33. Reasoning, Guessing, and the Four Arguments

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Lecture Notes

Main Topics #

Reasoning vs. Understanding #

• Reasoning is distinct from understanding; it is the movement of mind from one statement to another
• Understanding is static (like rest); reasoning is discursive and kinetic (like motion)
• Both concern the intellect, but in different modes

The Nature of Guessing and Reasonable Guesses #

• Not all guesses are wild; there are reasonable guesses (guesses with reasons)
• Examples: weatherman predicting rain, economist forecasting economic trends, experimental physicist proposing freely-imagined hypotheses
• The difference between guessing and knowledge: guessing lacks certainty; knowledge grasps necessity
• Reasonable guessing is distinguished from wild guessing by having evidentiary or rational basis

Definition of Reasoning #

• Reasoning is coming to know or guess a statement from other statements already known or accepted, and because of them
• The key phrase “because of” indicates that the conclusion flows from premises, not merely follows them
• Alternative formulation: reasoning is coming to know or guess a statement through other statements known or accepted

Calculating vs. Reasoning #

• Calculating is similar to reasoning: it is coming to know or guess a number from other numbers
• Even correct arithmetic operations (addition, subtraction, multiplication, division) may yield only a guess if the starting numbers are themselves guesses
• Like the syllogism, calculating produces a third element from two elements, and both arts imitate nature (two parents produce offspring)
• The conclusion may follow necessarily while still remaining uncertain if premises are uncertain

The Four Arguments as a Progression #

Arguments move along a “road from the senses into reason,” becoming progressively more difficult and more universal:

• Example (exemplum): singular to singular
• Induction (epagoge): many singulars to universal
• Enthymeme (enthymema): from something more universal or probable
• Syllogism: completely universal, most removed from senses

Argument as Speech #

• An argument is speech bringing together the statements from which we reason
• The statements from which we reason are called premises (Latin praemissa, “sent before”)
• The statement to which we reason is called the conclusion
• The Greek term ποτόθις (potosis) is more accurate than praemissa because it suggests premises “stretch forward, producing the conclusion”

Logic and Logistic as Parallel Arts #

• Logike (logic, reasoning) and logistike (calculating) are two distinct arts
• Both involve coming to know something unknown from things already known
• Both imitate nature: as two parents produce offspring of similar kind, two premises produce a conclusion, and two numbers produce a third number
• Arthur Eddington’s observation: “If you put in numbers, you get out numbers” (natural limitation of operations)

Key Arguments #

Example (Exemplum) #

• Definition: An argument from one singular to another singular of the same kind
• Structure: Reasoning from a past singular case to a future singular case
• Necessity: Conclusion does not follow necessarily; it is a reasonable guess
• Strength depends on: The likeness between the two singulars; the greater the likeness, the stronger the argument
• Usage: Common in rhetoric, political discourse, everyday decision-making (restaurant selection, car purchase, course enrollment)
• Etymology note: Example differs from sample; a sample is a part of an integral whole (e.g., cheese sample), while an example illustrates a universal through a particular

First Meaning of “Example” (Non-argumentative) #

• A singular used to illustrate the universal
• Necessary in all teaching because of human dependence on the senses
• A professor must use examples (particular instances) to teach universal concepts
• This is not itself an argument, but a pedagogical aid

Induction (Epagoge) #

• Definition: An argument from many singulars to the universal
• Etymology: From Greek verb meaning “to lead in”; premises lead the mind into universal statements
• Process: Examining multiple cases (e.g., frog A has three-chambered heart, frog B has three-chambered heart, frog C has three-chambered heart, therefore all frogs have three-chambered hearts)
• Necessity: Does not guarantee necessity; conclusion is a reasonable guess from enumeration of cases
• Movement: More advanced along the road from senses to reason than example; moves from particular to universal

