Natural Beginnings of Philosophy: Wonder, the Natural Road, and Axioms

Orientation #

He opens by reviewing the first three of the four introductory questions (what is a philosopher, what is philosophy, what are its kinds and parts) as settled, and turns to the fourth. He points forward: the road of reason as reason “when we begin logic,” the private roads and their “seven or eight elements” when natural philosophy starts, and the Physics ch. 1 text “later on”; “we’re going to do some logic before that.” Verified sources place the class on the handout “An Introduction to the First Road in Our Knowledge” (pp. 3-9) and “Friar Laurence on Stumbling” (p. 9); the latter is not audible in the transcript, which has a gap. The previous class treated wisdom as the most divine science and the true philosopher; the next continues with the natural beginnings, Euclid and Heraclitus.

The class, in order #

1. Review of the first three questions (“knowledge over a road”) #

The point: philosophy is a methodos, knowledge that follows a road, because it is a work of reason and every work of reason has order.

• Philosopher: lover of wisdom; wisdom is knowledge of causes and at the end of the very first cause, “looking” knowledge, free, not really a human possession, most honorable because most divine; loved for its own sake, as the end of life and as a common good (of reason and of mankind).
• Two ways of having philosophy: knowing the road to follow vs. going down it. At the end the mind halts: episteme, “reasoned-out knowledge.” At the beginning it is a search, zetesis or historia.
• Kinds: looking philosophy (end: to understand) vs. practical (end: to do); logic as the third, tool kind. Looking has three parts (mathematical, natural, first philosophy/wisdom), practical three (ethics: good of the individual; domestics: good of the family; political: good of city or nation), plus logic: seven “parts,” in the sense of subject parts, not parts composing a whole.
• Each is a reasoned-out knowledge of a subject: geometry of continuous quantity (lines, angles, figures), arithmetic of numbers, natural philosophy of natural things, wisdom of “what is, completely universal,” ethics of human happiness and virtue, domestics and politics of family and city, logic of definition, statement and argument (syllogism).
• Student asks him to repeat geometry’s subject: continuous quantity is divisible forever, its parts meet at a common boundary (line, surface, three-dimensional continuum).
• Three roads in our knowledge: the natural road (senses into reason), made by nature; the common road of reason as reason (from reasonable guesses toward reasoned-out knowledge); the private road of each reasoned-out knowledge.

2. The fourth question answered in one sentence (“from its natural beginnings through the use of reason”) #

The point: how should one come into philosophy? From its natural beginnings, through the use of reason.

• This raises four questions: what the natural beginnings are; why one should start from them; what it is to use reason; why one should enter through reason (the last “almost obvious”: philosophy is a work of reason).
• Natural beginnings divide: some in desire, some in knowledge.

3. The two beginnings in desire (“men begin to philosophize out of wonder”) #

The point: wonder is the beginning of looking philosophy; the desire to live well, of practical philosophy.

• Wonder, defined: the natural desire to know, for its own sake, the cause. Democritus: he would rather discover one cause than be master of the kingdom of the Persians (the greatest king of the time), showing the strength of that desire.
• Alternative definition: natural desire to know what and why; the question “what” appears in Theaetetus’ words, “why” in Socrates’; “Twinkle, twinkle, little star, how I wonder what you are.”
• Both questions seek the cause (Posterior Analytics II, “the center of logic”): what is an eclipse of the sun? The cutting off of its light by the moon coming between earth and sun. Why is the sun eclipsed today? Because the moon came between. Same answer, different arrangement. Definition answers “what,” demonstration “why”; a definition may be the beginning or the conclusion of a demonstration or differ from it only by arrangement, so the two definitions of wonder are equivalent.
• Wonder is the beginning of looking philosophy (knowledge for its own sake); practical philosophy seeks knowledge for the sake of doing well. Its natural desire “doesn’t have a name”: the natural desire to live well, not merely to live. Ethics asks when the individual lives well; domestics and politics, when the life of family and city is good.
• Theological footnote: looking and practical philosophy are two kinds; dogmatic and moral theology are not two theologies but one, because theology shares in God’s knowledge, which is one and simple, chiefly theoretical but also practical. Vatican I’s “faith and morals” (infallibility) should not be read as two knowledges. Philosophy divides because it is on the human level.

4. The two beginnings in knowledge: the natural road and the axioms (“known through themselves and by all men”) #

The point: besides the road from sense into reason (met already), there is a natural understanding of the axioms and their parts.

