How Reliable Is Logic? -- By: John V. Dahms
JETS 21:4 (December 1978) p. 369
How Reliable Is Logic?
The basic laws or principles of logic are commonly said to be three in number: the law of identity, the law of contradiction and the law of excluded middle. They may be set forth in the following form: “If anything is A it is A; nothing can be both A and not A; anything must be either A or not A.”1 Though it may be that the other principles of logic—the principle of the syllogism, the principles of tautology, simplification, absorption, and so forth—cannot be derived from them2 these three are at least the foremost of the laws of thought.3 Moreover, though the other two apparently cannot be derived from it4 writers often mention the law of contradiction when they have logic generally in mind.5
What is of interest to us is the fact that orthodox thinkers commonly believe that logic is of unlimited applicability. Though sometimes this faith is tacit, often it is explicit. For example, E. J. Carnell insists on “a rigid application of the law of contradiction” and says that “God does not break the law of contradiction.”6 Likewise, Francis Schaeffer says, “Historic Christianity stands on a basis of antithesis.” By antithesis he means, as he says, “If you have A it is not not-A)”7 Both of these writers leave the impression that no exception to or modification of these statements is permissible. And N. Geisler argues that “the rationally inescapable is real.”8
*John Dahms is professor of New Testament at Canadian Theological College, Regina, Saskatchewan.
JETS 21:4 (December 1978) p. 370
This absolute and unconditional commitment to the law of contradiction is quite surprising in view of the evidence that there are limitations to its applicability.
1. There is the problem posed by irrational numbers. According to E. Cell. “Russell and Whitehead… [have] shown that irrational numbers (N-l) were, derived from rational numbers (-1), which in turn were similarly built out of real numbers (1), and these were still further constructions out of simple ‘logical’ statements.”9 If Cell is correct, irrational numbers pose an insurmountable problem for those who believe that the logically necessary is always real.
2. There is t...
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