universal proposition

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universal proposition

A philosopher writes a universal proposition on a chalkboard.

Definition
  1. 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.
universal proposition

A philosopher writes a universal proposition on a chalkboard.

Noun
  1. (logic) a proposition that asserts something of all members of a class

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