• Euclid distinguishes postulates, private to geometry (all right angles are equal), from the more general statements (the whole is larger than its part; things equal to the same are equal to each other). [He calls the second group “postulates” once, then “axioms”; the axioms are meant.]
• Axioms here: statements known through themselves, not proved by others, and known by all men. If anyone denies the whole is larger than the part, “we’ll give him a part of his celery,” of his dinner, of the car he bought; his ranting shows he is lying.
• We seem born knowing them, but actually come to know them through common experience: once one understands what whole and part are, it is obvious.
• Why there must be such statements (argument):
  1. If you understood nothing before reasoning, you would have nothing to reason from.
  2. What is so through itself is before and a cause of what is so through another: sugar is sweet through itself; coffee, if sweet, is sweet through another, so something sweet through itself must be before it.
  3. So if some statements are known through others, statements known through themselves must be before them: the axioms.
• Euclid also distinguishes statements known through themselves by all men (axioms) from those known through themselves by the learned in a science: no odd number is even (to one who knows odd and even); an obtuse angle is greater than an acute (to one who knows the definitions). The peasant might not know these but knows whole and part.
• Summary: four natural beginnings, two in desire, two in knowledge.

5. The natural road: before and after in kinds of knowing (“Mummy, a dog!”) #

The point: a road is an order, a before and after; in the natural road there are two before-and-afters, in kinds of knowing and in things known, to be considered separately.

• From Aristotle’s “Premium to Wisdom” (prev. lecture): sensing first (seeing, hearing, smelling, tasting, touching); then memory (he remembers nothing before his fifth birthday, kindergarten); then experience, a collection of many memories of the same sort of thing; only after experience the universal, proper to reason, by separating out what many individuals have in common.
• The child: “See the dog in the yard” (an individual sensed and remembered), another dog next day, memories accumulate into experience of dogs, until one day he looks out on his own and says “Mummy, a dog!”, recognizing a new individual under the universal.
• Sensing, memory, experience are knowledge of the singular. Among universals: first natural understanding (whole and part, etc.), then reasoned-out understanding in its many forms (geometry, arithmetic, natural philosophy, ethics, domestics, politics), and at the very end wisdom, which perfects both natural and reasoned-out understanding, “a kind of unique thing.”
• Student: is wisdom metaphysics? Aristotle usually says first philosophy; “metaphysics” comes from Andronicus of Rhodes, meta ta physica, after the books in natural philosophy, since in the order of learning it comes after (so placed even in the Random House Basic Works); Thomas says transphysica, across or after the natural books.

6. The order in which different things are known (“I don’t know why they fall to the ground”) #

The point: along the road from senses into reason, sensible things are known before what cannot be sensed, and more sensible before less; under this fall three befores, ascending from particular to general.

1. Material before immaterial. Hence natural philosophy (material things) before wisdom (immaterial). The first philosophers knew only material things and thought everything material; not until Anaxagoras, Plato and Aristotle were there reasons to think immaterial things exist, and then they saw there is a knowledge after the study of natural things.
2. Effects before causes (more general, since immaterial things are causes of material, but causes exist within the material world too). Reason: the senses know effects more than causes. Day and night: everyone agrees there is day and night, but people have disagreed whether it is caused by the sun going round the earth or the earth turning; disagreement about the cause with agreement about the effect is a sign the effect is more known. Alcohol’s effect on you is known, why it has it is hidden, and the chemist’s formula does not tell you. Trees grow; why is hidden. Every question “why” is a sign we know effect before cause. Historians agree there was a French Revolution and disagree why; we know what people do and are puzzled or mistaken about why. Newton: people think he answered why stones fall with gravity; reading his text he says “I don’t know,” the editor made it appear otherwise; Einstein, speaking on Newton in England, admired more his knowing what he didn’t know; Newton’s remark that he seemed a little boy playing with seashells while the ocean of truth lay undiscovered; the poets (“God said let Newton be, and all was light”) give him an ignorance of his ignorance he did not have. Einstein was still trying to find out why stones fall.
   • Consequence: wisdom comes last. We know effect before cause and cause before cause of the cause, so knowledge of the first cause comes at the end. Also from (1): mathematics defines material things without concrete matter; wisdom is about immaterial things, and if there were none natural philosophy would be wisdom. “From both of these, you can see why wisdom comes last in the order of learning.”
3. Composed before simple (generalizing 2: the cause tends to be simpler than the effect). God, the first cause, is the simplest thing there is: Summa Theologiae I, q. 2 on God’s existence, q. 3 on his simplicity, so the last thing we know is the simplest. Physics likewise: the principle of simplicity; Planck, the more universal an equation the simpler; Einstein at Columbia, “simple doesn’t mean easy,” relativity’s equations simple but not easy. The West Point professor asking Cadet MacArthur “do you understand this?” “No, sir.” “Neither do I. Class dismissed.” God is simplest yet hardest to understand.
   • Even in mathematics we define the simple by the composed: body has length, width, depth (three affirmations); surface has length and width but no depth (one negation); line, length but no width or depth (two negations); point, position but no length, width or depth; Euclid: that which has no parts. Even where grammatically affirmative (“God is simple”), theology shows it by showing he is not composed in any way. As we know cause through effect, so simple through composed.

