Dr. Peter Redpath

Dr. Peter Redpath

Recovering Our Understanding of Philosophy and Science

by Peter A. Redpath, Ph.D.

As the above title indicates, I devote this article to recovering our understanding of philosophy and science. This title will likely perplex those readers who were unaware that we had lost, or ever had, this understanding. I have two requests to make of such readers: (1) Read on. If, after having finished this paper, you still hold the same opinion, write an article or book and please show me where I have gone wrong. (2) Read my trilogy of works, Cartesian Nightmare: An Introduction to Transcendental Sophistry; Wisdom’s Odyssey from Philosophy to Transcendental Sophistry; Masquerade of the Dream Walkers: Prophetic Theology from the Cartesians to Hegel; and John N. Deely’s, Four Ages of Understanding: The First Postmodern Survey of Philosophy from Ancient Times to the Turn of the Twenty-first Century.

[i] Again, if after having read these works and this article you still disagree with me, please write an article or book and show me where I have gone wrong.

While I am now certain the thesis I propose is true, I can understand the trouble some readers might have accepting it. I experienced a similar difficulty when, in the late 1980s, my reading of Jacques Maritain’s The Peasant of the Garonne, and some other works, caused me to start to take seriously Maritain’s bold assertion that modern subjective idealists “impugn the basic foundation of philosophic research. They are not philosophers”; that what such thinkers practice today is a kind of “secularized theology.”[ii] Étienne Gilson, no historical or philosophical ignoramus, reinforced this initial shock when I found him saying, “The magnificent ‘systems’ of those idealists who bear the title of ‘great thinkers,’ and wholly deserve it, belong to the realm of art more than in that of philosophy. . . . No more than science, philosophy cannot be a system, because all systematic thinking ultimately rests upon an assumption, whereas, as knowledge, philosophy must rest on being.”[iii]

1. For Everyone and All Time, Philosophy is the Study of the One and the Many

Like most of my colleagues, before reading Maritain and Gilson, under the influence of René Descartes, I mistook philosophy for a kind of systematic logic. I mistakenly thought that the ancient Greek discovery of philosophy arose as a result of the Greek discovery of the principles of logic. By 1998, I no longer thought so.

Hence, in my Masquerade of the Dream Walkers: Prophetic Theology from the Cartesians to Hegel, I correctly wrote:

Often, philosophy teachers assert that the problem of the one and the many was a main issue of ancient Greek philosophy. This is not accurate. Ancient Greek philosophy was the problem of the one and the many. For the ancient Greeks, philosophy was a study of measured being. The major Greek philosophers considered philosophy to involve knowing a multiplicity of substances and substantial properties through a one. Aristotle tells us to measure something means to know it through a one. Hence, to know a substance as a one is to measure it.

. . . Substance and its two intrinsic accidents account for the three intrinsic principles of measuring. These principles, in turn, account for the intelligible ground, and subsequent rules, of all our scientific knowledge.[iv]

This explains why Aristotle divided the speculative sciences into physics, mathematics, and metaphysics. Because forms are unit measures, and to be one means to be indivisible, qualities and quantities are intrinsic forms, or limit measures, that inhere in and necessarily limit a substance, internally, and necessarily determine the way it can relate to things around it in the real world. These accidental forms, or essential properties, just like substantial form, necessarily limit their subjectifying matters because, as intrinsic indivisibles (what St. Thomas, at times, refers to, when known, as “indivisible intelligibles”), they act as boundaries, that beyond which something cannot exist.[v]

As St. Thomas maintained, philosophy studies a real, not a logical, subject or genus. It studies a proximate subject, a generic substance (a one) considered as a multitude of hierarchically ordered species (a many). While this subject (this one generic body, for example, a geometrical body) resembles a logical genus because we include it in the definition of beings that participate in it (for example, linear, square, and triangular bodies; its intrinsic, or per se accidents, its species [a many]), strictly speaking, this subject genus that the philosopher studies is a multitude of hierarchically ordered specific substances considered as the proper subject of intrinsic, necessary operations, or per se accidents (necessary effects [a many] flowing from a necessary cause, its per se subject [a one]). [vi]

Our job as philosophers is chiefly to consider the behavior of individually existing things in terms of this proximate, per se subject and its intrinsic and necessary, per se, accidents, a hierarchical order of species, contrary opposites, that a generically-considered, substantial body causes to flow from its existence, matter, and form. These species are contrary opposites because contraries of higher and lower species are extreme differences that exist within a genus, and Aristotle asserted that contraries are extreme differences sharing a common genus.[vii]

Thus, following Aristotle, St. Thomas asserted that the proximate subject, or generic substance, about which the geometrician wonders is the surface body. This body is the immediate, chief, proximate, and principle subject of all plane figures, its intrinsic and necessary, or per se, accidents. Because these accidents intrinsically and necessarily flow from, and are intrinsically subjectified in, this geometrical body, these plane figures comprise a multitude of species (a many), of hierarchically ordered opposites, subjectified in, and caused by, a surface body, their generic body or substance. They are its many necessary effects. The geometrician considers this subject analogously, that is, according to the same formal aspect and, also, according to unequal relationships, “just,” as he said, “it is clear that one science, medicine considers all health-giving things.”[viii]

Hence, this multitude of species essentially flows from this generic body as from a principle (a one, because principles are starting points and points are unit measures, indivisibles, or ones). Since this concrete body, abstractly considered as the one generic body of all the members of its many species, proximately gives rise to these necessary and intrinsic accidents whose properties and behavior the philosopher causally seeks to understand, this generic body is their per se, or proper, subject; and they are its per se, or proper, accidents.

For example, “Socrates the musician” (the generic body), not “Socrates the philosopher” (incidental, or accidental body or subject), or “Socrates the human being (incidental, or accidental body or subject, and the generic body of “Socrates the musician”), is the proper and per se principle, cause, and subject of flute playing (the per se effect). “Socrates the musician” is the proper, or per se, accident of “Socrates the human being,” because being a musician is incidental to being human (not all human beings are musicians). “Socrates the musician” has specific, intrinsic, and necessary properties (intrinsic and necessary accidents) as a musician. The philosopher chiefly seeks to understand the first causes of these properties through reference to their proper and per se, not incidental, subject, body, or matter.[ix]

The geometrical body (subject, matter, subject-matter, or genus, or generic substance), not the sentient body, living body, or political body (all incidental bodies in reference to a geometrical body), is the body upon which the geometrician as geometrician chiefly, primarily, reflects, for the purpose of considering how the principles of this subject give rise to its different species, or per se accidents, and their ways of behaving through their properties.[x] Hence, this is the body about which the geometrician chiefly talks, or predicates his terms per se. As a result, Aristotle stated that science involves per se predication and that philosophy starts in wonder, not in universal methodic doubt or impossible dreams of pure reason.[xi]

St. Thomas added to Aristotle’s observation that wonder is a species of fear that results from ignorance of a cause. Because the object of fear calls to mind a difficulty of some magnitude and a sense of personal weakness, an immediate sense of opposition, dependency, and privation, our desire to philosophize must arise within all of us as the product of a natural desire to escape from the natural fear we have of the real difficulty, danger, and damage ignorance can cause us. Hence, strictly speaking, we are not born philosophers. And people cannot pour philosophy into us like into an empty jug. Only those who have some knowledge and experience of this initial sort of fear, accompanied by the appropriate desire to put it to rest, can become philosophers.

St. Thomas explained that this initial sense of fear grips us in two stages: (1) Recognition of our weakness and fear of failure causes us to refrain immediately from passing judgment. Then (2) hope of possibility of understanding an effect’s cause prompts us intellectually to seek the cause.

Thomas added that, since philosophical investigation starts with wonder, “it must end in the contrary of this.” We do not wonder about the answer to questions we already know, or about what is evident. And, strictly speaking, when working as philosophers, we do not seek to remain in a state of wonder. We seek to put wonder to rest by discovering the causes of the occurrences of things.[xii]

Since wonder is the first principle of all theoretical, practical, or productive philosophy for everyone and all time, initially, all philosophical first principles arise from our human senses, emotion, intellect, and something that causes in us the awareness of real opposition, not simply difference. Hence, for the ancient Greeks, philosophy involved a study of opposites and relations, and, more precisely, of contrary opposites, because cause and effect are a species of relation and contrary opposites (precisely speaking, because relation is, as Aristotle claimed, one of the four kinds of opposition). But because, as Aristotle said, opposition between the one and the many is basic and the principle of all other opposition, because all other opposites are analogous transpositions of this sort of opposition, fundamentally, all philosophy, for all time, involves reflection upon the problem of the one and the many.[xiii]

2. Why Plato Thought Philosophy Starts in Wonder and Wonder Starts with the Problem of the One and the Many

To prove more completely that the ancient Greeks realized that philosophy starts with wonder understood as arising from awareness of opposition and sustained reflection of consideration of the problem of the one and the many, I will first consider some things Plato, chiefly through the character of Socrates, told us about becoming a philosopher in one of his most famous dialogues, The Republic. Throughout his dialogues, Plato repeatedly made reference to the opposition between the one and the many and the peculiar way philosophers speak is connected to this opposition. The examples are so many that I need not cite them in particular to prove my point. Readers may simply check dialogues such as the Meno, Symposium, Crito, Phaedo, Ion, Laches, Lysis, Charmides, Protagoras, Parmenides, Sophist, Laws, and Republic and, if they pay attention, they should easily be able to verify that my claim is true. I will, however, initially focus on what Plato said in Republic, Book 7, to support my paper’s major thesis because, in this section of this work, Plato engaged in a sustained reflection on the pedagogy involved in becoming a philosopher.

Republic, Book 7, starts with Plato’s famous “Myth of the Cave.” Plato presented this story at this point in his dialogue as an example to show how, as he just finished saying in Book 6, “Philosophy . . . the love of wisdom, is impossible for the multitude” (the many), and how strange, alien, the nature of philosophical education is likely to appear to the many.[xiv]

Since most people conversant with philosophy are familiar with this story, I need not go into it in detail, other than to mention that, within the context of his account, Plato made sure to indicate that “in naming the things they saw” the people in the cave would be naming appearances, but would think they were naming the things that were causing the appearances.[xv] Only the person who was able to escape from the cave and, eventually, come to know the Good, which causes everything else but is the last thing seen, is the philosopher and would rightly understand how to name things.[xvi]

In preparing to explain the nature of philosophical education, Plato had Socrates tell Glaucon that they have to use this image of turning the soul’s vision from appearances to the Good.[xvii] Then Socrates proceeded to explain the nature of this sort of psychic turning in more precise, less metaphorical, detail.

He started to do this by saying, “education is not in reality what some people proclaim it to be in their professions. What they aver is that they can put true knowledge into a soul that does not possess it, as if they were inserting vision into blind eyes.” Next, he stated that his argument indicates the proper analogy for the change education effects is not that of filling an empty vessel.

[T]he true analogy for this indwelling power in the soul and the instrument whereby each of us apprehends is that of an eye that could not be converted to the light from the darkness except by turning the whole body. Even so this organ of knowledge must be turned around from the world of becoming together with the entire soul, like the scene shifting periactus in the theater, until the soul is able to endure the contemplation of essence and the brightest region of being. And this, we say is the good, do we not?[xviii]

Socrates then speculated that “an art of the speediest and most effective shifting or conversion of the soul, not an art of producing vision in it,” might exist. But it could only do so for an eye that already possesses vision, “but does not rightly direct it and does not look where it should.”

He maintained that such an art would resemble servile, or bodily, arts, inasmuch as it does not pre-exist in the soul; and we have to cause it by habit and practice. But such a liberal art, or as Socrates more precisely called it, this intellectual virtue or

excellence of thought, it seems, is certainly of a more divine quality, a thing that never loses its potency, but, according to the direction of its conversion, becomes useful and beneficent, or, again, useless and harmful. Have you never observed in those who are popularly spoken of as bad, but smart, men, how keen is the vision of the little soul, how quick it is to discern the things that interest it, a proof that it is not a poor vision, which it has but one forcibly enlisted in the service of evil, so that the sharper the sight the more mischief it accomplishes?[xix]

Plato might have had in mind Alcibiades as the sort of precocious man possessed of some the liberal art of learning but lacking in the requisite moral virtue to become a philosopher.[xx] Whatever the case, Socrates continued by saying that, had the moral part of this small-souled person’s psyche “been hammered from childhood” and had it freed more the intemperate dispositions that turned its vision downward, if “it had suffered a conversion toward the things that are real and true (that is, toward first principles and causes), that same faculty of the same men would have been most keen in its vision of the higher things, just as it is for the things toward which it is now tuned.”[xxi]

Socrates asserted that, strictly speaking, people uneducated and inexperienced in truth, and people who want to spend their lives in uninterrupted learning for the sake of learning, can never adequately rule a city because the first live aimless lives, and direct all their actions aimlessly, and the second will not voluntarily seek to engage in politics because they believe “that while still living they have been transported to the Islands of the Blessed.”

Since the wider context of Plato’s consideration of education was his consideration of how to establish the ideal city so as to find there true justice, he had Socrates maintain that the only way he will be able to do so is to force philosophers “to live an inferior life when the better is in their power.” The just city that he is founding is concerned with the happiness of the whole city, not that of one group, even of philosophers. Hence, he told Glaucon, with whom he was then speaking, that, in forcing philosophers to rule, “[W]e shall not be wronging . . . the philosophers who arise among us, but . . . we can justify our action when we constrain them to take charge of the other citizens and be their guardians.”

In this way, unknowingly anticipating the modern city sprung from Cartesian doubt and modern subjective idealism, Socrates said, “our city will be governed by waking minds, and not, as most cities now, which are inhabited and ruled darkly as in a dream by men who fight one another for shadows and wrangle for office as if that were a great good.”

Socrates claimed that philosophers “will assuredly approach office as an unavoidable necessity, and in the opposite temper from that of the present rulers in our cities.”[xxii] Plato’s ideal city only becomes a determinate, or real, possibility on the condition that some way of living better, some happiness higher, than political life exists.

For only in such a state will those rule who are really rich, not in gold. But if, being beggars and starvelings from lack of goods of their own, they turn to affairs of the state thinking that it thence that they should grasp their own good, then it is impossible. For when office and rule become the prizes of contention, such a civil and internecine strife destroys the office seekers themselves and the city as well.[xxiii]

Socrates said that only the life of the true philosopher looks with scorn upon political office, for this precise reason: only true philosophers are worthy of holding political office because “those who take office should not be lovers of rule. Otherwise there will be a contest with rival lovers.”[xxiv] Clearly, this is because, in Plato’s mind, the philosopher is unique, different from, and opposed to the many, those who seek political office for personal gain.

