🧠 What Is a Definition?
A definition assigns meaning to a term — using words, examples, or context.
Two Kinds of Meaning
| Type | Description | Example |
|---|
| Extension (Denotation) | The set of things a term applies to | “Dog” → all dogs |
| Intension (Connotation) | The traits or characteristics required for something to fall under the term | “Dog” → furry, mammal, domestic animal |
🔹 Rule: As intension increases, extension decreases.
⚖️ Ordering by Intension
As specificity grows, fewer things qualify.
Examples (in order of increasing intension):
- Horse < Mammal < Animal < Living thing
- Figure < 4‑sided figure < Rectangle
- Car < Vehicle < Motorized vehicle < Inexpensive car
- Sport < Team sport < Baseball < Hardball
🧾 Types of Definitions
🔹 Extensional (Denotative)
- Define by pointing to or listing instances.
| Type | Description | Example |
|---|
| Ostensive | Point directly | “That is a cat.” |
| Quasi‑Ostensive | Pointing + words | “A car is that thing over there.” |
| By Example | List examples | “Cars are Fords, Toyotas, Hondas.” |
| By Subclass | Name subtypes | “A house is a ranch, colonial, bungalow.” |
🔹 Intensional (Connotative)
Define by giving essential characteristics.
| Type | Description | Example |
|---|
| Etymological | Based on word origin | “Ambulance” from ambulo (Latin: “walk”). |
| Synonymous | Replace with known term | “Oculist” = “Eye doctor.” |
| Operational | Specifies measurable criteria | “Intelligence is your IQ test score.” |
| Genus & Difference | Places term in class (genus) + distinguishing feature (difference) | “A triangle is a 3‑sided polygon.” |
🧪 Practice Classifications
| Definition | Type | Likely Use |
|---|
| “Derivative of y = xⁿ is nxⁿ⁻¹.” | Operational / Mathematical | Theoretical |
| “Matrix = collection of numbers in rows and columns.” | Genus & Difference | Stipulative / Precising |
| “Computer is a Dell, Mac, or IBM.” | Extensional by Example | Lexical |
| “‘Principle’ from Latin ‘principium,’ meaning fundamental.” | Etymological | Lexical |
| “In Britain, a ‘chemist’ = U.S. ‘pharmacist.’” | Synonymous | Lexical |
🧭 Uses of Definitions
| Type | Purpose | Example |
|---|
| Stipulative | Introduce a new meaning or term | “10ⁿ =df 10 × 10 × … × 10 (n times)” |
| Precising | Make vague term clearer | “DUI =df BAC ≥ 0.08.” |
| Lexical | Record ordinary usage & clarify ambiguity | Dictionary definitions — “Organ = 1) tissue group, 2) instrument.” |
| Theoretical | Embedded in theory, allows prediction | “PV = nRT” ⇒ predicts pressure given T, etc. |
| Persuasive | Loaded wording to influence attitudes | “A senator is a greedy official who takes perks.” |
🧩 More Definition‑Use Practice
| Definition | Int/Ext | Type | Use |
|---|
| “A car is a motorized vehicle for transportation.” | Intensional | Genus & Difference | Lexical |
| “Kinetic energy = ½ mv².” | Intensional | Theoretical / Operational | Theoretical |
| “‘Wristovision’ = television worn as a watch.” | Intensional | Stipulative | Stipulative |
| “An SUV is a gas‑guzzling, unsafe vehicle.” | Intensional | Persuasive | Persuasive |
| “Website = region of cyberspace w/ info.” | Intensional | Genus & Difference | Theoretical or Lexical |
| “‘Solitude’ from Latin ‘solus’ (alone).” | Intensional | Etymological | Lexical |
| “Hypothesis = educated guess / bold conjecture.” | Intensional | Synonymous | Lexical |
| “Morality = forcing your opinion on others.” | Intensional | Persuasive | Persuasive |
📏 Evaluating Genus & Difference (G&D) Definitions
| Rule | Description | Example / Problem |
|---|
| R1 — Essential Attributes | Include necessary traits | “Car = 4‑door vehicle” ❌ (too specific) |
| R2 — Not Circular | Don’t define with the same term | “Sound = emission of sound waves.” ❌ |
| R3 — Not Too Broad/Narrow | Fit exactly the extension | “Car = 4‑door vehicle.” ❌ excludes coupes |
| R4 — Not Figurative/Vague | Avoid metaphorical language | “Poetry = music of the soul.” ❌ |
| R5 — Not Negative | Define positively | “Light = absence of darkness.” ❌ |
🧰 Improving Poor G&D Definitions
| Weak Definition | Problem | Improved Version |
|---|
| “Teacher = one who instructs children.” | Too narrow (adults excluded) | “Person who gives instruction to others.” |
| “Knowledge = true opinion.” | Too narrow/misleading | “Justified true belief.” |
| “Belief = attitude towards something.” | Vague | “Mental state of accepting a proposition as true.” |
| “Work of art = idea expressed in paint/sculpture.” | Too narrow | “Creative expression intended to evoke aesthetic response.” |
| “Music = poetry of the mind.” | Figurative | “Structured combination of sounds arranged rhythmically and harmonically.” |
| “Faith = illogical belief in the unbelievable.” | Persuasive/emotive | “Trust or confidence in propositions without empirical proof.” |
| “Life = art of drawing conclusions.” | Figurative, vague | “Condition distinguishing living from nonliving organisms.” |
✏️ Quick Reference: Types & Tests
| Dimension | Category | Key Idea / Example |
|---|
| By Form | Extensional / Intensional | “Ford, Toyota” vs. “Motorized vehicle” |
| By Origin | Etymological, Synonymous | “Ambulance,” “Eye‑doctor” |
| By Application | Operational, G&D | “IQ test,” “Triangle = 3‑sided polygon” |
| By Purpose | Stipulative, Precising, Lexical, Theoretical, Persuasive | Introduce, Clarify, Record, Predict, Influence |
💡 Key Takeaways
- Intension determines extension.
- Every term has degrees of specificity → more traits = fewer referents.
- Good definitions are clear, precise, non‑circular, appropriately scoped, and neutral.
- Definitions differ by form (ext/int) and purpose (stipulative → persuasive).
- Apply evaluative rules to ensure clarity and logical rigor in definitions.