7. The order in which the same thing is known (“singular when sensed, but universal when understood”) #

The point: because of the natural road we also know one and the same thing in one way before another.

• Boethius, Consolation of Philosophy, repeated through the Middle Ages: a thing is singular when sensed, universal when understood. The chair seen and touched is an individual chair; what I understand, what a chair is, is common to many.
  • So people asked “what is X?” by Socrates invariably give examples, and he says “you’re giving too much, I want what’s common to all these.” A child asked what a chair or a nose is points: “That’s a chair.” Defining a chair takes time (something to sit on? so is a bench, a saddle…). His children came home from kindergarten with “this is a circle, that’s a square,” not “a plane figure contained by one line.” Natural to give examples before defining; logic will show a road from examples to the definition: reading many Shakespearean sonnets and comparing them, one notices 14 lines, then the meter, and thinks out the definition.
  • Likewise in reasoning: the universal statements from which a syllogism proceeds are usually established by induction, an argument from many singulars to the universal, so induction comes before syllogism for us; in the Phaedo Socrates first makes an induction, then syllogizes to the immortality of the soul.
  • Hence Aristotle’s reason wisdom is hardest: most universal, so furthest from the senses; students complaining “this is so abstract” mean “so universal.”
• Second: we know things in an outward way before inwardly. “Outward” in English is nearly a synonym for sensible (the catechism’s sacrament, “an outward sign instituted by Christ to give grace”). Meeting someone for the first time you know them outwardly; through talk, listening, seeing them on the battlefield, inwardly. Especially true in ethics and natural philosophy (plane geometry deals with surfaces anyway). Senses know outwardly; reason tries to see into things, hence “insight,” “penetrating,” a “sharp” mind.
  • Important in logic: asking what a thing is, we first draw a line around it. Aristotle at the end of Nicomachean Ethics I calls virtue a praiseworthy quality (vice, blameworthy), an outward notion, since praise is in the one praising; the real definition comes in Book II. The child knows what he is praised or criticized for without seeing inwardly why. One can reason from outward to inward: what is praised in eating? The man who eats neither too much nor too little; so virtue is a habit in the middle. In treating happiness Aristotle uses graphe, to draw a line around, an outline, then begins.
  • “Wisdom is the best knowledge” is likewise outward: “best” means better than all the rest and does not say what wisdom is knowledge of; the road inward is to ask why one knowledge is better than another.
• [Recording gap here; the transcript resumes mid-example.] A point is fixed by longitude and latitude: an infinity of points share the longitude, but only one has both; so a definition narrows to one. This explains why we name a thing before defining it (naming needs less distinct knowledge) and why definition begins with the general, “animal” for dog. (The gap likely covers the confused/distinct before-and-after, referred to below.)

8. Aristotle’s reflection: more known to us is less fully known (“the more specific I try to get, the less sure I am”) #

The point: both before-and-afters share this: what is more known to us is before what is less known to us; and, “the most subtle thing he sees,” what is more known to us is less fully known.

• More known to us: the confused over the distinct, the outward over the inward, the singular, material over immaterial, effects over causes, composed over simple.
• What is known outwardly or confusedly is imperfectly known yet more known to us, so we are more sure of the confused than the distinct: handed a glass, “a dry red wine” is surer than “Cabernet Sauvignon,” surer than “Cabernet from Napa Valley.” Students asked his age: over twenty, yes; over thirty, yes; fifties or sixties, they start to fight. His weight: over 100, yes; over 300, no; more precise, less certain.
• Descartes, in the Discourse on Method, identifies certitude with clarity and distinctness; a man on Main Street would agree at first, but for us they do not go together.
• Student asks him to repeat Aristotle’s two thoughts: what is more known to us comes before what is less known to us; but what is less known to us is the more known, i.e. more fully or perfectly known, and what is more known to us is the less, imperfectly, known. Plato and Aristotle compare the mind to going from darkness toward light; where there is more light it blinds us at first. The effect is known more by itself than in the light of its cause (diseases whose causes are sought), but the effect is not fully understood until the cause is known.
• Student asks where Aristotle discusses this: not in the Nicomachean Ethics but in the first chapter of the Physics, to be read when natural philosophy begins, after some logic.

