by John M. Frame
[“Self-Refuting Statements, ” for IVP Dictionary of Apologetics.]
Several kinds of statements have been described as “self-refuting:”
(1) Logical contradictions, such as “Socrates is mortal and Socrates is not mortal.” If the two occurrences of mortal in this sentence are predicated of Socrates at the same time and in the same respect, then the sentence cannot be true. The first clause refutes the second, and vice versa.
(2) Some self-referential statements, that is, statements that refer to themselves, are self-refuting, such as “All statements are false.” If that statement is true, then it is false.
(3) Some statements refute themselves, not because of their explicit content, but because of the one who utters them. An example is “I am lying now.” Generally, there is no contradiction involved in saying that someone is lying. Replace the first person with the third, “He is lying now,” and the contradiction disappears. But in the first person the statement is self-refuting, because the very act of asserting something involves a claim to be telling the truth. So “I am lying now” means, in effect, “I am telling the truth, and I am also lying now,” which is a contradiction.
(4) There are other “practical” forms of self-refutation that pertain more to the speaker than to the actual words he utters. If a person says that he hates beans, but he gorges himself with large helpings of them, observers may well claim that his behavior refutes his statement. His statement itself is not self-refuting, but in an important sense the person has refuted himself. To argue against such practical self-contradictions is, of course, to argue ad hominem.
(5) Some philosophical theories are said to be self-refuting because they set up conditions of meaning, rationality, and/or truth that they themselves are unable to meet. Ludwig Wittgenstein in his Tractatus Logico-Philosophicus, for example, candidly admitted at the end that the propositions of his book did not measure up to his own criteria of meaning; so he suggested that those propositions were a kind of ladder that one throws away after he uses it to reach a higher vantage point. Later, the logical positivists insisted that a piece of language cannot meaningfully state an empirical fact (either truly or falsely) unless it is empirically verifiable by methods akin to those of natural science. But many observed that this “verification principle” itself could not be empirically verified in that way. That argument led to the demise of logical positivism as an influential philosophical movement.
(6) One philosophical view often accused of self-refutation is the general form of skepticism, which claims that there are no truths or that nothing can be known. The antiskeptic accuses the skeptic of making the error noted above under (2): trying to state truly that there are no truths or claiming to know that nothing can be known. In response, skeptics may either (a) abandon their skepticism, (b) modify it to exclude their own claim (a move that can easily be criticized as arbitrary or self-serving), or (c) modify their view to allow for a few knowable truths. Alternative (c) might involve some sort of distinction between first-order truths and second-order truths (i.e. truths about truths), limiting skepticism to truth-claims of the first order. But it is hard to imagine any reason for first-order skepticism that would not apply equally to second-order skepticism. In any case, such a distinction naturally invites further arguments.
(7) Immanuel Kant argued that the truth of mathematics and science cannot be proved by rational deduction (as Leibniz) or by sense experience alone (Hume), but rather by a “transcendental” argument that shows the conditions under which alone knowledge is possible. To deny this theory, Kant believed, is to deny the necessary conditions of knowledge while claiming to have knowledge, a self-refuting position. Similar claims, however, have been made for many epistemological theories, some very different from Kant’s.
Christian apologists have often employed the concept of self-refutation against alternatives to Christian theism. Gordon H. Clark, in A Christian View of Men and Things and other writings is one of many apologists who emphasizes the logical contradictions of non-Christian thinkers, particularly those that entail skepticism. Stuart Hackett’s The Resurrection of Theism, which develops a modification of Kant’s transcendental argument, is another example of an apologetic work in which this approach is prominent.
Francis Schaeffer frequently employed the “practical” sense of self-refutation (4). In The God Who is There (72-74) he refers to John Cage, who wrote “random” music expressing his view that pure chance governs reality. But Cage also collected mushrooms as a hobby, and he came to realize he would die if he applied his philosophy of chance to the gathering of mushrooms. In Schaeffer’s view, Cage refuted himself in that his practice was inconsistent with his theory.
Cornelius Van Til mentions often in his writings (such as Essays on Christian Education, 89) a man he saw on a train whose little daughter was slapping his face. But she could not have reached him if he had not kept her on his lap. Van Til uses this incident to illustrate his view that the non-Christian cannot even argue against Christian theism without depending on it. To argue at all, even against Christianity, presupposes that the world is meaningful, knowable, and expressible in language. In Van Til’s view, only Christian theism provides the conditions that make such rational discourse possible. Therefore, the unbeliever’s very decision to argue against God refutes his position. This type of self-refutation is akin to (3) and (4) above, because the self-refutation is found not directly in the content of the assertion, but in the decision of a speaker to state that assertion.
Gordon H. Clark, A Christian View of Men and Things (Grand Rapids: Eerdmans, 1952).
Stuart Hackett, The Resurrection of Theism (Chicago: Moody Press, 1957).
William Hasker, “Self-Referential Incoherence,” in Robert Audi, ed., The Cambridge Dictionary of Philosophy (Cambridge: Cambridge University Press, 1995), 721.
Francis Schaeffer, The God Who Is There (Chicago: Inter-Varsity Press, 1968).
Cornelius Van Til, Essays on Christian Education (No date: Presbyterian and Reformed, 1974).
Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London: Routledge and Kegan Paul, 1921, 1963).