Since rule in the ideal city necessarily demands involvement of philosophers, Socrates’ next question to consider was how do we produce philosophers and how may they “be led upward to the light even as some are fabled to have ascended from Hades to the gods?” Socrates’ answer is that, as he had said in his Myth of the Cave, true philosophy is that ascension to reality that is “a conversion and turning about of the soul from a day whose light is darkness to the veritable day.”

All well and good. Most people who call themselves philosophers probably get his message. But, metaphors aside, more precisely, what did Socrates and Plato mean by this conversion and turning of the soul? Socrates immediately explained his meaning by considering the question what powers effect this turning and conversion.

Since the general education thus far under consideration in the Republic had been for rulers, or guardians, Socrates maintained that this study must be useful to soldiers but must go beyond the training in “music,” the liberal arts, or poetry as he and Glaucon have already described music. The reason for this, as Glaucon explained, is that music had “educated the guardians through habits, imparting by the melody a certain harmony of spirit that is not science, and by the rhythm measure and grace, and also the qualities akin to these in words of tales that are fables and those that are more nearly true. But it included no study that intended to any such good as you are now seeking.”

Since music, gymnastic, and the servile arts as then popularly understood and taught, were inadequate propaedeutics for effecting the philosophical habit of mind, Socrates suggested that Glaucon and he should “take something that applies to all alike.” He then referred to the “common thing that all the arts and forms of thought and all sciences employ, and which is among the first things that everybody must learn.” Since this thing is common to all the arts and all the forms of thought, and is something all science uses, while Socrates did not refer to it as such, at first glance, it would appear to be some sort of logical or metaphysical being because logical reasoning and metaphysical principles apply to everything we know.

The way Socrates explained this common thing, however, was as “that of distinguishing one, two, and three. I mean, in sum, number and calculation. Is it not true of them that every art and science must necessarily partake of them?” While Glaucon readily agreed, at first glance, the correct answer to the question Socrates just posed appears to be, “No,” unless Socrates was referring these predicates to their subjects in some sort of metaphysical, not mathematical, way. For example, by predicating the term analogously to mean measuring. At the same time, in a way, what Socrates said is true, even mathematically considered, for, in a way, all linguistic development (a necessary condition for developing science), presupposes our ability to limit the length of sounds we produce to form words, and ordering words one after the other (word order), to form sentences. Both require some rudimentary arithmetical and geometrical skill. We derive our first understanding of all our concepts of measuring from our sensible experience of real quantity.

Whatever the case, Socrates’ point was that mathematical study is conducive to awakening philosophical wonder in us. Hence, he said, “It seems likely that it is one of those studies which we are seeking that naturally conduce to the awakening of thought, but that no one makes the right use of it, though it really does tend to draw the mind to essence and reality.”

Why ? Socrates immediately explained by indicating to Glaucon that some reports our perceptions give us “do not provoke thought to reconsideration because the judgment of them by sensation seems adequate, while others always invite the intellect to reflection because the sensation yields nothing that can be trusted.” Apparently, then, Plato thought that the philosophical habit of mind presupposes our experience of “reports” or “communications” from perceptions that provoke our minds to engage in reconsideration of what we have perceived and that, absent such provocation, we cannot become philosophers. Becoming philosophers, in some respect, involves semiosis and awareness of opposition. [xxv] (Later in philosophy’s history, St. Thomas will go so far as to say all our knowledge starts with sensible signs: “[K]nowledge of a thing starts with certain external signs.”)[xxvi]

Glaucon thought he understood what Socrates meant and immediately said, “You obviously mean distant appearances . . . and shadow painting.”

In reply, Socrates told Glaucon that he had totally missed Socrates’ meaning. So, Socrates immediately clarified his point:

The experiences that do not provoke thought are those that do not at the same time issue in a contradictory perception. Those that do have that effect I set down as provocatives when the perception no more manifests one thing than its contrary, like whether its impact comes from nearby or afar.[xxvii]

Socrates then illustrated his point to make his meaning more clear. He held up three fingers (the little, second, and middle). Whether he spoke of them as near or far, he said:

Each one of them appears to be equally a finger, and in this respect it makes no difference whether it is observed as intermediaries or at either extreme, whether it is black or white, thick or thin, or of any other quality of this kind. For in none of these cases is the soul of most men impelled to question the reason and to ask what in the world is a finger, since the faculty of sight never signifies to it at the same time that the finger is the opposite of a finger.[xxviii]

Clearly, Plato’s argument immediately above involves the problem of how we signify, or think, and talk about what we perceive and the problem of opposition. The problem is clearly semiotic. Communication from sense perception that provokes us to become philosophers changes the way we think and talk about, or signify, what we perceive. Many ways we sense things do not impel us to question, to ask the reason why. And those that do arise from sense perceptions that simultaneously involve us in a sense and intellectual experience of opposition conveyed by apparently conflicting signs. Since, in Socrates’ example to Glaucon, our sense faculty never signifies to itself that a finger is not a finger, is the opposite of a finger, whence comes our simultaneous sense and intellectual experience of opposition?

Since the experience of a finger being a finger is not the cause, Socrates immediately asked Glaucon, “what about the bigness and smallness of these objects?” Or consider “the relation of touch to thickness and thinness, softness and hardness.” Is it not the case that the operation of each of our senses to objects is as follows?: “In the first place, the sensation that is set over the hard is of necessity related also to the soft, and it reports to the soul that the same thing is hard and soft.” In short, is it not the case that our different sense faculties report to us different objects and opposing relations, or opposites, related to those objects?

Such being the case, Socrates, again, directed Glaucon’s attention to the problem of communication, signification. Simultaneously, something we perceive causes the soul to receive opposite communications, significations, reports. Hence, Socrates continued:

Then, said I, is not this again a case where the soul must be at a loss as to what significance for it the sensation of hardness has, if the sense reports the same thing as also soft? And, similarly, as to what the sensation of light, and heavy means by light and heavy, if it reports the heavy as light and the light as heavy?

Glaucon conceded, “Yes, indeed, . . . these communications to the soul are strange and invite reconsideration.”[xxix]

Such being the case, Socrates replied that “naturally,” in such cases, “the soul first summons to its aid the calculating reason and tries to consider whether each of these things reported to in is one or two. . .. And if it appears to be two, each of the two is a distinct unit.”

That is, given our experience of conflicting reports from our perception, our intellectual faculty immediately starts to consider whether our opposing communication is coming from one perceived object and perception or from two. For example, is perceiving a finger and perceiving a small, versus large, finger, one perception or two? Clearly, such determination involves counting. And if we do not, or cannot, count to two, we cannot have any perception of sensory opposition and opposing communications.

Each perception considered in itself is one, and of separate, singular, objects. But considered together (thought of as two) we think of them as if they were not really separate. We are now thinking of one and one, while really separate, as not separate. Hence, of this simultaneously-and-newly-thought-of-one-and-one (considered together [as a unit]: this single, or separate, two considered as one unit measure, this single two), Socrates immediately said: “If, then, each is one and both two, the very meaning of “two” is that the soul will conceive them as distinct. For if the were not separate, it would not have been thinking of two, but one.”

When our sense of sight so unites really separate beings, such as the “the great and the small,” and thereby sends a miscommunication to the human intellect that things that exist separated and need not co-exist in reality, things that are really two (or many), nevertheless now, in this perception, do so co-exist and are not separated, but are one Socrates maintained that “it confounds” these qualities in its report to the soul. In so doing, it compels “the intelligence” to separate them, “to contemplate the great and the small not as confounded but as distinct entities, in the opposite way from sensation.”[xxx]

According to Socrates, this is just the sort of sense experience of opposition that gives rise to philosophic wonder. Hence, the following discussion between Socrates and Glaucon immediately ensued:

And is it not in some such experience as this that the question first occurs to us. What is the world, then is the great and the small?

By all means.

And this is the origin of the designation intelligible for the one, and visible for the other.

Just so, he said.

This, then, is just what I was trying to explain a little while ago when I said that some things are provocative of thought and some are not, defining, as provocative things that impinge on the senses together with their opposites, while those that do not I said do not tend to awaken reflection.[xxxi]

Clearly, Socrates maintained that philosophic wonder, wonder in any respect at all, is impossible absent “provocative” awareness, or sense perception that communicates to our intelligence perception of semiotic opposition, of multitude signifying opposition to unity. Absent such semiotic sense experience, we cannot distinguish intellectual experience from sensory, much less philosophical from non-philosophical.

Immediately, Socrates asked Glaucon, “To which class, do you think number and the one belong?” That is, are number and unity visible, or intelligible, entities?

Given Glaucon’s inability to conceive the answer, Socrates told him to reason the problem out from what they have already said. If we could adequately see unity through our sense of sight or some other sense faculty, unity would have no need to draw our minds to apprehend its being in cases like that of simultaneously conflicting perception of the finger just described. If we coincidentally, simultaneously, experience some opposition confounded with our sensory perception of unity “so that it no more appears to be one than the opposite,” then Socrates maintained, “there would forthwith be need of something to judge between them, and it would compel the soul to be at a loss and to inquire, by arousing thought in itself, and to ask, whatever then is the one as such, and thus the study of unity will be one of the studies that guide and convert the soul to the study of true being.”

Glaucon claimed that visual perception, especially, involves such opposing communication. “For we see the same thing at once as one and as an indefinite plurality.” For example, we see the same kind of thing (specifically, say, “finger”), as tall and short. Since experience of this sort of communicative opposition is true of unity, Socrates reasons that it must also be true of “all number.”

Moreover, since counting and “the science of arithmetic are wholly concerned with number . . . [a]nd the qualities of number appear to lead to the apprehension of truth,” Socrates concluded that he and Glaucon would have to include counting and the science of arithmetic among the studies they seek. “For a soldier must learn them in order to marshal his troops, and a philosopher because he must rise out of the region of generation and lay hold on essence or he can never become a true reckoner.”

That is, to become a philosopher, we must do more than sense differences or possess an art that never attempts to understand first principles and causes considered as such, like the simple art of counting, or singing, which put to right use principles whose causes a person with mathematical science and the science of music are able abstractly to consider and understand but the singer or student of mathematics need never grasp considered as such.

Hence, Socrates maintained that counting and the scientific pursuit of mathematics are philosophically useful to us for arousing wonder in us. Philosophers are not interested in knowing about counting to buy and sell merchandise. We are interested in it because it is an area of human perception that often leads to provocative thought, which inclines us to wonder about causes and first principles. Some mathematical knowledge is a necessary, but not sufficient, condition for experiencing the wonder that generates philosophy. As Socrates said, the philosophical soul finds interest in numbering when such consideration:

strongly compels the soul upward, and compels it to discourse about pure numbers never acquiescing if anyone proffers to it in the discussion of numbers attached to visible and tangible bodies. For you are doubtless aware that experts in this study, if anyone attempts to cut up the “one” in argument, laugh at him and refuse to allow it, but if you mince it up, they multiply, always on guard lest the one should appear not to be one but a multiplicity of parts.

Clearly, the numbering about which Socrates was talking as philosophically provocative is abstract. The numbers that concerned him philosophically were those that involve “unity equal to every other without the slightest difference and admitting no division into parts.” People who talk in such a way, he said, “are speaking of units which can only be conceived by thought, and which it is not possible to deal with in any other way.”

Such study, Socrates maintained, appears to be “indispensable” for philosophical purposes because “it plainly compels the soul to employ pure thought with a view to truth itself” (that is, it forces us to think abstractly and generally, or universally, about first causes and principles of provocative experiences, or our awareness of experienced opposition).

Socrates then described how, beyond simple counting and the science of arithmetic, such liberal arts studies as plane and solid geometry are related to astronomy and music and how all these investigations encourage wonder in us and lead us toward first philosophy, or metaphysics.

Socrates had noticed that people who demonstrate a facility at calculation tend to be quick learners and that slow learners trained in calculation start to become better learners. Assuming he had established the worth of numbering and the study of mathematics for becoming philosophical, he proceeded to examine the specific worth of geometry, politically and in other respects. Given the nature of his interest in education for producing good rulers, whom he also assumes to be soldiers, Plato had Socrates immediately indicate some military benefits of geometry, like constructing encampments and devising military formations in battle and on march. Socrates asserted that these will not require much geometrical skill, but will make a military officer a much different officer than he would have been otherwise.

Socrates’ concern, however, was with intensive and extensive, not rudimentary, geometrical skill. He wanted to consider, “whether the greater and more advanced part of it tends to facilitate the apprehension of the idea of the good.” That is, will advanced study of geometry likely lead us to become more philosophical, more metaphysical? Will it change the way we look at, and tend to pursue, happiness altogether, which is the sort of thing he thought happens when we experience subjects of study that encourage philosophical reflection? Will it tend to change the way we look at everything by turning our eyes around, by turning our souls and bodies around, by forcing us to think in a totally different way than we had formerly done? Will it, in short, make us generally consider things more abstractly and reflectively?

Hence, Socrates immediately added, “That tendency,” to make us better able to apprehend the idea of the good, “is to be found where dwells the most blessed part of reality, which it is imperative that it,” the human soul, “behold.”

He mentioned that anyone with the slightest familiarity with geometricians will see how strange, how filled with opposition to the proper object of geometry, is their speech, the way they talk about what they do: “Their language is most ludicrous, though they cannot help it, for they speak as if they were doing something and as if all their words were directed toward action. For all their talk is of squaring and applying and adding and the like, whereas in fact the real object of the entire study is pure knowledge.”

Strictly speaking, however, the object of the science of geometry is abstract, theoretical, general consideration of the principles and causes that constitute the makeup of figured bodies. This science is not chiefly concerned about how to construct individual, figured bodies. It is concerned about the principles and causes that make such construction possible. Hence, the proper, or per se, object that the geometrician chiefly has in view is the abstractly and theoretically considered triangle, not the side of this pyramid, or how to construct this A-frame house.

For this reason Socrates said that the science of geometry studies “that which always is” (the abstractly-considered, non-moving, unchanging triangle), not “something which at sometime comes into being and passes away” (like a person’s increasingly-becoming-less-slender figure).

So, because the science of geometry inclines us to think abstractly and theoretically about sensible objects, Socrates concluded, “it would tend to draw the soul to truth, and would be productive of a philosophical attitude of mind, directing upward the faculties that now wrongly are turned earthward.” In short, wittingly or not, it inclines us to become more philosophical and metaphysical about the way we consider the things around us.

Next, Socrates suggested that Glaucon and he consider whether the liberal art of astronomy might be of benefit for their political and philosophical education. Glaucon immediately recognized its worth for agriculture, navigation, and, more so, “to the military art.”

