Ends and Limits, and the Dependence of Philosophy on the Natural

Orientation #

He begins because “brother asked me to go over again briefly the word end or limit” from “that first reading” (the Physics VI passage on the edge/limit), and refers back to “what we learned last time in that first reading” and to the example of “before” he “mentioned last time” (prev. lecture). He ends by returning to the second paragraph of page one of the reading. Verified sources: the handout “Friar Laurence on Stumbling” p. 14 (read from) and the printed volume DHB Vol III p. 1058. The neighbouring classes treat Physics VI on the continuous and on the divisibility of magnitude, motion and time.

The class, in order #

1. The four senses of end or limit (“the first meaning of end or limit”) #

Point: the word translated “edge” in the first reading (Aristotle there probably uses eschaton, “last”; the usual Greek is peras or horos) has four ordered senses, which he gives from the fifth book of “wisdom” [ed.: Metaphysics].

1. End of a magnitude — the beginning and end of the desk. Most obvious to the senses; we name what we sense first and carry words over to less sensible things, a gradual process.
2. End or limits of a motion — in the motion from hot to cold, hot and cold.
3. End of intention — that for the sake of which, the goal; one of the four kinds of causes.
4. Definition — definitio comes from horismos, “limit”; the definition is called horos; cf. “horizon”, limit of the sky. Thomas’s two reasons (commentary on Met. V) why definition is an “end”: (a) knowing what something is comes last in knowing, since we start from the senses in an outward way — hence Heraclitus, “nature loves to hide”; Aristotle spends all of On the Soul I looking for what the soul is and reaches it only at the start of book II. (b) A definition draws a line around the thing, separating it from everything else — likeness to the first sense: the city limits of Worcester, no part of Worcester outside, no neighbouring town inside; the logician’s “tight fit”, convertibility: every square is an equilateral right-angled quadrilateral and vice versa. Simple grasping (first act of the mind, Thomas): grasping the glass is easy, the air moves away; grasping the centre of the table needs a knife to cut it out — so in logic you divide in order to define. Worked example: quadrilateral separates the square from all non-quadrilaterals; equilateral separates it from oblong, rhomboid, trapezium but not the rhombus; right-angled separates it from all except the oblong; together they separate it from everything. Objection of some early Greeks: you cannot define, because separating a thing from an infinity of others is “a long story” (one with no end). Reply: they forget the universal; “perfect number is a composed number” separates it from an infinity of primes at once, because the universal is said of many.

2. Telos, the two ends of the table, and the equivocation of “end” (“happiness is the end of human life”) #

Point: telos translated “end” can be extended to the senses; the senses are alike and yet distinct, and mixing them is the commonest error.

• Arche / telos: beginning and end of the table; Aristotle notes we also say “both ends” of the table. Running to the end of the table and back: beginning and end of motion very close to the first sense (as in book VI).
• Purpose is like that: when I run to the end and stop, you know where I was going; the end is pursued for its own sake, so you come to a stop. Thomas: I consider body for the soul, soul for the angels, angels for God, “and that’s it”.
• Sophism he gives students: happiness is the end of human life; the end of human life is death; therefore happiness is death. Death is the limit in time (reducible to the second sense), not the third sense; Aristotle himself points this out. Students still fall for it in exams: equivocation is the most common mistake according to “the father of logic”.
• A student’s argument: if nature acted for an end, all things would have come to an end — same confusion.
• Aside: a candidate speaking of a “teleological end” — moderns use words not to be understood; Hegel admitted writing obscurely to be admired; De Koninck (twelve children, lecture tours) inserted a meaningless sentence and listeners praised it; his friend Jim tells women “I don’t understand you” and they love it — people enjoy what they don’t understand and resent things made plain.

3. The Greek words (“eschaton, horos, peras”) #

Point: eschaton, horos, peras (P-E-R-A-S, the common one in the Physics and Met. V); a student notes Euclid uses both — “the boundary (horos) is the limit (peras)”; basically synonyms. He is unsure of his own translation “edge”; “end” or “limit” better.

4. The axiom behind the reading: nothing is an end of itself (“nothing is an end of itself”) #

Point: distinguishing these words also clarifies the axioms, which rest on such common words.

