On a different topic, I also want to go back to the idea of the first principles being "sense-verifiable", because in re-reading some of Posterior Analytics I think I understand now what you are referring to, and I think it just requires some clarification.
Posterior Analytics begins with the assertion that all instruction begins with preexisting knowledge, whether it's instruction in math, rhetoric, or deductive or inductive reasoning. (Note: this first sentence of the book also makes clear that it intends to speak of a topic that applies to both categorical logic and scientific induction, even though he often uses mathematical examples) He goes on to say that one of the kinds of preexisting knowledge is knowledge of premises, which are assumed without prior argument. ("In some cases admission of the fact must be assumed.")
As the book develops this idea of premises, and as it is further elaborated in book 4 of the Metaphysics, there is a division of premises into types, the first being the kinds of basic truths that are appropriate to some given field of study, and a second being "axioms" of the type we are discussing in this thread, i.e the law of non-contradiction and the law of identity. The first mention of this separation is in Posterior Analytics I,2:
"I call an immediate basic truth of syllogism a 'thesis' when, though it is not susceptible of proof by the teacher, yet ignorance of it does not constitute a total bar to progress on the part of the pupil: one which the pupil must know if he is to learn anything whatever is an axiom. I call it an axiom because there are such truths and we give them the name of axioms par excellence."
Much of book 1 develops the idea of premises further, including the idea that the most basic truths can't be given demonstrations, and finally we arrive at the end of book 2, in part 19:
"As regards syllogism and demonstration, the definition of, and the conditions required to produce each of them, are now clear, and with that also the definition of, and the conditions required to produce, demonstrative knowledge, since it is the same as demonstration. As to the basic premises, how they become known and what is the developed state of knowledge of them is made clear by raising some preliminary problems.
We have already said that scientific knowledge through demonstration is impossible unless a man knows the primary immediate premises. But there are questions which might be raised in respect of the apprehension of these immediate premises: one might not only ask whether it is of the same kind as the apprehension of the conclusions, but also whether there is or is not scientific knowledge of both; or scientific knowledge of the latter, and of the former a different kind of knowledge; and, further, whether the developed states of knowledge are not innate but come to be in us, or are innate but at first unnoticed.
Now it is strange if we possess them from birth; for it means that we possess apprehensions more accurate than demonstration and fail to notice them. If on the other hand we acquire them and do not previously possess them, how could we apprehend and learn without a basis of preexistent knowledge? For that is impossible, as we used to find in the case of demonstration. So it emerges that neither can we possess them from birth, nor can they come to be in us if we are without knowledge of them to the extent of having no such developed state at all. Therefore we must possess a capacity of some sort, but not such as to rank higher in accuracy than these developed states. And this at least is an obvious characteristic of all animals, for they possess a congenital discriminative capacity which is called sense-perception. But though sense-perception is innate in all animals, in some the sense-impression comes to persist, in others it does not. So animals in which this persistence does not come to be have either no knowledge at all outside the act of perceiving, or no knowledge of objects of which no impression persists; animals in which it does come into being have perception and can continue to retain the sense-impression in the soul: and when such persistence is frequently repeated a further distinction at once arises between those which out of the persistence of such sense-impressions develop a power of systematizing them and those which do not.
So out of sense-perception comes to be what we call memory, and out of frequently repeated memories of the same thing develops experience; for a number of memories constitute a single experience. From experience again-i.e. from the universal now stabilized in its entirety within the soul, the one beside the many which is a single identity within them all-originate the skill of the craftsman and the knowledge of the man of science, skill in the sphere of coming to be and science in the sphere of being.
We conclude that these states of knowledge are neither innate in a determinate form, nor developed from other higher states of knowledge, but from sense-perception."
It seems clear to me that this passage is what leads you (or whichever commenters you are relying on) to conclude that something like the PNC is known from sense-perception, but I think it oversimplifies Aristotle's view, for a few reasons:
1) Aristotle draws a distinction between axioms like the PNC and the kind of immediate premises being discussed here. The distinction is that of I,2 quoted before, elaborated further in Metaphysics book 4. Aristotle is something of an empiricist in this sense that he thinks the basic data of scientific investigation must be known by induction from sense-experience, but if you compare this passage to the discussion of the PNC in The Metaphysics (IV, 3), he appeals to no such inductive argument on its behalf, but states it as being necessary strictly on the grounds that without it no logic is possible. His brief treatment of the law of identity is similar. It follows from the fact that the metaphysics is the investigation into being qua being, and is therefore higher than and prior to the other sciences.
