25. Definition: Nature, Kinds, and Distinctions

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Lecture Notes

Main Topics #

The Nature of Definition #

Three Formulations:

• Primary: Speech signifying what a thing is (or signifying it distinctly)
• Secondary: Speech making known what a thing is
• Tertiary: Speech bringing out what a thing is (emphasizing active discovery and drawing forth what is hidden)

The third formulation connects to Heraclitus’s maxim that “nature loves to hide.” Since nature (φύσις/natura) means what is within and therefore hidden, definition is the act of bringing out what is concealed within a thing.

Definition versus Name:

• A name is a single vocal sound signifying by custom, with no parts that signify by themselves
• A speech (λόγος) has parts that signify by themselves; composed of multiple names
• Example: “Square” (name) versus “equilateral and right-angled quadrilateral” (speech/definition). Both signify what the thing is, but the speech signifies more distinctly because it can “blow up” or expand the meaning through its constituent parts.

Definition of a Thing versus Definition of a Name:

• Definition of a thing: Makes known the nature of reality; the primary philosophical concern
• Definition of a name: Makes clear the meaning of a word; secondary but often necessary
• The definition of a name may precede the definition of a thing because:
  • We must understand what a word means before asking if the thing exists
  • Definitions are composed of names, so we may need to clarify component terms
  • We can define names even for non-existent things (unicorn, mermaid, centaur)
• In Aristotle’s four questions (from Posterior Analytics), the order proceeds: Does it exist? → What is it? → Is this that? → Why is this that?

First Distinction: Definition in the Full Sense versus Encircling (περιγραφή) #

Definition in the Full Sense (Definitio proprie dicta):

• Uses genus and specific differences (species-making differences)
• Expresses the essential nature of a thing
• Penetrates inwardly to what the thing is
• Example: “A square is an equilateral and right-angled quadrilateral”

Encircling (Περιγραφή):

• Uses genus and a property or collection of common attributes
• Provides confused, outward knowledge rather than distinct, inward knowledge
• More sensible and accessible to our natural mode of knowing
• Examples:
  • “Wisdom is the best knowledge” (best is a property/effect, not essence)
  • “A dog is a four-footed animal that barks” (barking is an effect, not essential)

Why We Know Confusedly Before Distinctly:

• Our knowledge begins with the senses, which provide outward, sensible knowledge
• We naturally tend to encircle things before penetrating to their essence
• We should respect this natural progression in teaching and learning, not attempt to begin with perfect definitions
• Example of defining a dog: “It’s an animal” → “It’s a four-footed animal” → “It’s a four-footed animal that barks” (as far as the mind can penetrate)
• The same occurs with learning virtue: as a child, we know praise and blame (outward effects) before understanding inward goodness or badness

Second Distinction: Definition by Cause versus Definition by Effect #

Definition by Cause:

• Defines a thing through what makes it to be what it is
• More perfect and complete
• Reflects true understanding of the thing’s nature

Definition by Effect:

• Defines a thing through its results or manifestations
• More commonly known to us because knowledge begins with sensation
• We naturally perceive effects before understanding causes
• Examples from the lecture:
  • “Good is what all desire” (desire is an effect of goodness)
  • “Comedy is a likeness of the laughable” (laughter is an effect)

The Socratic Question:

• Applied in Plato’s Euthyphro: “Is the pious pious because the gods approve of it, or do the gods approve of it because it is pious?”
• The question reveals whether we are defining by cause or by effect
• Applied more broadly: “Is something good because we desire it, or do we desire it because it is good?”
• This distinction is fundamental to ethics and metaphysics

The Composition of Definition #

Parts of a Complete Definition:

• Genus: The more general category
• Specific Difference (species-making difference): What distinguishes this species within the genus

Alternative Components:

• Property: Something that follows upon the nature; an effect or result of the essential nature
• Collection of common attributes: May substitute for difference when full definition is not yet available

Superficiality in Definition:

• In geometry and arithmetic, things are superficial (on the surface)
• Example: Defining a triangle as “a rectilineal figure with the least sides” is stupid because having three sides is a result, not an essence
• In ethics and metaphysics, vices and virtues are deep within us (like the roots of a tree), not on the surface
• The word “stubborn” comes from stub (tree root), reflecting what is deep and resistant

Euclid’s Definitions and the Role of Existence #

• Some of Euclid’s definitions (Elements, Book I) may initially be definitions of names rather than things
• The existence of the equilateral triangle is not presupposed in Proposition 1 but established through construction
• Only after construction does the definition become a definition of a thing
• This shows that logic cannot be separated from geometry; understanding definitions requires understanding the role of existence

Key Arguments #

Why Definition is Not Merely Linguistic #

1. Modern philosophers (following certain strands of thought) mistakenly treat definition as primarily concerned with the meaning of names
2. Berquist cites Heisenberg’s reference to Plato’s dialogues as seemingly focused on “the meaning of names,” claiming this idea “got into the modern mind somewhere”
3. This makes definition “something relatively secondary” when actually it is our chief philosophical interest
4. Definition of a thing is often a major accomplishment requiring extensive intellectual work and long thought
5. Even when someone has achieved a good definition, it takes the rest of us a long time to understand it

Examples of profound definitions:

• Descartes quoted the definition of motion “in a garbled fashion”
• Understanding the definition of reason (“ability for discourse looking before and after”) took time to penetrate
• The definition of eternity required Thomas Aquinas to think out each word carefully
• The definition of person is similarly profound

Why Effects Are More Known Than Causes #

1. The natural road of knowledge proceeds from sensation to reason
2. We perceive effects directly through our senses before we understand causes
3. When we ask “why?” we already know the effect but seek the cause
4. Therefore, we naturally define by effect before defining by cause
5. This is the “before and after” according to us (quoad nos) versus according to nature (quoad se)