Glaucon’s reaction bemused Socrates, who commented that, apparently, Glaucon responded the way he did, emphasizing astronomy’s practical, not theoretical, benefit, out of fear of what “the many” might suppose were he to recommend “useless studies.” Socrates comments that, after we have been blinded by our “ordinary,” that is, daily practical, pursuits, we have a difficult task realizing that every soul has an intellectual faculty that theoretical study purifies and refreshes, “a faculty whose preservation outweighs ten thousand eyes, for by it only is reality beheld. Those who share this faith will think your words superlatively true. But those who have and have had no inkling of it will naturally think them all moonshine.”[xxxii]

After Glaucon admitted that he spoke, asked, and answered, questions for his, not anyone else’s, sake, Socrates told him they needed to back track a bit because they made a mistake in their order of investigation. The natural order of scientific investigation, and philosophical learning, requires that we first study solid geometry, or as Socrates called it, “the dimension of cubes and of everything that has depth” (a deep body, as opposed to a surface body) after we study plane geometry (which studies the surface body). The reason for this, Socrates said, is that, properly considered, astronomy studies “solids in revolutions,” not “plane surfaces.”[xxxiii] Consequently, even though Socrates maintained that the thinkers of his time only “languidly pursued” such studies “owing to their difficulties,” the proper order of investigation requires that we understand the principles and causes of solid bodies and the way they behave before we attempt to study the principles and causes of movement of solid bodies, as does the science of astronomy.

At this point in their conversation, Glaucon attempted to move Socrates along to investigate other sciences to include in the city by agreeing with Socrates that they should include “geometric astronomy” among those disciplines that he would now praise on Socrates’ principles. By this Glaucon meant he would not praise theoretical astronomy on the basis of the way the many praise it, or, as Glaucon more precisely put it, not on the basis of its “vulgar utilitarian commendation,” because, “[I]t is obvious to everybody . . . that this study certainly compels the soul to look upward and leads it away from things here to those higher things.”

Socrates, however, immediately, replied that this appears to be evident to everyone but Socrates. “As it is now handled by those who are trying to lead us up to philosophy, I think that it turns the soul’s gaze very much downwards.”

Socrates said he responded in this negative fashion because he thought Glaucon had “put a most liberal interpretation on the ‘study of higher things.’” Apparently, Glaucon would incorrectly call “contemplative using higher reason” (not higher vision) anyone whose head were thrown back to learn something about decorations on a ceiling. Strictly speaking, Socrates said, the only sort of study that “turns the soul’s gaze upward” is “that which deals with being and the invisible.” Strictly speaking, he claimed that any person who studies a subject whose matter (that is, its generic subject) concerns sensible reality (that is sensible qualities), “whether gaping up or blinking down . . . never learns—for nothing of the kind admits of true knowledge—nor would I say that his soul looks up, but down, even though he study floating on his back on sea or land.”

While, Socrates said, we have to regard heavenly bodies, “these sparks that paint the sky, . . . decorations on a visible surface, . . . as the fairest and most exact of material things,” we have to recognize that such realities “fall far short of the truth,” by which he means, in this instance, “the movements . . . of real speed and real slowness in true number and in all true figures both in relation to one another and as vehicles for the things they carry and contain,” Socrates maintained that we apprehend such realities “only by reason and thought, . . . not by sight.”

That is, while all species of heavenly mobile body (heavenly mobile body being the astronomer’s generic subject) are worthwhile subjects of consideration inasmuch as a species of such a generic subject are of a more immaterial kind than an earthly body, and their motion is closer to the divine [because it is perpetual]), precisely considered, the philosopher’s job is abstractly (and, therefore, exactly) to consider (to reason about) the principles and causes (or, as Socrates said, “the truth”) of the properties, the necessary and essential accidents, of such species of body as they move across the visible surface of the sky, including the effects these specific bodies produce through their properties (like acting on each other in relation to time [speed], or twinkling, going through retrograde motion), as these specific bodies act through principles and causes they effect through the power of their generic subject (that is, inasmuch as they are species of heavenly body involved in circular movement). The philosopher, in short, considers per se effects in light of their per se causes.

Socrates maintained, further, that, while astronomy has to use such complicated, visible, surface decorations as models to help us study the principles and causes of the motion of heavenly bodies, we should not expect that mapping the heavens in this sort of architectural fashion will give us the absolute truth, the exact conclusion, about the mathematical ratio of their movements. The astronomer is in the same sort of situation as would be any geometrician who happened upon the blueprints or diagrams of a craftsman or painter like Socrates’ ancestor Daedelus. While he might admit that such a person’s workmanship to be beautiful, he would not expect that the mathematical ratios would exactly match those that exist in the physical world.

Socrates thought that, when astronomers reflect upon the motions of the stars, they will likely agree with him that heaven’s architect fashioned the heavens and everything in them in the most beautiful and best possible way for the nature of the whole. And when they consider the order of heavenly motions, the regularity of the relation between night and day, month to month, to year, of the motion of star to star, they will have to consider absurd the belief that heavenly realities, bodily and visible things, exist “forever without change or the least deviation” and that astronomer’s “unremitting quest is the realities of these things.” That is, they would have to admit that astronomers will never find the principles and causes (the permanent realities) of the motions of heavenly bodies through bodily vision in what these bodies reveal to human sight. They will only get at these principles and causes through abstract, intellectual consideration and reasoning from visible effects in abstractly-considered specific bodies to invisible causes in abstractly-considered generic bodies.

Socrates explained that, if we want to transform astronomy and the soul’s natural power of intelligence from being useless to being truly useful, we will have to attack problems in astronomy the way we do in geometry, “and leave the starry heavens alone.” That is, we cannot expect to find principles and causes with our external vision. We have to reason to these, abstractly, by turning our minds away from visible effect to seek the invisible cause.

We have to do the same sort of thing with our ears in one of astronomy’s mathematically-related sciences, music. Just as our eyes are fashioned for astronomy, the orderly motion of whose sensible object fixes their movement and attention and limits our gaze, Socrates maintained our ears are fashioned for music, because harmonic movements of audible sounds fix and limit what we musically hear. And Socrates said he agreed with Pythagoras that many other mathematically-subalternated sciences like astronomy and music can exist, suited for other sense faculties.

As in the case of astronomy, Socrates claimed that, in his time, musicians made the same mistake as astronomers. Instead of looking for inaudible causes (in this case, numbers) of the harmony of audible sounds that account for their mathematical proportion, a harmony, some students of musical theory tried to hear these inaudible causes (numbers, the causes of the harmonies) with their ears as if they were sensible, minima notes that exist between notes, while others maintained the strings are the cause.

They talk of something they call minims and, laying their ears alongside, as if trying to catch a voice from next door, some affirm that they can hear a note between and that this is the least interval and the unit of measurement, while others insist that the strings now render identical sounds, both preferring their ears to their minds.

“Their method,” Socrates said, “exactly corresponds to that of the astronomer, for the numbers they seek are those found in these heard concords, but they do not ascend to generalized problems and the consideration (of) which numbers are inherently concordant and which not and why in each case.”[xxxiv]

Socrates realized that the task of reforming the methods of human investigations and arts to transform them into sciences is daunting. He knew that experts in practical pursuits are not experts in philosophical reasoning, or what he called “dialectic.” At the very least, he hoped that the study Glaucon and he had been conducting had gone far enough to show “the community and kinship” of these studies and to allow them “to infer their affinities.” If, at least, he had been able to show how they are alike, their work had helped come closer to achieving his goal and has not been in vain.

Socrates maintained that people who cannot give explanations, who cannot give or follow an argument in discussion will never be able to know anything about the things he said “must be known,” that is, philosophy’s real subject and generic method. They resemble people still held prisoner within Plato’s mythical cave.

For this reason, at this point in the dialogue, Socrates returned to the cave analogy to elucidate the way we have to proceed to do philosophy, dialectic. He asserted that the human mind has an ability to achieve progress in learning by following the “law of dialectic,” which he thought is a law regulating the operation of the human mind that we see imitated in the faculty of sight. He said he had already described this likeness in our attempt to use our faculty of sight to find first principles and causes, or, as he said, “to look at living things themselves and the stars themselves and finally the very sun.” Dialectic’s law, however, “belongs to the intelligible” realm, in human reason’s power of abstract consideration that results from the wonder caused in us by sensibly-perceived-and-reported provocative communications. We see this law at work, in short,

when anyone by dialectic attempts through discourse of reason and apart from all perceptions of sense to find his way to the very essence of each thing and does not desist till he apprehends by thought itself the nature of the good itself, he arrives at the limit of the intelligible, as the other our parable came to the goal of the visible.

This “limit” of the intelligible about which Socrates spoke here is what Plato called the Good. This was clearly Socrates’ meaning because he identified this limit with the Sun, or the Sun’s light, that was the goal in his Myth of the Cave, to which he directly referred here. He called the Good a limit of the intelligible because an intelligible limit, as a limit, is that beyond which we cannot intellectually go. As such, it is an indivisible, or, as Plato often called it, “the One.” For this reason, also, while Plato did not say so here, the highest, or maximum, as a limit, is an indivisible, one, and a measure, because we always measure everything, even things we know, in terms of a one. Hence, we measure our knowledge in terms of intelligible indivisibles, or intellectual, but not necessarily mathematical, ones, units, first principles, or per se nota starting points.

When Plato said that “dialectic attempts through discourse of reason and apart from all perceptions of sense to find his way to the very essence of each thing” he was not thinking like dissatisfied young Descartes, fresh out of La Flèche, hoping entirely to escape from sensory input, clean out all the intellectual junk he has stored for years in his spiritual attic to follow the whispering voice of conscience (in addition to whatever handy dreams or divine signs might reinforce this voice) calling him to get in contact with his pure reason in the hidden recesses of his mind.

Plato’s understanding of dialectical progress involved initially receiving conflicting communications from sensible being trustworthy enough to start us on, and reinforce along the way, our abstract, philosophical quest for invisible first principles and causes of a per se effect that relates to a proximate and per se subject. Plato did not entirely distrust the human senses. He thought that their object, the world of becoming, as he would often call it, has some reality, but is imprecise. He thought it “exists,” but is somewhat false, because he identified truth and reality with precision, exactness, permanence, and unity. And he maintained sensible reality lacks the level of reality that he would call “true being,” the “really real,” or “beingly-being” (which level of reality entities in the World of Forms possess), and the Good has, to which he refers as “beingly-beingly-being” or the “really, really, real” (or, sometimes, as beyond being or not-being).[xxxv]

To explain dialectic’s nature and method more precisely, Socrates started a short, but detailed, exegesis of part of the Myth of the Cave at the point where a prisoner had broken free from his subterranean world and had ascended to the world above. When he first exited the cave, this escaped inmate had a “persisting inability to look directly at animals and plants and the light of the Sun.” He was only able to see divine-like reflections in the water and shadows of real beings cast by the Sun, similar to the shadows he had seen in the cave cast by a light that, compared to the Sun’s light, is as unreal as shadows. Socrates maintained that the practice of the arts and sciences as Glaucon and he had been describing them shows their power to stir the human soul upward to contemplate the best realities, just as, in the fable he had told, the best sense organ, sight, “was turned to the contemplation of what is brightest in the corporeal and visible region.”

Such being the case, Glaucon urged Socrates to show him (1) the nature of dialectic’s power, (2) its divisions, and (3) its methods so that they can come to the end of their journey and rest.

In reply, Socrates told Glaucon he would show Glaucon these things, not their image, if he could, but, unhappily, he was unable to show him the real truth as it appears to him, whether it appears rightly to Socrates or not. Still, Socrates had to affirm that the real truth must be something like what they had affirmed. And they may properly state that only dialectic’s power could show it, and only to a person experienced in studies they have described (that is, like theoretical geometry, astronomy, and music).

Still, Socrates maintained that no one will be able to refute their claim that any other method of investigation exists that tries progressively and universally to determine what each thing really is (that is, the principles and causes of the behavior of things). Mostly all the other arts have human opinions and wants as their object, are totally concerned with generation and composition, care and cultivating “things that grow and are put together.” Those few arts, like geometry and its subalternate studies, astronomy and music, dream about being, but never reach it, because their method of investigation always starts with assumption, belief, not with absolutely, or assumptionless, first principles of knowing, per se nota truths.

Evidently, Socrates did not use the Latin. Instead, he said:

[T]he clear waking vision of it (reality or real being) is impossible for them as long as they leave the assumptions which they employ undisturbed and cannot give any account of them. For where the starting point is something that the reasoner does not know, and the conclusion and all that intervenes is a tissue of things not really known, what possibility is there that assent in such cases can ever be converted into true knowledge or science?

Socrates claimed that dialectic is the only method of inquiry that eliminates assumptions, hypotheses, to advance “up to the first principle itself to find confirmation there.” Only philosophy, as he had described it, utilizes a starting point of scientific investigation that is entirely assumptionless, is not based upon any hypothesis. Philosophy uses no assumptions because it finds confirmation in awareness of the first principle of knowing considered in itself. It does not take its first principles from the conclusions of another, higher science. Philosophy is the science that, with dialectic’s help, knows the first principles that all the other sciences assume.

Socrates continued by saying that when the soul’s eye, the human intellect, is buried deep in a kind of primeval mud,

dialectic gently draws it forth and leads it up, employing as helpers and co-operators in this conversion the studies and sciences which we enumerated, which we called sciences often from habit, though they really need some other designation, connoting more clearness than opinion and more obscurity than science. “Understanding,” I believe, was the term, we employed. But I presume we shall not dispute about the name when things of such moment lie before us for consideration.

Clearly, this passage indicates that Plato thought that, while he called studies like geometry and its subalternate disciplines of astronomy and music “sciences,” or “philosophy,” he was predicating the terms “science” and “philosophy” analogously. Toward the end of the Republic Book 6, Socrates had described to Glaucon a divided line of learning, ascending from the lowest form of human learning to the highest. He now revisited what he had said about the divided line toward the end of Book 6 to express his thinking more precisely.

He recalled how he had given a simile of a straight line, cut in two, with each half, similarly subdivided. The result was a fourfold division of two major sections, one representing higher learning, the other lower. The two subdivisions of higher learning he had designated “knowledge”; the lower two he had called “opinion.” The higher division he had subdivided into (1) science and (2) understanding. The lower division he had subdivided into (3) belief and (4) imagination. Socrates stated that knowing relates to being, and opinion relates to becoming. Expressing this in a proportion, he said that as being is to becoming so science is to belief and understanding to imagination.