2) Aristotle's view of induction and sense-knowledge is not a pure empiricism, and shouldn't be read to imply that basic truths are directly experienced in Nature as such. His views are more complex, being in some sense a middle ground between the pure rationalism of the platonic forms and a pure empiricism. In Metaphysics IV,5 he deals with arguments against the PNC based on sense-experience, and in rejecting them makes clear he doesn't think that the PNC is known directly by the senses:
"Those who really feel the difficulties have been led to this opinion by observation of the sensible world. They think that contradictories or contraries are true at the same time, because they see contraries coming into existence out of the same thing. If, then, that which is not cannot come to be, the thing must have existed before as both contraries alike, as Anaxagoras says all is mixed in all, and Democritus too; for he says the void and the full exist alike in every part, and yet one of these is being, and the other non-being...
And in general it is because these thinkers suppose knowledge to be sensation, and this to be a physical alteration, that they say that what appears to our senses must be true; for it is for these reasons that both Empedocles and Democritus and, one may almost say, all the others have fallen victims to opinions of this sort...
But the reason why these thinkers held this opinion is that while they were inquiring into the truth of that which is, they thought, 'that which is' was identical with the sensible world; in this, however, there is largely present the nature of the indeterminate-of that which exists in the peculiar sense which we have explained; and therefore, while they speak plausibly, they do not say what is true...
Regarding the nature of truth, we must maintain that not everything which appears is true; firstly, because even if sensation-at least of the object peculiar to the sense in question-is not false, still appearance is not the same as sensation.
And, in general, if only the sensible exists, there would be nothing if animate things were not; for there would be no faculty of sense. Now the view that neither the sensible qualities nor the sensations would exist is doubtless true (for they are affections of the perceiver), but that the substrata which cause the sensation should not exist even apart from sensation is impossible. For sensation is surely not the sensation of itself, but there is something beyond the sensation, which must be prior to the sensation; for that which moves is prior in nature to that which is moved, and if they are correlative terms, this is no less the case."
Here, Aristotle is arguing directly against a kind of pure empiricism, and that "prior to sensation" in his view is nous, mind, which must be understood in relation to Plato as a faculty which is prior to and "higher" than the sensible world, but through which we have the capacity to grasp both universals and through pure reason to apprehend principles like the PNC. If we go back to Prior Analytics II,19, which I quoted above, it concludes with this text:
"Let us now restate the account given already, though with insufficient clearness. When one of a number of logically indiscriminable particulars has made a stand, the earliest universal is present in the soul: for though the act of sense-perception is of the particular, its content is universal-is man, for example, not the man Callias. A fresh stand is made among these rudimentary universals, and the process does not cease until the indivisible concepts, the true universals, are established: e.g. such and such a species of animal is a step towards the genus animal, which by the same process is a step towards a further generalization.
Thus it is clear that we must get to know the primary premisses by induction; for the method by which even sense-perception implants the universal is inductive. Now of the thinking states by which we grasp truth, some are unfailingly true, others admit of error-opinion, for instance, and calculation, whereas scientific knowing and intuition are always true: further, no other kind of thought except intuition is more accurate than scientific knowledge"
The word translated as "intuition" is a reference to this capacity of nous. While sense experience and induction play a crucial role in knowledge, the knowledge of the "earliest universal" is present in the soul through intuition. Without sense experience we could not connect the universal with the particular, but the apprehension of the universal depends also on the apprehension of nous via intuition, which is more reliable than scientific knowledge through induction. So that the basic premises of a science may arise through sense experience, but the PNC or the law of identity are different, being the sort of necessary, universal and immutable truths which must be apprehended through intuition alone.
This is why I think it's wrong to say that, to Aristotle, these first principles are "sense-verifiable".
