Summary of Logic: Language, Meaning, and Definitions
Logic: Language, Meaning, and Definitions Explained for Students
Introduction
Understanding "meaning" in language is essential for clear communication, academic analysis, and constructing precise definitions. This module explores different kinds of meanings, rules for good lexical definitions, common defects (vagueness and ambiguity), special definition types, and practical ways to evaluate and create definitions.
Definition: The study of meaning examines how words stand for concepts (intension) and for the sets of things they apply to (extension).
1. Intension and Extension
Intension (Connotative meaning)
- The intension of a term consists of the attributes, properties, or qualities the term connotes.
- Example: The intension of "triangle" includes "three-sided" and "plane figure."
Definition: Intension = the set of attributes or properties a term implies.
Extension (Denotative meaning)
- The extension of a term is the set of all objects or members the term denotes.
- Example: The extension of "triangle" is the class of all triangles drawn, imagined, or observed.
Definition: Extension = the set of actual things a term applies to.
| Concept | Focus | Example |
|---|---|---|
| Intension | Attributes | "Four-legged, mammal" for "dog" |
| Extension | Members | All individual dogs on Earth |
2. Rules for Good Lexical Definitions
Lexical definitions are the everyday definitions we consult in dictionaries. Good lexical definitions follow these rules:
- Conform to proper grammar — A definition must be a well-formed sentence.
- Convey the essential meaning — Capture the core concept without adding irrelevant features.
- Be neither too broad nor too narrow — Include all appropriate cases and exclude inappropriate ones.
- Avoid circularity — Don’t define a word using the word itself or its direct root.
- Prefer affirmative forms — Use positive statements when possible rather than negative descriptions.
- Avoid figurative, obscure, vague, or ambiguous language — Be literal and clear.
- Avoid affective terminology — Don’t rely on value-laden or emotionally charged words.
- Indicate relevant context — Specify the domain or context if the definiens is context-dependent.
Definition: Lexical definition = the standard dictionary-style meaning of a word used in ordinary language.
Example: Applying the rules
- Poor: "Rich = not poor." (Rule 5 and 3 violated; negative and too narrow.)
- Better: "Rich = having substantial financial resources beyond basic needs." (Affirmative, more informative.)
3. Defects of Meanings: Vagueness and Ambiguity
Vagueness
- A vague expression allows borderline cases where it is unclear whether the term applies.
- Examples: "rich," "fresh," "normal," "conservative."
- Practical problem: Hard to make precise decisions or build logical arguments when terms have borderline cases.
Definition: Vagueness = the presence of unclear borderline cases where membership is indeterminate.
Ambiguity
- An ambiguous expression can be interpreted in two or more clearly distinct ways in the same context.
- Examples: "light" (not heavy vs. low intensity), "bank" (financial institution vs. river bank), "race" (competition vs. ethnic group).
Definition: Ambiguity = more than one distinct and plausible meaning for a single expression in a given context.
Practical tip: When you encounter ambiguity, provide context or rephrase the sentence to a single intended meaning.
4. Stipulative, Persuasive, and Other Special Definitions
Stipulative Definitions
- A stipulative definition assigns a meaning to a word for the first time or gives a new meaning to an existing word.
- Uses: coining terms, abbreviations, technical jargon, or secret codes.
- Note: A stipulative definition cannot be true or false in the same way as a descriptive
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Meaning of Terms
Klíčové pojmy: Meaning splits into intension and extension, Intension = set of attributes a term connotes, Extension = set of members the term denotes, Follow 8 rules for lexical definitions, Avoid circular and negative definitions when possible, Vagueness allows borderline undecidable cases, Ambiguity permits multiple distinct meanings, Stipulative definitions assign new meanings, Persuasive definitions use value-laden wording to influence, Always indicate context in definitions, Test definitions with examples and borderline cases, A term must function as a subject to be definable