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On Arguing about Entailment

Published online by Cambridge University Press:  09 June 2010

John Woods
John Woods
Affiliation:
University of Toronto
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Extract

In 1919, G. E. Moore introduced into technical philosophy the term “entailment.” He used it to name the converse of the relation which holds between two propositions when the one follows from or is deducible from the other. Moore believed this latter to be exemplified by the relation in which the conclusion of an argument in Barbara stands to the conjunction of its premises and by the relation in which x is coloured stands to x is red.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 3 , Issue 4 , March 1965 , pp. 405 - 421
Copyright
Copyright © Canadian Philosophical Association 1965

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References

1 Philosophical Studies, London, 1922, pp. 276–309Google Scholar.

2 See Lewis, and Langford, C. H., Symbolic Logic, New York, 1932Google Scholar, for what to Lewis remained the “definitive” account of strict implication.

3 Thus Lewis took his own “strict implication” and Moore's “entailment” to name the very same relation. Let us call this the identification-thesis.

4 Of course this is just one of four “paradoxes” of strict implication. It is a matter of indifference, for the points I argue in this paper, which of the “paradoxes” are taken as examples.

5 See, for example, Nelson, E. J., “On Three Logical Principles in Intension,” Monist, 1933, p. 271Google Scholar.

6 I might here add that I shall use the phrase “the paradox” neutrally, to refer to the proposition that an impossible proposition entails any proposition whatever, without implying that it is or is not genuinely paradoxical to say this.

7 “Necessary Propositions and Entailment-Statements”, Mind, 1948, pp. 184–200.

8 “Entailment”, Symposium, Aristotelian Society, Supplementary Volume, 1958.

9 Idem.

10 Logical Studies, London, 1957, pp. 166–191Google Scholar.

11 Logically unsatisfiable not in the sense that the proof is valid, and hence cannot be invalidated; but unsatisfiable in any sense that does not countenance or involve the validity of the proof.

12 Op. cit., p. 270.

13 See Goodman, N., Fact, Fiction and Forecast, Harvard, 1955, p. 67Google Scholar; White, Morton, Toward Reunion in Philosophy, Harvard, 1956, Part IVGoogle Scholar, and Quine, W. V. O., From a Logical Point of View, Harvard, 1953, pp. 17–19Google Scholar.

14 The nontransitivity of entailment is actually proposed by Geach, op. cit., and by Smiley, T. J., Aristotelian Society, Proceedings, 1958–1959, pp. 233–254Google Scholar.

15 The more general thesis, of course, is as follows. If with respect to a relation R, and relations R* and R**, which two differ in respect of properties P1, P2, …, Pn, then no proof that R = R* or that R = R** can be valid if it presupposes the truth (or falsity) of any statement, (R (R*, R**) has Pj). But absolute undecidability obtains only when there is no proof of R = R* or R = R** which does not invoke at least one of these statements. Even if this situation obtains, all that follows is that the identity question is undecidable. This does not necessarily mean that a great deal of common agreement about the nature of R could not be achieved, and achieved by deductive means. Of course the area of disagreement about R would shrink proportionately to any increase in the set of disputed properties, P1, P2, …, Pn. The absolute undecidability of any dispute about R obtains only when there is no deductive proof which does not invoke the truth (or falsity) of some disputed proposition about R. Needless to say, the undecidability-thesis, in this sense, is hardly likely to be maintained.

16 I have no wish to hang this part of the paper on what may be an untenable theory of concepts. To preclude this possibility the reader is invited to read my “inconsistent concept” in terms of incompatible rules for the correct use of a word or phrase; if this is to legislate a technical sense for “concept”, so be it.