29. Division, Whole and Part, and the Four Senses of Causality

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Lecture Notes

Main Topics #

Division as a Method for Finding Beginnings #

• Division (divisio) is the process of distinguishing the parts of a whole to arrive at its principles and causes
• Different methods of division correspond to different philosophical schools and reveal different fundamental principles
• Division is essential to understanding how thinkers arrive at their answers about what is fundamental

Four Senses of Whole and Part #

1. Quantitative Whole and Part (τὸ συνθετόν)

• Parts that meet at a common boundary (continuous quantity)
• Examples: dividing a line, circle, or body into organs
• Most familiar sense; the parts can be physically separated and counted
• Quantity by its nature has parts

2. Universal Whole and Part (τὸ καθόλου)

• The universal is a set of its particulars, not composed from them
• Universals are not “put together” from particulars
• Parts here are called “particulars” (from Latin pars)
• Example: “animal” is the universal whole; dogs and cats are particulars
• Aristotle in Physics makes an analogy: general relates to particular as whole to part
• The general (from Greek kathalou = “according to the whole”) precedes knowledge of the particular

3. Definitional Whole and Part

• Definition composed of genus and differences
• Example: “square” = “equilateral and right-angled quadrilateral”
• Genus and differences are parts composing the definition
• This is a composed whole but not in the quantitative sense

4. Matter-Form Whole and Part

• Most hidden and difficult sense to understand
• Matter and form are intrinsic principles of being
• Example: body and soul in a human being
• Not apparent to the senses; they are “in things” (in reality), not merely in the mind
• The distinction between composed wholes (quantitative, definitional) versus those “in the mind” versus those “in reality”
• Matter and form are like “order” in the word—essential but not obvious as a “part” in the ordinary sense

The Problem of Understanding Matter-Form Division #

• When we think of our parts, we ordinarily think of quantitative parts (head, arms, legs)
• But body and soul are parts of us in a quite different sense—more like the order of letters in a word
• If you cut up a word “cat” into letters c-a-t, what happened to the order? It seems to disappear
• Yet the order is not a quantitative part; it is intrinsic to the word’s being
• Analogy to materialism: A doctor who dissects a body and finds no soul is “looking for the wrong kind of part”
• The matter-form distinction is the most important for knowing what a thing truly is, yet it remains hidden

The Method of Dividing and Its Implications #

Two ways of dividing universals:

1. Division by genus into species (downward)

   • Dividing a genus into less universal species
   • Each step produces something less universal
   • Example: dividing “quadrilateral” → “equilateral quadrilateral” → “square”
   • Eventually arrives at the least universal (the indivisible species)

2. Division by definition into more universal principles (upward)

   • Starting with a definition and dividing its parts into their definitions
   • Example: “square” (equilateral, right-angled, quadrilateral) → “quadrilateral” (rectilineal plane figure contained by four sides) → “plane figure” (figure contained by straight lines)
   • Each step produces something more universal
   • Eventually arrives at the most universal

Two different results from two methods:

• One method proceeds to the least universal (species, individuals)
• The other method proceeds to the most universal (being, highest genera)
• These represent fundamentally different answers to what the beginning of things is

Three Possible Answers to “What is the Beginning of Things?” #

1. Materialist answer (Empedocles, Democritus)

• Beginning is material parts: earth, air, fire, water (Empedocles) or atoms (Democritus)
• Divide things quantitatively into material constituents
• Discovery through dissection and reduction to elements

2. Platonic answer

• Beginning is the most universal (forms, being)
• Proceed upward through division of definitions
• All thinkers pursuing universals and definitions follow this path conceptually

3. Aristotelian answer

• Beginning is matter and form (and act and potency)
• The matter-form distinction reveals what is most fundamental in changing things
• This answer is not immediately apparent; it requires intellectual understanding

The Hidden Nature of Matter-Form in Understanding #

• In Aristotle’s Physics, the beginning of natural philosophy (physica) involves understanding that we know confusedly before distinctly
• Examples: sensible whole (a salad) before distinguishing its parts; a name (“square”) before its definition
• But the matter-form distinction remains hidden from first appearance
• It is the most important distinction for understanding what changes, yet it does not appear obviously
• People miss this distinction because they think of parts primarily in the quantitative sense

Key Arguments #

The Intelligibility of Matter and Form as Parts #

• The analogy of the word: The word “cat” seems to have parts c-a-t, but what about the order?

