The threefold division

This is a collection of quotes I have gathered regarding the ancient division between physics, ethics, and logic, whether regarded as a division of philosophy, of the sciences in general, or of anything, really. I have tried to reach as wide as I could, capturing also the use of the Latin words natural or real, moral, and rational, as well as any reference made to mathematics instead of logic or rational philosophy, and the different combinations and orderings that the division could take. As you will notice, I have usually chosen to include rather than to exclude something.

Aristotle always says about Socrates that he confined himself to ethical enquiries. This entirely coincides with the saying of Xenophon, that he never ceased discussing human affairs, asking, What is piety? what is impiety? what is the noble? what the base? what is the just? what the unjust? what is temperance? what is madness? what is a state? what constitutes the character of a citizen? what is rule over man? what makes one able to rule? (Memor. I. i. 16.) In all this we see the foundation of moral philosophy as a science, and hence Socrates is always called the first moral philosopher. But we have already remarked (see above, pp. 142 and 149) that the way was prepared for Socrates by Archelaus, by the Sophists, and by the entire tendencies of the age. There is another saying about Socrates which is a still greater departure from the exact historical truth, namely, that he divided science into Ethics, Physics, and Logic. It is quite a chronological error to attribute to him this distinct view of the divisions of science. He never separated his method of reasoning from his matter, nor could he ever have made the method of reasoning into a separate science. In Plato even, Logic has no separate existence; there is only a dialectic which is really metaphysics. And we may go further, and say that in Aristotle Logic has no one name, and does not form a division of philosophy. Again, Socrates probably never used the word Ethics to designate his favourite study. If he had used any distinctive term, he would have said Politics. With regard to Ethics also, we may affirm that in Plato they are not as yet a separate science, and in Aristotle only becoming so. As to Physics, Socrates appears rather to have denied their possibility, than to have established their existence as a branch of philosophy. The above-mentioned division is probably not older than the Stoics.

— Sir Alexander Grant, Bart., M.A., LL.D., On the History of Moral Philosophy in Greece previous to Aristotle,
in: The Ethics of Aristotle, Illustrated with Essays and Notes, p.160

It is interesting, however, that later Platonists, who started to interpret Plato as holding doctrines, take up enthusiastically the idea that Plato’s philosophy is tripartite, and should be approached via the division of physics, ethics, and logic—usually called just that, though at least one author [— Alcinous, Handbook, ch. 3 —] find names for them that sound more Platonic. We find this claim about Plato’s philosophy in a number of authors, Platonists and others, who agree that Plato should be interpreted doctrinally. Nor is this simply the unreflective following of philosophical fashion. It seems clear that ancient Platonists found it peculiarly appropriate to read Plato this way, since Plato is seen as being the first person to do philosophy in a way which covers a wide area but can be divided into three different areas of differing methodologies and subjects. Atticus, with characteristically violent language, says that Plato was the first to gather together the parts of philosophy, which had hitherto been torn apart and scattered like the limbs of Pentheus. [frag, i des Places.]

— Julia Annas, Platonic Ethics, Old and New, p. 109

In the first cycle of [the curriculum that the Neoplatonists used to teach Plato’s dialogues], after the introductory I Alcibiades, students began with a pair of ethical dialogues, the Gorgias for political virtue and the Phaedo for cathartic. Then, leading up to a summative treatment of the Good in the Philebus, they read three pairs of logical (Cratylus and Theaetetus), physical (Sophist and Statesman) and theological (Phaedrus and Symposium) texts, all interpreted as teaching theoretical virtue to those who had moved beyond politics and catharsis. The clearest presentation of this curriculum survives in an anonymous Prolegomenon to Platonic philosophy, probably written in the sixth century and much influenced by Iamblichus.[...]

— Brian P. Copenhaver, The Secret of Pico’s Oration: Cabala and Renaissance Philosophy, in: Renaissance and Early Modern Philosophy, p. 65

Of propositions and problems there are—to comprehend the matter in outline—three divisions; for some are ethical propositions, some are on natural science, while some are logical. Propositions such as the following are ethical, e.g. ‘Ought one rather to obey one’s parents or the laws, if they disagree?’; such as this are logical, e.g. ‘Is the knowledge of opposites the same or not?’; while such as this are on natural science, e.g. ‘Is the universe eternal or not?’ Likewise also with problems. The nature of each of the aforesaid kinds of proposition is not easily rendered in a definition, but we have to try to recognize each of them by means of the familiarity attained through induction, examining them in the light of the illustrations given above.

— Aristotle, Topics, Α 14.105b19–30

Let us begin by examining the categories “logical,” “ethical" and “physical.” In the Topics, as I said, they serve to distinguish summarily (ώς τύπω περιλαβει̑ν) different species of propositions or of problems. There is no question here of three philosophical disciplines or sciences but, simply, three points of view permitting classification, so to speak, of all types of propositions and problems. Do these viewpoints correspond to “sciences” in the sense of formal objects recognized and distinguished elsewhere in Aristotle? One is tempted to grant this in light of a passage of the Posterior Analytics where, after having established the difference between having an opinion (δοξάζειν) and knowing (ἐπίστασθαι), he writes: “As for how the rest should be distributed among discursive thought and intellect and science and art and prudence and wisdom—some of these questions belong rather to physical study, others to ethical study” (τὰ μεν φυσικη̑ς, τὰ δὲ ἠθικη̑ς θεορίας μα̑λλόν ἐστιν). As for the Analytics, they exhibit the perspective of “logical” study. The fact that the Stoics happened to divide philosophy systematically into three parts described as “logical,” “ethical” and “physical” might suggest that such a system of sciences was previously drawn up by Aristotle himself. But the texts do not really authorize our being so affirmative.

— Richard Bodeus, Political Dimensions of Aristotle’s Ethics, pp. 16–17

In Topics 1.14 Aristotle says there are three classes of dialectical propositions: ethical, physical, and logical. Ethical can be understood to include political propositions. Since rhetoric does not ordinarily deal with questions of physics, ethical and logical propositions are those useful to a speaker. In these chapters, and continuing in Book 2, chapters 1–17, Aristotle gives lists of opinions (called endoxa in dialectic) on political and ethical matters that are commonly held and could be used as premises in the formation of arguments; however, he does not provide much in the way of illustrating how they might be used in practice. Logical propositions will be discussed when he returns to the dialectical features of rhetoric in Book 2, chapters 18–26. Chapters 2–17 of Rhetoric for Alexander treat some of the same matters; they use some of the same terminology, but often defined differently, and they are far more practical in their advice for application of topics, making an interesting comparison with what we find in Aristotle’s text.

— George Kennedy, introduction to chapters 4–15 of Aristotle’s Rhetoric (p. 51)

It being our determination to discourse of Natural Philosophy, we judge it necessary, in the first place and chiefly, to divide the body of philosophy into its proper members, that we may know what is that which is called philosophy, and what part of it is physical, or the explanation of natural things. The Stoics affirm that wisdom is the knowledge of things human and divine; that philosophy is the exercise of that art which is expedient to this knowledge; that virtue is the sole and sovereign art which is thus expedient; and this distributes itself into three general parts, —natural, moral, and logical. By which just reason (they say) philosophy is tripartite; of which one is natural, the other moral, the third logical. The natural is when our enquiries are concerning the world and all things contained in it; the ethical is the employment of our minds in those things which concern the manners of man's life; the logical (which they also call dialectical) regulates our conversation with others in speaking. Aristotle, Theophrastus, and after them almost all the Peripatetics give the following division of philosophy. It is absolutely requisite that the complete person be contemplator of things which have a being, and the practiser of those things which are decent; and this easily appears by the following instances.[...]

— Pseudo-Plutarch, Placita Philosophorum, 1.0 (Prooem.)  = SVF 2.35

Chrysippus is of opinion, that young students should first learn logic, secondly, ethics, and after these, physics, and likewise in this to meddle last of all with the disputes concerning the Gods. Now these things having been often said by him, it will suffice to set down what is found in his Fourth Book of Lives, being thus word for word: ‘First then, it seems to me, according as it has been rightly said by the ancients, that there are three kinds of philosophical speculations, logical, ethical, and physical, and that of these, the logical ought to be placed first, the ethical second, and the physical third, and that of the physical, the discourse concerning the Gods ought to be the last; wherefore also the traditions concerning this have been styled Τελεταί, or the Endings. ’ But that very discourse concerning the Gods, which he says ought to be placed the last, he usually places first and sets before every moral question. For he is seen not to say any thing either concerning the ends, or concerning justice, or concerning good and evil, or concerning marriage and the education of children, or concerning the law and the commonwealth; but, as those who propose decrees to states set before them the words To Good Fortune, so he also premises something of Jupiter, Fate, Providence, and of the world's being one and finite and maintained by one power. None of which any one can be persuaded to believe, who has not penetrated deeply into the discourses of natural philosophy.

— Plutarch, De stoicorum repugnantiis, 9

The pseudo-Plutarchean treatise De vita et poësi Homeri (Homer’s Life and Poetry) deals with Homer’s rhetoric and his purported knowledge of all sciences, a theme that appeared already in Crates and Stoic commentators. Sections 92–160 are dedicated to the ‘theoretical arguments’ in the epics, those that demonstrate truths or theorems concerning the basic divisions of knowledge into logic, physics and ethics—the typical Stoic tripartition of philosophy. The author finds in Homer the doctrine of the four elements and Empedocles’s forces of Love and Strife. The story of Circe is treated as a reflection of Pythagorean metempsychosis. Plato, Aristotle, Epicurus and the Stoics are said to have derived their ideas from Homer.

— Ilaria L. E. Ramelli, The Role of Allegory, Allegoresis, and Metaphor in Paul and Origen, p. 138

Here we encounter problems of translation again: the Stoics use the names of the philosophical disciplines physics, logic (or dialectic) and ethics as the names of (generic) virtues and speak of physical, logical and ethical virtues. This sounds a little odd to modern ears and it is important to bear in mind that in speaking of physical virtue, it is not a virtue of the (human) body that is meant but a virtue that relates to (the knowledge of) physics. This, however, is a minor awkwardness compared to the constructions which would be consequent upon translating physikē - as ‘understanding of nature’ etc. (as has been suggested by Martha Nussbaum 1995 against Menn’s pathbreaking 1995 article on ‘Physics as a Virtue’).

