The passages above named in the Nikomachean Ethica are remarkable: λέγοιτο δ’ ἂν ἱκανῶς, εἰ κατὰ τὴν ὑποκειμένην ὕλην διασαφηθείη· τὸ γὰρ ἀκριβὲς οὐχ ὁμοίως ἐν ἅπασι τοῖς λόγοις ἐπιζητητέον, ὥσπερ οὐδ’ ἐν τοῖς δημιουργουμένοις. τὴν ἀκρίβειαν μὴ ὁμοίως ἐν ἅπασιν ἐπιζητεῖν (χρή), ἀλλ’ ἐν ἑκάστοις κατὰ τὴν ὑποκειμένην ὕλην, καὶ ἐπὶ τοσοῦτον ἐφ’ ὅσον οἰκεῖον τῇ μεθοδῷ. Compare Metaphys. E. p. 1025, b. 13: ἀποδεικνύουσιν ἢ ἀναγκαίοτερον ἢ μαλακώτερον.
The different degrees of exactness attainable in different departments of science, and the reasons upon which such difference depends are well explained in the sixth book of Mr. John Stuart Mill’s System of Logic, vol. II. chap. iii. pp. 422-425, 5th ed. Aristotle says that there can be no scientific theory or cognition about τὸ συμβεβηκός which he defines to be that which belongs to a subject neither necessarily, nor constantly, nor usually, but only on occasion (Metaphys. E. p. 1026, b. 3, 26, 33; K. p. 1065, a. 1, meaning τὸ συμβεβηκὸς μὴ καθ’ αὑτό, — Analyt. Post. I. 6, 75, a. 18; for he uses the term in two different senses — Metaph. Δ. p. 1025, a. 31). In his view, there can be no science except about constant conjunctions; and we find the same doctrine in the following passage of Mr. Mill:— “Any facts are fitted, in themselves, to be a subject of science, which follow one another according to constant laws; although those laws may not have been discovered, nor even be discoverable by our existing resources. Take, for instance, the most familiar class of meteorological phenomena, those of rain and sunshine. Scientific inquiry has not yet succeeded in ascertaining the order of antecedence and consequence among these phenomena, so as to be able, at least in our regions of the earth, to predict them with certainty, or even with any high degree of probability. Yet no one doubts that the phenomena depend on laws.… Meteorology not only has in itself every requisite for being, but actually is, a science; though from the difficulty of observing the facts upon which the phenomena depend (a difficulty inherent in the peculiar nature of those phenomena), the science is extremely imperfect; and were it perfect, might probably be of little avail in practice, since the data requisite for applying its principles to particular instances would rarely be procurable.
“A case may be conceived of an intermediate character between the perfection of science, and this its extreme imperfection. It may happen that the greater causes, those on which the principal part of the phenomena depends, are within the reach of observation and measurement; so that, if no other causes intervened, a complete explanation could be given, not only of the phenomenon in general, but of all the variations and modifications which it admits of. But inasmuch as other, perhaps many other, causes, separately insignificant in their effects, co-operate or conflict in many or in all cases with those greater causes, the effect, accordingly, presents more or less of aberration from what would be produced by the greater causes alone. Now if these minor causes are not so constantly accessible, or not accessible at all, to accurate observation, the principal mass of the effect may still, as before, be accounted for, and even predicted; but there will be variations and modifications which we shall not be competent to explain thoroughly, and our predictions will not be fulfilled accurately, but only approximately.
“It is thus, for example, with the theory of the Tides.… And this is what is or ought to be meant by those who speak of sciences which are not exact sciences. Astronomy was once a science, without being an exact science. It could not become exact until not only the general course of the planetary motions, but the perturbations also, were accounted for and referred to their causes. It has become an exact science because its phenomena have been brought under laws comprehending the whole of the causes by which the phenomena are influenced, whether in a great or only in a trifling degree, whether in all or only in some cases, and assigning to each of those causes the share of effect that really belongs to it.… The science of human nature falls far short of the standard of exactness now realized in Astronomy; but there is no reason that it should not be as much a science as Tidology is, or as Astronomy was when its calculations had only mastered the main phenomena, but not the perturbations.�
In setting out the process of Demonstration, Aristotle begins from the idea of teaching and learning. In every variety thereof some præcognita must be assumed, which the learner must know before he comes to be taught, and upon which the teacher must found his instruction.[8] This is equally true, whether we proceed (as in Syllogism) from the more general to the less general, or (as in Induction) from the particular to the general. He who comes to learn Geometry must know beforehand the figures called circle and triangle, and must have a triangular figure drawn to contemplate; he must know what is a unit or monad, and must have, besides, exposed before him what is chosen as the unit for the reasoning on which he is about to enter. These are the præcognita required for Geometry and Arithmetic. Some præcognita are also required preparatory to any and all reasoning: e.g., the maxim of Identity (fixed meaning of terms and propositions), and the maxims of Contradiction and of Excluded Middle (impossibility that a proposition and its contradictory can either be both true or both false.)[9] The learner must thus know beforehand certain Definitions and Axioms, as conditions without which the teacher cannot instruct him in any demonstrative science.
[8] Analyt. Post. I. i. pp. 71-72; Metaphys. A. IX. p. 992, b. 30.
[9] Aristot. Analyt. Post. I, i. p. 71, a. 11-17. ἅπαν ἢ φῆσαι ἢ ἀποφῆσαι ἀληθές.
Aristotle, here at the beginning, seeks to clear up a difficulty which had been raised in the time of Plato as between knowledge and learning. How is it possible to learn at all? is a question started in the Menon.[10] You either know a thing already, and, on this supposition, you do not want to learn it; or you do not know it, and in this case you cannot learn it, because, even when you have learnt, you cannot tell whether the matter learnt is what you were in search of. To this difficulty, the reply made in the Menon is, that you never do learn any thing really new. What you are said to learn, is nothing more than reminiscence of what had once been known in an anterior life, and forgotten at birth into the present life; what is supposed to be learnt is only the recall of that which you once knew, but had forgotten. Such is the Platonic doctrine of Reminiscence. Aristotle will not accept that doctrine as a solution; but he acknowledges the difficulty, and intimates that others had already tried to solve it without success. His own solution is that there are two grades of cognition: (1) the full, complete, absolute; (2) the partial, incomplete, qualified. What you already know by the first of these grades, you cannot be said to learn; but you may learn that which you know only by the second grade, and by such learning you bring your incomplete cognition up to completeness.
[10] Plato, Menon. p. 80.
Thus, you have learnt, and you know, the universal truth, that every triangle has its three angles equal to two right angles; but you do not yet know that A B C, D E F, G H I, &c., have their two angles equal to two right angles; for you have not yet seen any of these figures, and you do not know that they are triangles. The moment that you see A B C, or hear what figure it is, you learn at one and the same time two facts: first, that it is a triangle; next, by virtue of your previous cognition, that it possesses the above-mentioned property. You knew this in a certain way or incompletely before, by having followed the demonstration of the universal truth, and by thus knowing that every triangle had its three angles equal to two right angles; but you did not know it absolutely, being ignorant that A B C was a triangle.[11]