43. Demonstration, Necessity, and the Perfect Argument

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Lecture Notes

Main Topics #

Demonstration as the Perfect Argument #

• Demonstration is a syllogism that makes known the cause and that of which it is the cause, showing that it cannot be otherwise
• It is the “perfect argument” because both form and matter are perfect:
  • Form: conclusion follows necessarily from premises
  • Matter: premises are necessarily true and seen as necessarily true
• Other arguments fall away from this perfection in various ways
• Demonstration is the measure by which all other arguments are judged

The Intimate Connection: Cause, Necessity, and Definition #

• Cause answers the question “why” and is essentially connected with necessity
• Thomas Aquinas: causes produce necessary consequences (just as straight lines necessarily produce equal opposite angles)
• Definition is one meaning of peras (limit) and tends to be the middle term in demonstration
• What belongs to something per se (through itself) or as such belongs necessarily
• Example: Two is necessarily half of four through being two, not accidentally

Per Se (Through Itself) and Necessity #

• What belongs to something per se belongs in virtue of what that thing is
• Man is rational per se (belongs to man as such); triangle is green per se (accidental)
• Can be expressed as: “by its very nature” or “in the definition of the thing”
• Tightly connected to necessity: if something belongs per se, it must be so
• Aristotle discusses per se in both Metaphysics Book 5 (in connection with perfection) and Posterior Analytics Book 1 (in connection with necessity)

Demonstration Propter Quid vs. Demonstration Quia #

• Demonstration propter quid (“on account of what”): proceeds from cause to effect
• Demonstration quia (“that it is so”): proceeds from effect to cause
• Natural philosophy uses quia more often because effects are more known to us than causes
• Geometry typically uses propter quid because causes are evident on the surface

Dialectic vs. Demonstration #

• Demonstration: determines mind to one side of contradiction; produces necessary knowledge
• Dialectic: leaves mind undetermined between both sides; produces probable opinion
• Dialectician asks “which do you think?”; demonstrator takes one side and excludes the other
• Dialectic can reason from both sides of a contradiction; demonstration never can
• In demonstration, one cannot demonstrate the contradictory of what has been demonstrated
• The mind in demonstration is limited to one side of contradiction in both premises and conclusion

Plato Anticipating Aristotle on Cause and Certainty #

• Meno: Knowledge differs from right opinion because knowledge is “tied down” (logismos) by an account of the cause
• Right opinion can be lost; knowledge cannot, because grounded in causes
• Phaedo: Socrates appeals to natural philosophy to find causes for necessity (e.g., why the soul must be immortal)
• Plato connects certainty, necessity, and cause in both dialogues

Definition and Limit (Peras) #

• Definition comes from Latin finis meaning end or limit
• Definition enables certitude and shows why something must be so
• Limit also means the determination of mind to one side of a contradiction
• God as “beginning and end” of all things: both the limit in sense of first principle and final principle
• Limiting thought (as by definition) perfects thinking, contrary to modern notion of “unlimited thinking”

The Four Questions in Speculative Knowledge #

1. Does it exist?
2. What is it?
3. Is this that?
4. Why is this that?

• First question must be answered before the second (cannot ask “what is a unicorn?” if unicorns don’t exist)
• Third question must be answered before the fourth
• Both “what” and “why” are answered by knowing causes
• The eclipse example: defining what an eclipse is requires the cause (moon between sun and earth); explaining why the sun is eclipsed uses the same cause

Key Arguments #

The Best Reason Argument #

• The best reason for a statement is the reason why it must be so
• “Why” asks for cause; cause is what enables necessity
• Example (geometry): Why are opposite angles equal? Not because “they look equal” or “we measured them”—because these are straight lines, and by necessity of straight lines, the angles must be equal

Plato’s Argument for Knowledge as “Tied Down” by Cause #

• Right opinion can change; knowledge cannot
• Knowledge is secure because it is held by the logismos (account of the cause)
• Therefore: knowing the cause is what distinguishes knowledge from mere opinion

The Sacrament Definition as Causal #

• “A sacrament is an outward sign instituted by Christ to give grace”
• This definition gives multiple kinds of causes:
  • Efficient cause: instituted by Christ
  • Final cause: to give grace
  • Material cause: outward sign
  • Formal cause: the words and matter together

Important Definitions #

• Demonstration (ἀπόδειξις / apodeixis): A syllogism that makes known the cause and that of which it is the cause, showing that it cannot be otherwise
• Cause (αἴτιον / aition): That which answers “why”; intimately connected with necessity
• Per se (δι’ αὑτό / per se): What belongs to something in virtue of its essence; what is necessary to it by its very nature
• Limit (πέρας / peras): Can mean: (1) definition, (2) the determination of mind to one side of contradiction, (3) beginning and end
• Dialectic: Reasoning from probable opinions; the power to argue both sides of a question
• Demonstration propter quid (“on account of what”): Demonstration from cause to effect
• Demonstration quia (“that it is so”): Demonstration from effect to cause

Examples & Illustrations #

The Geometric Demonstration #

• Straight lines intersect; opposite angles are equal
• Why? Because these are straight lines, angle A + X must equal two right angles, AND angle B + X must equal two right angles
• By axiom (quantities equal to the same equal each other): A = B
• The cause: straightness of lines
• The effect: equality of angles
• This is necessary, not accidental

Simple Mathematical Example #

• Two is half of four
• Why? Because two as two is half of four; it belongs to two through being two (per se)
• Necessarily true, not accidental
• Contrast: A triangle being green is not per se; it doesn’t belong to triangle as triangle

The Eclipse Questions #

• Does the sun’s light get eclipsed? (existence question)
• What is an eclipse? (definition question: cutting off of light by moon between sun and earth)
• Why is the sun’s light eclipsed? (cause question: the moon is between the sun and the earth)
• The cause answers both “what” and “why”

Notable Quotes #

“Demonstration is a syllogism making us know the cause and that of which it is the cause, and that it cannot be otherwise.”

“The best reason you can give for a statement is the reason why it must be so.”

“Cause answers the question why.”

“In demonstration you have the truth. In dialectic you’re still guessing the truth.”

“The mind in demonstration is limited to one half of a contradiction, both in the premises and in the conclusion. While in dialectic it’s kind of unlimited.”

“Definition tends to be the middle term in a demonstration.”

Questions Addressed #

Why is Knowledge Better Than Right Opinion? #

• Right opinion can be lost or changed
• Knowledge is “tied down” by the account of the cause (logismos)
• The cause makes the connection between premises and conclusion necessary and perduring

How Do “What” and “Why” Relate? #

• Both are ultimately answered by knowing causes
• To define what an eclipse is requires knowing the cause (moon between sun and earth)
• To answer why the sun is eclipsed requires the same cause
• The questions are closely connected and can be transformed into one another

Why Does Definition Matter for Demonstration? #

• Definition provides the middle term
• Definition shows what belongs to something per se (necessarily)
• Definition enables the mind to see the necessary connection between cause and effect
• Limit (definition) is essential to the perfection of demonstration

Why Is Demonstration More Perfect Than Dialectic? #

• Demonstration’s form is perfect: conclusion necessarily follows from premises
• Demonstration’s matter is perfect: premises are necessarily true
• Dialectic’s form may be perfect (conclusion follows necessarily), but matter is not (premises are only probable)
• Demonstration determines the mind; dialectic leaves it undetermined
• Demonstration produces knowledge; dialectic produces opinion