— Christoph Jedan, Stoic Virtues, ch. 7, fn. 10 (p. 191)
(note: a much earlier version of this book, without the note quoted, is free on his Academia.edu profile)

A threefold system of philosophising, then, was already received from Plato. One, on the subject of life and morals. A second, on nature and abstruse matters. The third, on discussion, and on what is true or false; what is right or wrong in a discourse; what is consistent or inconsistent in forming a decision.

And that first division of the subject, that namely of living well, they sought in nature herself, and said that it was necessary to obey her; and that that chief good to which everything was referred was not to be sought in anything whatever except in nature. And they laid it down that the crowning point of all desirable things, and the chief good, was to have received from nature everything which is requisite for the mind, or the body, or for life. But of the goods of the body, they placed some in the whole, and others in the parts. Health, strength, and beauty in the whole. In the parts, soundness of the senses, and a certain excellence of the individual parts. As in the feet, swiftness; in the hands, strength; in the voice, clearness; in the tongue, a distinct articulation of words. The excellences of the mind they considered those which were suitable to the comprehension of virtue by the disposition. And those they divided under the separate heads of nature and morals. Quickness in learning and memory they attributed to nature; each of which was described as a property of the mind and genius. Under the head of “morals” they classed our studies, and, I may say, our habits, which they formed, partly by a continuity of practice, partly by reason. And in these two things was contained philosophy itself, in which that which is begun and not brought to its completion, is called a sort of advance towards virtue; but that which is brought to completion is virtue, being a sort of perfection of nature and of all things which they place in the mind; the one most excellent thing. These things then are qualities of the mind.

The third division was that of life. And they said that those things which had influence in facilitating the practice of virtue were connected with this division. For virtue is discerned in some good qualities of the mind and body, which are added not so much to nature as to a happy life. They thought that a man was as it were a certain part of the state, and of the whole human race, and that he was connected with other men by a sort of human society. And this is the way in which they deal with the chief and natural good. But they think that everything else is connected with it, either in the way of increasing or of maintaining it; as riches, power, glory, and influence. And thus a threefold division of goods is inferred by them.

— Cicero, Academica Posteriora, 1.5

Cicero occupies a leading position among the doxographers of Plato and Platonism. In common with many writers of the Hellenistic period, he divides the study of philosophy as a whole - defined as the love of knowledge regarding divine and human things - into three parts. The pedagogic order of these parts varies for him, being given as physics, ethics, and logic in the Tusculanae disputationes [5,68] and Lucullus [116] and as ethics, physics, and logic in the Academica [15–19] and De legibus [1,60–62].

— Stephen Gersh, The Medieval Legacy From Ancient Platonism, §2, in: The Platonic Tradition in the Middle Ages: A Doxographic Approach, p. 13

The greatest authors, and the greatest number of authors, have maintained that there are three divisions of philosophy – moral, natural, and rational. The first keeps the soul in order; the second investigates the universe; the third works out the essential meanings of words, their combinations, and the proofs which keep falsehood from creeping in and displacing truth. But there have also been those who divided philosophy on the one hand into fewer divisions, on the other hand into more. Certain of the Peripatetic school have added a fourth division, “civil philosophy,” because it calls for a special sphere of activity and is interested in a different subject matter. Some have added a department for which they use the Greek term “economics,” the science of managing one’s own household. Still others have made a distinct heading for the various kinds of life. There is no one of these subdivisions, however, which will not be found under the branch called “moral” philosophy. The Epicureans held that philosophy was twofold, natural and moral; they did away with the rational branch. Then, when they were compelled by the facts themselves to distinguish between equivocal ideas and to expose fallacies that lay hidden under the cloak of truth, they themselves also introduced a heading to which they give the name “forensic and regulative,” which is merely “rational” under another name, although they hold that this section is accessory to the department of “natural” philosophy. The Cyrenaic school abolished the natural as well as the rational department, and were content with the moral side alone; and yet these philosophers also include under another title that which they have rejected. For they divide moral philosophy into five parts: (1) What to avoid and what to seek, (2) The Passions, (3) Actions, (4) Causes, (5) Proofs. Now the causes of things really belong to the “natural” division, the proofs to the “rational.” Aristo of Chios remarked that the natural and the rational were not only superfluous, but were also contradictory. He even limited the “moral,” which was all that was left to him; for he abolished that heading which embraced advice, maintaining that it was the business of the pedagogue, and not of the philosopher – as if the wise man were anything else than the pedagogue of the human race!

— Seneca, Letter 89, 9–13

The goal of Stoic philosophy, like that of other philosophical schools of the Hellenistic era, was to give the pupil a flourishing life free from the forms of distress and moral failure that the Stoics thought ubiquitous in their societies. Unlike some of their competitor schools, however, they emphasized the need to study all parts of their threefold system—logic, physics, and ethics—in order to understand the universe and its interconnections. To the extent that a Roman such as Cicero believed he could uphold the moral truths of Stoicism without a confident belief in a rationally ordered universe, he held a heretical position (one shared many centuries later by Immanuel Kant).

— Elizabeth Asmis, Shadi Bartsch, and Martha Nussbaum, Seneca and His World
in: Natural Questions, pp. x–xi (this essay is included in a few other volumes of the collection)

For when some persons affirm that the world is infinite, while others pronounce it to be confined within limits; or while some look upon the world as uncreated, and others assert that it is created; or when some persons look upon it as destitute of any ruler and superintendent, attributing to it a motion, deprived of reason, and proceeding on some independent internal impulse, while others think that there is a care of and providence, which looks over the whole and its parts of marvellous power and wisdom, God ruling and governing the whole, in a manner free from all stumbling, and full of protection. How is it possible for any one to affirm that the comprehension of such objects as are brought before them, is the same in all men? And again, the imaginations which are occupied with the consideration of what is good, are not they compelled to suspend their judgment rather than to agree? While some think that it is only what is good that is beautiful, and treasure that up in the soul, and others divide it into numbers of minute particles, and extend it as far as the body and external circumstances. These men affirm that such pieces of prosperity as are granted by fortune, are the body-guards of the body, namely strength and good health, and that the integrity and sound condition of the organs of the external senses, and all things of that kind, are the guards of that princess, the soul; for since the nature of good is divided according to three divisions, the third and outermost is the champion and defender of the second and yielding one, and the second in its turn is a great bulwark and protection to the first; and about these very things, and about the different ways of life, and about the ends to which all actions ought to be referred, and about ten thousand other things which logical, and moral, and natural philosophy comprehends, there have been an unspeakable number of discussions, as to which, up to the present time, there is no agreement whatever among all these philosophers who have examined into such subject.

— Philo of Alexandria, On Drunkenness, §§199–202

At all events, men say, that the ancients compared the principles of philosophy, as being threefold, to a field; likening natural philosophy to trees and plants, and moral philosophy to fruits, for the sake of which the plants are planted; and logical philosophy to the hedge or fence: for as the wall, which is erected around, is the guardian of the plants and of the fruit which are in the field, keeping off all those who wish to do them injury and to destroy them, in the same manner, the logical part of philosophy is the strongest possible sort of protection to the other two parts, the moral and the natural philosophy; for when it simplifies twofold and ambiguous expressions, and when it solves specious plausibilities entangled in sophisms, and utterly destroys seductive deceits, the greatest allurement and ruin to the soul, by means of its own expressive and clear language, and its unambiguous demonstrations, it makes the whole mind smooth like wax, and ready to receive all the innocent and very praiseworthy impressions of sound natural and moral philosophy.

— Philo of Alexandria, On Husbandry, §14–16

There are three topics in philosophy, in which he who would be wise and good must be exercised. That of the desires and aversions, that he may not be disappointed of the one, nor incur the other. That of the pursuits and avoidances, and, in general, the duties of life; that he may act with order and consideration, and not carelessly. The third includes integrity of mind and prudence, and, in general, whatever belongs to the judgment.

— Epictetus, Discourses, 3.2 [2]

9.6. Be satisfied with your present opinion, if certain; with your present course of action, if social; with your present mood, if well pleased with all that comes upon you from without.

9.7. Wipe out impression; stay impulse; quench desire; and keep the governing part master of itself.

— Marcus Aurelius, Meditations (see also: 4.33, 7.54, 8.7) [2]

[Plato wrote] so as to be the first to link philosophy up as tripartite, and to show that its parts, which are reciprocally necessary, not merely do not conflict among themselves but even help one another with mutual aid. For although it was from different workshops that these parts of philosophy were taken by him (philosophy of nature from the Pythagoreans, logic from the Eleatics, and moral philosophy right from the source of Socrates), he produced a single thing from them all, like a living thing he had given birth to himself.

— Apuleius, De Platone 1.3, tr. Annas

The study of wisdom, which we call philosophy, seems to most people to have three species or parts: the natural, the moral and the rational, in which is contained the art of arguing [ars disserendi], and which I have proposed to treat at this point.

— Apuleius, Peri Hermeneias, 1

[S]ince, in order to discover the nature of the body, and the distinctions between diseases, and the indications for remedies, he must exercise his mind in rational thought, and since, so that he may persevere laboriously in the practice of these things, he must despise riches and exercise temperance, he must already possess all the parts of philosophy: the logical, the scientific, and the ethical.

— Galen, That The Best Physician is also a Philosopher (Opt. Med.)

Well, these people seem to have been deficient in their approach; by comparison, the approach of those who say that one part of philosophy is physics, another ethics, and another logic seems to have been more complete. Of this group Plato is in effect the founder, since he engaged in discussion on many matters in physics, many in ethics, and not a few in logic. But the most explicit adherents of this division are Xenocrates, the Peripatetics, and the Stoics.

— Sextus Empiricus, Against the Mathematicians, VII, 16

Socrates, then, was a hearer of Archelaus, the natural philosopher; and he, reverencing the rule, “Know yourself”, and having assembled a large school, had Plato (there), who was far superior to all his pupils. (Socrates) himself left no writings after him. Plato, however, taking notes of all his (lectures on) wisdom, established a school, combining together natural, ethical, (and) logical (philosophy). But the points Plato determined are these following.[...]