• Axiom used in the first reading: nothing is an end/limit of itself; positively, an end is always an end of something other than itself. Parallel in Physics I: nothing is a beginning of itself.
• Nobody, to his knowledge, has enumerated all the axioms; Aristotle’s Met. IV defends the axioms of being and non-being (cannot both be and not be; must either be or not be); Thomas’s stock example is “the whole is larger than its part”; these two are further examples.
• Use in Physics I: Parmenides and Melissus (everything is one) do away with beginnings and causes, since nothing is a beginning or cause of itself; without some multiplicity no beginning or cause is possible. Aside: interesting to apply to the Buddhists’ unity of everything.

5. Understanding the axiom distinctly through the four senses (“what’s the end of a body”) #

Point: run the axiom through the senses to see it more distinctly than the man in the street.

• Sense 1: end of body is surface (not a body: no depth); of surface a line (no width); of line a point; of a point — no end. A point cannot have an end, since that would distinguish edge from rest of the point and it would not be indivisible. Hence (first reading) two points cannot be contiguous — no ends to put together — so they could only coincide.
• Student: better to say the point “lacks” a limit than is “limitless”? His correction: lack strictly is the non-being of what one is able and ought to have; the stone is not blind, you or I would be. So the point does not lack an end; it does not have one (negation, not privation).
• Sense 2: the end of a motion is not a motion. Sense 3: the purpose is not the purpose of itself but of the means. Sense 4: the definition of definition is not a definition of itself; it fits every definition — “think about that”.
• Another axiom he is fond of: nothing is before or after itself. Thomas on order (Sentences): order involves distinction and before/after, then corrects: distinction is presupposed to order — reason must see distinction before before-and-after.

6. Axioms are naturally known (“the whole is more than the part”) #

Point: reason naturally comes to know these; one cannot avoid it, though a sophism can make someone think he doesn’t know what he knows. Student: do they arise from repeated experience? — you cannot live without experiencing wholes and parts, so you come to see the whole is more than one part. Composed whole is composed of more than one part; universal whole is said of more than one part.

7. The complete dependence of philosophy upon the natural (“complete dependence of philosophy upon the natural”) #

Point, flagged as “very important”: three statements, each true alone, together show the dependence.

1. Some statements and their parts our reason naturally knows, or naturally comes to know. Nobody can say when he first knew a whole is more than a part; the denier is either pretending (give him part of his salary, part of his dinner, part of his car — he’ll scream) or deceived by a sophism. His sophism: man is an animal with reason, so animal is only part of man; but animal includes cat, dog, horse; so the part is more than the whole. Diagnosis: “part” is equivocal by reason (like “in”), not by chance — chance equivocals don’t deceive (Roger Maris hit 61 home runs with the bat; a bat is a flying rodent). Animal is a composing part of the definition of man; man is a subject part (species) of the genus animal — universal whole vs. composed whole. Recalls last time’s harder example: breathing before philosophizing in the second sense of before (can be without it, not vice versa) does not make it before in the fourth sense (better) — like saying Chaucer is better than Shakespeare because earlier. Aside: reading the Contra Gentiles, Thomas finds Averroes, “the commentator” by antonomasia, deceived by equivocation; his rule of thumb: Aristotle means what Thomas says he means. So natural that, as Plato said, it seems we always knew them and just recall them.
2. We have a natural desire to know the things we do not naturally know. No desire for what we already have. Aside on “want” as lack: Hamlet’s “a beast that wants discourse of reason would have mourned longer”; telling students “you’re sadly wanting”. This is the desire to know what and why Socrates speaks of.
3. We come to know the things we do not naturally know through the things we do naturally know — applies to statements and to their simple parts. Euclid’s theorems are reasoned to through other statements; if every statement had to be reasoned to, there would be none to reason from, so we would know none. Terms: natural understanding = Aristotle’s nous, Thomas’s intellectus (both also name the faculty; here the habit that arises from the mind itself); he translates episteme “reasoned-out understanding”. Wonder, the beginning of philosophy, is this natural desire. What we learned last time was learned through such axioms (nothing is an end of itself). Student: is the order “one, three, two”? He restates: naturally known statements (axioms; Boethius: statements known of themselves to all men); the Pythagorean theorem not naturally known, pursued by natural desire; known ultimately through what we naturally know. Friar Laurence (Romeo and Juliet, handout): those who revolt from true birth — from the natural — stumble on abuse; a revolt from the natural means the complete collapse of philosophy.

8. The modern revolt from the natural (“a revolt from the natural”) #

Point: modern philosophy revolted from statements 1 and 2, hence from 3.

