28. Division, Distinction, and the Rule of Two or Three

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Lecture Notes

Main Topics #

Division vs. Distinction #

Division (strict sense): The distinction of the parts of some whole. Requires an actual whole and its parts.

Distinction (broader sense): Opposition or separation between things. Does not necessarily require a whole.

Key relationship: Every division is a distinction, but not every distinction is a division.

Examples of distinctions that are NOT divisions:

• Distinguishing different senses of a word (like the word “before”)
• Distinguishing the simple from what is in some respect
• Distinguishing substantial from accidental

Two Kinds of Wholes #

Integral or Composed Whole (original meaning of “whole”)

• Put together from its parts
• NOT said of its parts individually
• Example: A chair is composed of seat, legs, back—but “chair” is not said of the seat or leg
• Definition itself is a composed whole: genus + differences = definition (the genus is not the definition, nor is the difference, but together they form the definition)

Universal Whole

• Said of its parts
• NOT composed of its parts
• Example: “Animal” is said of man, dog, cat, horse—but animal is not composed of these
• If you understand one definition, the other is simply the reverse

The Rule of Two or Three #

Historical Precedents

• Plato/Socrates: Always divided into two (in the Sophist and other dialogues)
  • Rationale: “We should divide by opposites, but opposites are two”
  • Examples: odd/even, prime/composite, vertebrate/invertebrate, male/female
• Aristotle: Criticized Plato for always dividing into two, yet himself recognized valid reasons for binary division
• Hegel (1770-1831): Always divided into three (thesis, antithesis, synthesis)
  • Three is the first number about which we say “all” (with two we say “both”)
  • Connection to beginning, middle, and end
  • Possible reflection of the Trinity in reasoning
• Karl Marx: Influenced by Hegel’s ternary method in his youth, later suspected it was artificial and forced

Berquist’s Synthesis

• Do not always divide into two, do not always divide into three
• But divide into two or three for the most part
• This combined rule has more probability than either Platonic or Hegelian approach alone
• Divisions into more than three typically result from one of two things:
  • Crisscrossing two separate divisions
  • Subdividing one part of a division into two or three

Why the mind prefers two or three

• The mind has difficulty understanding divisions beyond three without treating them as mere enumeration
• Divisions into more than three often obscure the rational structure when analyzed

Key Arguments #

Why Division Must Be Exhaustive #

• The word “divide” comes from dividere (to empty out)
• A proper division should leave nothing remaining
• Example of incomplete division: If you divide triangles into equilateral and isosceles, you’ve left out scalene

The Principle of Higher Knowledge #

• Universal principle: It belongs to the higher and wiser knowledge to distinguish itself from lower knowledge and to establish order between them
• Examples:
  • Reason (not sensation) distinguishes reason from sensation
  • Natural philosophy (not mathematics) determines how mathematics applies to nature and its limitations
  • Theology (not philosophy) distinguishes theology from philosophy
  • Speaking properly (not metaphorically) defines what a metaphor is—for metaphor cannot define itself
  • Knowledge in words (not mathematical symbols) can define what an equation is; mathematics cannot define itself

Application to Modern Philosophy #

• Modern philosophers abandoned revealed theology
• Without theology, they lack the knowledge to distinguish philosophy from theology
• Result: They confuse philosophy and theology, seeking in philosophy what belongs to theology
• They demand certitude that exceeds human capacity—demanding theological certainty from philosophy
• This explains chronic complaints about the senses being an imperfect means of knowing

Important Definitions #

Division (divisio): The distinction of the parts of some whole; requires both a whole and its parts

Distinction (distinctio): Opposition or separation; more universal than division; does not require a whole

Integral or Composed Whole (totum integrale/compositum): A whole put together from parts but not said of those parts

Universal Whole (totum universale): A whole said of its parts but not composed of those parts