— Hippolytus of Rome, Refutation of All Heresies, 1.15

The connection, on which we have been dwelling above, between philosophy in its earliest form and the drama was recognised by the Greeks themselves. The dialogue was defined as being ‘composed of question and answer, on some philosophical or political subject, with appropriate character-drawing of the persons who take part in it, and in an ornate style.’ This definition was a common-place of antiquity, for we find it not only in Diogenes Laertius, but in identically the same words in the ‘Introduction to Plato’s Dialogues’ by Albinus. Further, it was pointed out how the progress of philosophy presented an analogy to the progress of the drama. As Thespis first added a single actor to the original song of the chorus, then Aeschylus a second, and Sophocles a third: so philosophy had at first only a single department, namely, physical speculation, to which Socrates added moral science, while Plato perfected its structure with the third division of dialectic. Ever after this the form of philosophy was as rigidly fixed as the form of a tragedy; and every systematic exponent or critic started with the assumption of a tripartite division into φυσική, ἠθική, and διαλεκτική or, as it was called later, λογική. Nor is the division without ground of reason. For philosophy must study either nature (including the divine nature) or man, and if it studies man, it must regard him either from the side of the emotions or of the intellect.

— St. George William Joseph Stock,[1] Introduction to the Meno of Plato

But, just as long ago in tragedy the chorus was the only actor, and afterwards, in order to give the chorus breathing space, Thespis devised a single actor, Aeschylus a second, Sophocles a third, and thus tragedy was completed, so too with philosophy: in early times it discoursed on one subject only, namely physics, then Socrates added the second subject, ethics, and Plato the third, dialectics, and so brought philosophy to perfection. Thrasylus says that he published his dialogues in tetralogies, like those of the tragic poets. Thus they contended with four plays at the Dionysia, the Lenaea, the Panathenaea and the festival of Chytri. Of the four plays the last was a satiric drama; and the four together were called a tetralogy.

— Diogenes Laërtius, Lives of Eminent Philosophers, 3.56

Philosophic doctrine, say the Stoics, falls into three parts: one physical, another ethical, and the third logical. Zeno of Citium was the first to make this division in his Exposition of Doctrine, and Chrysippus too did so in the first book of his Exposition of Doctrine and the first book of his Physics; and so too Apollodorus and Syllus in the first part of their Introductions to Stoic Doctrine, as also Eudromus in his Elementary Treatise on Ethics, Diogenes the Babylonian, and Posidonius.

These parts are called by Apollodorus “Heads of Commonplace”; by Chrysippus and Eudromus specific divisions; by others generic divisions. Philosophy, they say, is like an animal, Logic corresponding to the bones and sinews, Ethics to the fleshy parts, Physics to the soul. Another simile they use is that of an egg: the shell is Logic, next comes the white, Ethics, and the yolk in the centre is Physics. Or, again, they liken Philosophy to a fertile field: Logic being the encircling fence, Ethics the crop, Physics the soil or the trees. Or, again, to a city strongly walled and governed by reason.

No single part, some Stoics declare, is independent of any other part, but all blend together. Nor was it usual to teach them separately. Others, however, start their course with Logic, go on to Physics, and finish with Ethics; and among those who so do are Zeno in his treatise On Exposition, Chrysippus, Archedemus and Eudromus.

Diogenes of Ptolemaïs, it is true, begins with Ethics; but Apollodorus puts Ethics second, while Panaetius and Posidonius begin with Physics, as stated by Phanias, the pupil of Posidonius, in the first book of his Lectures of Posidonius. Cleanthes makes not three, but six parts, Dialectic, Rhetoric, Ethics, Politics, Physics, Theology. But others say that these are divisions not of philosophic exposition, but of philosophy itself: so, for instance, Zeno of Tarsus. Some divide the logical part of the system into the two sciences of rhetoric and dialectic; while some would add that which deals with definitions and another part concerning canons or criteria: some, however, dispense with the part about definitions.

— Diogenes Laërtius, Lives of Eminent Philosophers, 7.39–41

It is possible that [Origen of Alexandria] offers us a further clue to the content of the psychic sense in the prologue to his Commentary on the Song of Songs (ed. Baehrens 1925: 75), where he argues that each of the three books ascribed to Solomon in the Hebrew canon corresponds to a branch of Greek philosophy, and also to one stage in the believer’s progress from the foothills to the summit of understanding. Ethics is represented in this itinerary by Proverbs, physics by Ecclesiastics, the science of contemplation (theorics, epoptics or enoptics) by the Song). The first of these texts is phrased and may be understood somatically; the third, in which Solomon forgoes his own name and becomes the bridegroom, lifts the veil between the enlightened soul and her Redeemer (see further King 2005: 222–263). If we pursue this seductive analogy, the second book of Solomon, which reveals our place in the cosmos, is a mine of cosmological or sapiential teaching which may be said to represent the soul of scripture.

This pattern would appear to have been suggested not by the usual division of philosophy into ethics, physics and logic, but by a passage in the Stromateis of Clement of Alexandria, where three edifying senses are accorded to the scriptures, the last of which is the epopteia, or discernment of the mysteries.

— Mark J. Edwards, Origen (SEP)

The term “epoptics” (or “enoptics”) is problematic. Latin authors often translated this Greek term as inspectiva and they usually viewed it as equivalent to theology. But Origen’s list presented a difficulty since it differed from the two common schemas, that of Aristotle (mathematics, physics, and theology) and that of the Stoics (logic, ethics, and physics). Origen’s list, which was subsequently accepted by Augustine and Isidore of Seville, therefore made room for logic. One can still find it in Letter 30 of Jerome, which organizes each category in relation to the biblical books: physics with Genesis and Ecclesiastes, ethics with Proverbs (and, Jerome tells us, all other books). As for logic, Jerome understands it as a problem and replaces it with theology, placed in relation to the Song of Songs and the Gospels, while also noting that the letters of Paul because of their use of reasoning could correspond to logic. This schema for theological reflection is also in Jerome’s commentary on Ecclesiastes. Relayed through Gregory the Great (in his commentary on Song of Songs) and Isidore of Seville, these corresponding categories are continued in many medieval commentaries. Latin terms that were used to describe aspects of philosophy include moralis, naturalis, contemplativa, and inspectiva. To my knowledge, only Denis the Carthusian presents a different schema at the beginning of his commentary on Proverbs[...]

— Gilbert Dahan, The Sapiential Books in the Latin Middle Ages,
in: The Wiley Blackwell Companion to Wisdom Literature, p. 440–441

Whereas Plato divided the whole subject of philosophy into three branches, Physics, Ethics, Logic, and then again divided his Physics into the examination of sensibles, and the contemplation of incorporeals, you will find this tripartite form of teaching among the Hebrews also, seeing that they had dealt with the like matters of philosophy before Plato was born.

It will be right then to hear Plato first, and so afterwards to examine the doctrines of the Hebrews. And I shall quote the opinions of Plato from those who give the highest honour to his system; of whom Atticus, a man of distinction among the Platonic philosophers, in the work wherein he withstands those who profess to support the doctrines of Plato by those of Aristotle, recounts the opinions of his master in the following manner:

Since therefore the entire system of philosophy is divided into three parts, the so-called Ethical topic, and the Physical, and also the Logical; and whereas the aim of the first is to make each one of us honourable and virtuous, and to bring entire households to the highest state of improvement, and finally to furnish the whole commonalty with the most excellent civil polity and the most exact laws; while the second pertains to the knowledge of things divine, and the actual first principles and causes, and all the other things that result from them, which part Plato has named Natural Science; the third is adopted to help in determining and discovering what concerns both the former. Now that Plato before and beyond all others collected into one body all the parts of philosophy, which had till then been scattered and dispersed, like the limbs of Pentheus, as some one said, and exhibited philosophy as an organized body and a living thing complete in all its members, is manifestly asserted by every one.

For it is not unknown that Thales, and Anaximenes, and Anaxagoras, and as many as were contemporary with them spent their time solely on the inquiry concerning the nature of existing things. Nor moreover is any one unaware that Pittacus, and Periander, and Solon, and Lycurgus, and those like them, applied their philosophy to statemanship. Zeno too, and all this Eleatic School, are also well known to have studied especially the dialectic art. But after these came Plato, a man newly initiated in the mysteries of nature and of surpassing excellence, as one verily sent down from heaven in order that the philosophy taught by him might be seen in its full proportions; for he omitted nothing, and perfected everything, neither falling short in regard to what was necessary, nor carried away to what was useless.

Since therefore we asserted that the Platonist partakes of all three, as studying Nature, and discussing Morals, and practising Dialectic, let us now examine each point separately.’

So speaks Atticus, And the Peripatetic Aristocles also adds his testimony to the same effect, in the seventh Book of the treatise which he composed Of Philosophy, speaking thus word for word:

If any man ever yet taught a genuine and complete system of philosophy, it was Plato. For the followers of Thales were constantly engaged in the study of Nature: and the school of Pythagoras wrapped all things in mystery: and Xenophanes and his followers, by stirring contentious discussions, caused the philosophers much dizziness, but yet gave them no help.

And not least did Socrates, exactly according to the proverb, add fire to fire, as Plato himself said. For being a man of great genius, and clever in raising questions upon any and every matter, he brought moral and political speculations into philosophy, and moreover was the first who attempted to define the theory of the Ideas: but while still stirring up every kind of discussion, and inquiring about all subjects, he died too early a death.

Others took certain separate parts and spent their time upon these, some on Medicine, others on the Mathematical Sciences, and some on the poets and Music. Most of them, however, were charmed with the powers of language, and of these some called themselves rhetoricians and others dialecticians.

In fact the successors of Socrates were of all different kinds, and opposed to each other in their opinions. For some sang the praises of cynical habits, and humility, and insensibility; but others, on the contrary, of pleasures. And some used to boast of knowing all things, and others of knowing absolutely nothing.

Further some used to roll themselves about in public and in the sight of all men, associating with the common people, while others on the contrary could never be approached nor accosted.

