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:
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—Robert Southey (1774–1843)