Quantification Theory Flashcards
Define: quantification.
A method for describing and symbolizing noncompound statements by reference to their inner logical structure; the modern theory used in the analysis of what were traditionally called A, E, I and O propositions.
Define: affirmative singular proposition.
A proposition in which it is asserted that a particular individual has some specified attribute.
Define: individual constant.
A symbol (by convention, normally a lower case letter, a through w) used in logical notation to denote an individual.
Define: individual variable.
A symbol (by convention, normally the lower case x or y) that serves as a placeholder for an individual constant.
Define: propositional function.
In quantification theory, an expression that contains an individual variable and becomes a statement when that variable i replaced with an individual constant. A propositional function can also become a statement by the process of generalization.
Define: simple predicate.
In quantification theory, a propositional function having some true and some false substitution instances, each of which is an affirmative singular proposition.
Define: universal quantifier.
In quantification theory, a symbol, (x), used before a propositional function to assert that the predicate following the symbol is true of everything. Thus “(x) x” means “Given any x, F is true of it.”
Define: existential quantifier.
In quantification theory, a symbol, ∃, used before a propositional function to assert that the function has one or more true substitution instances. Thus “(∃)xFx” means “there exists an x such that F is true of it.”
Define: instantiation.
In quantification theory, the process of substituting an individual constant for an individual variable, thereby converting a propositional function into a proposition.
Define: generalization.
In quantification theory, the process of forming a proposition from a propositional function by placing a universal quantifier or an existential quantifier before it.
Define: nominal-form formula.
A formula in which negation signs apply to simple predicates only.
Define: universal instantiation (U.I.).
In quantification theory, a rule of inference that permits the valid inference of any substitution instance of a propositional function from the universal quantification of the propositional function.
Define: universal generalization (U.G.).
In quantification theory, a rule of inference that permits the valid inference of a generalized, or universally quantified, expression from an expression that is given as true of any arbitrarily selected individual.
Define: existential instantiation (E.I.).
In quantification theory, a rule of inference that says that e may (with some restrictions) validly infer from the existential quantification of a propositional function the truth of its substitution instance with respect to any individual constant that does not occur earlier in that context.
Define: existential generalization (E.G.).
In quantification theory, a rule of inference that says that from any true substitution instance of a propositional function we may validly infer the existential quantification of the function.