Plato however, though he perceived that the science of things divine and human was one and the same, was the first to make a distinction, asserting that there was one kind of study concerned with the nature of the universe, and another concerned with human affairs, and a third with dialectic.

But he maintained that we could not take a clear view of human affairs, unless the divine were previously discerned: for just as physicians, when treating any parts of the body, attend first to the state of the whole, so the man who is to take a clear view of things here on earth must first know the nature of the universe; and man, he said, was a part of the world; and good was of two kinds, our own good and that of the whole, and the good of the whole was the more important, because the other was for its sake.

Now Aristoxenus the Musician says that this argument comes from the Indians: for a certain man of that nation fell in with Socrates at Athens, and presently asked him, what he was doing in philosophy: and when he said, that he was studying human life, the Indian laughed at him, and said that no one could comprehend things human, if he were ignorant of things divine.

Whether this, however, is true no one could assert positively: but Plato at all events distinguished the philosophy of the universe, and that of civil polity, and also that of dialectic.

Such being the philosophy of Plato, it is time to examine also that of the Hebrews, who had studied philosophy in the like manner long before Plato was born. Accordingly you will find among them also this corresponding tripartite division of Ethical, and Dialectical, and Physical studies, by setting yourself to observe in the following manner:[...]

— Eusebius of Caesarea, Preparation for the Gospel, Book 11, ch. 1–3

[I]n contrast to the numerous levels making up the Proclan chain, the Iamblichan universe is only four-layered. This is, basically, the triad deriving from the late Plato, of Metaphysical-Physical (i.e. ideal—phenomenal) and interposed Mathematical, to which there was added by Iamblichus one further stratum, the Ethical, i.e. the realm in which man exists as a political and historical entity.

— James A. Coulter, The Literary Microcosm: Theories of Interpretation of the Later Neoplatonists, p. 86

As the human sciences came from the pagan antique, the accepted classifications of them naturally were taken from Greek philosophy. They followed either the so-called Platonic division, into Physics, Ethics, and Logic, or the Aristotelian division of philosophy into theoretical and practical. The former scheme, of which it is not certain that Plato was the author, passed on through the Stoic and Epicurean systems of philosophy, was recognized by the Church Fathers, and received Augustine’s approval. It was made known to the Middle Ages through Cassiodorus, Isidore, Alcuin, Rabanus, Eriugena and others.

Nevertheless the Aristotelian division of philosophy into theoretical and practical was destined to prevail. It was introduced to the western Middle Ages through Boëthius’s Commentary on Porphyry’s Isagoge, and adopted by Gerbert; later it passed over through translations of Arabic writings. It was accepted by Hugo of St. Victor, by Albertus Magnus and by Thomas, to mention only the greatest names; and was set forth in detail with explanation and comment in a number of treatises, such as Gundissalinus’s De divisione philosophiae, and Hugo of St. Victor’s Eruditio didascalica, which were formal and schematic introductions to the study of philosophy and its various branches.

— Henry Osborn Taylor, The Mediaeval Mind, vol. 2, ch. 35 (p. 312)

For there are three most excellent things that the philosophers of this world have considered to constitute a threefold wisdom – the natural and the moral and the rational. These three things are already evident even in the Old Testament. For what else do those three wells signify—one being ‘vision’, the second ‘abundance’ and the third ‘oath’—if not that that threefold quality existed in the patriarchs (cf. Gen. 26:19–22, 33)? The rational well is ‘vision’ because reason sharpens the mind’s vision and cleanses the eye of the soul. The moral well is ‘abundance’ because, once the foreigners had departed (whose appearance symbolizes the vices of the body), Isaac discovered the limpidity of the living mind, for good morals flow forth pure, and native goodness itself abounds for others when it is more disciplined in its own regard. The third well is ‘oath’ (that is, natural wisdom, which includes things that are above nature and things that are of nature), for what it asserts and swears—with God as its witness, so to say—also embraces divine things, when the Lord of nature is cited as a witness to one’s credibility. Likewise, what do the three books of Solomon show us—the first being that of Proverbs, the second Ecclesiastes and the third that of the Song of Songs—if not that the holy Solomon was skilled in this threefold wisdom? [...]

— Ambrose, Commentary on Luke, prologue (this translation from here)

As the study of wisdom consists in action and contemplation, so that one part of it may be called active, and the other contemplative – the active part having reference to the conduct of life, that is, to the regulation of morals, and the contemplative part to the investigation into the causes of nature and into pure truth – Socrates is said to have excelled in the active part of that study, while Pythagoras gave more attention to its contemplative part, on which he brought to bear all the force of his great intellect. To Plato is given the praise of having perfected philosophy by combining both parts into one. He then divides it into three parts — the first moral, which is chiefly occupied with action; the second natural, of which the object is contemplation; and the third rational, which discriminates between the true and the false. And though this last is necessary both to action and contemplation, it is contemplation, nevertheless, which lays peculiar claim to the office of investigating the nature of truth. Thus this tripartite division is not contrary to that which made the study of wisdom to consist in action and contemplation.

— Augustine, City of God, 8.4

In the third place, let us ask where one should begin [reading Aristotle]. The natural sequence would be to begin with the ethical treatise, so that after first disciplining our own character, we might in that way get to the other writings. But he has used demonstrations and syllogisms in that [the ethical treatise], too, and we are likely to be ignorant of them, being untutored in this kind of discourse. So, for this reason, we must begin with logic, having first, of course, disciplined our own character without the ethical treatise. After logic we must go on to ethics, and then take up the physical [treatises], and after those the mathematical ones, and finally the theological ones.

— Ammonius, in Cat., 5,31–6,9 (see also: Olympiodorus, Prolegomena, 8.29–9,12)

Notably, when Sergius [of Reshaina] signifies his intentions to introduce and comment on Aristotle’s different writings he presents them in the order they were studied according the curriculum of the Alexandrian school, beginning with the Categories and the other logic books of what is called Organon, and continuing with the books on ethics, physics and mathematics, and finally the theological ones (see L.3rb5-3o/P.i7vi3-24; cf. also Hugonnard-Roche 2004: 80 and Watt 2011: 240 f.).

— Sami Aydin, Sergius of Reshaina: Introduction to Aristotle and his Categories, Addressed to Philotheos, p. 48

There are three kinds of philosophy: one natural (naturalis), which in Greek is ‘physics’ (physica), in which one discusses the investigation of nature; a second moral (moralis), which is called ‘ethics’ (ethica) in Greek, in which moral behavior is treated; a third rational (rationalis), which is named with the Greek term ‘logic’ (logica), in which there is disputation concerning how in the causes of things and in moral behavior the truth itself may be investigated. Hence physics involves the cause of inquiring, ethics, the order of living, and logic, the rationale of knowing.

— Isidore of Seville, Etymologies, II.24.3–4

Sub philosophia tres species contineri dicimus: physicam, ethicam, logicam. Physicam naturam dicimus scientiam, idest speculandis causis in rerum naturis. Ethicam vero magistram honestatis vocamus. Logicam vero idem dicimus quod dialecticam et indifferenter utroque nomine in designatione utimur eiusdem scientiae.

— Peter Abelard, Logica “Nostrorum petitioni sociorum”, l. 18–23
in: Abelard, P.: Peter Abaelards philosophische Schriften. 1. Die Logica ‘Ingredientibus’, 2. Die Logica Nostrorum petitioni sociorum, edited by B. Geyer. Aschendorff, Münster (1973), p. 506

The word physis means nature, and therefore Boethius places natural physics in the higher division of theoretical knowledge. This science is also call physiology, that is, discourse on the natures of things, a term which refers to the same matter as physics. Physics is sometimes taken broadly to mean the same as theoretical science, and, taking the word in this sense, some persons divide philosophy into three parts—into physics, ethics, and logic. In this division the mechanical sciences find no place, philosophy being restricted to physics, ethics, and logic alone.

— Hugh of St. Victor, Didascalicon, Book 2, ch. 16

The Compendium of Barcelona is a guide for the students who want to pass the final examination of the Faculty of Arts of Paris. Lafleur has dated it between 1230 and 1240. It is found in a single manuscript, since the production in series by the pecia system was only available for works written by theologians. The author of the guide has a plan divided in three parts : Logic, Ethics and Natural Philosophy. The part devoted to Ethics is divided in three: first the questions devoted to the subject and division of moral philosophy; second the questions devoted to the Ethics; and finally some questions on Plato’s Timaeus and on Boethius’ De Consolatione Philosophiae. The part on the Ethica Noua and Vetus is developed according to several questions established for the examinations. In addition, there is a pronounced interest on methodological issues within Ethics.

— Valeria Buffon, Philosophers and Theologians on Happiness: An analysis of early Latin commentaries on the Nicomachean Ethics, pp. 458–459

After I have treated grammar according to different languages as they assist and indeed are necessary for the study of the Latin writers, and also along with these have dealt with the logical arts and after I have treated in a second volume the parts of mathematics, now in this third volume I come to the natural sciences and in a fourth metaphysics will be joined with the moral sciences. For it is evident that grammar and logic are prior in the order of teaching, and the proper place for the natural sciences, as Avicenna says in his Metaphysics I, is that they should follow mathematics. And similarly Avicenna teaches that metaphysics follows natural science, since, according to him, the conclusions of the other sciences are principles in metaphysics. And this is certain from Aristotle, since through the conclusions of astronomy Aristotle teaches the unity of the first cause and the plurality of the intelligences, although the metaphysician also has, by another way, to prove the principles of all the sciences, as it should be shown in that science. But moral philosophy is the end of all the other sciences, and, therefore, obtains the last place in philosophical consideration. For all the others are speculations about truth, but this is practical or operative of the good, for which reason it follows in the order of nature, for the knowledge of the truth is ordered to love and good action.

