Demonstration: Cause, Necessity and Through Itself

Orientation #

He says he “might have said last time” that the best reason for a statement is the reason why it must be so (prev. lecture). He announces “a few more words about demonstration and dialectic,” and then a move to sophistic, Aristotle’s book “About Sophistical Refutations” (next time). The previous class worked through the second figure of the syllogism; the next takes up dialectic’s usefulness and the sophistical fallacies.

The class, in order #

1. Remembering the dead (“So just remember them a little bit”) #

Opening aside: he recalls several recently deceased people (a woman who tended the altar flowers, Monsieur Delacour whom he had for courses at the College of Saint Thomas, Mr. Rice met on the way to Rome) and asks the class to remember them. No doctrinal content.

2. Aristotle’s definition of demonstration, anticipated by Plato (“a syllogism making us know the cause”) #

Point: demonstration is a syllogism (its genus) making us know the cause, that of which it is the cause, and that it cannot be otherwise; Plato already sees the tie between certainty, necessity and cause.

• Meno: Socrates separates knowledge (episteme) from right opinion. Right opinion is as good for action while you hold it, but it can get up and go away; knowledge is tied down “by the logismō aitias,” an account of the cause. So the cause is what lets you see it must be so.
• Phaedo: Cebes finds the arguments for immortality good but not necessary and presses for a necessary one; Socrates says “you are asking for a lot” and goes back to his days as a natural philosopher, because the natural philosopher most of all knows causes, and the reason why the soul must be immortal has to be given in terms of the cause.
• He credits this to Plato rather than Socrates (“I am going to give Plato more”).

3. The best reason for a statement: the vertical angles (“the reason why it must be so”) #

Point: of the many reasons one can give for a statement, the best is the reason why it must be so; “why” touches the cause (cause answers “why,” also “what”), and so necessity. Example, vertical angles at intersecting straight lines:

1. “They look equal” — a reason, not the best.
2. “Euclid says so” — a reason, not the best.
3. Measure these two, or a few more — evidence for this case, not universal.
4. Euclid’s reason: because this is a straight line, a + x equals two right angles; because this is a straight line, b + x equals two right angles; then the axioms obvious to everyone (things equal to the same are equal; equals subtracted from equals leave equals). The basic “why” comes from the straightness. Applied to the definition: the lines intersecting is the cause of there being angles; the straightness is the cause of their being equal; that equality cannot be otherwise.

• Aside: “the man from Missouri — show it to me”: demonstration really shows it.

4. Cause and necessary in Metaphysics V (“a cause is that to which something else necessarily follows”) #

Point: cause and necessity are intimately connected, hence two ways of defining demonstration.

• In book V of “wisdom” Aristotle takes up the words used most in wisdom, in the axioms, and to some extent everywhere. The first group are names of causes: beginning, cause, element, and (as in the first sentence of natural philosophy) nature; then he attaches “necessary.”
• Thomas: “necessary” is attached to the causes because a cause is that on which something else necessarily follows — as equality follows on the lines being straight; as being half of four and a third of six follows on a number being two.
• Hence demonstration is defined either with emphasis on making known the cause, or as a syllogism from premises that are necessarily true. Two key words: cause, necessary.

5. “Perfect” and its three companions; why demonstration is the perfect argument (“This is a perfect argument”) #

Point: among the words for properties of being, Aristotle first takes “perfect” (three basic meanings; a sense for God and a sense for creatures), then, unusually, three words related to perfect: (1) limit or end; (2) through itself — per se, kath’ hauto; (3) have and having. Since we call dinners, tragedies, chairs and arguments perfect, these words apply to the perfect argument. Argument that demonstration is the perfect argument:

1. In form, nothing more can be asked than that the conclusion follow necessarily from the premises.
2. In matter, nothing more can be asked than that the premises be true, and necessarily true.
3. Demonstration has both; other arguments lack one or the other or both. Conclusion: demonstration is the measure of all other arguments, which fall away from it — e.g. the dialectical syllogism: conclusion follows necessarily, premises not necessarily true, so the conclusion is only probable.

6. Through itself (kath’ hauto): friendship, two and four, the four senses (“It belongs to two through being two”) #

Point: the premises of demonstration are per se, and per se is bound up with both cause and necessity.