  • Cutting the word yields the letters but seems to leave the order behind
  • Yet without the order, the letters spell “act” instead of “cat”
  • Therefore the order must be a part, though not a quantitative part
  • This is “like materialism”—if you cannot physically find the soul when dissecting, it does not mean it is not real

• The role of intrinsic principles: Matter and form are intrinsic to a thing’s being

  • They are not external causes (like a maker)
  • They compose the thing from within
  • Yet they are not apparent to ordinary perception

Why People Miss the Matter-Form Distinction #

• We naturally think of parts as quantitative divisions
• Body and soul are both parts of a human being, but not in the obvious quantitative sense
• This distinction is essential to knowing a thing truly, but it remains concealed from common understanding
• The mind must be trained to recognize this different sense of “part”

Important Definitions #

Διαίρεσις (divisio) – The process of distinguishing the parts of a whole to discover its principles (ἀρχαί)

Σύνθετον (compositum) – A composed whole; that which is put together from parts. The word literally means “put together” (from σύν + θέσις)

Κόλον (totum) – A whole; that which has parts. Can be understood in four distinct ways corresponding to the four senses of whole and part

Μέρος (pars) – A part; a constituent element. The meaning varies depending on the type of whole

Ὕλη (materia) – Matter; that from which something comes to be; the principle of potentiality and receptivity

Μορφή (forma) – Form; the principle that actualizes matter and determines what a thing is; the principle of actuality

Κατα-ὁλου (catholicam / universale) – General or universal; literally “according to the whole”

Κατα-ἰδιας (particulare) – Particular; the singular instances included in a universal

Examples & Illustrations #

The Word “Cat” #

• Quantitative analysis: c-a-t (three letters)
• The order problem: The word also requires the order of letters as a part
• Cut the word apart: You find the letters c, a, t but the order seems to vanish
• Contrast with “act”: Same letters but different order; clearly the order must be a real part
• But what kind of part? Not a quantitative part (you cannot separate it physically); rather a formal part
• The lesson: Just as you cannot find the soul when dissecting a body, you cannot find the order when separating letters, yet both are real

Berquist’s Typewriter #

• Intrinsic causes (the letters):

  • Limited in kind: only 26 letters in the English alphabet
  • Unlimited in number: Berquist can type infinite A’s, B’s, C’s on successive pages
  • These are the material constituents

• Extrinsic causes (Berquist and the typewriter):

  • Limited in number: one man, one typewriter
  • These are the maker and the instrument

• Application to the universe:

  • Intrinsic causes (matter/elements) may be limited in kind but not in number
  • Extrinsic causes (the unmoved mover) may be limited in number
  • This shows how different kinds of causality yield different answers about limitation

Knowing a Thing Before Defining It #

• Children: Call something a “square” before they can define it
• Name vs. definition: “Square” is less distinct than “equilateral and right-angled quadrilateral”
• The analogy: We know the general (confused) before the particular (distinct)
• Therefore: The knowledge of the general precedes ability to know the particular distinctly

Dividing Definitions Upward #

• Square: equilateral, right-angled, quadrilateral
• Divide quadrilateral: rectilineal plane figure contained by four sides (more universal)
• Divide further: plane figure contained by straight lines (even more universal)
• Pattern: Each division produces something more universal, approaching the most general

Notable Quotes #

“By its very nature, quantity has parts.” — Berquist, on Thomas’s observation about the nature of quantity

“In some way, the word cat is put together not only from those letters, but also from that order.” — Berquist, on the matter-form analogy

“You’re looking for the wrong kind of part there if you’re looking for it in that way.” — Berquist, on the materialist error regarding the soul and the order in the word

“Dust thou art, and to dust thou shalt return.” — Scripture (cited by Berquist), illustrating Anaximander’s principle that what you are made of is what you return to

“It doesn’t seem to be there… It’s like the materialist, you know, doctor saying, I cut off these bodies in the lab and never saw a soul there, right?” — Berquist, on the invisibility of form and the inadequacy of material dissection

Questions Addressed #

How should we understand “part” in different contexts? #

• Parts in the quantitative sense are distinct and separable
• Parts in the universal sense are predicates said of the whole
• Parts in the definitional sense are genus and differences
• Parts in the matter-form sense are intrinsic principles, not sensibly separable
• Resolution: The word “part” is equivocal; we must distinguish these senses to avoid confusion

Why do different philosophers give different answers about the beginning of things? #

• Because they use different methods of division
• The materialist divides quantitatively and finds material elements
• The Platonist divides definitions upward and finds universals
• The Aristotelian recognizes both but emphasizes the matter-form distinction as most fundamental
• Resolution: Understanding the method of division clarifies why thinkers reach different conclusions

What makes the matter-form distinction both real and hidden? #

• Matter and form are intrinsic to all changing things
• They are real parts of being, not merely abstract concepts
• Yet they are not apparent to ordinary perception (unlike quantitative parts)
• They require intellectual understanding to grasp
• Resolution: They are hidden by nature, not by defect of reality, and require philosophical training to understand