— Roger Bacon, Liber primus communium naturalium, dist. 1, c.l, ed. R. Steele, fasc. 2, pp. 1-2
cf. Fr. Benedict M. Ashley, O.P., St. Albert and the Nature of Natural Science, in: James A. Weisheipl, Albertus Magnus and the Sciences: Commemorative Essays 1980, p. 94, fn. 93

[T]he Peripatetics divided philosophy first into three parts, to wit, into physicam generaliter dictam, and ethicam generaliter dictam and rationalem likewise taken broadly. I call physica generaliter dicta that which embraces scientia naturalis, disciplinalis, and divina (i.e. physics in a narrower sense, mathematics which is called scientia disciplinalis, and metaphysics which is scientia divina). And I call ethica, that which, broadly taken, contains the scientia monastica, oeconomica and civilis. And I call that the scientia rationalis, broadly taken, which includes every mode of proceeding from the known to the unknown. From which it is evident that logic is a part of philosophy.

— Albertus Magnus, De praedicabilibus, tr. 1, c. 2

They offered him gifts…[Mt 2:11] Some assign a literal reason for these gifts and say that the Magi found three things: a squalid house, a helpless child and a poor mother. Therefore, they offered gold to sustain the mother, myrrh to sustain the child’s members, frankincense to remove the stench. But it should be noted that something mystical is involved here, such that those three refer to the three things we should offer, namely, faith, action and contemplation.

1. As to faith in two ways:
• first as to the things found in Christ, namely, royal dignity: “The king will reign and be wise” (Jer 23:5); and therefore, they offered gold in tribute. The greatness of the priesthood and, therefore, frankincense, as a sacrifice. Man’s mortality: and therefore, myrrh.
• Secondly, as to faith in the Trinity, because the persons of the Trinity are designated in us.
2. Secondly, they can be referred to our action. For by gold can be signified wisdom: “If you search for wisdom as for hidden treasures, then you will understand the fear of the Lord” (Pr 2:4). By frankincense devout prayer: “Let my prayer, O Lord, be directed as incense in your sight” (Ps 144:2). By myrrh mortification of the flesh: “Mortify your members which are on earth” (Col 3:5); “My hands dripped with myrrh” (Song of Songs 5:5).
3. As to contemplation by those three can be signified the three senses of Sacred Scripture, under which are included the allegorical, anagogical and moral; or the three parts of philosophy, namely, moral, logic and natural. For we ought to use all these for the service of God.

— Thomas Aquinas, Commentary on Saint Matthew’s Gospel, 2.3 (§11)

[A] method of proceeding in the sciences is called rational in three ways:

In one way, because of the principles from which we begin; for instance, when we proceed to prove something beginning with mental beings, like genus, species, opposite, and concepts of this sort, which the logicians study. In this sense a method will be called rational when in a science we use the propositions taught in logic; namely, when we use logic as having a teaching function in the other sciences. But this method of proceeding cannot belong properly to any particular science: it will fall into error unless it proceeds from its own proper principles. However, logic and metaphysics may properly and suitably use this method, because both are universal sciences and in a sense treat of the same subject.

In a second way, a method is called rational because of the end that terminates the thinking process. (1) For the ultimate end that rational inquiry ought to reach is the understanding of principles, in which we resolve our judgments. And when this takes place, it is not called a rational procedure or proof but a demonstration. (2) Sometimes, however, rational inquiry, cannot arrive at the ultimate end, but stops in the course of the investigation itself; that is to say, when several possible solutions still remain open to the investigator. This happens when we proceed by means of probable arguments, which by their nature produce opinion or belief, but not science. In this sense, rational method is opposed to demonstrative method. We can proceed by this rational method in all the sciences, preparing the way for necessary, proofs by probable arguments. This is another use of logic in the demonstrative sciences; not indeed as having a teaching function, but as being an instrument. ln these two ways, then, a method is called rational from rational science, for, as the Commentator says, in both of them logic (which is another name for rational science) is used in the demonstrative sciences.

In a third way, a method is called rational from the rational power, that is, inasmuch as in our procedure we follow the manner proper to the rational soul in knowing, and in this sense the rational method is proper to natural science. For in its procedures natural science keeps the characteristic method of the rational soul in two ways. (1) First, in this respect, that just as the rational soul receives from sensible things (which are more knowable relatively to us) knowledge of intelligible things (which are more knowable in their nature), so natural science proceeds from what is better known to us and less knowable in its own nature. This is evident in the Physics. Moreover, demonstration by means of a sign or an effect is used especially in natural science. (2) Secondly, natural science uses a rational method in this respect, that it is characteristic of reason to move from one thing to another; and this method is observed particularly in natural science, where we go from the knowledge of one thing to the knowledge of another; for example, from the knowledge of an effect to the knowledge of its cause. (a) And the procedure in natural science is not only a movement from one thing to another distinct from it in the mind and not in reality, as when we go from the concept animal to the concept man. In the mathematical sciences we proceed only by means of what is of the essence of a thing, since they demonstrate only through a formal cause. In these sciences, therefore, we do not demonstrate something about one thing through another thing, but through the proper definition of that thing. It is true that some demonstrations about the circle are made by means of the triangle or vice versa, but this is only because the triangle is potentially in the circle and vice versa. (b) But in natural science, where demonstration takes place through extrinsic causes, something is proved of one thing through another thing entirely external to it. So the method of reason is particularly observed in natural science; and on this account natural science among all the others is most in conformity with the human intellect. Consequently, we say that natural science proceeds rationally, not because this is true of it alone, but because it is especially characteristic of it.

[...]

Reply to 4. In that place the Philosopher considers the reasoning and deliberative parts of the soul to be identical: so it is clear that they are related to the second mode of rational procedure mentioned above. In the same place, moreover, because of their contingency he assigns human actions, which are the objects of moral science, to the reasoning or deliberative part of the soul. From what has been said, then, we can gather that the first mode of rationality is most characteristic of rational science, the second of moral science, and the third of natural science.

— Thomas Aquinas, On Boethius’s ‘De Trinitate’, Q.6, A.1c, respondeo & ad. 4

In summary[, Leonardo] Bruni listed the main fields of the Stagirite’s interest, giving four headings. He placed rhetoric (“eloquence and persuasion”) first, followed by civic and moral philosophy, logic (“the precepts of discourse”), and natural philosophy (“the secrets of nature and the causes and reasons of the most occult things”). The basis of this list was the traditional division of philosophy into ethics, logic, and natural philosophy, but Bruni altered it by adding rhetoric as a separate category at the beginning.

— Jerrold E Seigel, Leonardo Bruni and the New Aristotle, in: Rhetoric and philosophy in Renaissance Humanism, p. 112

A nuanced remark concerning Academic Scepticism can be found in De consolatione theologiae, where [Jean] Gerson distinguished three kinds of certainty: supernatural, natural, and moral or civil. Supernatural certainty guarantees infallible belief and comes in three forms. One is the clear and intuitive knowledge of blessed souls in heaven, the next pertains to revealed but evident prophetic knowledge, the last is a supernatural certainty of faith which is based on God’s authority. Gerson remarked that not even God’s absolute power could render supernatural certainty, which was unknown to the ancient philosophers, fallible. Next follows natural certainty. Assent to propositions is naturally certain if its wrongness would conflict with the nature of things. Aristoteles, the Peripatetics, and the Stoics assume this certainty for first principles of the kind, for example, that something is or is not. Furthermore, it is the certainty of correct mathematical deductions. At this point Gerson introduced the Academic Sceptics, of whom he mentioned Socrates, Carneades and Cicero in particular. The Academic Sceptics professed to know nothing at all, not even that they know nothing. Thus, they denied the possibility of supernatural and natural certainty. However, Gerson reminded his readers that a third kind of certainty exists, discussed by Aristotle in the Ethics. This certainty may be called moral or civil (the already discussed certitudo moralis). It does not arise from mathematical proof but from probable and gross reasoning. If the Academics should deny that moral certainty suffices for moral action, they would have to abandon all rational attempts to strive for the good and avoid the bad, and thereby make virtue impossible.

— Rudolf Schüssler, Jean Gerson, moral certainty and the Renaissance of ancient Scepticism,
in: Braun & Vallance, The Renaissance Conscience, pp. 11–28 (the quote is in p. 24)

Ibn Sina holds that there are three kinds of problems that may be discussed in a dialectical way, and consequently there must be three kinds of topics to be used in the art of dialectic; logical, moral and natural. He gives an example for each of the problems in a brief phrase.

Logical problems, such as whether the opposite property belongs to the opposite of the subject in question; moral problems, such as the question of the desirability of pleasure and its beauty or choice worthiness; and natural problems, such as the question of the temporally eternity of the Universe, each question has its own topic.

It seems that Ibn Sina followed Aristotle in his classification of the different branches of knowledge and does not include logic among the philosophical sciences.

— Mohsen Javadi, Ibn Sina and the status of moral sentences, p. 248

[The commentary of the music theory treatise titled Parvulus musice, in Leipzig MS 1236, probably copied in the early 1450s,] begins by dividing the liberal arts into the trivium and quadrivium according to whether the art deals with discourse or with quantity. The arts of the trivium are then subdivided according to the nature of discourse without any of them ever being named. The arts of the quadrivium are not detailed here because the commentator or lecturer had outlined these previously as an explanation of the word science. There, following a line of writers reaching back to Aristotle into natural, moral and mathematical. Discarding the first two, he then, still following this tradition, divided mathematical sciences according to whether they dealt with multitude or magnitude. The first of these terms was then subdivided according to whether it was handled in relationship to another measure or not, resulting in the distinction between arithmetic and music. Finally, motion and then weight were introduced in order to lay out not only geometry and astronomy, but optics and the science of weights as well. In this as in his dealing with some other subjects, the lecturer did not bring together all of his information on a topic in the same place. (One hopes, on behalf of his students, that he at least read them in the same lecture.) None of this information is new. Most of it goes back to Boethius and Cassiodorus, in spirit, if not in formulation. I am rather sure that a more proximate source can ultimately be identified.

— Tom R. Ward, 1990, Music and Music Theory in the Universities of Central Europe during the Fifteenth Century,
in: Cristle Collins Judd, Musical Theory in the Renaissance, p. 567

Born c. 1480 in the diocese of Sens, [Jacques Almain (c. 1480-1515)] probably studied the arts at the College de Montaigu of the University of Paris. During the years 1503-1512, he taught the arts at the College de Montaigu, College de Sainte Barbe, and College de Coqueret. In January 1503 Jan Standonck appealed to the Parlement of Paris to prevent Almain from moving his teaching away from College de Montaigu. Almain served as rector of the university in 1507 and as proctor of the French nation the following year, but he vainly sought a good benefice during the same period. During these years, Almain published works on logic, physics, and moral philosophy. Of these, the Moralia attained the widest diffusion.

