, belong to science in general and are not part of a specific science (in saying this, he must be implying that metaphysics is a type of unifying science, above all others). Thus, because the PNC is a general condition and statement about knowledge - or understanding being - it must be part of our study of metaphysics.
"The grounds for thinking that the examination does not belong to a specialized science, is that principles of reasoning, such as PNC, are true of all things, not just some things; and this is confirmed by the fact that everyone and all sciences make use of them." (Politis [digital] Ch. 5, Sec. 4)
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