Fallacy of Quantificational LogicType: Formal Fallacy
Quantificational logic is an extension of propositional logic which examines the logical properties of some of the internal grammatical structure of simple, non-compound propositions. Consider the proposition:
Socrates is wise.
This is a simple proposition because it does not contain any propositional parts joined by truth-functional connectives. However, in quantificational logic, it has an internal structure consisting of a name and a predicate. "Socrates", of course, is a name. In addition to names, quantificational logic has individual variables which stand in for names. So, in the example, "x is wise" is the predicate, with the variable "x" acting as a placeholder for a name; replace the variable with the name "Socrates" and we get the example proposition. For this reason, quantificational logic is sometimes called "predicate logic".
The final new grammatical element in quantificational logic, which gives it that name, is the category of quantifier. There are many quantifiers, just as there are many truth-functional connectives, but the two most frequently encountered in quantificational logic, and which you need to know about to understand quantificational fallacies, are the following:
All dogs hate some cat.
As with propositional fallacies, to show that a quantificational argument form is non-validating, it suffices to find an instance of that form with true premisses and a false conclusion, that is, a counter-example.
Robert Audi (General Editor), The Cambridge Dictionary of Philosophy (Second Edition), 1995, pp. 272-3.