— Henrik Lagerlund, Encyclopedia of Medieval Philosophy: Philosophy Between 500 and 1500, “Jacques Almain” entry

Superficially, natural light is nothing more complicated than innate concepts, which [Philipp Melanchthon (1497–1560)] calls noticiae. His scriptural basis is the classic natural law passage, Romans 2:15, where Saint Paul declares a divine rule to be written in the hearts of men, so that even Gentiles can abide by the precepts of Jewish law. Melanchthon simply extends this knowledge of law to include logic, mathematics, and physics. It is not strange that the natural philosophical should mix with the ethical. Mathematics and physics are ethical for Melanchthon. In the Erotemata dialectices, he notes that moral philosophy receives from natural philosophy the principle that man is made for a certain end[...]

— Jonathan Regier, Logic, Mathematics and Natural Light: Liddel on the Foundations of Knowledge,
in Duncan Liddel (1561-1613): Networks of Polymathy and the Northern European Renaissance, ed. Pietro Daniel Omodeo (Leiden: Brill, 2016), 113–29.

In the course of the centuries, God has shown more than one way of drawing men to Him. So it was not to be wondered at that the fishers of men employed their own particular ways of attracting souls into their nets. Whoever may think that ethics, physics and mathematics are not important in the work of the Church is unacquainted with the taste of the Chinese, who are slow to take a salutary potion, unless it be seasoned with an intellectual flavoring.

— Matteo Ricci, Journals, p. 235

In late 1553 and early 1554, Ignatius, with the help of Polanco, wrote the section on universities in the Constitutions, which the Society adopted as binding in 1558. However, Ignatius offered only brief and general guidance on philosophy. In part 4, chapter 12, he wrote this unhelpful sentence: “Logic, physics, metaphysics, and moral philosophy should be treated, and also mathematics with the moderation appropriate to secure the end which is being sought.” And in part 4, chapter 14, he ordered that Aristotle should be followed in logic, and natural and moral philosophy. The First General Congregation (1558) added the words "and metaphysics,” making the statement: “In logic, natural and moral philosophy, and metaphysics, the doctrine of Aristotle should be followed, as also in the other liberal arts.”

— Cristiano Casalini, Jesuit Philosophy on the Eve of Modernity, p. 16

Characteristic of Latitudinarian epistemology was to place logical, physical and moral assent in order of decreasing certainty.

— Paul McHugh, Knowledge and Scepticism in Newman and Locke: Background Considerations Religious, Cultural and Philosophical, f.n. 23

[Paolo] Sarpi had privately taught Micanzio, not with ordinary lessons, but using the Socratic method, setting reading then seeking the truth with him in open discourse. He had in this way perfected many gentlemen and clerics in the moral, mathematical, and natural disciplines, never expounding an author such as Aristotle or Aquinas ex professo, but instead preparing his students sincerely to seek the truth.

— Warren Boutcher, The School of Montaigne in Early Modern Europe, vol. 2, p. 145

In his final years, [Pierre] Gassendi relented to pressure from his friends and released a major portion of his Epicurean studies to the public, publishing his Latin translation of Diogenes Laertius’s Book X on Epicurus, along with ample commentary, in his Animadversiones of 1649. He continued to work on this interpretive material, however, steadily incorporating his philosophical and scientific insights, until his death in the Paris apartment of Montmor in 1655. Montmor, acting as executor, collected this material in manuscript form and with Gassendi’s other Parisian friends arranged to have it published as the posthumous Syntagma Philosophicum. The Syntagma is more systematic than the Animadversiones, largely eschewing the sometimes philological character of the earlier commentary and principally discussing logic, the natural sciences, psychology, and ethics from the perspective of what he deems philosophically, historically, and theologically supportable. His interests in Epicurus are ever-present, not least in the structure of the work, which is divided into a Logic (including his textbook-format Institutio Logica), Physics, and Ethics.

— Saul Fisher, Pierre Gassendi’s Philosophy and Science: Atomism for Empiricists, p. 5 (PDF p. 32)

These are the several kinds of Evidence whereby we attain to the Knowledge or Belief of Things.

The Kinds of Assent proceeding from them, are reducible to these Two Heads.

I. Knowledge or Certainty, which distinguished into three Kinds, which I crave leave to call by the Names of

1. Physical.
2. Mathematical.
3. Moral.

II. Opinion or Probability.

I. That kind of Assent which doth arise from such plain and clear Evidence as doth not admit of any reasonable Cause of doubting, is called Knowledge or Certainty.

1. I call that Physical Certainty, which doth depend upon the Evidence of Sense, which is the first and highest Kind of Evidence of which human Nature is capable.

Nothing can be more manifest and plain to the Appearance of such a Colour or Figure, than that I have in my Mind such a Thought, Desire, or Purpose, and do feel within myself a certain Power of determining my own Actions, which is called Liberty.

To say that we cannot tell whether we have Liberty; because we do not understand the manner of Volition, is all one as to say, that we cannot tell whether we see or hear; because we do not understand the manner of Sensation.

He that would go about to confute me in. any of these Apprehensions, ought to bring a Medium that is better known, and to derive his Argument from somewhat that is more evident and certain than these Things are, unless he can think to overthrow and confute that which is more plain and certain, by that which is less plain and certain; which is all one as to go about to out-weigh a heavy Body by somewhat that is lighter, or to attempt the proving of Ten to be more than Eleven; than which nothing can be more absurd.

2. I call that Mathematical Certainty, which doth more eminently belong to Mathematical Things, not intending hereby to exclude such other Matters as are capable of the like Certainty; namely, all such simple abstracted Beings, as in their own Natures do lie so open, and are so obvious to the Understanding, that every Man’s Judgment (though never lo much prejudiced) must necessarily assent to them. ’Tis not possible for any Man in his Wits (though never so much addicted to Paradoxes) to believe otherwise, but that the Whole is greater than the Part; That Contradictions cannot be both true; That three and three make six; That four is more than three.

There is such a kind of Connexion betwixt the Terms of some Propositions, and some Deductions are so necessary as must unavoidably enforce our Assent : There being an evident Necessity that some Things must be so, or not so, according as they are affirmed or denied to be, and that supposing our Faculties to be true, they cannot possibly be otherwise, without implying a Contradiction.

3. I call that Moral Certainty, which hath for its Object such Beings as are less simple, and do more depend upon mixed Circumstances. Which though they are not capable of the same kind of Evidence with the former, so as to necessitate every Man’s Assent, though his Judgment be never so much prejudiced against them; yet may they be lo plain, that every Man whose Judgment is free from prejudice will consent unto them. And though there be no natural Necessity, that such things must be so, and that they cannot possibly be otherwise, without implying a Contradiction; yet may they be so certain as not to admit of any reasonable Doubt concerning them.

Under each of these Heads there are several Propositions, which may be stiled Self-evident and first Principles.[...]

— John Wilkins, FRS, Of the Principles and Duties of Natural Religion, 9th ed., pp. 4–7 (PDF pp. 27–30)

No one disputes the Usefulness of those Arts, which supply the Necessities, or contribute to the Convenience of Human Life.

As to Sciences; some may be stiled Useful; others Curious, and others again Vain.

In the Number of useful Sciences, I reckon Logick, which teaches to reason justly, closely, and methodically; those Sciences which have any respect to Morality, Physick, and all such Parts of Mathematicks as lay the Foundation of those practical Arts, which serve to procure and augment the Necessaries or Conveniencies of Life.

By Curious, or Elegant Sciences, I understand such as are not indeed of so necessary Use, as to render the Life of Man less sociable, or less convenient upon the Want of them; but yet such as serve to gratify and please an innocent Curiosity, to polish and adorn our Wit, and to embellish and render our Understanding more compleat: Such Sciences are, Natural and Experimental Philosophy, the more fine and subtile Parts of Mathematicks, History, Criticism, Languages, Poetry, Oratory, and the like.

By Vain Sciences, I mean such as are made up of false and erroneous Notions, or are employ’d about frivolous, trifling, and unprofitable Speculations; such are the Amusements of old Philosophers, the Dreams of Astrologers, and the Subtilties of the School-men.

— Samuel Pufendorf, The Whole Duty of Man, According to the Law of Nature, 1.5.9

Dico primò: rectè partitur Philosophia in sua latitudine accepta in naturalem, moralem, & rationalem. Ita comunis olim Platonicorum, & Stoicorum, uti habetur apud Eusebium lib. 2 de præparat. Evangel. Et Alcinat. de doctrina Platonis. Et Ciceronem 1. de orat. ad. Quintum. [...]

— Bernard Sannig, Schola Philosophica Scotistarum, prologus, quæstio iii

At the [Amsterdam] Athenaeum, the traditional philosophical subjects were presented in a hierarchy which reflected the Aristotelian divisions of logic, physics and moral philosophy. It may come as a surprise that this order, maintained at a Protestant institute, reflected the Jesuit Ratio studiorum of 1599; but this was not the only way in which Protestants borrowed from the Jesuit tradition, as we will see.[...]

— Dirk van Miert, Humanism in an Age of Science: The Amsterdam Athenaeum in the Golden Age, 1632–1704

[I]t appears that necessary truths, such as we find in pure mathematics and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances nor, consequently, on the testimony of the senses, although without the senses it would never occur to us to think of them. This is a distinction that should be noted carefully, and it is one Euclid understood so well that he proves by reason things that are sufficiently evident through experience and sensible images. Logic, together with metaphysics and morals, of which the one shapes natural theology and the other natural jurisprudence, are full of such truths, and consequently, their proof can only arise from internal principles, which are called innate. It is true that we must not imagine that we can read these eternal laws of reason in the soul from an open book, as the edict of the praetor can be read from his tablet without effort and scrutiny. But it is enough that they can be discovered in us by dint of attention; the senses furnish occasions for this, and the success of experiments also serves to confirm reason, a bit like empirical trials help us avoid errors of calculation in arithmetic when the reasoning is long. Also, it is in this respect that human knowledge differs from that of beasts. [...]