Socrates then stated they would give the name “dialectician” to the person who can give an account of the being, or essence, of each thing to himself and others. But they would deny this designation to the person unable to do this because this person does not “possess full reason and intelligence about the matter.”

He added that, in the same way, denial of this designation applies to the person who cannot “define in his discourse and distinguish and abstract from all other things the aspect or idea of the good.” Socrates thought that truly to know something is to know it philosophically or scientifically. And this means to know it abstractly. This involves being able to explain something in terms of its first principles and causes, to be able to state the reasons why something is the way it is, in terms of principles we have abstracted from our experience of the being of things. He described someone incapable of doing this to be like someone going through life half-awake, dreaming his way through. He said we would say of such a man that he

does not really know the good itself or any particular good, but if he apprehends any adumbration of it, his contact with it is by opinion, not by knowledge, and dreaming and dozing through his present life, before he awakens here he will arrive at the House of Hades and fall asleep forever.

Especially in an ideal city, where philosophers will be rulers, Socrates maintained we cannot neglect having children learn that discipline whereby they will be able “to ask and answer questions in the most scientific manner.” For this reason, Socrates said he had put this study of dialectic higher than all others, like “a coping-stone,” so no higher learning could be put above it and to make their discussion of studies complete.[xxxvi]

Having thus completed their investigation into the nature, division, and methods of the sciences, Socrates stated that what remained for them was to determine to whom to assign studies and how. In the Republic, Book 6, Socrates had already stated that traits of a philosophical nature included: “quickness at learning, memory, courage, and magnificence.” Toward the end of Book 7, he reiterated many of these traits, and recalls something else he had said in Books 6 and 7, “Our present mistake . . . and the disesteem that has in consequence fallen upon philosophy are, as I said before, caused by the unfitness of her associates and wooers. They should not have been bastards, but true scions.”

So as not to be a philosophical bastard, Socrates maintained we have to be industrious, not half-hearted. A true philosopher loves learning and hard work. We must also hate mistakes in ourselves and others, as much as we hate lies in both. No true philosopher “cheerfully accepts involuntary falsehood,” is undisturbed when convicted of ignorance, or “wallows in the mud of ignorance as insensitively as a pig.” True philosophers are also temperate, courageous, and great-souled.

Socrates maintained that, since philosophers will be rulers or their advisors, we have to be careful that philosophical natures possess, and can recognize in others, temperance, courage, and greatness of soul. Otherwise, we will undermine, not preserve, our city, and “we shall pour a still greater ridicule upon philosophy.”

Moreover, we cannot take Solon’s advice that, as we get older, we will be able to learn many things. We must train the young for philosophy through liberal education. Or, as Socrates stated:

Now all this study of reckoning and geometry and all the preliminary studies that are indispensable preparation for dialectic must be presented to them while still young, not in the form of compulsory education. . .. Because . . . a free soul ought not to pursue any study slavishly, for while bodily labors performed under constraint do not harm the body, nothing that is learned under compulsion stays with the mind. . .. Do not . . . keep children in their studies by compulsion but by play.

After a period of primary education in the liberal arts, at about age twenty, Socrates said, those who will be given preference to higher learning in philosophy would have to demonstrate their ability to unify “the studies which they disconnectedly pursued as children in their former education into a comprehensive survey of their affinities with one another and with the nature of things.” That is, they would have to be able to show how all their many former studies are one with each other and the world.

“That,” Socrates maintained, “is the only instruction that abides with those who receive it.” This is the only kind of learning that lasts. “And,” he added, “it is also . . . the chief test of the dialectic nature and its opposite. For he who can view things in their connection is a dialectician; he who cannot is not.” That is, the person who can intellectually comprehend how many things are one, the person who can reason abstractly, is the philosopher. The person who cannot do this is not.

Socrates warned, however, about the dangers of premature study of dialectic. He did so, among other reasons, because Plato tended to conflate philosophy, which he called here “dialectic,” with first philosophy, or metaphysics. Socrates thought that premature study of metaphysics is dangerous because metaphysical study requires that a person be able “to disregard the eyes and other senses and go on to being itself in company with truth.” Because most young people are not prepared to embark upon such a rigorous journey in abstract reasoning about most general first principles and causes (first principles and causes that all arts and science take for granted, or assume), he noted how great is the harm cause by the way the Greeks were treating dialectic in his time: “Its practitioners are infected with lawlessness.”

Sad that Descartes’s instructors at La Flèche did not take this warning to heart. Premature study of metaphysical subtleties by precocious youth under the influence of sophists often winds up producing sophists (like Descartes), and eventually, in their wake, corrupt lawyers, judges, politicians, and intellectuals, much as sophists like Protagoras and Gorgias had done in Socrates’ and Plato’s time and subjective idealists and other “philosophical bastards” have done in modernity and post-modernity.

Socrates maintained that the situation of such prematurely metaphysically-exposed youth is similar to that of an intelligent, spoiled rich kid, doted over all his life by family flatterers, and raised by others like an orphan, almost as if by adopted parents. When he reaches physical adulthood he perceives that he has no parents, and does not know how to find his natural ones. A young person in that sort of situation would likely start to have a higher opinion of his flatters and those who raised him, would be more inclined to listen to them and live by their rule and less inclined to disobey them in great matters, than he would his natural parents.

From childhood rearing, Socrates said, we have received specific convictions about higher things, great, important, matters, such as about the nature of truth and the honorable. We have been raised from childhood under obedience to these convictions. At the same time, practices opposite to what we have learned exist “that have pleasures attached to them and that flatter and solicit our souls.” Such practices do not corrupt decent people because they continue to honor and obey what they have been taught.

But what are such people to do when they run into questions about the highest and most important things, questions we commonly call “metaphysical” and “moral,” when they find their traditionally-held beliefs about what they hold to be true about everything refuted by subtle arguments they cannot adequately answer? What is the honorable person to do, Socrates asked, “when he has had the same experience about the just and the good and everything that he chiefly held in esteem”? How will he conduct himself thereafter regarding respect and obedience to his former beliefs?

Glaucon’s answer was that, inevitably, this person will disrespect and disobey the former beliefs.

And, then, Socrates wanted to know, what will happen to him? He will now be in a situation where he ceases to honor his former metaphysical and moral principles, will think they no are no longer are binding on him, and he will be unable to discover true ones. Such a person will be like putty in the hands of any flatterer or dictator who comes along and will adopt the life the flatterer or dictator desires. In so doing, such a person will become rationally ungovernable, a rebel against traditional law and morality.

Plato gave us a similar warning in his classic work the Gorgias, in which we find Socrates critiquing the famous sophist Gorgias for making the same absurd and grandiose claim, which Descartes would later make, that he possessed one art, or the specific method, to know everything, and “without learning any other arts . . . to prove in no way inferior to the specialists.” The discussion continued:

SOCRATES: Therefore when the rhetorician is more convincing than the doctor, the ignorant is more convincing among the ignorant than the expert. Is that our conclusion, or is it something else?

GORGIAS: That is the conclusion in this instance.

SOCRATES: Is not the position of the rhetorician and of rhetoric the same with respect to the other arts also? It has no need to know the truth about things but merely to discover a technique of persuasion so as to appear among the ignorant to have more knowledge than the expert.

GORGIAS: But is this not a great comfort, Socrates, to be able without learning any other arts but this one to prove in no way inferior to the specialists?[xxxvii]

Socrates did not think so. For this reason, in the same work, in his discussion with the corrupt politician Callicles, Socrates told Callicles (who, like Gorgias’ student, Polus had admired the despot Archelaus as the happiest of men) that men like Archelaus are the most miserable of men and fools. Callicles’ problem was that confounding sophistry with wisdom eventually tends to turn a person into a dictator or a panderer to dictators.[xxxviii]

Rightly considered, Socrates thought, the practice of dialectic, or philosophically abstract reasoning, is ordered toward enabling us to become metaphysicians, to help us to understand the first principles and causes about everything, especially about the highest, or most important things for us to know as human beings. When it is not rightly ordered, it tends to degenerate into sophistry, ideology, and argument for the sake of victory, not truth. No wonder then so many contemporary descendants of Descartes, Kant, and Hegel glory in thinking that their philosophical work is chiefly to get students “to question their belief systems.” This is not philosophy. It is a secularized understanding of St. Augustine’s reduction of philosophy to theology in which philosophy becomes “faith seeking understanding.”

As a result of the perennial dangers of mistaking sophistry for philosophy, we have to be careful not to introduce students too early to philosophical argumentation involving metaphysical issues. When this happens, when young people “first get a taste of disputation,” Plato thought they “misuse it as a form of sport, always employing it contentiously, and, imitating confuters, they themselves confute others. They delight like puppies pulling about and tearing with words all who approach them.”

Plato maintained that the person who “makes a jest and sport of mere contradiction” is a sophist, not a true philosopher or dialectician. When young people run into such sophists, mistaking them for philosophers, and start to imitate them, he thinks “they quickly fall into a violent distrust of all that they formerly held true, and the outcome is that they themselves and the whole business of philosophy are discredited with other men.” They become like contemporary students have become under the influence of modern subjective idealists and their subjective critique: moral and metaphysical relativists.

Socrates and Plato did not object to questioning traditional beliefs. Socrates was put to death for refusing to stop questioning the poor educational practices of his time fostered by poets and sophists. Both philosophers objected to confounding philosophy with sophistry and sophistry with metaphysics. Hence, Plato had the character Socrates maintain that his requirement would be that “those permitted to take part in such discussions must have orderly and stable natures, instead of the present practice of submitting it to any chance and unsuitable applicant.”

Because, Plato, also, tended to conflate philosophy with first philosophy, or metaphysics, he ended Book 6 of the Republic by recommending, in striking similarity with his student Aristotle, that the study of metaphysics, or dialectics, start about age fifty. At this time, he said of those who would have passed all prior tests and would have been approved to become philosophers:

We shall require them to turn upward the vision of their souls and fix their gaze on that which sheds light on all, and when they have thus beheld the good itself they shall use it as a pattern for the right ordering of the state and the citizens and themselves throughout the remainder of their lives, each in his turn, devoting the greater part of their time to the study of philosophy, but when the turn comes for each, toiling in the service of the state and holding office for the city’s sake, regarding the task not as a fine thing but a necessity. And so, when each generation has educated like themselves to take their place as guardians in the state, they shall depart to the Islands of the Blessed and there dwell. And the state shall establish public memorials and sacrifices for them as to divinities if the Pythian oracle approves or, if not, as to divine and godlike men.[xxxix]

Like his teacher Plato, Aristotle recognized the dangers of sophistry. Perhaps, for this reason, among others, he said thinkers like Protagoras “say nothing…while they appear to say something remarkable, when they say ‘man is the measure of all things.’”[xl] And, perhaps, also, for this same reason, in his Metaphysics, Aristotle went out of his way to defend the principle of contradiction as the ground of the possibility of scientific thought and put such emphasis on issues like understanding the relationship between the problem of the one and the many and issues such as opposition and contrariety.[xli]

3. Why Aristotle Maintained that Philosophy Starts is Wonder and with the Problem of the One and the Many

Like his teacher Plato, Aristotle thought that philosophy is essentially (1) a study of the one and the many, and of opposites; (2) unity is related to plurality as a measure to a being measured; and (3) measures of things are mind-independent indivisibles, unities, ones, forms. Aristotle simply relocated such measures from a Platonic World of Forms to individual subjects so as to make his understanding of philosophy more coherent.

That Aristotle thought the way I am saying is easy to show simply by reading his Metaphysics. Consider, for example, the way he started the last Book of this work: “All the philosophers make the first principles contraries: as in natural things (that is, in physical beings), so also in the case of unchangeable substances (that is, in metaphysical beings).”[xlii] Aristotle included the pre-Socratics, Socrates, and Plato in the phrase “All the philosophers.” Since Aristotle maintained that contraries are extreme differences, opposites, belonging to the same genus, and that species that share a common genus share a common matter, he was maintaining that all philosophers prior to him, including Plato and Socrates, wittingly or not, thought that opposition was the first principle of everything. Moreover, since Aristotle maintained that the opposition between the one and the many was the ground of all other opposition, by considering first principles to be contraries, Aristotle believed that all philosophers prior to him were involved in attempting to understand the opposition between the one and the many.

Aristotle rejected the notion that contrariety can be the first principle of everything because, he maintained, the notion of contrariety involves the notion of being generated from a common matter or subject and first principles must have no underlying subject. Hence, he stated:

But all things which are generated from their contraries involve an underlying subject, and none can exist apart; a subject, then, must be present in the case of contraries, if anywhere. All contraries, then, are always predicable of a subject, and none can exist apart, but just as appearances suggest that there is nothing contrary to substance, argument confirms this. No contrary is the first principle of all things in the full sense; the first principle is something different.[xliii]

Nonetheless, Aristotle did not reject the notion that philosophy essentially involves studying opposites and that we initially derive the problem of the one and the many from conflicting communications about sensible measures we first uncover, as the pre-Socratics, Socrates, and Plato maintained, in the being of sensible things. Whatever the first principle is, Aristotle maintained that it involves the notion of being one, because a principle is a one and indivisible, and being one involves the notion of being a measure.

He explained that being a measure involves being homogeneous with the thing measured. This is the case, he said, in music (a quarter-tone in a scale), in spatial magnitude (a finger, a foot, or something similar), in rhythms (a beat or syllable), in heaviness (a definite weight, an indivisible limit), “and in the same way in all cases, in qualities, a quality, in quantities a quantity (and the measure is indivisible, in the former case in kind, and in the latter to sense), which implies that the one is not in itself the substance of anything.”

Aristotle immediately added, “And this is reasonable (that is, that the one not be the substance of anything). For, he said that, while substances are composites of matter and form:

“the one” means the measure of some plurality, and ‘number’ means a measured plurality and a plurality of measures [that is, of things measured]. Thus it is natural that the one is not a number; for the measure is not measures [that is, things measured], but both the measure and the one are starting points. The measure must always be some identical thing predicated of all the things it measures, e.g., if things are horses, the measure is “horse,” and if they are men “man.” If they are a man, a horse, and a god, the measure is perhaps “living beings.”[xliv]

Aristotle thought that all divisions of philosophy, not just metaphysics, study a substance considered per se. He maintained that all human knowledge originates in the being of sensible things. Sensible things are composite beings, complexes of form and matter, or act and potency, in which and from which we derive our knowledge of first principles.[xlv] Aristotle even attributed to Socrates, Plato, and Plato’s followers the procedure of deriving universals from sensible singulars.[xlvi]

Aristotle considered philosophy to be identical with science: certain knowledge demonstrated through causes.[xlvii] He maintained that philosophy, or science, considers a multitude of beings, a genus, a many, contrary opposites, and tries to demonstrate essential properties of the genus by reasoning according to necessary principles, or measures, universal, or one, to the genus.[xlviii] Aristotle thought that causes are principles, and principles are starting points, and measures, of being, becoming, or knowing.[xlix] For this reason, he thought of philosophy as a study of causes, principles of effects, which we first encounter in our experience of sensible being.

