Deductions Involving Complex Propositions

Some deductions involve complex propositions. A complex proposition is a proposition that is made from simpler propositions combined with connectives like "and," "or," and "if... then."

When discussing the form of such propositions, we use lowercase letters to represent the simple propositions.

In this article we will cover arguments involving conditionals (complex propositions joined by "if... then..." and disjunctions (complex propositions joined by "or").

Arguments involving conditionals

In a conditional, the proposition following the "if" is called the "antecedent" and the one following the "then" is called the consequent.

Modus Ponens

Modus Ponens (or "affirming the antecedent") is a two-premise deduction of which one premise is a conditional, the other is the antecedent of the conditional, and the conclusion is the consequent of the same conditional.

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Modus ponens should not be confused with the fallacy of affirming the consequent.

Modus Tollens

Modus Tollens (or "denying the consequent") is a two-premise deduction of which one premise is a conditional, the other is the denial of the consequent, and the conclusion is the denial of the antecedent.

Modus Tollens should not be confused with the fallacy of denying the antecedent.