Examples & Illustrations #

Grammar #

• Sentence divides into parts of speech (noun, verb, adjective, adverb)—this is a composed whole
• Sentence divides into affirmative/declarative, interrogative, imperative, and prayer—this is a universal whole
• Both divisions are valid for the same subject

Geometry #

• Circle divides into two semicircles—composed whole
• Parallelogram divides into square, oblong, rhombus, rhomboid—universal whole
• Euclid uses both kinds of division

Chemistry #

• Atom divides into proton, electron, neutron—composed whole (the proton is not an atom)
• Atoms divide into hydrogen, nitrogen, oxygen (periodic table)—universal whole

Government #

• Greeks divided government into three: monarchy, oligarchy, democracy (rule by one, few, or many)—seems more natural as a ternary division
• Aristotle’s six forms of government results from crisscrossing two divisions:
  • Division into good and bad (criterion: good of whole vs. good of rulers)
  • Division into rule by one, few, or many
  • Result: monarchy, tyranny, aristocracy, oligarchy, democracy, tyranny

Sacraments: Thomas Aquinas’s Seven #

Thomas uses five divisions to arrive at seven sacraments, showing the rational structure:

1. Those ordered to individual good vs. those ordered to directing others (matrimony/orders)
2. Matrimony vs. orders
3. Baptism, confirmation, Eucharist vs. penance and extreme unction
4. First three according to bodily life analogy (generation, growth, nourishment)
5. Last two according to defects (sickness, death)

Each division uses either two or three parts. Only by understanding the divisions can one understand the seven sacraments in their relations and distinctions.

Shakespeare’s Plays #

Berquist notes working for years on dividing Shakespeare’s 27 plays (setting aside 10 history plays) into four kinds—demonstrating that while he advocates the rule of two or three, he is “not a fanatic” and recognizes exceptions when the material demands it.

Notable Quotes #

“Division is a distinction of the parts of some whole.”

“Every division is a distinction, but not every distinction is a division.”

“The basis of distinction is opposition, and opposites are two. Therefore, you should divide into two.”

“Three is the first number about which we say ‘all’—with two we just say ‘both’.”

“If you divide into more than three, you are probably either crisscrossing two divisions or subdividing one part.”

“It always belongs to the higher knowledge, the knowledge that has more the character of wisdom, to distinguish between itself and the lower knowledge.”

“The modern philosophers have given up revealed theology, and therefore they can’t distinguish between theology and philosophy—because they can’t distinguish between them, they start to mix them up.”

“When you distinguish the senses of a word, like we did with the word ‘before’… is that really a division? Or should it be called a distinction, but not a division?”

Questions Addressed #

Q: What is the difference between division and distinction? A: Division (strict sense) requires an actual whole and distinguishes its parts; distinction (broader sense) is any opposition or separation and does not require a whole. Every division is a distinction, but not every distinction is a division.

Q: What are the two kinds of wholes? A: The composed/integral whole is put together from parts but not said of those parts (like a chair made from seat, legs, back). The universal whole is said of its parts but not composed of them (like animal said of man, dog, cat).

Q: Why should divisions be into two or three? A: Two reflects the nature of opposition (opposites are two); three is the first number about which we say “all.” Most natural divisions in the sciences follow one of these patterns.

Q: Does every division always use two or three parts? A: Not always—Berquist examines exceptions like Aristotle’s quality (four) and his own analysis of Shakespeare (four). However, analysis shows these either involve crisscrossing divisions or subdivision within a binary or ternary framework.

Q: To whom does it belong to distinguish between rhetoric and political philosophy? A: Political philosophy, because it has more the character of wisdom. The rhetorician, even if skilled, cannot make this distinction because lower knowledge cannot define itself against higher knowledge.

Q: Why can’t mathematics define an equation, while words can define mathematical symbols? A: Because knowledge in mathematical symbols cannot know itself—it lacks the universality and reflexivity of verbal knowledge. Therefore, the knowledge in words and statements has more the character of wisdom.