Mr. Nance,
Question 6 of Intermediate Logic Quiz 2 asks to symbolize this proposition: “The knight attacks the dragon only if the dragon devours the damsel.” The answer key says K ⊃ D (“If K then D”). I would have thought the answer was D ⊃ K (“If D then K”). Am I wrong? Continue reading Translating “only if”
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
Hi Mr. Nance!
I had a student ask me a question about the biconditional in Lesson 5 of Intermediate Logic the other day that had not occurred to me. She asked for written explanation of why if both sides of the biconditional were false then the truth table was true. Conceptually I understood it because of the definition of equivalency and from working through the truth tables, but verbally, I could not give her an example. Could you give a verbal example of each possibility of true and false like you did for the conditional, disjunction, and conjunction? I told her just to memorize the truth values, but honestly it would make more sense if I could give her an example that would explain why. Thanks! Continue reading The Biconditional Truth Table