The Four Questions and the Order of Knowing #

1. From Aristotle’s Posterior Analytics II: Does it exist? What is it? Is this that? Why is this that?
2. We cannot ask “what is it?” without some name or meaning already in mind
3. Therefore, definition of a name (understanding what the word means) may precede even asking whether the thing exists
4. But we cannot have a true definition of a thing unless the thing exists in some way
5. Example: We can define “unicorn” as a name, but without unicorns existing, there is no definition of a thing

Important Definitions #

Definition (ὁρισμός/definitio): Speech signifying what a thing is, or speech bringing out what is hidden within a thing

Name (ὄνομα/nomen): Vocal sound signifying by custom, having no parts that signify by themselves

Speech (λόγος/sermo): Vocal sound having parts that signify by themselves; composed of multiple names

Genus: The more universal category within which species are contained

Difference or Species-Making Difference: What distinguishes one species from another within the same genus

Property (ἴδιον/proprium): Something that follows upon the nature of a thing; an effect or result of the essential nature rather than the essence itself

Encircling (περιγραφή/circumlocutio): A less rigorous definition using genus and a property rather than genus and difference; provides confused, outward knowledge

Discourse (διάλεξις/discursus): Coming to know what you don’t know through what you do know

Examples & Illustrations #

Definition in the Full Sense versus Encircling #

Square:

• Name: “Square”
• Encircling: “A four-sided figure” or “A figure with equal sides”
• Full definition: “An equilateral and right-angled quadrilateral”

Wisdom:

• Encircling: “The best knowledge”
• Analysis: “Best” is a property indicating excellence, not the essence of wisdom
• Full definition would require deeper penetration into the nature of wisdom

Dog:

• Encircling: “A four-footed animal that barks”
• Problem: Barking is an effect of dog-nature, not its essence
• We know the dog barks (outward, sensible knowledge) but not why it barks

Definition by Cause versus Definition by Effect #

The Pious (from Plato’s Euthyphro):

• Definition by effect: “What the gods approve of” or “What pleases the gods”
• Socratic question: Is it pious because it pleases the gods, or does it please the gods because it is pious?
• Definition by cause would reveal what makes something pious in itself

Good:

• Definition by effect: “What all desire”
• Ethical question: Do we desire something because it is good, or is it good because we desire it?
• This distinction is fundamental to ethics

Perfect Numbers #

Definition: “A number equal to the sum of everything that measures it (where ‘measures’ means divides evenly)”

Examples:

• Six: measured by 1, 2, and 3; sum = 1 + 2 + 3 = 6 ✓
• Twenty-eight: measured by 1, 2, 4, 7, and 14; sum = 1 + 2 + 4 + 7 + 14 = 28 ✓
• Four: measured by 1 and 2; sum = 1 + 2 = 3 ≠ 4 ✗

Theological significance:

• Augustine and Thomas Aquinas see meaning in the number six (first perfect number) in Genesis’s account of creation in six days
• The things that measure six (1, 2, 3) are “perfect in order: one, two, three”
• Connection to Plato’s Symposium: six speakers arranged from lesser to greater (three rhetoricians, two poets, one philosopher)

Blank Verse #

Problem: Students don’t know what blank verse is

Definition by encircling: “Unrhymed iambic metameter”

Definition of “iambic”: “Two syllables with the accent on the second”

Process: Making known through progressive definition when component terms are unknown

Notable Quotes #

“Nature loves to hide.” — Heraclitus (cited as expressing a central truth)

“It’s laughable” to make the meaning of names the main thing in philosophy (referring to a modern tendency)

“The definition of a thing is what we’re chiefly interested in. And the definition of a thing is very often a major accomplishment.”

“We should try to say some things better than our predecessors, and other things as well as they said them. And sometimes a thinker says something so well that you don’t try to improve upon it.” — Aristotle (cited on method)

“Is it pious because the gods approve of it, or do the gods approve of it because it is pious?” — Socratic question (from Euthyphro)

“Speech making known what a thing is” (defining definition as an active process of bringing knowledge)

Questions Addressed #

What is the relationship between definition of a thing and definition of a name? #

Answer:

• Definition of a name may be necessary as a preliminary step
• We must understand what a word means before asking if the thing exists
• But the primary goal is always definition of the thing itself
• A definition of a name does not require that the thing exist
• Once we know the thing exists, we seek to define the thing itself more perfectly

How does the order of knowing differ from the order of being? #

Answer:

• “Before and after according to us” (quoad nos): We know confusedly before distinctly, outwardly before inwardly
• “Before and after according to nature” (quoad se): The essential nature is prior to properties and effects
• Our pedagogical progression from encircling to full definition reflects this order

Can a definition apply to a non-existent thing? #

Answer:

• Yes, we can have a definition of a name for non-existent things (unicorn, mermaid)
• But we cannot have a true definition of a thing unless the thing exists
• This is why existence is a question that precedes the question “what is it?”

How do we know when we have a good definition? #

Answer:

• Through extended intellectual work and thought (as exemplified by Aristotle’s thinking on motion)
• Through understanding each part distinctly (genus and difference)
• Through seeing that the definition is convertible with what it defines
• This is shown in Thomas Aquinas’s method: objections to each part, then explanation, then application

Why does Euclid begin with constructions rather than existence proofs? #

Answer:

• Some of Euclid’s initial definitions (like equilateral triangle) are definitions of names
• The existence of the thing must be established before the definition becomes a definition of a thing
• This shows that in geometry, as in other sciences, existence and definition must be properly ordered
• Understanding Euclid requires some knowledge of logic