His words #

• methodos; knowledge over a road, knowledge that follows a road; road = order, before and after in our knowledge
• episteme; “reasoned-out knowledge,” “reasoned-out understanding” [ed.: science]
• zetesis, historia; search, investigation, the beginning stage of philosophy
• looking philosophy; whose end is to understand [ed.: theoretical/speculative]
• practical philosophy, “philosophy of doing”; whose end is to do
• domestics; philosophy of the good of the family [ed.: economics, oikonomia]
• subject parts; the sense in which the seven knowledges are parts of philosophy, not parts composing a whole
• natural road; from the senses into reason, made by nature
• road of reason as reason; from reasonable guesses toward reasoned-out knowledge
• private road; the road proper to each reasoned-out knowledge
• wonder; natural desire to know, for its own sake, the cause; or to know what and why
• natural desire to live well; unnamed beginning of practical philosophy
• axioms; statements known through themselves and by all men
• postulates; statements private to geometry
• through itself / through another; what is so through itself is before and a cause of what is so through another
• experience; a collection of many memories of the same sort of thing
• natural understanding; understanding of the very basic universals like whole and part, before reasoned-out understanding
• Premium to Wisdom; Aristotle’s Metaphysics I [ed.: proemium]
• meta ta physica; “after the books in natural philosophy”; transphysica in Thomas
• outward vs. inward knowledge; outward nearly synonymous with sensible; reason seeks insight
• graphe; to draw a line around, an outline definition
• induction; argument from many singulars to the universal
• more known to us / more known (fully, perfectly); Aristotle’s pair; the more known to us is the less fully known

Texts #

Read in class

• Euclid, Elements: axioms and postulates; definition of point (that which has no parts); definitions of body, surface, line (his summary)
• Boethius, Consolation of Philosophy: “a thing is singular when sensed, but universal when understood”
• Democritus, fragment: one cause over the kingdom of the Persians
• Handout, “An Introduction to the First Road in Our Knowledge,” pp. 3-9 (verified source)
• Handout, “Friar Laurence on Stumbling,” p. 9 (verified source; not audible in transcript)

Mentioned

• Plato, Theaetetus (Socrates and Theaetetus on wonder); Phaedo (induction then syllogism to immortality)
• Aristotle, Metaphysics I (sensing, memory, experience); Posterior Analytics II (what and why); Nicomachean Ethics I end (virtue a praiseworthy quality) and II; Physics I ch. 1 (more known to us)
• Thomas Aquinas, Summa Theologiae I, q. 2 (existence of God), q. 3 (simplicity of God)
• Descartes, Discourse on Method (certitude as clarity and distinctness)
• Vatican I, definition of infallibility in faith and morals
• Newton’s text on gravity and his seashore remark; Einstein’s talk on Newton and his Columbia lecture; Planck on universality and simplicity; Andronicus of Rhodes; Random House Basic Works of Aristotle
• “Twinkle, twinkle, little star”; catechism definition of sacrament; Shakespearean sonnets

His questions #

• How should one come into philosophy? From its natural beginnings, through the use of reason.
• What are the natural beginnings of philosophy? Two in desire (wonder, desire to live well), two in knowledge (natural road, natural understanding of the axioms).
• Is coffee sweet through being coffee? No; if sweet, sweet through another, so something sweet through itself is before it.
• Is wisdom to be understood as metaphysics? (student) Yes; Aristotle says first philosophy; “metaphysics” is Andronicus’ name, after the books on nature.
• Is day and night caused by the sun going round the earth or the earth turning? Not obvious; the disagreement shows effect is more known than cause.
• Question three of the Prima Pars is on the what? Simplicity of God.
• “Virtue is a praiseworthy quality”: inward or outward knowledge of virtue? Outward; praise is in the one praising.
• What kind of definition is “wisdom is the best knowledge”? Outward; it does not say what wisdom is knowledge of.
• Do certitude and clarity-and-distinctness go together for us? No; the more distinct we get (wine, age, weight), the less sure.
• Where did Aristotle discuss that? (student) First chapter of the Physics, to be read later.