• Friendship shows per se as a mark of perfection: loving you because useful or pleasant is not loving you for yourself; in the highest friendship I love you for what you are in yourself.
• Man is an animal with reason, and because he is, capable of laughter: rational belongs to man as such; capable of laughter belongs to rational animal as such.
• Two is half of four vs. triangle green: two is half of four because it is two (cause), so it belongs to two as such, through itself, necessarily. Green does not belong to triangle through being a triangle; it is accidental, not necessary. So as-such / through-itself links to cause and to necessity.
• Student: is “through itself” just “by its very nature”? — Yes, ultimately, by its nature.
• Four senses of through itself in the Posterior Analytics: (1) what is in the definition of a thing said of it (square as such is equilateral, a quadrilateral); (2) what belongs to a thing as a property — these two are the basic ones; (3) the Greek idiom “by yourself” (alone in your room you are kath’ hauto); (4) applied to the other causes [unclear in recording: “they move in the end too”].
• Student: does Aristotle distinguish necessary from as-such/through-itself? — They are connected. It is necessary that two is a number and necessary that two is half of four, though these are two different senses of through itself (one from the definition, one the property).
• Through itself appears in Metaphysics V because it follows on “perfect,” and in Posterior Analytics I because it is connected with “necessary”; since demonstration is the perfect argument, no surprise it is central there.

7. Limit or end: definition, and being determined to one half of a contradiction (“How to Limit Your Thinking”) #

Point: “limit” applies to demonstration in two ways — definition, and the mind’s determination to one side of a contradiction.

• Joke against “opening horizons”: his book would be “How to Limit Your Thinking,” i.e. how to perfect it.
• Definition comes from finis, end or limit; definition gives certitude, and the middle term of a demonstration tends to be a definition.
• Demonstrator vs. dialectician (Prior Analytics): the demonstrator takes one half of a contradiction and throws away the other; the dialectician asks “which do you think?” and may incline to one side with some fear. Socrates asked whether virtue can be taught says virtue is not yet defined, then in the third part of the Meno argues with probability both that it can and that it cannot; Aristotle says dialectic reasons to probable opinions, even to contradictory conclusions; Thomas in the Quaestiones disputatae may give fifteen arguments yes and ten no before resolving.
• So in demonstration the mind is determined to one half of a contradiction in premises and conclusion; the contradictory of what is demonstrated is never demonstrated. Demonstration has the truth; dialectic is still guessing — a reasonable guess, but no firm hold. Chess image: “I got you, no way out.”
• Beginning and end: on a line one point is the beginning, the other the end, yet both are called endpoints. God, most perfect, is beginning and end of all things, “alpha and omega,” more like a circle — not that he has a limit, but is the limit of all things.
• Having: God is being to himself, good to himself, has everything. Euthyphro problem: how give anything to God? Christmas: what to give the man who has everything. Thomas on Scripture’s “follow me and I will show you every good”: that is, myself. A creature is perfect in its kind, lacking perfections of other genera; God has the perfections of every genus without their imperfections — and to “have” an imperfection (blindness, poverty, ignorance) is not really having, only a metaphor.

8. Student question: dogmatics vs. moral theology (“as you descend to the particular”) #

Student: would one find more demonstration in speculative/dogmatic theology and more dialectical syllogism in moral theology? — Yes: as you descend to the particular there is less certainty, more to be considered, and necessary reasons become hard (how many bites of steak to have). The moral manuals deal in probable opinions. The Secunda Secundae gives the common principles of ethics and moral theology; for the proper and particular ones you go to St. Alphonsus de Liguori, patron of moral theologians and confessors, because he descends more to particulars. The Secunda Secundae is nearly larger than the rest of the Summa together, because perfecting these things means descending to particulars.

9. Demonstration propter quid and demonstration quia (“going from the effect to the cause”) #

Point: besides the demonstration from cause to effect (propter quid, “on account of what”), Aristotle in Posterior Analytics I speaks of a demonstration that it is so (quia), going from effect to cause. It is used more in natural philosophy, where the effect is more known to us than the cause, than in geometry, where things are on the surface and one goes from cause to effect.

10. The four questions and wonder (“how I wonder what you are”) #

Point: Posterior Analytics II opens with the four questions of speculative knowledge, and what and why are both answered by the cause.

