Quantification Theory Flashcards
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.
Affirmative Singular Proposition
A proposition in which it is asserted that a particular individual has some specified attribute.
Individual Constant
A symbol (by convention, normally a lower case letter, a through w) used in logical notation to denote an individual.
Individual Variable
A symbol (by convention, normally the lower case x or y) that serves as a placeholder for an individual constant.
Propositional Function
In quantification theory, an expression that contains an individual variable and becomes a statement when that variable is replaced with an individual constant.
A propositional function can also become a statement by the process of generalization.
Simple Predicate
In quantification theory, a propositional function having some true and some false substitution instances, each of which is an affirmative singular proposition.
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) Fx” means “Given any x, F is true of it.”
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 “(∃x) Fx” means “there exists an x such that F is true of it”.
Instantiation
In quantification theory, the process of substituting an individual constant for an individual variable, thereby converting a propositional function into a proposition.
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.
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.
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.
Existential Instantiation (E.I.)
In quantification theory, a rule of inference that says that we 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.
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.
Asyllogistic argument
An argument in which one or more of the component propositions is a form more complicated than the form of the A, E, I and O propositions of the categorical syllogism and whose analysis therefore requires logical tools more powerful than those provided by Aristotelian logic.
