Fallacy of Propositional LogicType: Formal FallacyExposition:Propositional logic is a system which deals with the logical relations that hold between propositions taken as a whole, and those compound propositions which are constructed from simpler ones with truthfunctional connectives. For instance, consider the following proposition: Today is Sunday and it's raining. This is a compound proposition containing the simpler propositions:
Moreover, the connective "and" which joins them is truthfunctional, that is, the truthvalue of the compound proposition is a function of the truthvalues of its components. The truthvalue of a conjunction, that is, a compound proposition formed with "and", is true if both of its components are true, and false otherwise. Propositional logic studies the logical relations which hold between propositions as a result of truthfunctional combinations, for instance, the example conjunction implies "today is Sunday". There are a number of other truthfunctional connectives in English in addition to conjunction, and the ones most frequently studied in propositional logic are:
Since a validating argument form is one in which it is impossible for the premisses to be true and the conclusion false, you can use the truthfunctions to determine that forms in propositional logic are validating. For instance, the earlier example involving conjunction is an instance of the following argument form:
This form is validating because, no matter what propositions we put for p and q, if the premiss is true, then both p and q will be true, which means that the conclusion will also be true. Thus, to show that a propositional argument form is nonvalidating, all that you have to do is find an argument of that form which has true premisses and a false conclusion. Subfallacies:
Source:Robert Audi (General Editor), The Cambridge Dictionary of Philosophy, 1995. Resources:This discussion of propositional logic is by necessity brief, since I am only trying to give the minimal background required to understand the subfallacies above. For a lengthier explanation of propositional logic, see the following:
