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The Logical Form of Counterfactual Conditionals

Published online by Cambridge University Press:  09 June 2010

J. A. Eisenberg
J. A. Eisenberg
Affiliation:
Ontario Institute for Studies in Education
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Extract

I shall here propose specific logical forms to express the structures of the counterfactual conditional and its cognate forms, the semifactual conditional and the undetermined conditional. Some of the proposals have been previously made in a different context by Nelson Goodman, but to my knowledge they have never been incorporated into definite, all-embracing logical schemata. Because of this failure, the astounding assertion that there is no definite logical form of the counterfactual conditional could be made.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 7 , Issue 4 , March 1969 , pp. 568 - 583
Copyright
Copyright © Canadian Philosophical Association 1969

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References

1 Cf. Fact, Fiction and Forecast, Ch. 1. Though Goodman's major concern is to discover the justification for going from the antecedent to the consequent of a counterfactual, many of his insights are relevant for the analysis of the purely logical structure of the counterfactual.

2 M. R. Ayers: “Counterfactuals and Subjunctive Conditionals”, MIND, July 1965, p. 349.

3 Ibid., p. 350.

4 Op. cit., p. 355.

5 On strictly formal grounds counterfactuals are materially equivalent to only two of the four elements, (1) the general proposition (x)(Fx ⊃ Gx) and (4) the denial of the instantiated consequent ∼ Ga. From (1), Fa ⊃ Ga can be deduced and from Fa ⊃ Ga and (4), ∼ Fa can be deduced. Element (2) has t o be included in order to indicate the specific context and individuals referred o t in the counterfactual and element (3) has been included to provide emphasis for something quite explicitly affirmed in all counterfactuals.

6 It is not my intention here to become embroiled in the disputes surrounding the various notions of implication and the paradoxes resulting from them. I have chosen the logical operator ⊃ to express implication because it is most commonly used to do so. However, it should be interpreted in a way which is general enough to cover any form of implication, so that when there may indeed be differences, as between material and strict implication, the appropriate notion can be used. By doing this I hope to simplify the proposed logical schemata and to avoid controversy which properly belongs to a prior or more basic, though distinct area of philosophical investigation, concerned with the interpretation of logical operators.

7 Fact, Fiction and Forecast, p . 25 et seq.

8 M. R. Ayers, he. cit., p. 352.

9 M. R. Ayers, loc. cit. Cf. pp. 347–348 for a brief discussion on past confusions of these categories.

10 Once again all the elements are not necessary on the basis of formal requirements alone. But one may justify the inclusion of the denial of the general proposition ∼ [(x)(Fx ⊃ ∼Gx)] in (1) in as much as it clearly indicates the general proposition rebutted by the semifactual.

11 This variation was suggested by Professor W. H. Dray.