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:
Genesis 43:4-5, “If you will send our brother along with us, we will go down… But if you will not send him, we will not go down.”
2 Kings 7:4, “If they spare us, we live; if they kill us, then we die.”
John 6:53-54, “Unless you eat the flesh of the Son of Man and drink his blood, you have no life in you. Whoever eats my flesh and drinks my blood has eternal life.”
The first example could be translated as “We will go down if and only if you send our brother with us.” The second, “We will live if and only if they spare us.” The third, “You have eternal life if and only if you eat Christ’s flesh and drink His blood.”
Can you find any other biblical examples of statements that could be translated with the “if and only if”?