— G.W. Leibniz, Preface to the New Essays, ¶3
in: Philosophical Essays, p. 293

Vico’s system undeniably shows him to have been a profound thinker, and to have carefully meditated the problems of intelligence. His line dividing the certainty of sciences is exceedingly interesting. At first sight, nothing is more specious than the difference marked between mathematical, natural, and moral sciences. Mathematics is absolutely certain, because the work of the understanding, it is as the understanding, which constructed them, sees them to be. On the other hand, the natural and moral sciences regard objects independent of reason, having by themselves an existence of their own; wherefore, the understanding knows little of them, and even in this little it is the more liable to err as it penetrates deeper into a sphere where it cannot construct. We call this system specious, because when examined, it is found to be destitute of all solid foundation. We recognize, however, a profound thought in its author; for one he must have had to consider science under such a point of view.

— Jaime Luciano Balmes, Fundamental Philosophy, 1§296

[T]his is one Argument whereby, as I remember, the late ingenious Mr. Norris somewhere proves the Being of a God, viz. that there are certain eternal Truths or Propositions, Natural, Mathematical and Moral, such as, Three and three make six; Two Parallel Lines will never meet; The Whole is greater than any one of its Parts; and God is to be honoured by his intelligent Creatures. Now these eternal unchangeable Truths are not a mere Nothing, and therefore they must have an eternal Existence somewhere, and this cannot be but in some eternal Mind, which is GOD. However it be, this is certain, that all these eternal Fitnesses lie open to the Divine Mind, and are part of his unchangeable Ideas, which is all that my present Argument requires.

— Isaac Watts, An Essay on the Freedom of Will in God and in Creatures, §4, prop. 10 (p. 41 of 1732 ed.)

Three sorts of useful knowledge—that of Coexistence, to be treated of in our Principles of Natural Philosophy; that of Relation, in Mathematics; that of Definition, or inclusion, or words (which perhaps differs not from that of relation), in Morality.

— George Berkeley, Philosophical Commentaries, entry 853 (spelling updated cf. Conroy, 1961)

There are, therefore, three species of knowledge, which we must consider as equally certain, provided we employ the precautions necessary to secure us against error. And hence, likewise, result three species of certainty.

The first is called physical certainty. When I am convinced of the truth of any thing, because I myself have seen it, I have a physical certainty of it; and, if I am asked the reason, I answer, that my own senses give me full assurance of it, and that I am, or have been, an eye-witness at it. It is thus I know, that Austrians have been at Berlin, and that some of them committed great irregularities there. I know, in the same manner, that fire consumes all combustible substances; for I myself have seen it, and I have a physical certainty of its truth,

The certainty which we acquire by a process of reasoning, is called logical or demonstrative certainty, because we are convinced of its truth by demonstration. The truths of geometry may here be produced as examples, and it is logical certainty which gives us the assurance of them.

Finally, the certainty which we have of the truth of what we know only by the report of others, is called moral certainty, because it is founded on the credibility of the persons who make the report. Thus, you have only a moral certainty that the Russians have been at Berlin, and the same thing applies to all historical facts. We know with a moral certainty, that there was formerly at Rome a Julius Cæsar, an Augustus, a Nero, &c. and the testimonies respecting these are so authentic, that we are as fully convinced of them, as of the truths which we discover by our senses, or by a chain of fair reasoning.

We must take care, however, not to confound these three species of certainty, physical, logical, and moral, each of which is of a nature totally different from the others. I propose to treat of each separately; and shall begin with a more particular explanation of moral certainty, which is the third species.[...]

— Leonhard Euler, Letters to a German Princess, 4 (p. 12–16, 1802 ed.)

You are no more wanting, I am persuaded, in prudence, than in industry. I shall, therefore, communicate to you a maxim, which I have observed with regard to my own children, that I may learn how far it agrees with your practice. The method I follow in their education is founded on the saying of an ancient, “That students of philosophy ought first to learn logics, then ethics, next physics, last of all the nature of the gods.” [Chrysippus apud Plut: de repug: Stoicorum] This science of natural theology, according to him, being the most profound and abstruse of any, required the maturest judgement in its students; and none but a mind enriched with all the other sciences, can safely be entrusted with it.

— David Hume, Dialogues Concerning Natural Religion, part 1

Q. What Distinctions are made of Necessity?

A. It is distinguished into natural, logical, and moral. By natural Necessity Water congeals with Cold, and Ice melts with Heat. By logical Necessity a Conclusion flows from the Premisses of a Syllogism. By moral Necessity Virtue will be finally rewarded, and Vice punished; and it is morally necessary that intelligent Creatures should worship their Creator. It is to be observed, that both Necessity and Contingence are frequently applied to Events in the Natural World; but those in the Moral World are usually called contingent, being voluntary Actions of intelligent Beings.

— John Newbery, Logic Made Familiar and Easy: To which is Added a Compendious System of Metaphysics Or Ontology: Being the Fifth Volume of The Circle of the Sciences, &c. Published by the King's Authority, p. 202 (1789 ed.)

In 1765, Kant issued an Advertisement for the four lecture courses he would be delivering in the winter semester of 1765/66, on Metaphysics, Logic, Ethics, and Physical Geography (Kant 1905). Instead of merely outlining the course syllabuses, Kant prefaced the document with what would nowadays be called a ‘statement of teaching philosophy’. [...]

— George MacDonald Ross, Kant on Teaching Philosophy, p. 65

Ancient Greek philosophy was divided into three sciences: physics, ethics, and logic. This division is perfectly suitable to the nature of the thing; and the only improvement that can be made in it is to add the principle on which it is based, so that we may both satisfy ourselves of its completeness, and also be able to determine correctly the necessary subdivisions. 

All rational knowledge is either material or formal: the former considers some object, the latter is concerned only with the form of the understanding and of the reason itself, and with the universal laws of thought in general without distinction of its objects. Formal philosophy is called logic. Material philosophy, however, which has to do with determinate objects and the laws to which they are subject, is again twofold; for these laws are either laws of nature or of freedom. The science of the former is physics, that of the latter, ethics; they are also called natural philosophy and moral philosophy respectively.[...]

— Immanuel Kant, Groundwork of the Metaphysic of Morals, preface

Although Kant never uses this term in the Critique of Judgement, its first pages offer a brief overview of an encompassing “transcendental topology.” There, Kant says that our rational capacities relate to two “fields”: the natural and the ethical. He refers to the regions of the fields of which we can have cognition as “territories” and to those of the fields where reason is legislative as “domains.” We should think here of mathematics, physics, and ethics. Those parts of the territory for which reason is not legislative he calls “dwelling-places.” Here, we should think of aesthetics, natural and ethical teleology, and—following Makkreel—history, culture, religion, and other human sciences.

— Simon Truwant, Kant’s Transcendental Reflection: An Indispensable Element of the Philosophy of Culture, §3

The knowledge that is suited to our situation and powers, the whole compass of moral, natural, and mathematical science, was neglected by the new Platonists; whilst they exhausted their strength in the verbal disputes of metaphysics, attempted to explore the secrets of the invisible world, and studied to reconcile Aristotle with Plato, on subjects of which both these philosophers were as ignorant as the rest of mankind.

— Edward Gibbon, The History of the Decline and Fall of the Roman Empire, §13.4

[Moses] Mendelssohn’s collaborator on the Bible translation project, Hartwig Wessely, issued a pamphlet in March (“Words of Peace and Truth”), strongly supporting Joseph’s Edict of Tolerance, and to allay the fears of the rabbis. “The human law prepares the soul for its eventual perfection by the higher studies” of divine matters. The “refinement of morals” now includes the secular culture of “moral, mathematical, and physical sciences.” Mastering German, as Mendelssohn had intended, would uplift Hebrew learning.

— David Shavin, Philosophical Vignettes from the Political Life of Moses Mendelssohn

The Principle of Sufficient Reason in all its forms is the sole principle and the sole support of all necessity. For necessity has no other true and distinct meaning than that of the infallibility of the consequence when the reason is posited. Accordingly every necessity is conditioned: absolute, i.e., unconditioned, necessity therefore is a contradicto in adjecto. For to be necessary can never mean anything but to result from a given reason. By defining it as “what cannot not be,” on the other hand, we give a mere verbal definition, and screen ourselves behind an extremely abstract conception to avoid giving a definition of the thing. But it is not difficult to drive us from this refuge by inquiring how the non-existence of anything can be possible or even conceivable, since all existence is only given empirically. It then comes out, that it is only possible so far as some reason or other is posited or present, from which it follows. To be necessary and to follow from a given reason, are thus convertible conceptions, and may always, as such, be substituted one for the other. The conception of an “ABSOLUTELY necessary Being” which finds so much favour with pseudo-philosophers, contains therefore a contradiction: it annuls by the predicate “absolute” (i.e., “unconditioned by anything else”) the only determination which makes the “necessary” conceivable. Here again we have an instance of the improper use of abstract conceptions to play off a metaphysical artifice such as those I have already pointed out in the conceptions “immaterial substance,” “cause in general,” “absolute reason,” &c. &c. I can never insist too much upon all abstract conceptions being checked by perception.

There exists accordingly a fourfold necessity, in conformity with the four forms of the Principle of Sufficient Reason:—

1º. Logical necessity, according to the principle of sufficient reason of knowing, in virtue of which, when once we have admitted the premisses, we must absolutely admit the conclusion.

2º. Physical necessity, according to the law of causality, in virtue of which, as soon as the cause presents itself, the effect must infallibly follow.

3º. Mathematical necessity, according to the principle of sufficient reason of being, in virtue of which, every relation which is stated in a true geometrical theorem, is as that theorem affirms it to be, and every correct calculation remains irrefutable.

4º. Moral necessity, in virtue of which, every human being, every animal even, is compelled, as soon as a motive presents itself, to do that which alone is in accordance with the inborn and immutable character of the individual. This action now follows its cause therefore as infallibly as every other effect, though it is less easy here to predict what that effect will be than in other cases, because of the difficulty we have in fathoming and completely knowing the individual empirical character and its allotted sphere of knowledge, which is indeed a very different thing from ascertaining the chemical properties of a neutral salt and predicting its reaction. I must repeat this again and again on account of the dunces and blockheads who, in defiance of the unanimous authority of so many great thinkers, still persist in audaciously maintaining the contrary, for the benefit of their old woman’s philosophy. I am not a professor of philosophy, forsooth, that I need bow to the folly of others.