• Revolt from natural understanding: Oliver Wendell Holmes would leave blank the paper of statements he is sure of (is he sure of that?). Reply: “statements exist” is proved by making one and cannot be denied without one. Mill, On Liberty, chapter on liberty of the mind: freedom to think because we know nothing; this dominates universities — teaching that a statement is true violates their morals; “present all points of view” — otherwise (student:) a terrorist. Student: is this Thomas’s intellectus? — used in many senses, like nous.
• Revolt from the natural desire: replaced by desire for power — Descartes’s tree (metaphysics roots, physics trunk, medicine and mechanics the fruit, all ordered to the practical); Hobbes explicitly: the end of knowledge is to do or make; Marx rejects any knowing not tied to making. Are these lovers of wisdom or of power?
• Contrast: Greek philosophy from Thales to Aristotle is seeds, growth, grown plant; modern philosophy is a zigzag, no building on predecessors’ partial truths.
• Asides: an interviewee who could not say what a name is; Heidegger colleague at St Mary’s still asking what “being” meant after three years — time should go to judging true or false, as with Thales’s “water is the beginning of all things”; a Notre Dame professor’s abstruse vocabulary that vain professors won’t ask about; Locke apologizing for the length of the Essay — attacking “a whole cloud”; Heraclitus, “wisdom is to speak the truth and act according to nature”, versus Kant’s second preface: summon nature like a judge, not listen like a student.

9. Back to the reading (“the edge and that of which it is an edge are other”) #

Point: end of second paragraph, page one — this is a statement we naturally know or come to know, and through such statements we come to know other things. Aside (before the prayer): “physician” comes from physis, so the abuse at issue violates what a doctor should be.

His words #

• end / limit / edge — his translations of peras, horos, eschaton; four senses: of magnitude, of motion, purpose, definition.
• wisdom, fifth/fourth book of — [ed.: Metaphysics V, IV].
• Natural Hearing — [ed.: Physics].
• simple grasping — Thomas’s first act of the mind [ed.: simple apprehension].
• tight fit — the logician’s convertibility of definition and defined.
• long story — the early Greeks’ story with no end.
• lack — non-being of what one can and should have (privation), vs. mere not having (negation).
• equivocal by reason vs. by chance — related meanings that deceive, vs. unrelated that don’t.
• composing part vs. subject part; composed whole vs. universal whole.
• natural understanding — nous, intellectus; reasoned-out understanding — episteme.
• want — as lack (Hamlet).
• the commentator — antonomastic title of Averroes; Thomas as “the commentator” of Aristotle.
• zigzag — the history of modern philosophy.

Texts #

Read in class

• Aristotle, Physics VI, first reading, p. 1, second paragraph: “the edge and that of which it is an edge are other”.
• Shakespeare, Romeo and Juliet, Friar Laurence on those who revolt from true birth (handout “Friar Laurence on Stumbling”, p. 14, verified). Mentioned
• Aristotle, Metaphysics V (end/limit, with Thomas’s commentary); Metaphysics IV (axioms); Physics I (Parmenides, Melissus; beginning); On the Soul I–II.
• Euclid (boundary and limit); Pythagorean theorem.
• Heraclitus fragments (“nature loves to hide”; “wisdom is to speak the truth and act according to nature”).
• Thomas, Sentences commentary (order); Summa Contra Gentiles (Averroes); Boethius (statements known of themselves).
• Plato (recollection); Shakespeare, Hamlet (beast that wants discourse of reason).
• Holmes; Mill, On Liberty; Descartes (tree of knowledge); Hobbes; Marx; Hegel; Heidegger; Locke, Essay; Kant, Critique of Pure Reason, second preface.
• DHB Vol III, The School of Aristotle, p. 1058 (verified printed volume).

His questions #

• What is the end of a body? of a surface? of a line? of a point? Surface, line, point, no end — a point with an end would not be indivisible.
• Does the point lack a limit? No: it does not have one; lack is of what one can and should have.
• Is the end of a motion a motion? Is the purpose the purpose of itself? Is the definition of definition a definition of itself? No in each case — it is always of something other.
• Is happiness death, since both are the end of human life? No: death is the limit in time, happiness the end as purpose — equivocation.
• Do we come to know all statements by reasoning? No; then there would be nothing to reason from.
• Does Holmes’ man doubt that statements exist? He cannot deny it without making a statement.
• Are Descartes, Hobbes, Marx lovers of wisdom or of power? Seemingly lovers of power.
• Is this natural understanding Thomas’s intellectus? Yes, though intellectus and nous are used in many senses.
• Is the order of the three statements one, three, two? He restates: naturally known; natural desire; known through the naturally known.