universal proposition
Definition
- Noun:
- (Logic) A proposition that asserts something of all members of a class: A statement in logic that claims a specific property or relationship holds true for every single member within a defined category or set.
Usage
- This term is primarily used in formal contexts such as logic, philosophy, mathematics, and scientific discourse.
- It describes a type of logical statement that is universally quantified, often contrasted with a "particular proposition" or "existential proposition," which asserts something about only some members of a class.
Examples
- Noun:
- "All humans are mortal" is a classic example of a universal proposition.
- In the syllogism, the major premise must be a universal proposition.
- The philosopher analyzed the truth conditions of the universal proposition "Every swan is white."
Advanced Usage
- Logical Form: A universal proposition is typically expressed using quantifiers like "all," "every," "each," or "no." For example, "No planets are stars" is also a universal proposition (a universal negative).
- In Syllogistic Logic: Universal propositions (both affirmative and negative) form the basis of categorical syllogisms, a type of deductive argument.
Variants and Related Words
- Universal Affirmative: A type of universal proposition that affirms a predicate of all subjects (e.g., "All S are P").
- Universal Negative: A type of universal proposition that denies a predicate of all subjects (e.g., "No S are P").
- Particular Proposition: A proposition that asserts something about only some members of a class (e.g., "Some birds can fly").
- Categorical Proposition: A broader category of statements that affirm or deny something about a subject, which includes universal and particular types.
Synonyms
- Universal Statement
- Universal Quantification (more common in formal/mathematical logic)
- General Proposition
Related Concepts (Not Phrasal Verbs or Idioms)
- Quantifier: A logical operator (like "for all" ∀) that specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
- Deductive Reasoning: A type of reasoning where conclusions are drawn from universally accepted premises, often involving universal propositions.
Noun
-
(logic) a proposition that asserts something of all members of a class
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