Limits of Logic

Since reasoning is a part of life, and part of our total responsibility before God, it is never something “neutral.” As a part of human life, reasoning is something that we can do in a godly or an ungodly way, obediently or disobediently, competently or incompetently. Such sciences as logic, mathematics, and epistemology may usefully be classified as “ethical” sciences; for they seek to help us determine what we ought (ethical “ought”) to believer, granted certain data or certain other beliefs. But we must also say that not only the conclusions but also the premises, the presuppositions, the starting points of these sciences are subject to ethical – ultimately religious – evaluation.

The idea that human reason, or at least the “laws of logic,” are a neutral, even infallible basis for human decision-making is an idea that dies hard. Here, it would be wise to remind ourselves briefly of various specific limits on the ultimacy, the powers and the reliability of reason in general and logic in particular.

a) The law of non-contradiction is only “necessary” to those who acknowledge a practical (“ethical”) necessity to think logically.

b) Logic presupposes that those using it are able to agree on the nature of and criteria for truth and falsity; but these concepts are controversial, and religiously so. The agreement to say that “p may not be both true and false in the same respect and at the same time” is a formal (and thus in an important sense meaningless) agreement unless there is agreement on the meaning of “true” and “false.”

c) The disciplines of mathematics and logic, far from consisting of truisms, are riddled with controversy.

d) No one has succeeded in justifying induction from within the discipline of logic; yet all non-deductive reasoning presupposes it.

e) We do not know all the “laws of logic;” in fact, our systems fail to account for many everyday forms of inference, such as the examples under II, A,1,(a).

f) The discovery of one fact apparently contrary to one’s belief, or even an apparent contradiction within that belief, does not serve to refute it. When faced with such a challenge, one may simply treat it as a “problem” to be worked out within one’s alreadyexisting system of thought. One cannot specify in precise terms how much unresolved discrepancy will, or ought to, cause someone to reject a belief; the point at which “refutation” occurs will depend greatly on practical, personal – even religious – factors. And generally such discrepancy will produce modifications in one’s position rather than abandonment of it.

g) Logical rigor by itself does not guarantee truth; one also needs true premises. And our knowledge of the truth of premises is always conditioned by our fallibility.

h) The principle of non-contradiction states that “A is A and not non-A at the same time and in the same respect;” thus it is limited in its application to aspects of reality which are unchanging.

i) Logical syllogisms generally require some restatement of an argument, some translation from ordinary language into the technical language of logic. There are acknowledged discrepancies which enter here: the logical “if-then” (material implication), for example, is generally not equivalent to the use of “if-then” in ordinary language. Thus an otherwise adequate argument may fail by inadequately translating the ordinary language which it purports to test. Thus it is evident that we do not find in human reason alone, even in logic, an infallible criterion of truth that might compete with Scripture as our ultimate covenant rule. Scripture, indeed, must be seen to rule over our reasoning as over every other aspect of life.

(John Frame, Rationality in the Calvinian Tradition, “Rationality and Scripture,” pp. 305-306. Note the whole article is worth the read – D2.)

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