(related to Lemma: Affirming the Consequent of an Implication)
We want to prove that the affirming the consequent of an implication is a fallacy. * The fallacy can be formulated in propositional logic as $(p\Rightarrow q)\wedge q\Rightarrow q.$ * The definition of implication "$\Rightarrow$" gives us the following truth table of the function:
$[[p]]_I$ | $[[q]]_I$ | $[[p\Rightarrow q]]_I$ | $[[p]]_I$ |
---|---|---|---|
$0$ | $0$ | $1$ | $0$ |
$0$ | $1$ | $1$ | $0$ |
$1$ | $0$ | $0$ | $1$ |
$1$ | $1$ | $1$ | $1$ |