Fallacy of Propositional Logic

Type: Formal Fallacy

Exposition:

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 truth-functional connectives. For instance, consider the following proposition:

Today is Sunday and it's raining.

This is a compound proposition containing the simpler propositions:

  • Today is Sunday.
  • It's raining.

Moreover, the connective "and" which joins them is truth-functional, that is, the truth-value of the compound proposition is a function of the truth-values of its components. The truth-value 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 truth-functional combinations, for instance, the example conjunction implies "today is Sunday". There are a number of other truth-functional 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 truth-functions to determine that forms in propositional logic are validating. For instance, the earlier example involving conjunction is an instance of the following argument form:

Simplification
p and q.
Therefore, p.

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 non-validating, 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:


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