Metaphysics

​We must say whether it belongs to one or to another science to inquire both about the so-called axioms in mathematics and about substance. It is clear, then, that the inquiry about these also belongs to one science, and that of the philosopher; for they belong to all beings, and not to some genus separate and private from the others. And all make use of them, because they belong to being qua being, and each genus is being; but they use them to such an extent as is sufficient for them, and this is as far as the genus extends about which they bring their proofs. So that, since it is clear that they belong to all things qua being (for this is what is common to them), the contemplation about these also belongs to the one who cognizes being qua being. Therefore, none of those who inquire into particulars attempts to say anything about them, whether they are true or not, neither geometer nor arithmetician, but some of the natural philosophers do so, and naturally enough; for they alone thought they were inquiring about the whole of nature and about being. But since there is someone still higher than the natural philosopher (for nature is one particular genus of being), the inquiry about these would belong to the one who contemplates the universal and the first substance. Natural philosophy is also a kind of wisdom, but not the first. And as for the attempts of some of those who speak about the truth to state in what way one should accept it, they do this through lack of education in analytics; for they should come prepared with knowledge about these, and not inquire while they are listening to lectures. That, therefore, it belongs to the philosopher, and to the one who contemplates all substance qua its natural being, to inquire also about the principles of syllogism, is clear. And it is fitting for the one who most cognizes about each genus to be able to state the most certain principles of the matter, and so also for the one who cognizes about beings qua beings to state the most certain principles of all. And this is the philosopher. And the most certain principle of all is that about which it is impossible to be mistaken; for such a principle must be both the most cognizable (for all are deceived about what they do not cognize) and non-hypothetical. For that which one who understands anything at all of beings must possess is not a hypothesis; and what one must cognize who cognizes anything at all, he must come possessing. That, therefore, such a principle is the most certain of all is clear; let us state next what this is. For it is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect (and whatever other specifications we might add, let them be specified against logical difficulties). This, then, is the most certain of all principles; for it has the stated specification. For it is impossible for anyone to believe that the same thing is and is not, as some think Heraclitus says. For it is not necessary that what one says, one must also believe. And if it is not possible for contraries to belong to the same thing at the same time (and let the usual specifications be added by us to this premise too), and a contrary opinion to an opinion is that of contradiction, it is manifest that it is impossible for the same person to believe at the same time that the same thing is and is not; for the one who is mistaken about this would have contrary opinions at the same time. Therefore, all who demonstrate refer to this ultimate belief; for this is by nature the principle also of all the other axioms.