• The questions and their order: does it exist? before what is it?; is this that? before why is this that? Unicorns: if none exist, you discuss the word but there is no thing to know. Is the sun’s light eclipsed? then why? Does snow melt? then why?
• The questions almost change into one another. “What is an eclipse of the sun?” — a cutting off of the sun’s light by the moon coming between sun and earth. “Why is the sun’s light eclipsed at midday?” — because the moon is coming between. Same cause answers both.
• Sacrament: “an outward sign instituted by Christ to give grace” states its causes — Christ the maker, grace the end, outward/sensible the matter, sign (words etc.).
• “Twinkle, twinkle, little star, how I wonder what you are”: wanting what the star is made of is wanting its causes. At the start of natural philosophy Aristotle says understanding what and knowing why both come by knowing beginnings, causes and elements.
• Posterior Analytics II is “the centerpiece of logic”, because logic is the tool of the man who wonders; wonder, the beginning of philosophy, is a natural desire to know the cause, i.e. what and why (the Theaetetus reading he gave mentions what and why).
• Aside: the rhyme is in trochaic meter, the unusual meter of wonder, like the witches’ “Fair is foul and foul is fair, hover through the fog and filthy air”; the last foot is cut short.
• Aside: a University of Minnesota logician told one of his professors that symbolic logic is useless for knowing reality — Aristotle’s logic serves the questions what and why, definition and demonstration.

His words #

• demonstration: a syllogism making us know the cause, that of which it is the cause, and that it cannot be otherwise; also, a syllogism from necessarily true premises.
• episteme: “knowledge” in the strict sense, the effect of demonstration.
• logismō aitias (Meno): “an account of the cause,” what ties down right opinion.
• because: “cause being.”
• wisdom, fifth book [ed.: Metaphysics V].
• thoughts of nature / natural philosophy [ed.: Physics], first sentence: the word nature.
• perfect: three basic meanings; a sense for God, a sense for creatures.
• limit or end: includes definition (from finis); also beginning and end as endpoints.
• through itself: per se, kath’ hauto; as such; “by its very nature” (accepted from student); four senses.
• have and having: God has everything; to have an imperfection is not really having.
• determined: the demonstrator’s mind fixed to one half of a contradiction.
• demonstration propter quid (“on account of what”): from cause to effect; demonstration quia (“that it is so”): from effect to cause.
• the four questions: does it exist, what is it, is this that, why is this that.
• wonder: natural desire to know the cause, i.e. what and why.

Texts #

Read in class

• Aristotle, Posterior Analytics I, definition of demonstration (quoted); four senses of through itself (summarised); demonstration quia / propter quid.
• Aristotle, Posterior Analytics II, opening: the four questions, eclipse example.
• Aristotle, Metaphysics V: words for cause and “necessary”; “perfect” and its three companion words.
• Euclid, vertical angles equal (worked at the board) (inferred: Elements I.15).
• Handout “Shakespeare on Error,” p. 3 (verified source; the witches’ lines).
• DHB Vol. III, The School of Aristotle, p. 1030 (verified source, printed volume).

Mentioned

• Aristotle, About Sophistical Refutations (next topic).
• Aristotle, Prior Analytics (demonstrator vs. dialectician on the contradiction).
• Plato, Meno (knowledge vs. right opinion; third part, virtue taught / not taught); Phaedo (Cebes; Socrates as natural philosopher); Theaetetus (earlier reading); Euthyphro.
• Thomas Aquinas on Metaphysics V (“necessary” attached to causes); Quaestiones disputatae; Summa Theologiae, Secunda Secundae; gloss on “I will show you every good.”
• St. Alphonsus de Liguori.
• Scripture: “I am the alpha and the omega”; God’s words to Moses (or Abraham).

His questions #

• What is the best reason you can give for a statement? The reason why it must be so.
• What is the reason those opposite angles are equal? Because the lines are straight, each pair sums to two right angles; the rest is axioms.
• Why is demonstration the perfect argument? The conclusion follows necessarily and the premises are necessarily true.
• Why is two half of four — does it just happen to be, like a triangle green? No: because it is two; it belongs to two through itself.
• Is “through itself” just “by its very nature”? (student) Yes, ultimately.
• Are necessary and through itself distinguished or connected? (student) Connected; two senses of through itself (definition, property), both necessary.
• Is there more demonstration in dogmatics and more dialectic in moral theology? (student) Yes; descending to particulars lessens certainty (moral manuals, St. Alphonsus).
• Why is the sun’s light eclipsed / what is an eclipse? Both answered by the cause: the moon coming between sun and earth.
• What is a sacrament? An outward sign instituted by Christ to give grace — i.e. its causes.