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Published online by Cambridge University Press: 14 March 2022
Deduction has frequently been condemned as a useless intellectual instrument because of its tautological character. To thoroughgoing opponents of rationalism, the pretensions of deduction are on the same level with those of induction. Both presume to yield more knowledge from the fact that we have some knowledge; and this is an impossible paradox, which not even so powerful an opponent of the “Philosophy of Experience” as Bradley could resolve to his own satisfaction. I wish in this brief note to indicate how this semblance of paradox may very easily be removed without having to deny, as has often been thought necessary, the tautologicality of deduction.
1 E.g., for three modern examples of this condemnation, cf. L. Wittgenstein, Tractatus Logico-Philosophicus, 6.1 ff.; D. W. Prall, “Implication,” University of California Publications in Philosophy, 1931, pp. 127 ff.; and F. C. S. Schiller, “Is Socrates Mortal?,” Mind, 1935, pp. 204ff.
2 Poincaré, Foundations of Science, p. 155; N. Campbell, Physics: The Elements, p. 161.
3 Principles of Logic, second edition, vol. II, p. 599.
4 E.g., M. R. Cohen, “The Subject Matter of Formal Logic,” Journal of Philosophy, 1918, p. 681.
5 W. E. Johnson, Logic, Part II, Chapter I.
6 Thus, the classical syllogism in Barbara, “All men are mortal; Socrates is a man; therefore Socrates is mortal,” has an appearance of non-tautologicality because the collective term ‘all’ obscures the presence of the proposition ‘Socrates is mortal’ in the major premiss. Similarly, when it is inferred that something is colored because it is red, the use of two different terms, ‘colored’ and ‘red,‘ hides the tautologicality of the inference.
7 Symbolically expressed, if a proposition s can be deduced from propositions p, q and r, s may be novel with respect to either p, or q, or r, or pq, or pr, or qr; but it cannot be novel with respect to pqr. In general, where n is the number of premisses, there seems to be 2n – 2 ways in which the conclusion of a deduction may be novel with respect to its premisses.
8 “Take the classical example: A priest says: ‘My first penitent was a murderer, and a baron soon thereafter entering the room says, ‘I was the reverend father's first penitent.’ The dramatic conclusion is surely not contained in either premiss” (M. R. Cohen, Reason and Nature, p. 194).
9 Cf. C. S. Peirce, Collected Papers, vol. II, p. 387.