Symbolic logic has five standard logical operators, each of which has a standard translation in English:

negation is “not”
conjunction is “and”
disjunction is “or”
conditional is “if/then”
biconditional is “if and only if”

While the translations of the first four logical operators are frequent in English, the phrase “if and only if” is used very infrequently, and then only occasionally among mathematicians, philosophers, and lawyers.

For instance, while it is easy to find hundreds of nots, ands, ors, and if/thens in the Bible, the phrase “if and only if” is completely absent. However, for those who look carefully, biconditional reasoning is used several times in scripture. Keeping in mind that p if and only if q means if p then q and if q then p — and remembering other equivalences we have learned — the following verses all reflect biconditional reasoning: Continue reading The Biblical Biconditional →