Important Definitions #

Reasoning (λογισμός - logismos) #

• Coming to know or guess a statement from other statements already known or accepted, and because of those statements
• The phrase “because of” is essential: it distinguishes reasoning from mere sequence

Premise (praemissa / ποτόθις - potosis) #

• Latin: literally “sent before”
• Greek: from πρωτείνω (proteino), meaning “to stretch forward”
• The Greek term better captures that premises actively stretch forward to produce the conclusion

Conclusion #

• The statement to which we reason
• Follows from premises either necessarily (in syllogism) or as a reasonable guess (in other arguments)

Argument (argumentum) #

• Speech bringing together the statements from which we reason
• A tool of logic; logos means reason, so logic concerns speeches involving reasoning

Reasonable Guess (vs. Wild Guess) #

• A guess with a rational or evidentiary basis
• Distinguished from mere random speculation
• Examples: meteorologist’s forecast based on weather patterns, economist’s projection based on data trends

Examples & Illustrations #

Plymouth Car Purchase #

• First Plymouth lasted 10 years; therefore, buyer reasons that another Plymouth will also be good
• Father-in-law observes this reasoning and also purchases a Plymouth
• Illustrates argument from one singular (past purchase) to another singular (future purchase)

Restaurant Selection: Joseph’s Restaurant in Boston #

• Had excellent meal on Saturday night; recommended restaurant to connoisseur friend
• Friend dined on Monday evening and had ordinary meal
• Illustrated that likeness between two singulars matters: Saturday evening may have had head chef; Monday may have had lesser kitchen staff
• Shows weakness of example argument: even with good reason for the guess, conclusion is not guaranteed

Automobile Selection: Honda vs. Chevrolet #

• Past experience: Hondas started reliably in winter; Chevrolets sometimes failed to start
• Reasoned preference: better to buy another Honda than another Chevrolet
• Illustrates strengthening of argument when similarity is greater and reasons more substantial

Shakespeare’s Henry V #

• Context: Hundred Years’ War between England and France; English preparing second invasion
• King’s argument: “It fits us then to be as provident, as fear may teach us out of late examples, left by the fatal and neglected English upon our fields”
• Reasoning: King recalls devastation from first English invasion; therefore prepares carefully for second invasion
• Contrast: Young Dauphin wasn’t present at first invasion and remains overconfident; lacks experiential basis for his argument
• Shakespeare’s phrase: “Looking before and after” - examining past similar cases to foresee future outcomes
• Term: Shakespeare uses “provident” (from Latin providentia, foresight)

MacArthur’s Incheon Landing #

• Military establishment opposed landing as too risky
• MacArthur argued: “I’m going to do exactly what Wolfe did in Quebec”
• Parallel case: Wolfe unexpectedly climbed hills to Plains of Abraham, attacking where French didn’t expect
• MacArthur’s principle: “Hit them where they ain’t” - apply strategy from past successful singular case to new situation
• Illustrates example argument in military strategy

Munich Appeasement (1938) #

• Chamberlain appeased Hitler; believed this would satisfy him and avoid war
• Churchill warned: “You’re just going to have to fight them under less favorable circumstances now”
• Modern usage: When facing other dictators, argument returns to Munich as example: appeasing dictators only makes them more voracious
• Shows how example argument is used in political rhetoric

Course Selection by Students #

• Student takes course from Professor X and receives good mark; therefore takes another course from Professor X
• If student received low mark, less likely to take another course from same professor
• Shows spontaneous use of example argument without explicit awareness
• Limitation: Different courses may be quite different in content and difficulty; strength of argument depends on likeness of courses

Professor Quality vs. Subject Matter #

• Student likes Professor X in logic course; may not like Professor X in philosophy of nature course
• Love and Friendship course may have over-enrollment while logic course does not
• Illustrates how strength of example argument depends on specific likeness between cases

Historical Analogy and Uniqueness #

• Historian argues that every historical period is unique; purpose of history is to show fallacy of historic analogies
• Historian emphasizes differences over similarities
• Shows methodological tension: historians may resist example arguments because they focus on singular particularity

