Implicational Converse
If S is a statement of the form P implies Q (P → Q), then the converse of S is the statement Q implies P (Q → P). In general, the verity of S says nothing about the verity of its converse, unless the antecedent P and the consequent Q are logically equivalent.
For example, consider the true statement "If I am a human, then I am mortal." The converse of that statement is "If I am mortal, then I am a human," which is not necessarily true.
On the other hand, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition. Thus, the statement "If I am a bachelor, then I am an unmarried man" is logically equivalent to "If I am an unmarried man, then I am a bachelor."
A truth table makes it clear that S and the converse of S are not logically equivalent unless both terms imply each other:
| P | Q | P → Q | Q → P (converse) |
|---|---|---|---|
| T | T | T | T |
| T | F | F | T |
| F | T | T | F |
| F | F | T | T |
Going from a statement to its converse is the fallacy of affirming the consequent S and its converse are equivalent (i.e. if P is true if and only if Q is also true), then affirming the consequent will be valid.
Read more about this topic: Converse (logic)
Famous quotes containing the word converse:
“The Anglo-American can indeed cut down, and grub up all this waving forest, and make a stump speech, and vote for Buchanan on its ruins, but he cannot converse with the spirit of the tree he fells, he cannot read the poetry and mythology which retire as he advances. He ignorantly erases mythological tablets in order to print his handbills and town-meeting warrants on them.”
—Henry David Thoreau (1817–1862)