He considered principles to be measures because principles are starting points and points are ones, unities, or indivisibles. He said that points are ones, indivisibles, with position, principally spatial position or position in a continuum. Principles, then, are indivisibles, ones.[l] As known they are indivisible intelligibles, limits of knowing.

As is well known, Aristotle considered being and unity convertible concepts. In reality, what we call being and one are identical. They differ only conceptually, in reason. We derive our idea of unity by adding the concept of indivisibility and principle to our idea of being, just as we derive our idea of number by dividing a unity (a continuum). Hence, Aristotle thought that adding the notion of unity to being adds to being the ideas of being a principle and measure.[li]

In his Posterior Analytics Aristotle said that demonstration demands that a one exist “in many and about many” and that science involves knowledge of the fact that something is and demonstration of the reason why. He claimed that demonstration must make manifest a thing’s proximate, or fully commensurate, cause.[lii] Demonstration, requires a middle term, a one that is the same in many, or a universal unequivocally predicable of a many. If no one something exists the same in a multitude, in a many, no universal exists unequivocally predicable of many beings. Lack of such a one existing in a many makes demonstration, and philosophy, impossible.[liii]

Because Aristotle maintained that demonstration involves knowledge of the fact and of the reason why, he asserted that science requires necessary, or per se, predication, predication of a proximate, not a remote, cause. Such a cause is the principle of proximate substance and its essential accidents, accidents that have their cause in a proximate subject and necessarily and always inhere in the subject.[liv] For Aristotle, no science considers accidents as such because no science can study an infinite number of things, can be involved in infinite predication. Science can only study accidents that have determinate causes in a subject.[lv]

In making such statements, Aristotle appears clearly to have been following the lead of Socrates and Plato as Plato described their behavior in his dialogues. Aristotle did not develop the notion of per se predication. We have already seen many examples of it in Book 7 of Plato’s Republic involving Socrates’ discussion of the division and methods of the arts and sciences of arithmetic, geometry, astronomy, and music. And it is present as far back as Book 1 of the Republic, where Plato portrayed Socrates utilizing it in conversation with the sophist Thrasymachos.

At that point in the dialogue, Thrasymachos had just ridiculed Socrates for needing a nurse to wipe his nose because Socrates thought that, strictly speaking, the art of shepherding concerns the welfare of sheep, not the monetary benefit of shepherds. In reply, Socrates told Thrasymachos, that, precisely speaking (that is, predicating the term per se of its proximate or subject considered per se) the art of shepherding relates to a different specific subject than does the art of money-making. It concerns a different matter.

This is one of, if not the, first instances of the explicit articulation of the notion of per se predication in philosophy’s history. Clearly, Plato had this notion consciously in mind when he wrote Book 7 of his Republic. The notion of per se predication underlies it because, as is clear from our study of the Republic, Book 7, Plato thought that we can distinguish the different arts and sciences based upon the different psychological powers to which different matters relate in unequal ways for possible human investigation.

Aristotle took from Plato his notion of the order of the arts and sciences, he often referred the hierarchy of the arts and sciences, and he started his Metaphysics with reference to it. For Aristotle, science, or philosophy, studies the many different ways many things relate to one proximate subject: the way many things, more or less, share in the unity of a primary subject.

Every science, not just metaphysics, therefore, chiefly and analogously studies the principles and causes of substances to understand the properties of the many species of which we predicate a genus.[lvi] Hence, Aristotle said that as many parts of philosophy exist “as there are kinds of substance.”[lvii] And, following Aristotle, Aquinas stated, “demonstration is concerned with things which are per se in something.”[lviii]

Aristotle claimed that science, or philosophy, chiefly studies the principles and causes of a proximate substance and its per se accidents. It does not study not just any substance and any accidents.[lix] Through these substantial principles we come to know the proper accidents, or properties, of all the species that belong to the genus.

Aristotle maintained that no science could possibly study all the accidents that relate to its subject because science must study a finite multitude and we can relate an infinite number of accidents to a subject. The scientist’s study bears only on those accidents that are essential properties of its subject, such as intrinsic shape and size, relate to a geometrical figure.[lx]

For Aristotle, then, in some way, all philosophy, and every science, involves coming to know how a many is essentially one. He maintained that (1) as many species of being exist as species of unity exist; (2) just as we can predicate the term being analogously, so we can predicate the term unity analogously; and (3) one science, metaphysics, has the job to study these species of unity: “the same and the similar and the other concepts of this sort.” [lxi]

Since being and unity are convertible notions, Aristotle maintained that we can analogously predicate unity of all the different genera. Hence, he claimed that we may refer almost all contraries to unity as to their principle.[lxii] St. Thomas Aquinas explained Aristotle’s meaning thus:

since being and unity signify the same thing . . . there must be as many species of being as there are species of unity, and they must correspond to each other. For just as the parts of being are substance, quantity, quality, and so on, in a similar way the parts of unity are sameness, equality and likeness. For things are the same when they are one in substance, equal when they are one in quantity, and like when they are one in quality. And the other parts of unity could be taken from the other parts of being, if they were given names. And just as it is the office of one science [first] philosophy to consider all the parts of being, in a similar way it is the office of this same science to consider all the parts of unity, i.e., sameness, likeness, and so forth.[lxiii]

Aristotle viewed a genus is a kind of whole. Philosophically or scientifically considered, he thought of it as a generic body, the immediate, proximate, first, or proper subject of different per se accidents, unities, or properties within the genus.[lxiv] Aquinas explained that this sense of genus is not the same as the sense of genus as signifying the essence of a species, which is the way the logician uses the term “genus”:

This sense of genus is not the one that signifies the essence of a species, as animal is the genus of man, but the one that is the proper subject in the species of different accidents. For surface is the subject of all plane figures. And it bears some likeness to a genus, because the proper subject is given in the definition of an accident just as a genus is given in the definition of its species. Hence the proper subject of an accident is predicated like a genus.[lxv]

Since surface is the immediate subject of all colors and plane figures, it is the referential source of intelligibility of all surface bodies, the proper subject of all the accidents that emanate from a proximate subject. We must refer color and figure to surface to comprehend their natures. By proximately subjectifying them, surface gives quantitative unity to all plane figures. For this reason, when geometricians predicate surface of different plane (surface) figures they predicate surface analogously as a common matter or subject.

In so doing, analogously, geometricians resemble logicians. When geometricians and logicians predicate a genus, both include the genus in the species’s definition. And both predicate the genus that signifies the essence of a species. In both cases the definition of the species refers to its subject genus, its substance, for its intelligibility.

But logicians do not predicate their genus of their subjects as per se, or proper, accidents of a proximate and per se subject. They totally abstract from such a concrete understanding of a subject. The substance the geometrician studies is a surface body as a per se cause of per se effects, the proper subject of an accident, not the essential definition of the logician. The logician’s abstract logical universal in not identical with the scientist’s, or philosopher’s, concrete universal because the logician and the scientist, or philosopher, consider the same subject under distinct formal aspects. The logician considers it abstractly and as existentially neutral. The philosopher, or scientist, considers it concretely and as existentially related, or loaded.

As part of their essential scientific activity, scientists, philosophers, look for the per se subject of an activity by referring the activity to an existing per se property, as an effect caused here and now by a per se subject acting through the per se property as through a per se accident. For example, Socrates the musician, Socrates (the per se subject), not Socrates the human being or philosopher (incidental subjects), is now producing music (the per se action) as a result of his possession of a per se musical property, his musical habit or quality, and per se accident.

Socrates produces the music because of his existing musical ability or habit, not because of his philosophical ability, or habit, or because he is a human being. All musical action presupposes production by an existing musical quality and an existing musical subject. Socrates’ action is musical. Therefore, Socrates’ action presupposes production by musical quality and an existing musical subject.

Hence, despite the fact that, logically considered, and according to the logician’s way of abstract talking or predicating, and, in truth, Socrates is essentially a human being, philosophically and scientifically considered, and according to the philosopher’s and scientist’s way of talking or predicating terms, being human is incidental to being a musician. Precisely speaking, predicating philosophically, or scientifically, per se, being a musician involves a principle and cause more proximate than being human, just as being a geometrical body involves a principle and cause more proximate than being a material body. The generic body, or subject, the philosopher, the scientist, studies in music is the musical, not the human, body, or subject. Similarly, the subject of study in ancient and contemporary physics is the mobile, not the corruptible or incorruptible, body, whether, logically and abstractly considered, matter is essentially corruptible or incorruptible.

The essential way of reasoning and talking, and the skills, of the philosopher, or scientist, are radically different from the logician’s. Consequently, Aristotle maintained that, philosophically or scientifically considered, we cannot reduce one proximate subject to another. Generically diverse beings in a philosophical or scientific sense are those “whose proximate substratum is different, and which are not analyzed the one into the other nor both into the same thing (e. g., form and matter are different in genus).”[lxvi] Aquinas clarified Aristotle’s meaning by referring, as I have just done, to the idea of a proximate subject as a subjectifying common matter of necessary accidental species. He said: “[A] solid is in a sense reducible to surfaces, and therefore solid figures and plane figures do not belong to diverse genera, . . . but celestial bodies and lower bodies are diverse in genus inasmuch as they do not have a common matter.”[lxvii]

That is, philosophically, or scientifically, considered, solid and plane figures are species of surface bodies. Both are kinds of surface body. Surface body proximately causes them and the necessary accidents that are subjectified in them. So considered, surface body is their proximate, or subjectifying, common matter, their generic matter. They share surface body as a proximate, or subjectifying common matter, or common material subject. This is the reason we can study them in one science.

Logically considered, we can include celestial bodies, sublunary bodies, surface bodies, and mobile bodies in the same genus, an abstract genus, because all are species of body. But they do not belong to a common science because they share no proximate, subjectifying common matter. They share a remote matter, a logically abstract “body.”

In ancient physics, in one way celestial bodies and sublunary bodies share no proximate, subjectifying, existential, common matter. The matter of celestial bodies is everlasting. The matter of sublunary bodies is corruptible. Considered as such (as corruptible, as opposed to incorruptible, bodies), they are separate, not identical, subjects of philosophical, or scientific, study in ancient physics. They share no proximate subjectifying cause. They share a common matter for philosophical, or scientific, purposes of study, as mobile, not as corruptible or incorruptible, bodies because this last formal difference (being mobile) distinguishes them relationally as essential accidents in reference to a common principle, cause, and proximate subject, and accounts for their essential being as proximate causes of motion. For this reason, physics can study both.

Recall that Aristotle tells us that all science chiefly studies substance. This means philosophy, physics, mathematics, and metaphysics study substance. Metaphysics, however, studies immaterial and material substance as part of its subject, even though, logically considered, immaterial and material substance cannot be reduced to a common “matter,” subject, or being. Immaterial substance has no matter. Yet part of metaphysics involves studying beings that have no bodies at all.

Logically considered, apparently we should not include corruptible bodies as part of the study of metaphysics. And metaphysics should not be a science because science involves study of specific multitudes in terms of a common, or generic, matter. And immaterial substances have no matter. Nonetheless, as a philosophical discipline, philosophers can claim that metaphysics studies a “common matter” by saying that metaphysics studies common being as its matter, or proximate subject, somewhat like the mathematician studies “intelligible matter” as the common matter of quantitative beings.

Moreover, philosophers, and scientists, can justify their right to make such distinctions by rightly maintaining that their way of predicating terms essentially differs from the way logicians predicate terms. Logicians predicate terms univocally using abstract, existentially neurtal, universals, universals that abstract from the notion of sharing a proximate subject as the cause for inclusion within the genus. Philosophers predicate terms analogously using concrete, existenially related, universals, universals that include the notion of sharing a proximate subject, principle, and cause for inclusion within the genus.[lxviii]

Inasmuch as philosophy studies real being, or substance, as the proximate cause of per se accidents within a multiplicity of beings, or a genus, Aristotle maintained that every science studies opposites and first principles because every science studies a multiplicity of differences according to a principle of unity.

Every science considers opposition, negation, completeness, privation, and necessity, precisely because it studies substances through a principle of unity. Opposition, negation, completeness, privation, and necessity, however, essentially relate to the idea of being one, unity, not of being many, multiplicity.

The one is undivided, does not possess, is deprived of, division, and is the opposite of division or plurality. Plurality, not number, is the opposite of unity and the ground of all division and difference. Hence, Aquinas maintained, we derive the idea of unity from the idea “of order or lack of division.”[lxix] The concept of unity entails, depends on, negation and privation, a species of opposition.

Aristotle held that our idea of “unity” includes an implied privation, “a negation in a subject,” like blindness in a human being.[lxx] He added that we can reduce all our concepts of necessity to that which can be in only one way.[lxxi] Hence, our notions of unity, privation, and opposition even precede our notion of necessity!

Aristotle appears to have contradicted himself by maintaining that our idea of unity includes an implied privation because he also had held that the one is the principle by which we know number.[lxxii] His reply to such an objection was that sensation is the starting point, or first principle, of all of our knowledge, even our knowledge of notions like unity, cause, and principle.[lxxiii]

He maintained that our first perception is of a many, of composite things, that we first confusedly grasp as a one. Hence our first positive concept of unity and plurality is a conflation in which we do not clearly distinguish unity and plurality. We identify them together as a coincidence of opposites. Perhaps this is what the ancient Greeks understood as chaos and why the ancient physicists thought of all philosophy in terms of contrariety.

Whatever the case, Aristotle held that we derive all our concepts, definitions, and first cognitions of first principles by privative negations of the way we sensibly perceive them as composite beings. He thought of unity as the most primary privation, consisting of negation in a subject. Since Aristotle maintained that plurality stems from unity, and causes diversity, difference, and contrariety, he viewed diversity, difference, and contrarity as effects of unity’s pluralization and claimed that we know first principles negatively in reference to the way we perceive their contraries.[lxxiv]

Hence, Aristotle said that “all things are contraries or composed of contraries, and unity and plurality are the starting points of all contraries.”[lxxv] Since contraries are extreme differences within a genus that relate as most complete and most deprived possession of a form, as Plato recognized in Book 7 of the Republic, contrariety, as such, is a kind of plurality, because difference is a pluralization of unity, and an opposition between possession and privation, which Aristotle calls the fundamental opposition. This means that contrariety consists in the greatest distance of difference, or inequality, between extremes of species within a genus.[lxxvi]

Aristotle thought that all otherness derives from dividing and, thereby, pluralizing, unequalizing, unity. And he claimed that unity, or what is undivided, is the principle of all sameness, equality, and similarity. Similarity, equality, and sameness are simply analogous extensions of the notion of unity. Aristotle referred to them as unity’s “proper accidents” or “parts.” As such, he considered them to be the principles of all plurality. Since, in turn, Aristotle held that plurality grounds all difference, he maintained that similarity, equality, and sameness are the principles of all difference.