Frog Example for Induction #

• This frog has three-chambered heart; this frog has three-chambered heart; this frog has three-chambered heart; therefore all frogs have three-chambered hearts
• Illustrates movement from enumeration of many singulars to universal statement

Questions Addressed #

Why distinguish reasonable guessing from wild guessing? #

• Because people in various professions are paid to make reasonable guesses (weathermen, economists)
• Reasonable guessing has some basis or reason
• Wild guessing has no basis; purely arbitrary
• Philosophy of nature should examine the reasonable guesses of early natural philosophers, not dismiss them as mere speculation

How do we know or guess statements? #

• Through reasoning: moving from other statements already known or accepted to new statements
• The new statement must follow from the earlier statements not merely sequentially, but because of them

What is the relationship between certainty and necessity? #

• In syllogism, conclusion follows necessarily from premises
• But even if conclusion follows necessarily, we may not be certain of it if premises are uncertain
• Example: Multiply number of guests by average beers per guest correctly, yet remain uncertain of result because initial numbers were guesses
• For certainty, need both true premises AND necessary inference

How do logic and calculation parallel natural reproduction? #

• Two dogs produce another dog (not a cat or elk); natural offspring resemble parents
• Two statements produce a third statement (conclusion)
• Two numbers produce a third number (result of arithmetic operation)
• Both arts follow principle that two elements produce a third of like kind

Why do guesses precede knowledge even in geometry? #

• In isosceles triangle, one typically guesses that base angles are equal before proving it rigorously
• Before finding reason why angles must be equal, one already suspects it is true
• Reasoning backward: search for explanation of something already believed

How does fear teach us? #

• Shakespeare notes that “fear may teach us”
• Fear makes us take counsel, become careful and wise
• Referenced in Adonis: small animal being chased displays wisdom; “wit waits on danger”
• Also: “Wisely and slow, they stumble that run fast” (Friar Lawrence)

Logical Structure and Pedagogy #

Why philosophy professors don’t define reasoning #

• Many philosophy professors, when asked “What is reasoning?” have no clear definition
• They know it when they see it but haven’t thought distinctly about it
• Yet this is foundational to their teaching

Why begin with example arguments? #

• Example is closest to senses; easiest to understand
• Students use example arguments spontaneously without recognizing them
• Concrete, familiar from everyday life
• Prepares mind for more abstract arguments (induction, enthymeme, syllogism)

The “road from senses into reason” #

• Singular things are known to us first (through sensation)
• Universal things are known later (through understanding)
• Arguments progress from sensible to intelligible
• Each step moves further from senses, closer to reason

References to Classical and Modern Sources #

Aristotle #

• Framework for four types of arguments
• Distinction between logos and reasoning

Euclid #

• Geometry as model of rigorous syllogistic demonstration
• Isosceles and equilateral triangles as examples

Einstein #

• Characterization of scientific guess as “freely imagined” (not reasonable guess)
• Scientific hypotheses must be tested by consequences

Arthur Eddington (Astrophysicist) #

• Head of scientific team confirming general relativity
• Quote: “If you put in numbers, you get out numbers”

Shakespeare #

• Henry V: King’s use of example argument; Dauphin’s overconfidence
• Romeo and Juliet: Friar Lawrence’s maxim “Wisely and slow, they stumble that run fast”
• Venus and Adonis: “Wit waits on danger”
• Hamlet: “This above all, to an own self be true, and it must follow as the night the day, thou canst not then be false to any man”

Winston Churchill #

• Preference for word “foresight” over “prudence”
• Reference to Munich appeasement and lesson thereof

Thomas Aquinas #

• Virtue of prudence (prudencia) with integral parts
• Providentia (foresight) as principal part of prudence
• Objection: How can prudence and providence mean same thing if one is part of other?
• Answer: Whole virtue named from principal part