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 shepherdi