Monthly Archives: January 2016

The Biblical Biconditional

Intermediate Logic, Why learn logic?, ,

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 →

If/Then Truth Table

Intermediate Logic,

One of the difficulties new students of symbolic logic must overcome is understanding the defining truth table for the conditional, the “if/then” logical operator. The defining truth table tells us what the truth value of the proposition is, given the truth value of its component parts. For the conditional, it looks like this:

p    q     p ⊃ q
T    T         T
T    F         F
F    T         T
F    F         T

One way to defend this is to look at real-life conditional propositions with known truth values, for which we also know the truth value of the component parts. We will take our examples from the Bible. Continue reading If/Then Truth Table →

Negations and Parentheses

Lesson 3 states the order for completing truth tables is: standard variables, negated variables, propositions in (). Yet I noticed while watching the Lesson 3 session on the DVD and in the example at the bottom of page 23, the operations are not always followed in that precise order; sometimes the parenthesis are completed prior to the negation. How important is this order? Does it matter only if there is a negation within the parenthesis, as in the example at the top of p 23? Continue reading Negations and Parentheses →

“Not both” v. “Both not”

Mr. Nance,

I am having a hard time with problem 3 in Exercise 3 of Intermediate Logic.  For the first proposition, ~(J ⋅ R), the answer key says “Joe and Rachel are not both students.” For the second proposition, ~J ⋅ ~R, the answer key says “Both Joe and Rachel are not students.” Those sound the same to me. Continue reading “Not both” v. “Both not” →