For Aristotle, in short, difference is pluralization of unity, and unity’s opposite. The analogous extensions and properties of unity, however, are unities. To be similar, equal, or the same, therefore, is, analogously, to be one.[lxxvii]

Hence, to be dissimilar, unequal, or different is to be many, a pluralization of unity and the respective opposites of being similar, equal, and the same. Since the one and the many are opposed, since, along with being and privated being, they are the principles of all opposition and contrariety, they (1) are the primary contraries into we reduce all other contraries and (2) make all other contraries intelligible as their first principles.[lxxviii]

This being so, if Aristotle is correct, the principles of similarity, equality, and sameness and their opposites and contraries (dissimilarity, inequality, and difference) are the first principles of all per se accidents and of the relative first principles of all philosophy and science. This must be the case because they are the most fundamental oppositions between unity and plurality. The opposition between unity and plurality is the first principle of all other oppositions and is the principle into which all others are reduced and made intelligible. Since science, or philosophy, studies the principles of opposition within a genus, it must chiefly study the opposition between, or problem of, the one and the many related to the principle kinds of per se subjects.[lxxix]

A main reason, then, that Aristotle divided the speculative sciences into three classes is clear. He recognized the existence of three pairs of specifically distinct, kinds of unity, plurality, and opposition (similarity/dissimilarity, equality/inequality, and sameness/difference) as the primary first principles of per se accidents and contrariety that exist within real substances. Using these primary sets of opposition, or contrariety, as first principles, he thought, we are able scientifically to understand the different sorts of necessary relations that exist between per se subjects and their per se accidents, or properties. He thought of these per se subjects as proximate subjects constituted by distinctive kinds of common matter involving distinctive kinds of contrary opposites. Hence, the actions performed through their properties reflect the same sort of opposition existing in their common matters.

Aristotle said we are able to sense two of these common matters. He claimed the third is “immovable and imperceptible.”[lxxx] Following much of what Plato said in Book 7 of the Republic about mathematics, music, and geometry, Aristotle limited the two classes of sensible substance to corruptible substances like animals and plants, and incorruptible substances, like movers of the celestial bodies, which ancient physics claimed to investigate.

Whether their matter is corruptible or not, scientifically or philosophically considered, as per se subjects of science or philosophy, we study both classes of bodies through abstract consideration of sensible effects they produce through their qualified matter (a surface body acting as the subject of qualities). The third class consists of objects with intelligible matter (mathematical objects, abstractly considered quantified bodies), and separate substances (beings that can, do, or can be considered to exist apart from any and all matter).[lxxxi] Hence, Aquinas maintained that “as many parts of philosophy” exist “as there are parts of substance, of which being and unity are predicated and of which it is the principle intention or aim of this science to treat.”[lxxxii]

St. Thomas said that, in the case of the speculative sciences of physics, mathematics, and metaphysics, we derive the formal object of such sciences “according to differences between objects of speculation.” He added that we derive this formal object partly “from the side of the power of the intellect” and partly “from the side of the habit of science that perfects the intellect.”

Thomas maintained that, because all three sciences are speculative, they must involve the human intellect in their scientific or philosophical operation of simply wondering about occurrences flowing from a proximate subject in the hope of simply knowing the per se principles of these occurrences. Hence, from the side of the power of the intellect, we derive a speculative formal object, one that essentially activates our intellects as operating speculatively, not practically. Our scientific habits are speculative precisely because they conform to the ontological needs of the human intellect when we use it with the aim of thinking speculatively.

Simultaneously, since our intellects are immaterial faculties, immaterial being, being abstractly removed from the identity conditions of matter and motion, essentially activates them. Hence, St. Thomas asserted that one of the necessary identity conditions of the formal object of speculative science is that it be a proximate subject immaterially, or abstractly, considered. In short, what makes our thinking scientifically speculative is that we think about an abstractly considered proximate, per se, subject simply as such.

Because all three sciences are habits, or qualities, that inhere in the same intellectual faculty, St. Thomas maintained that all principles that give them specifically scientific ways of existing, that is necessity, must activate them. Necessity is the mark of science. Strictly speaking, science, philosophy, is thinking about what must be. Consequently, what makes our speculative way of thinking scientific, philosophical, is that we possess our immaterial, speculative habit of thinking in relation to consideration of necessary, not contingent or incidental, relations of essential accidents and their activities to a proximate subject.

We can think speculatively about what is not a subject of science or philosophy (something contingent, what need not be or can be in more than one way, or what is incidental to a proximate subject), and we can think scientifically or philosophically about what is not a subject of speculation (an subject of productive science or philosophy). Our habit of knowing reacting to some necessary relation in the speculatively-considered subject makes a subject of speculation a scientific subject: a subject having within it a one and unchangeable principle upon which we may scientifically according to the degree to which our different intellectual habits are able to operate in separation from, or connection with, matter and motion.[lxxxiii]

Furthermore, St. Thomas said that we use different methods of doing this in different sciences. He maintained that we take the methods of the sciences “from the powers of the soul” because these powers operate in different ways. And we determine how our powers operate by relating them to their formal objects.

Hence, we take the methods of the sciences from the different formal objects, or identity conditions, that determine a proximate subject to be one and unchanging, in this, not that, way.[lxxxiv] Hence, continuing in the philosophical tradition of Socrates, Plato, and Aristotle, St. Thomas distinguished the speculative sciences according to proximate, or per se, subject by saying that the ancient physicist’s proximate subject is a qualified surface body, the mathematician’s proximate subject is quantified material being (the surface body), and the metaphysician studies substantial being that can be material or immaterial.

Just as Socrates, Plato, and Aristotle had done before him, St. Thomas maintained, that we proceed in this way when studying subjects scientifically because we derive scientific principles partly from the natural constitution of our faculties and partly from the way things exist according to mind-independent relations. Scientifically, we think the way we can (according to the way our powers operate in relation to different formal objects), not the way we wish. As Socrates had, in a more roundabout way, told Thrasymachos centuries before Aquinas, the being of things and the way this essentially relates to our natural faculties, not our dreams or wishes, determines the methods by which we can think about objects at all or scientifically. The being of things and the natural constitution of our knowing powers, not our dreams, provide the unity and necessity that grounds all knowledge and science.

Precisely speaking, what makes common matters proper subjects of scientific or philosophical investigation is not simply that they are common to a multiplicity. They are proper subjects of science or philosophy precisely because their common matters comprise those of a proximate subject containing a specific principle of unity that necessarily grounds the per se differences and principles of opposition and contrariety within the limits of a proximate-subject genus. Their common matters contain first principles of scientific reasoning.

For this reason St. Thomas said, “geometry speculates about a triangle being a figure having ‘two right angles,’ i.e., having its three angles equal to two right angles; but it does not speculate about anything else, such as wood or something of the sort because these things pertain to a triangle accidentally.” Geometry speculates about its subject genus in this limited way, through the quantitative principle of equality, and does not speculate about other sorts of likenesses or differences because, strictly speaking they do not relate to its per se subject and “science studies those things which are beings in a real sense, . . . and each thing is a being insofar as it is one.”[lxxxv]

Geometry’s proximate subject, its common matter, is not material substance or body. It is quantified material substance, surface body. The accidental property of quantity makes a substantial body a geometrical body by giving it surface unity. Since equality is the principle of unity by which we grasp all the samenesses and differences that relate to a body as a continuum body, such as having three angles quantitatively the same as two right angles, since, that is, equality is, considered per se, a quantitative principle, the surface body that it unifies through the equality of its parts is the proper subject for geometrical study.

Simply put, sameness, equality, and similarity are the formal objects through which we conceive all the different sciences because these per se accidents of unity are necessarily principles of their common matters and the contrariety that exists in these matters.

To put all this in another way, Aristotle=s notion of philosophy, or science, like Socrates and Plato before him, rests upon his understandings of proximate material substance and per se predication. And his understanding of proximate material substance and per se predication rest upon his teaching about unity. He maintained that beings that belong to the same genus share a common matter and a common unit measure: the properties of sameness, equality, and similarity. For he claimed that “to be a measure” is a property of unity.[lxxxvi] And he held that sameness, equality, and similarity are unity’s primary accidents or properties. Through these common unit measures we know a subject’s common matter and can predicate their proximate effects per se of their proximate and per se subjects.[lxxxvii]

Aritstotle maintained, further, that unity measures “all things.”[lxxxviii] St. Thomas said that Aristotle made this claim because unity stops division. The undivided terminates division, is that beyond which no further division exists.[lxxxix] Aristotle explained that we know those principles that constitute each thing’s substance by analysis, by dividing or resolving a whole into its component parts, be the parts quantitative or specific (like matter, form, or elements). “Thus,” he said, “the one is the measure of all things, because we come to know the elements in the substance by dividing the things either in respect of quantity or in respect of kind.”[xc]

Analogously, Aristotle claimed we can call knowledge and perception “measures” of things because we know something by knowledge and perception. “[A]s a matter of fact,” he said (specifically criticizing Protagoras for saying nothing while pretending to say something remarkable in his dictum, “man is the measure of all things”), human knowledge and perception “are measured,” they do not “measure other things.”[xci]

According to Aristotle, a measure is the means by which we know a thing’s quantity. That is, a measure is a unit, number, or limit.[xcii] Like Plato, Aristotle, recognized that we first derive the notion of measure from the genus of quantity. But, unlike Plato, Aristotle did not confound mathematical and philosophical unity. He recognized that the proper opposite of unity is plurality, not number. Hence, he criticized Plato for conflating the notion of unity that is convertible with being with the unity that is the principle of number.[xciii]

Aristotle maintained, that, once we arrive at the notion of unity negatively from its association with as a principle and measure of quantity, we can analogously transfer this notion and the idea of being a measure to other genera. Hence, in a way, Aristotle asserted, unity and quantity are the means by which we even know substance, knowledge, and quality:

Evidently, then, unity in the strictest sense, if we define it according to the meaning of the word, is a measure, and most properly of quantity, and secondly of quality. And some things will be one if they are indivisible in quantity, and others if they are indivisible in quality; and so that which is one is indivisible, either absolutely or qua one.[xciv]

Aquinas later commented on this passage that we find indivisibility in things in different, not the same, ways. Some things, like a natural unit, the principle of number, or a natural length, the principle of measured length, are definite and totally indivisible. Other things, like an artificial and arbitrary measure, “are not altogether indivisible but only to the senses, according to the authority of those who instituted such a measure wished to consider something as a measure.”[xcv]

Aristotle thought that a natural body has per se unifying and formal principles, per se formal objects, that differentiate it from a quantified body, and a quantified body has per se unifying and formal principles, per se formal objects, that differentiate it from a qualified body. Each of these bodies differs from the other according to a distinctive kind of unity that acts as the principle and measure of distinctive kinds of contrariety and opposition based upon a distinctive kind of common matter.

A natural body’s unity is composed of opposites, of matter and form. These opposites constitute it as a material nature and as a substantial nature in the genus of substance. This body is not the same as a quantitative body, the body in the genus of quantity, or as a qualified body. The natural body is the subject of the quantitative body, and the quantitative body is the subject of the qualified body.

Three properties of unity (sameness, equality, and likeness [or similarity]) allow us to conceive of a natural body in this way. And these properties give us the threefold division of speculative philosophy, based upon unity’s properties. Consequently, following Aristotle, St. Thomas said that we distinguish the parts of philosophy “in reference to the parts of being and unity.” And he added that, according to Aristotle, “there are as many parts of philosophy as there are parts of substance, of which being and unity chiefly are predicated, and of which it is the principle intention or aim of this science [that is, metaphysics] to treat.” Aquinas identified these “parts of being” as “substance, quantity, quality, and so on.”

The parts of unity are sameness, equality and likeness. For things are the same when they are one in substance, equal when they are one in quantity, and like when they are one in quality. And the other parts of unity could be taken from the other parts of being, if they were given names. [xcvi]

According to St. Thomas, in short, we divide philosophy, or science, according to the order of proximate natural subjects and the respective properties of unity that constitute the necessary and sufficient conditions for a proximate subject’s ability to be the sort of subject it is.

As Charles B. Crowley has rightly observed, Aristotle maintained that, as a natural body, a substantial body emanates in three magnitudinal directions from its substantial matter. These dimensions are extensions, divisions, and arrangements of the natural body within terminal parts in different directions in place.[xcvii] They divide the natural body into parts that have a positional relation to each other and to bodies around them because position is contained within the notion of quantity.[xcviii] These emanations quantify a natural body as a magnitudinal, extended, quantitative, or continuum body. “This extension occurs both intrinsically to a body inasmuch as it places limits upon it within terminal parts internal to its substantial matter and externally inasmuch as it places limits upon the substantial body in the way it relates to its surrounding place.”[xcix]

When a material substance extends in one direction, Aristotle maintained it becomes a magnitudinal body terminated by a point. It becomes a linear body reaching from one point to another point. When it extends in two directions (from one point to another and one line to another), the substantial body becomes a surface, or wide, body stretching from one line to another. When the substantial body stretches from one surface to another surface, it becomes a solid, or deep, body and has depth. In this way, a quantified bodily substance acquires three natural intrinsic unit measures and termini (a point, line, and surface) that constitute it as a quantitative subject, a substance with quantity, the extended spatial unity and measure of which we call a quantitative “equal.”

As Aristotle noted, three kinds of magnitude exist: (1) a linear body, (2) a surface body; and (3) a solid body, all of which St. Thomas maintained, are essentially measurable and limited:

if magnitude is divisible into continuous parts in one dimension only, it will be length; if into two, width; and if into three, depth. Again, when plurality or multitude is limited, it is called number. And a limited length is called a line; a limited width, surface; and a limited depth, body. For if multitude were unlimited, number would not exist, because what is unlimited cannot be numbered. Similarly, if length were unlimited, a line would not exist, because a line is a measurable length (and this is why it is stated in the definition of a line that its extremities are two points). The same things hold true of surface and of body.[c]

Aristotle thought that we initially derive our idea of measure from sensation, primarily from our sense awareness of a numbered length that arises from cutting a continuum body from which we also derive such ideas as before and after, principle, and order.[ci]

By cutting a continuum body, we divide it into a plurality of unit lengths. The unit that terminates the division is the limit of the division, an indivisible. Hence, it formally constitutes the division as a one and a number, an ordered and limited plurality. A number is an ordered and limited plurality, a one, and a measure. It is a measure precisely because it is a one, an indivisible, and a limit. Hence, as I have already noted, Aristotle said, “the one is the measure of all things.”[cii]

Since a measure is a one, just as we can predicate unity analogously, along with its accidental properties, which include being a measure, so we can analogously predicate continuous and discrete quantity and their accidental properties. So predicated, all these properties become analogous unit measures, ways we can use to comprehend an extended or qualified substance as limited and one, and, hence, knowable because we cannot know anything totally indeterminate.

