Classical logic represents the Truth of God and Sound Reason is the foundation of the Christian faith. Reason comprises a sequence of logical steps based, in this case, on Scripture, personal experience and the great traditions of the church.
Some basic principles of logic can be found in the “Logical Preliminaries” portion of Christian Handbook of Reason and Insight for Scientists and Technologists. In this Section, we examine the Contradiction Method for proving that a conditional proposition is, in fact, true. A conditional proposition is represented by if P then Q, where the thesis P and the thesis Q are each of the form (α is β). Also, true can be represented by 1 and false can be represented by 0.
The Truth Table for a conditional proposition is given by:
P Q if P then Q P and not-Q
1 1 1 0
1 0 0 1
0 1 1 0
0 0 1 0
Notice a conditional proposition is true unless P is true and Q is false. Therefore, if we postulate that P is true and demonstrate that Q is true whenever P is true, then the second row of the truth table will never be reality and we can say that if P then Q is always a true statement. But notice that a fourth column has been added to the truth table. If it can be shown that P and not-Q can never be true, then if P then Q can never be false.
We begin by postulating that P and not-Q is true and showing that such an assumption leads to a contradiction.
Consider the following example:
P = God cannot identify a single false teaching in Old Testament autographs
Q = Old Testament autographs were inspired by God.
P and not-Q = God cannot identify a single false teaching in Old Testament autographs and Old Testament autographs were not inspired by God.
In other words, even though the Old Testament autographs were not inspired by God and were written over a period of 1000 years by at least 40 different authors, God views them as infallible and inerrant. Such a conclusion is contrary to all of human history.