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 Contrapositive 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 contrapositive of if P then Q is defined as if not-Q then not-P.
The Truth Table for a conditional proposition and the corresponding contrapositive is given by:
P Q if P then Q if not-Q then not-P
1 1 1 1
1 0 0 0
0 1 1 1
0 0 1 1
A conditional proposition and the contrapositive proposition have the same truth table.
Notice that a contrapositive proposition is true unless not-Q is true and not-P is false. Therefore, if we postulate that not-Q is true and demonstrate that not-P is true whenever not-Q is true, then the second row of the truth table will never be reality and we can say that the propositions if not-Q then not-P, and correspondingly, if P then Q are always true.
Consider the following example:
P = God cannot identify a single false teaching in Old Testament autographs
Q = Old Testament autographs were inspired by God.
not-Q = Old Testament autographs were not inspired by God.
not-P = God can identify one or more false teachings in Old Testament autographs.
The truth of not-Q can be postulated for the sake of argument. The assertion that not-P is true whenever not-Q is true is based on the fact that the 39 Old Testament books were written over a period of approximately 1000 years by at least 40 different authors. In the absence of divine inspiration, at least one author would have made at least one mistake.