Lecture 34

34. The Principle of Three Across All Knowledge

Summary
Berquist explores the principle that ’three is enough’ and often ‘all that is needed’ across multiple domains of human knowledge and experience. Beginning with Aristotle’s observation about three dimensions and the structure of change, he demonstrates how three emerges as a fundamental organizing principle in logic, rhetoric, grammar, poetry, music, natural science, and daily life. The lecture argues that this principle reflects something deep about the structure of reality and represents an optimal balance between necessity and sufficiency.

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Lecture Notes

Main Topics #

The Universal Principle of Three #

  • Three appears across all arts, sciences, and domains of human knowledge
  • Two is often insufficient; four is unnecessary
  • The principle is not arbitrary but reflects something fundamental about reality
  • This is distinct from but related to Aristotle’s observation about three dimensions

Linguistic Evidence #

  • In common speech, “both” applies to two, but “all” first applies to three or more
  • Language itself carries signs of this principle
  • Example: “We’re both going” vs. “We’re all going”

The Principle of Fewness Applied #

  • Fewer principles are better if they are sufficient to explain phenomena
  • Two was insufficient; three proves adequate and necessary
  • No need to posit more than three without necessity

Key Arguments #

Geometric Argument #

  • You can draw at most three lines, each at right angles to the others
  • A fourth line cannot be perpendicular to all three
  • This is why there are only three dimensions in space
  • Aristotle uses this as evidence that three is the natural limit

From Daily Experience #

  • Meals: Three meals per day seem necessary; two feels incomplete
  • Complete meal (repas complet): three components needed—appetizer, main course, dessert
  • Main course structure: meat/fish, starch, vegetable—without the third, something feels missing
  • Bread as solution: When cooking only two items, bread as a third completes the plate

Important Definitions #

No specific formal definitions are introduced in this lecture, though the concept of sufficiency (having enough to explain phenomena completely) is central throughout.

Examples & Illustrations #

Logic and Grammar #

  • Three operations of mind: Understanding what a thing is (simple apprehension), understanding true or false (judgment), reasoning
  • Syllogism: Two premises but three terms
  • Definition: Requires at least three parts (a grammarian explained this)
  • Parts of speech: Noun (substance), adjective (presupposes noun), adverb (presupposes adjective)—these three suffice to express thoughts; no fourth is needed

Rhetoric #

  • Three means of persuasion: Ethos (speaker’s character/image), pathos (audience emotion), logos (argument/reasoning)
  • Three species of rhetoric: Political/deliberative, judicial/courtroom, ceremonial
  • Three kinds of examples: Historical example, proportional example, fable
  • Othello example: Iago persuades Othello through all three means—establishing credible ethos as trusted friend, arousing jealousy (pathos), and presenting flimsy arguments (logos) that seem convincing when emotions are inflamed

Poetry and Drama #

  • Plot structure: Beginning, middle, end (Aristotle’s Poetics)
  • Sophocles’ achievement: Introduction of the third actor perfected drama; greatest plays came when this occurred
  • Shakespeare’s sonnets: Three quatrains plus concluding couplet
    • Sonnet on old age: Three images of old age (late fall/winter, twilight, dying fire) arranged in proper order of diminishing duration
  • Trilogies: Common in fiction; works often naturally fall into three parts
  • Paradise Lost: Twelve books naturally divide into three parts (books 1-4: action approaches; 5-8: interruption with angel’s warning and cosmic history; 9-12: action resumes with temptation and fall)
  • Tom Jones: Eighteen books divide into three geographical sections (countryside, inns/roads to London, London)
  • No Exit: Sartre’s play with three characters on stage creates interesting conflict; three people seem necessary for drama

Music #

  • Baroque trio sonatas: Two treble instruments plus continual bass—three lines sufficient for displaying musical craft (counterpoint, independent motion, harmonies, virtuosity)
  • Corelli and Handel: Established trio sonata as complete and perfect form
  • Mozart piano concertos: Always three movements (unlike symphonies which typically have four)
    • First movement: orchestral prelude followed by solo exposition
    • Second movement: typically andante
    • Third movement: generally rondo
  • Concerto form: Double exposition, development, recapitulation—naturally divides into three parts (more natural than four-part textbook division)
  • Mozart’s 23rd Piano Concerto in A Major:
    • First movement: joyful but with underlying sadness and hints of what’s to come
    • Second movement: F-sharp minor (rarely used key), sadness emerges fully
    • Third movement: bright melodies (like sunlight into dark room), confidence to overcome the sadness
    • Creates a dramatic arc of beginning (joyful anticipation), middle (sadness), end (triumph)

Natural Science #

  • Three dimensions: Only three perpendicular lines possible (geometric proof)
  • Three kinds of motion (Aristotle): Change of place (physics), change of quality (chemistry), growth (biology)
  • Heisenberg’s universal constants:
    • First: velocity of light (relativity theory)
    • Second: Planck’s constant of action (quantum theory)
    • Third: hypothetical universal length (~10^-13 cm, smaller than atomic radius)
    • For dimensional consistency, need three fundamental units minimum
  • CGS system: Centimeter, gram, second—three units sufficient for complete system of measurement

Cultural Evidence #

  • Speech course teaching: Professor advised never give more than three examples; audience cannot retain more than three
  • Shakespeare’s use: In tragedy (Macbeth), “Out, out, brief candle!” followed by three images of life (walking shadow, poor player on stage, tale told by idiot), then stops—three images suffice
  • Tavern signs: Historically named “Three Angels,” “Three Crowns,” etc.—reflects ancient cultural understanding

Notable Quotes #

“Three is enough, and sometimes three is all.”

“Never give more than three examples, because the audience can’t take in more than three.” (Professor cited in speech course)

“This is obvious. For purely dimensional reasons.” (Heisenberg, on necessity of three fundamental units)

“One needs at least three fundamental units for a complete set of units.” (Heisenberg, Physics and Philosophy)

Questions Addressed #

Why is three so common across all domains? #

  • The principle reflects something fundamental about the structure of reality
  • It represents the optimal balance between necessity (more than two needed) and sufficiency (more than three not needed)
  • This is neither arbitrary convention nor mere coincidence

How does this relate to Aristotle’s discussion of dimensions? #

  • Three dimensions are all that can exist geometrically (three perpendicular lines maximum)
  • Aristotle noted this through geometric demonstration
  • Language also witnesses to this (“all” first applies at three)

Why does Mozart’s 23rd Piano Concerto work with three movements? #

  • Three movements allow for dramatic structure (beginning, middle, end)
  • Each movement can explore a development of theme/emotion that creates an arc
  • First movement: anticipation; second: realization of sadness; third: resolution
  • This creates a complete action, which requires three parts