Aristotle maintained that these common properties are (1) of continuous quantity, large, or big, and small; (2) of number, much, many, large and little, few, small, and less; (3) of one-dimensional magnitude (length, or of a long body), long and short; of two-dimensional magnitude (a surface, or wide body), narrow and wide; of three-dimensional magnitude (a solid, or deep, body), high or deep, and low or shallow; (4) and of quality, heavy and light, hot and cold.[ciii]

Of all these analogously predicated accidents, Aquinas said that “quantity is the closest to substance.”[civ] Of all the accidents, that is, it is most per se. Quantity is a per se accident of a material body because it necessarily inheres in, and emanates from, the body’s natural matter. A quantitative body can thus be the proper subject of philosophical speculation for the geometrician as a proximate subject of accidents proper, or essential, to a point, line, and surface.

Similarly to the way in which dimensive quantity causes a material body to emanate extensively through its matter to natural intrinsic unit measures and limits, Aristotle claimed that a body emanates intensively through its form to natural intensive magnitudinal unit measures and limits of ability, positionally related to each other. By so doing, form constitutes a natural body as qualified, or a body with qualities, with limited and ordered abilities to act with more or less completeness or perfection, the proximate subject about which the ancient physicist, metaphysician, and ethician can speculate, depending upon, Aristotle held, whether the matter in question is corruptible or incorruptible, or human possessed of the faculty of free choice.

Following Aristotle, St. Thomas said that we can understand the term “perfect” in many senses. For example, (1) a thing is internally perfect when it “lacks no part of the dimensive quantity which it is naturally determined to have.” (2) We can understand the term internally to refer to “the fact that a thing lacks no part of the quantity of power which it is naturally determined to have.” (3) Or we can use the term teleologically to refer to external perfection. For example, we can say that “those things are said to be perfect ‘which have attained their end, but only if the end is ‘worth seeking’ or good.”[cv]

St. Thomas maintained that we can call a thing perfect in relation to this or that ability because:

[E]ach thing is perfect when no part of the natural magnitude which belongs to it according to the form of its proper ability is missing. Moreover, just as each natural being has a definite measure of natural magnitude in continuous quantity, as is stated in Book II of The Soul, so too each thing has a definite amount of its own natural ability. For example, a horse has by nature a definite dimensive quantity, within certain limits; for there is both a maximum quantity and minimum quantity beyond which no horse can go in size. And in a similar way the quantity of active power in a horse which is not in fact surpassed in any horse; and similarly there is some minimum which never fails to be attained.[cvi]

Hence, we can analogously transpose and predicate all the concepts of measure that we derive from our awareness of being as dimensively quantified and one to measure and comprehend quality and all the other accidents, like place and time.[cvii] In this way, we can talk about a color’s magnitude because of the intensity of its brightness, the strength of heat because of the greatness of its effects, the greatness of a sin because of the magnitude of its offense to God, the quantity of perfection of an animal’s ability to see, hear, or run, or the extent of perfection of someone’s happiness, or an animal being higher or lower in its genus or species.

To grasp Aristotle=s view of philosophy and science more completely we need to recognize a basic distinction he makes metaphysically between two types of quantity. Many philosophers familiar with Aristotle are aware that he distinguished between continuous and discrete quantity, continuous quantity being the proper, or per se, subject of the geometrician and discrete quantity being the proper, or per se, subject of the arithmetician.. Few philosophers, even Aristotelians, appear to be aware that, metaphysically considered, he made a more basic distinction between dimensive (molis) quantity and virtual (virtutis) quantity.

Aristotle said that continuous and discrete quantity are species of dimensive, or bulk, quantity. They result in a substantial body from the emanation of a natural substance’s matter to become a body divisible in one, two, or three magnitudinal limits, directions, or dimenstion: a long body, wide body, or deep body; or, more simply, as we say today, length, width, and depth.

He also maintained, however, that virtual quantity is a species of quantity. He said it emanates intensively from a natural substance’s form, not extensively from its matter. And he claimed that the accidental form “quality,” not dimensive “quantity,” produces it.

Commenting on this distinction, St. Thomas reported: “Quantity is twofold. One is called bulk (molis) quantity or dimensive (dimensiva) quantity, which is the only kind of quantity in bodily thing . . .. The other is virtual (virtutis) quantity, which occurs according to the perfection of some nature or form.” He added that we may also call this sort of quantity “spiritual greatness just as heat is called great because of its intensity and perfection.”[cviii]

Aristotle, in short, thought that forms and qualities have their own kind of quantity and magnitudinal limit of natural or supernatural power, one that consists in the greater or less intrinsic perfection, completeness, or quantity of form, not in the extension of matter throughout parts within a spatial continuum. This virtual quantitative property of form permits to exist within a subject and a genus the opposition between privation and possession that is the principle of all contrariety. Privation is the crucial addition that enables otherness, negation, or difference to involve contrariety.

Contrariety, which includes contradiction, is total or partial privative negation. Total privative negation is contradictory opposition, total privation of some being, the complete subject, upon the being of another. Partial privative negation is partial, limited, negation of some being within a genus that extracts from it some magnitude of its completeness of form.

Privation, in short, requires the disposition to have a form and the absence, in a definite subject at a definite time, of the form to which something is disposed.[cix] For this reason, Aristotle maintained that opposition between privation and possession is the basis of contrariety.[cx] Consequently, quality, or intensive quantity, as the foundation of all opposition and contrariety, (1) accounts for the limited possession of a finite being’s existence, (2) in a way, is the principle of all science and philosophy, and (3) is an essential principle of all wonder! And so, too, is privation.

Moreover, Aristotle, maintained that basically two kinds of qualities exist: (1) essential differences and (2) differences, or alterations, of mobile bodies, like cold and hot, heavy and light, white and black. This second kind refers to the way we generally talk about “quality,” “virtue and vice, and, in general, of evil and good.”[cxi] Aristotle considered this sense of quality to be an accident related to motion, an intensive quantitative change of something moved as moved. Consequently, about virtue and vice, he said:

Virtue and vice fall among these modifications; for they indicate differentiae of the movement or activity, according to which the things in motion act or are acted upon well or badly; for that which can be moved or act in one way is good and that which can do so in another—the contrary—way is vicious. Good and evil indicate quality especially in living things, and among these especially in those which have purpose.[cxii]

Regarding Aristotle=s assertion that virtues and vices enable something to move well or badly, St. Thomas said that the terms “well” and “badly” chiefly relate to living things and “especially” to things having “choice.” The reason Thomas gave for saying this is that living things, especially, act for an end and “rational beings, in whom alone choice exists know both the end and the proportion of the means to the end.”[cxiii]

Part of Aquinas’s reasoning in his above commentary was that quality limits a motion or action, places it within bounds, and, in a way, gives it order and proportion (properties that, strictly speaking, belong to, and it receives from, continuous quantity), especially in connection to acting for an end. This point is crucial to understand regarding any science involved in study of qualities because every science must study a genus in relation to opposition between contrary members of a species. Like all oppositions, such opposition is grounded in the principles of possession, privation, and limits. Hence, this notion should be especially helpful for modern and contemporary physics and could easily be used to reintegrate philosophy and this science because it appears to underlie all modern and contemporary physical science.

Aristotle thought that science studies one thing chiefly, a primary, or main, subject to which it analogously relates other subjects. Analogous predication, however, essentially involves predication of a term according to opposition of a many to a one. By this statement I mean that analogous predication involves predicating unequal relationships of existential possession and privation that different subjects have in reference to some one intelligible content that the predicate term conveys.

Hence, the medical doctor chiefly studies the subject of human health and its contrary opposite, disease, plus other unequally-health-related subjects and their opposites, like good and bad diet, exercise, operating procedures, medical instruments, and so on. Medical science chiefly studies human health because, strictly speaking, health exists chiefly and maximally, or in its main and maximum possession, in human bodies. Human health does not mainly and maximally exist in health-related subjects of study like human diet, exercise, operating procedures, or medical instruments.

Analogous predication involves predicating unequal reference of a common predicate, meaning, or term to different subjects according to different kinds of opposing relation, of greater and less (unequal, and, hence, not the same, or one) possession or privation by the subjects of the intelligible content the predicate term conveys and that maximally exists in a main subject. No science, then, can proceed without considering proportionate and unequal relationship of possession and privation, and hence, the kinds of opposition, that a multiplicity of unequally related subjects have to a chief proximate subject, to the maximum species in a genus, to a one to which other subjects of study are related as numerically one end.[cxiv]

One reason this last claim is true is that, as Aristotle rightly understood, substance is the chief subject of every science, or division of philosophy, not just of metaphysics. He criticized the ancient philosophers who made contraries their first principles because contraries cannot exist, without, and are attributes of, a common subject: “All contraries, then, are always predicable of a subject, and none can exist apart, but just as appearances suggest that there is nothing contrary to substance, argument confirms this. No contrary, then, is the first principle of all things in the full sense; the first principle is something different.”[cxv]

As Aristotle correctly noted, all science, philosophy, and knowledge chiefly concern a main subject, something about which the science, philosophical division, or knowledge chiefly talks and predicates terms. The first principle of no science, philosophical division, or knowledge can be an unconnected multitude, an indeterminate many. It must be some one being, or our talk is meaningless.

Aristotle stated, further, that (1) quantity is the means by which we know substance, (2) a measure is the means by which we know a thing’s quantity, (3) we first find unity as a measure in discrete quantity, number, and, (4), from this category, we analogously transfer the idea of a measure to other categories, like quality, time, place, and so on.[cxvi]

In the case of quality, Aristotle maintained that we first perceive the notion of measure by comparing one thing to another and by noticing that one thing exceeds another in a specific quality, by noticing the inequalities of larger and smaller, or more and less, properties and pluralities of unity. We notice, for instance, that one thing has more weight or heat than another.[cxvii] First and foremost, Aristotle considered equality and inequality to be quantitative divisions, of numeral proportions.[cxviii] He said that inequality is of two kinds: larger and smaller (or excessive and defective) and more and less. As inequalities, pluralizations of unity, we cannot understand excessive and defective, larger and smaller, and more and less apart from reference to equality. Equality, however, as a kind of unity (a one) is the measure of inequality, the means by which we know it.[cxix]

In the case of quality, Aquinas asserted that we cannot directly compare any two qualities. Quality as quality only directly refers to the subject in which exists. Its being is a referential being to its subject. St. Thomas claimed that we can only relate one quality to another quality (1) by referring the one quality to the other as an active or passive potency of the other, as being a principle or source of acting or being acted upon (like cause and effect, heating and being heated) or (2) by referring one quality to another through reference to quantity or something related quantity; for example, when we state that one thing is hotter than another because its quality of heat is more intense.[cxx]

4. Conclusion

Aristotle’s teaching on contraries makes intelligible how we can indirectly compare two qualities quantitatively, the way contemporary physicists often do. For Aristotle contrariety is one of four kinds of opposition: (1) contradiction, (2) contrariety, (3) possession and privation, and (4) relation.[cxxi] As partial, privative negations, not as contradictory opposites, contraries are forms, extreme differences, or specific extremes or limits, within the same genus between which a mean, middle, or intermediary can exist. When contraries have a mean or middle we can relate it to both extremes as a one, intermediate, or midpoint between possession and privation. In this situation, it is neither extreme, relates to both, and is opposed to both by an opposition of privative negation, not of contrariety, just as, for example, the midpoint between the extremely hot and extremely cold is not hot nor cold, and can become both, or a morally neutral person is not morally good or bad, and can become both.[cxxii]

Moreover, Aristotle said that passage from one extreme to another involves an order of change, a necessary passage through the midpoint. Such being the case, the midpoint (a one) stands in a condition of equality in relation to both extremes, just as passage from the great to the small and the fast to the slow must be through what is equidistant from both (an equal, or one). Because the equal stands as a mean or midpoint between extremes of possession and privation of a form within a genus, and is, consequently a one, we can use it as a measure to know both extremes.[cxxiii]

In relationship to the equal, a one, two opposites exist, comprising the unequal (in this case, excess and defect of some form). Analogously speaking, we may refer to these inequalities as multiplicities or pluralities. This being so, we can measure qualitative differences, or difference of intensity in possession or privation of a quality, by comparing excessive and deprived possession to possession of equal intensity as pluralities measurable by a homogeneous unit. We can compare one quality to another by relating both qualities to a third, standing midway between them in intensity, much like we can compare the heaviness of two different bodies by using a balance scale that compares their weight relative to a state of equilibrium (a one). This one qualitative state becomes the measure of the other two (a many) and the principle by which we know them.[cxxiv]

According to Aristotle, (1) all science seeks to understand its subject-matter in terms of its principles and (2) causes and effects are opposite terms of relational opposition. Consequently, by studying causes, all science, all philosophy, must study (1) opposition and (2) dependence and partial and total negation because partial or total negation of a subject are the causes of all opposition. This explains why a science like medicine must study causes of health and disease, like diet and exercise, medical operations, and medical instruments. All relate, as causes, to partial or total possession of health or disease in a human being.

Hence, in conclusion, no science, no division of philosophy, can study its subject-matter without, simultaneously, studying the problems of the one and the many and opposition. This is because, strictly speaking, (1) as the major philosophers of ancient Greece clearly understood, philosophy and science are identical; (2) philosophy, or science, chiefly studies substance in terms of contrary opposites; (3) contrariety and opposition always involve the problem of the one and the many; (4) all philosophical and scientific study for all time essentially involves the problem of the one and the many.