— Arthur Schopenhauer, On the Fourfold Root of the Principle of Sufficient Reason, §49

Progress, then, may be regarded under four successive aspects: Material, Physical, Intellectual, and Moral. Each of these might again be divided on the same principle, and we should then discover several intermediate phases. These cannot be investigated here; and I have only to note that the philosophical principle of this analysis is precisely the same as that on which I have based the Classification of the Sciences.

— Auguste Comte, A General View of Positivism, §2

I have spoken of the learning of Ligeia: it was immense—such as I have never known in woman. In the classical tongues was she deeply proficient, and as far as my own acquaintance extended in regard to the modern dialects of Europe, I have never known her at fault. Indeed upon any theme of the most admired, because simply the most abstruse of the boasted erudition of the academy, have I ever found Ligeia at fault? How singularly—how thrillingly, this one point in the nature of my wife has forced itself, at this late period only, upon my attention! I said her knowledge was such as I have never known in woman—but where breathes the man who has traversed, and successfully, all the wide areas of moral, physical, and mathematical science? I saw not then what I now clearly perceive, that the acquisitions of Ligeia were gigantic, were astounding; yet I was sufficiently aware of her infinite supremacy to resign myself, with a child-like confidence, to her guidance through the chaotic world of metaphysical investigation at which I was most busily occupied during the earlier years of our marriage.[...]

— Edgar Allan Poe, Ligeia

[T]he Scottish philosophical and the mathematical methods do not blend. [...] It should be noticed here that this approach is reflected in the curricula of the Scots universities, and always has been. It has been bred into Scots thinking over all the generations, and is now steadily acquired as well as inherited. This can be illustrated by the curricula of the eighteenth century. The course was in Humanity and Greek Philosophy (metaphysical and natural), Logic and Moral Philosophy, and, less securely though it was always there, Mathematics. [...]

— Alec Lawrence Macfie, The Scottish Tradition in Economic Thought [PDF], p. 393 (PDF p. 5)

Up to this point, it will be observed, we have been occupied with the relation of philosophy to one class of sciences only, the physical and mathematical. When we come to the other classes into which the sciences are usually, and exhaustively, divided, a similar conclusion will be forced upon us. A similar conclusion, because in these classes of sciences, the Moral and the Logical, the ultimate notions which are their distinguishing and characteristic marks are already subjective; for which reason it is that these sciences are most usually treated as forming a part of philosophy as distinguished from science. [...]

The several sciences then, in every case, yield us notions, their ultimate bases, which are susceptible of a further subjective analysis, whether these notions are themselves objective as in the physical and mathematical sciences, subjective as in the practical, or both at once as in logic. But besides these ultimate notions of the several sciences, there is yet one notion to be mentioned, a notion not peculiar to any one science, but common to all, and involved in the particular ultimate notions of each. This notion is that of Existence. Different as the three groups of sciences, physical, logical, and moral, are in point of subjectivity and objectivity, yet the notion of Existence is involved alike in all. [...]

— Shadworth H. Hodgson, Philosophy and Science

As is well known, we Germans are of a terribly ponderous Gründlichkeit, radical profundity or profound radicality, whatever you may like to call it. Whenever anyone of us expounds what he considers a new doctrine, he has first to elaborate it into an all-comprising system. He has to prove that both the first principles of logic and the fundamental laws of the universe had existed from all eternity for no other purpose than to ultimately lead to this newly-discovered, crowning theory. And Dr. Dühring, in this respect, was quite up to the national mark. Nothing less than a complete “System of Philosophy,” mental, moral, natural, and historical; a complete “System of Political Economy and Socialism”; and, finally, a “Critical History of Political Economy”—three big volumes in octavo, heavy extrinsically and intrinsically, three army-corps of arguments mobilized against all previous philosophers and economists in general, and against Marx in particular—in fact, an attempt at a complete “revolution in science”—these were what I should have to tackle.

— Friedrich Engels, Socialism, Utopian and Scientific

Philosophy may be divided into real, rational, and moral philosophy.— Every science may be divided into as many parts as there are different aspects under which the object of which it treats may be viewed. But the object of philosophy in general is being, which may be considered under three aspects: as real and possessing attributes independent of our cognition; as ideal and having attributes which result from our mental action; or as moral when regarded as the term of voluntary action. Philosophy, then, may treat of the ultimate principles of things either in the order of reality, or of cognition, or of morality; its divisions are, therefore, called physical, logical, and ethical; or, if we use the Latin equivalents, natural or real, rational, and moral. The ontological order, or order of existence would require us to begin with real philosophy or metaphysics; we must, however, first study rational philosophy, because it points out the laws of the human mind in acquiring knowledge, and trains it to discern the true from the false, thus furnishing the means to study real being more easily and securely.

— Louis of Poissy, Elementary Course of Christian Philosophy, intr.

[Brand Blanshard] insisted that there were genuine logical, moral, and natural necessities that are interlinked. For instance, logical necessities involve more than the connection of abstract elements – they involve the real connection of things. Further, natural causation involves logical necessity. Fundamental logical laws record not just an actual or recommended movement of thought in inference but genuine structural characteristics of nature: as Bradley had said, reality does not contradict itself. Moral necessities are revealed in such beliefs as that pleasure is better than pain. They do not just indicate preferences but are forced upon us by moral realities.

— F. Michael Walsh, “Brand Blanshard” entry in John R. Shook’s Dictionary of Modern American Philosophers

Are we then to conclude that reality is not physical, and look for other terms to which we may reduce physical terms? There is no lack of such other terms. Indeed, we could as fairly have begun elsewhere. Thus some parts of experience compose the consciousness of the individual, and are said to be known by him. Experience so contained is connected by the special relation of being known together. But this relation is quite indifferent to physical, moral, and logical relations. Thus we may be conscious of things which are physically disconnected, morally repugnant, and logically contradictory, or in all of these respects utterly irrelevant. Subjectivism, in that it proposes to conceive the whole of reality as consciousness, must attempt to reduce physical, moral, and logical relations to that co-presence in consciousness from which they are so sharply distinguished in their very definition. The historical failure of this attempt was inevitable.

— Ralph Barton Perry, The Approach to Philosophy, §210

On 31 January 1909, Keynes composed a list of proposed writings, most of which were never written. Last on the list was a textbook entitled ‘The Mathematical Organon of Economies’. Clearly, he viewed the matter as worth writing about in an educational context. Given his other writings, possible topics might have been the relevant types of mathematical technique, the question of the superiority of some methods over others, and the value and limits of mathematics in economics. Significantly, the title entails the existence of a mathematical organon of economics. The wording recalls his 1907 fellowship dissertation where he explicitly accepted the existence of an ‘organon’ of correlation theory while at the same time criticizing the particular analysis of its foundations by Pearson. Argument by analogy suggests that rejection of particular usages of mathematics in economics does not imply rejection of the entire apparatus.

This plan for a textbook on mathematics in economics provides informative background for later comments. In 1924 he lamented that ‘we still, after fifty years, lack the ideal textbook’ for the purpose of making diagrammatic analysis in economics ‘available to students in the fullest and clearest form possible’ (C.W. X: 188 & n. 3). Much later (c.1938), he referred to mathematics in another written work, ‘An Introduction to Economic Principles’, the opening volume of which was to discuss, inter alia, the ‘techniques’ of economics and their relations to ‘other moral, mathematical and natural sciences’.

— Rod O’Donnell, Keynes and Formalism,
in: Harcourt & Riach, A “second Edition” of The General Theory, Volume 2, p. 137

The ‘Twentieth Series’ of Logic of Sense is dedicated to Stoicism. It begins with the passage of Diogenes Laërtius mentioned above, where it emphasises sense of philosophy as an egg. ‘We must imagine’, he writes, ‘a situation in which a student [disciple] is posing a question of signification: O master, what is ethics? The Stoic sage then takes out a hard-boiled egg from his reversible cloak [manteau doublé] and designates the egg with his staff’ (LS 142). [...] [T]rying to talk about only the albumen, without referring to the yolk or shell, fails, just as trying to talk about only ethics, in isolation from physics and logic, is impossible, or at least misses the complicated yet necessary interrelations among all three. Deleuze knows this: ‘the place of ethics is clearly displayed between the two poles of the superficial, logical shell and the deep physical yolk’ (LS 142). [...]

— Ryan J. Johnson, Deleuze, a Stoic, introduction (pp. 8–9)

[I] think the orientation to value and axiology of Zhouyi is based on the understanding of the ultimate “truth” of the cosmos. The system of images and numbers is a system deriving from the principles of generation of the cosmos. Every single trigram and hexagram is based on a natural principle from which every behavior in human life is to derive. As explained by Mou Zongsan, there are three aspects of contents and meanings embodied in Zhouyi: First, physical aspect; second, arithmetical aspect; third, ethical aspect. All images imply “a kind of epistemology of realism” and “axiology of realism,” or “transcendental and immanent axiology” (Mou 1988, pp. 3–5). This means Zhouyi includes two types of content: philosophy of nature and philosophy of life.

— Li Shuhua, Natural Philosophy of “Zhouyi” and Life Practice, §3¶4 (p. 183)

Notes

[1] A note on Stock’s name. He was not canonized; his first name was “St. George”, with the title included, cf. https://www.zinzin.com/observations/2012/who-was-st-george-william-joseph-stock/

[2] The relation between the three disciplines pointed out by Epictetus and Marcus Aurelius and the threefold division of philosophy may not be clear to everyone. I include these quotes because the division is traditionally thought to be Stoic, and because the relation is drawn, not unreasonably, by Christopher Fisher’s helpful paper, Self-Coherence: The Fundamental Intuition of Stoicism. I recommend looking at it for an account of the division in modern Stoicism, supplemented with a table and four colorful diagrams. This post at Modern Stoicism also seems helpful.