Peter A. Redpath
Full Professor of Philosophy
St. John’s University
Staten Island, NY

[i] Peter A. Redpath, Cartesian Nightmare: An Introduction to Transcendental Sophistry (Amsterdam: Editions Rodopi, B. V., 1997), Wisdom’s Odyssey from Philosophy to Transcendental Sophistry (Amsterdam: Editions Rodopi, B. V., 1998), and Masquerade of the Dream Walkers: Prophetic Theology from the Cartesians to Hegel (Amsterdam: Editions Rodopi, B. V., 1998). John N. Deely, Four Ages of Understanding: The First Postmodern Survey of Philosophy from Ancient Times to the Turn of the Twenty-first Century (Toronto, Buffalo, London: University of Toronto Press, 2001). In this paper, I also draw heavily upon three previously published articles: (1) “Post-Post Modern Science and Religion: A Critique,” International Journal on World Peace, 18:1 (March 2001), pp. 61–90; (2) “Virtue as Intensive Quantity in Aristotle,” Contemporary Philosophy, 23:1, 2 (Jan./Feb. & Mar./Apr. 2001); and (3) “Thomist Humanism, Realism, and Retrieving Philosophy in Our Time,” Instituto Universitario Virtual Santo Tomas (Fundación Balmesiana–Universitat Abat Oliba CEU, 2003); (4) “Philosophical Realism, Classical Metaphysics, and the Contemporary World,” in David Murray (ed.) Metaphysical and Mystical Review/Revista de Metafísica y Mística (Rome, 2003).[ii] Jacques Maritain, The Peasant of the Garonne: An Old Layman Questions Himself about the Present Time (New York: Holt, Rinehard, and Winston, Inc., 1968), p. 102; The Dream of Descartes: Together with Some Other Essays, trans. Mabelle L. Andison (New York: Philosophical Library, 1944); Education at the Crossroads (New York and London: Yale University Press, 1970), p. 74.[iii]Étienne Gilson, Being and Some Philosophers (Toronto: Pontifical Institute of Mediaeval Studies, 2nd ed., 1952), pp. 212–213.[iv] Redpath, Masquerade of the Dream Walkers, p. 232. See also, Aristotle, Metaphysics, Aristotle, Metaphysics, in The Basic Works of Aristotle, ed. Richard Mc Keon (New York: Random House, 1968), Bk. 10, 1, 1052b20–30; and Charles B. Crowley, Aristotelian-Thomistic Metaphysics and the International System of Units (SI), ed. with a prescript by Peter A. Redpath (Lanham, Md.: University Press of America, 1996, pp. 1–47.[v] Aristotle, Metaphysics, Bk. 5, 17, 1022a1–13; Bk. 14, 1, 1087b34–1088b14. Aquinas, Commentary on the Metaphysics of Aristotle, trans. John P. Rowan (Chicago: Henry Regnery Company, 1961), Bk 5, l. 19, nn. 1045–1057.[vi] St.Thomas Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 22, n. 1121.[vii] Aristotle, Metaphysics, Bk. 4, 1, 1004a 1–38; Bk. 4, 2, 1004b 27–32; Bk. 10, 4, 1055a33–1055b3.[viii] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 1, n. 544. See Armand A. Muarer (ed.), Commentary on the de Trinitate of Boethius, Questions V and VI. St. Thomas Aquinas: The Division and Methods of the Sciences (Toronto: Pontifical Institute of Mediaeval Studies, 1963), q. 6, a. 3, c., fn. 15, p. 75.[ix] Aristotle, Metaphysics, Bk. 7, 4 1029b12–1030a17. Aquinas, Commentary on the Metaphysics of Aristotle, Bk 7, l. 4, nn. 1306–1330.[x] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 22, n. 1121, 1125–1127; Aristotle, Metaphysics, Bk. 5, 28, 1024b10–13.[xi] Aristotle, Metaphysics, Bk. 1, 2, 982a10–15.[xii] Ibid., Bk. 1, 1, 980a1–982a1. Aquinas, Commentary on the Metaphysics of Aristotle, Bk 1, l. 3, nn. 66–68; Summa theologiae, 1–2, 41, 4, ad 5.[xiii] Aristotle, Metaphysics, Bk. 4, 2, 1005a1–10.[xiv] Plato, Republic, trans. Paul Shorey, in Edith Hamilton and Huntington Cairns (eds.), Plato Collected Dialogues (New York: Pantheon Books, Bolingen Series 71, 1966), Bk. 6, 494A. My addition in parenthesis.[xv] Plato, Republic, Bk. 7, 515B.[xvi] Ibid., 515B–518B.[xvii] Ibid., 517B.[xviii] Ibid., 518C.[xix] Ibid., 518D–519A.[xx] See Plato, Symposium, Socrates’ discussion with Alcibiades, 213B–223D.[xxi] Plato, Republic, Bk. 7, 519A–B.[xxii] Ibidi., 7, 519B–520E. Italics are my addition.[xxiii] Ibid., 521A.[xxiv] Ibid.[xxv] Ibid., 521B–523C.[xxvi] Aquinas, Commentary on the Metaphysics of Aristotle, Bk 5, l. 19, n. 1048.[xxvii] Plato, Republic, Bk. 7, 521B–523C. Italics in the block quote are my emphasis.[xxviii] Ibid.. 523D.[xxix] Ibid.. 523D–524B. Italics are mine.[xxx] Ibid.. 523D–527C.[xxxi] Ibid.. 527C. The first italics are Plato’s. The second are mine.[xxxii] Ibid.. 527C–528E.[xxxiii] Ibid.. 528B.[xxxiv] Ibid.. 528E–531C. I add the “of” in parenthesis to clarify the translation.[xxxv] See, for example, Plato, Parmenides, 142A–144E; Sophist, 256E–259E; Republic, Bk. 6, 509B; Timaeus, 87D. See also Étienne Gilson’s lucid exposition of the problem of reality and being in Plato in Being and Some Philosophers, pp. 1–18.[xxxvi] Plato, Republic, Bk. 7, 531C–534E.[xxxvii] Plato, Gorgias, trans. W. D. Woodhead, in Edith Hamilton and Huntington Cairns (eds.), Plato Collected Dialogues (New York: Pantheon Books, Bolingen Series 71, 1966), 459B–D.[xxxviii] Ibid., 482C–527E.[xxxix] Plato, Republic, Bk. 7, 534E–540C.[xl] Aristotle, Metaphysics, Bk. 10, 1, 1053a32–1053b3[xli] Ibid., Bk. 4, 5, 1011a3–1011b24.[xlii] Ibid., Bk. 14, 1, 1087b29–1087b31. My explanation appears in parenthesis.[xliii] Ibid., 1087a36–1087b3.[xliv] Ibid., 1087b34–1088b14. My explanation appears in brackets.[xlv] Aristotle, Physics, trans. R. P. Hardie and R. K. Gaye, in The Basic Works of Aristotle, Bk.1, 1, 184a– 1925.[xlvi] Aristotle, Metaphysics, Bk.1, 990b1–4.[xlvii] Aristotle, Posterior Analytics, Bk.1, 1, 71b8–30.[xlviii] Ibid., Bk.1, 27, 87a37–87b4,[xlix] Aristotle, Metaphysics, Bk. 5, 1, 1012b34–1013a23.[l] Ibid., Bk. 3, 4, 1001b1–1002b10, Bk. 5, 6, 1016b18–32.[li] Ibid., Bk. 4, 1,1003b22–34, Bk. 10, 1, 1052a15–1053b8, and 1053b23–24.[lii] Aristotle, Posterior Analytics, Bk. 1, 11, 77a5–9. See, also, Joseph Owens, “The Aristotelian Conception of the Sciences,” in John R. Catan (ed.), Aristotle: The Collected Papers of Joseph Owens (Albany, N.Y.: SUNY Press, 1981), p. 24.[liii] Aristotle, Posterior Analytics, Bk. 1, 11, 77a5–9. See, also, St. Thomas Aquinas, Commentary on the Posterior Analytics of Aristotle, trans. F. R. Lacher, O.P. , based on the Leonine text (Albany, N.Y.: Magi Books, Inc., 1970), Bk. 1, l. 19.[liv] Aristotle, Posterior Analytics, Bk. 1, 11, 75a18–37. See Aquinas, Commentary on the Posterior Analytics of Aristotle, Bk. 1, l. 14.[lv] Aristotle, Metaphysics, Bk. 11, 8, 1064b30–1065b4.[lvi] Ibid., Bk. 12, 1, 1069a18–1069b32, Posterior Analytics, Bk. 2, 2, 90b14–16.[lvii] Aristotle, Metaphysics, Bk. 4, 2, 1004a2–3.[lviii] Aquinas, Commentary on the Posterior Analytics of Aristotle, Bk. 2, l. 2.[lix] Aristotle, Posterior Analytics, Bk. 2, 2, 90b14–16.[lx] Aristotle, Metaphysics, Bk. 6, 1, 1026b1–25.[lxi] Ibid., Bk. 4, 3, 1003b36–37, Bk. 10, 1, 1053b23–104a19.[lxii] Ibid.[lxiii] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 2, n. 561.[lxiv] Aristotle, Metaphysics, Bk. 5, 24, 1023a26-32, and 26, 1024a29–1024b4.[lxv] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 22, n. 1121.[lxvi] Aristotle, Metaphysics, Bk. 5, 28, 1024b10–13.[lxvii] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 22, n. 1125.[lxviii] For further expanation about the difference between these ways of predicating, see Maurer (ed.), The Division and Methads of the Sciences: Commentary on the de Trinitate of Boethius, Questions V and VI, q. 6, a. 3, c., fn. 15, p. 75.[lxix] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 2, n. 553.[lxx] Ibid., Bk. 4, l. 3, nn. 564–566.[lxxi] Aristotle, Metaphysics, Bk. 12, 1, 1069a18-1069b32, Bk. 5, 5, 1015b10–15.[lxxii] Ibid., Bk. 9, 10, 1052b19–22.[lxxiii] Aristotle, Physics, Bk. 1, 1, 184a17–21.[lxxiv] Aristotle, Metaphysics, Bk. 9, 10, 1052b19–22. See also Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 2, n. 553.[lxxv] Aristotle, Metaphysics, Bk. 4, 2, 1005a3–5.[lxxvi] Ibid., 1004b27-1005a13b, Bk 10, 3, 1055a32–39. See also Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 4, nn . 582–587.[lxxvii] Aristotle, Metaphysics, Bk. 4, 1, 1004a34–1005a18. See also Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 4, nn. 582–587.[lxxviii] Aristotle, Metaphysics, Bk. 10, 3, 1055a33–1055b39. See also Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 6, n. 2058.[lxxix] Aristotle, Metaphysics, Bk. 10, 3, 1054a20–1055b39. See also Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 4, nn.1998-2022, 2035.[lxxx] Aristotle, Metaphysics, Bk. 12, 1, 1069a30–1069b3.[lxxxi] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 4, l. 2, n. 563.51 Ibid.[lxxxiii] Aquinas, The Division and Methods of the Sciences: Commentary on the de Trinitate of Boethius, Questions V and VI, q. 5, a. 1, Reply.[lxxxiv] Ibid., Reply to 4.[lxxxv] Ibid., Commentary on the Metaphysics of Aristotle, Bk. 6, l. 2, n. 1176.[lxxxvi] Ibid., Bk. 5, 6, 1016b4-32. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 8, n. 432.[lxxxvii] Aristotle, Metaphysics, Bk. 10, 4, 1055a4–1055a32. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 5, nn. 2024–2026.[lxxxviii] Aristotle, Metaphysics, Bk. 10, 1, 1052b15-19.[lxxxix] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 2, n. 1951.[xc] Aristotle, Metaphysics, Bk. 10, 1, 1053a24–27.[xci] Ibid., 1053a32–1053b3.[xcii] Ibid., 1052b20–27.[xciii] Ibid., Bk. 14, Ch. 2, 1088a15–1093b30.[xciv] Ibid., Bk. 10, 1053b4–9.[xcv] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 2, n. 1953.[xcvi] Ibid., Bk. 4, l. 2, nn. 561–563.[xcvii] Charles B. Crowley, Aristotelian-Thomistic Philosophy of Measure and the International System of Units (SI).[xcviii] Aquinas, The Division and Methods of the Sciences, Commentary on the de Trinitate of Boethius, Questions V and VI, q. 5, a. 3.[xcix] Redpath, “Presecipt,” in Crowley, Aristotelian-Thomistic Philosophy of Measure and the International System of Units (SI), p. xiii.[c] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 15, n. 978.[ci] Aristotle, Metaphysics, Bk. 5, 1, 1013a1–24.[cii] Ibid., Bk. 10, 1, 1052b32–1053a23. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 1, n. 749.[ciii] Aristotle, Metaphysics, Bk. 5, 12, 1020a18–1020b12. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 15, n. 981, and l.16, n. 998.[civ] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 15, n. 982.[cv] Ibid., l. 18, nn. 1038-1039. See Aristotle, Metaphsyics, Bk. 5, 16, 10212b12–1022a3.[cvi] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 18, n. 1037.[cvii] Aristotle, Metaphysics, Bk. 10, 1, 1020a25–33. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 15, n. 984.[cviii] St. Thomas Aquinas, Summa theologiae, ed. Piana (Ottawa: Collège Dominicain d’Ottawa, 1941), q. 1, a. 42, ad 1. See also, IaIIae, q. 52, a. 1, c. For a more extensive treatment of the notion of virtual quantity in Aristotle and Aquinas, see Crowley, Aristotelian-Thomistic Philosophy of Measure and the International System of Units (SI), pp. 25-47, 249–260.[cix] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 14 nn. 962–965.[cx] Aristotle, Metaphysics, Bk. 10, 14 1055a33–1055b18.[cxi] Ibid., Bk. 5, 14 1020a33-1020b25. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 16, nn. 987–999.[cxii] Aristotle, Metaphysics, Bk. 5, 14 1020b18–25.[cxiii] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 16, n. 998.[cxiv] Aristotle, Metaphysics, Bk. 4, 1, 1003b11–19. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 5, l. 1, nn. 534–544.[cxv]Ibid., Bk. 14, 1, 1087b38–42[cxvi] Aristotle, Metaphysics, Bk. 10, 1, 1052b19–1053b8. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 2, nn. 1937–1960.[cxvii] Ibid.[cxviii] Aristotle, Metaphysics, Bk. 5, 14, 1020b26–1021a14. Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 2, n. 1008.[cxix] Ibid.[cxx] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 2, n. 1008.[cxxi] Aristotle, Metaphysics, Bk. 10, 4, 1055a33–1055b3.[cxxii] Ibid., 1056a10-30.[cxxiii] Aquinas, Commentary on the Metaphysics of Aristotle, Bk. 10, l. 7, nn. 2059-2074. For extensive analysis of the way contemporary physical scientists use the equal as a measure, see Crowley, Aristotelian-Thomistic Philosophy of Measure and the International System of Units (SI).[cxxiv] Crowley, Aristotelian-Thomistic Philosophy of Measure and the International System of Units (SI), p. 28.