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A Theory of Conditionals

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Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS,volume 15)

Abstract

A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is a truth function of those propositions. I may know the truth values of “Willie Mays played in the American League” and “Willie Mays hit four hundred” without knowing whether or not Mays, would have hit four hundred if he had played in the American League. This fact has tended to puzzle, displease, or delight philosophers, and many have felt that it is a fact that calls for some comment or explanation. It has given rise to a number of philosophical problems; I shall discuss three of these.

Keywords

  • Truth Condition
  • Modal Logic
  • Actual World
  • Conditional Statement
  • Impossible World

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I want to express appreciation to my colleague, Professor R. H. Thomason, for his collaboration in the formal development of the theory expounded in this paper, and for his helpful comments on its exposition and defense.

The preparation of this paper was supported in part by a National Science Foundation grant, GS-1567.

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Notes

  1. R. C. Stalnaker and R. H. Thomason, ‘A Semantic Analysis of Conditional Logic’, (mimeo., 1967). In this paper, the formal system, C2, is proved sound and semantically complete with respect to the interpretation sketched in the present paper. That is, it is shown that a formula is a consequence of a class of formulas if and only if it is derivable from the class in the formal system, C2.

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  2. N. Rescher, Hypothetical Reasoning, Amsterdam, 1964.

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  3. Cf. R. Chisholm, ‘The Contrary-to-fact Conditional’, Mind 55 (1946), 289–307, reprinted in Readings in Philosophical Analysis, ed. by H. Feigl and W. Sellars, New York, 1949, pp. 482–497. The problem is sometimes posed (as it is here) as the task of analyzing the subjunctive conditional into an indicative statement, but I think it is a mistake to base very much on the distinction of mood. As far as I can tell, the mood tends to indicate something about the attitude of the speaker, but in no way effects the propositional content of the statement.

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  4. F. P. Ramsey, ‘General Propositions and Causality’, in Ramsey, Foundations of Mathematics and other Logical Essays, New York, 1950, pp. 237–257. The suggestion is made on p. 248. Chisholm, op. cit., p. 489, quotes the suggestion and discusses the limitations of the ‘connection’ thesis which it brings out, but he develops it somewhat differently.

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  5. N. Rescher, op. cit., pp. 11–16, contains a very clear statement and discussion of this problem, which he calls the problem of the ambiguity of belief-contravening hypotheses. He argues that the resolution of this ambiguity depends on pragmatic consideration.

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  6. Cf, also Goodman’s problem of relevant conditions in N. Goodman, Fact, Fiction, and Forecast, Cambridge, Mass., 1955, pp. 17–24.

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  7. S. Kripke, ‘Semantical Analysis of Modal Logics, I’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9 (1963), 67–96.

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  8. The different restrictions on the relation R provide interpretations for the different modal systems. The system we build on is von Wright’s M. If we add the transitivity requirement, then the underlying modal logic of our system is Lewis’s S4, and if we add both the transitivity and symmetry requirements, then the modal logic is S5. S. Kripke, ‘Semantical Analysis of Modal Logics, I’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9 (1963), 67–96 Cf. S. Kripke, op. cit.

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  9. A.W. Burks, ‘The Logic of Causal Propositions’, Mind 60 (1951), 363–382. The causal implication connective characterized in this article has the same structure as strict implication. For an interesting philosophical defense of this modal interpretation of conditionals,

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  10. see B. Mayo, ‘Conditional Statements’, The Philosophical Review 66 (1957), 291–303.

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  11. Goodman, op. cit., pp. 15, 32.

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  12. Goodman, op. cit., pp. 15, 32.

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  13. Chisholm, op, cit., p. 492.

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  14. For a discussion of the relation of laws to counterfactuals, see E. Nagel, Structure of Science, New York, 1961, pp. 47–78. For a recent discussion of the paradoxes of confirmation by the man who discovered them,

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  15. see C. G. Hempel, ‘Recent Problems of Induction’, in R. G. Colodny (ed.), Mind and Cosmos, Pittsburgh, 1966, pp. 112–134.

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  16. Goodman, op. cit., especially Ch. IV.

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  17. Several philosophers have discussed the relation of conditional propositions to conditional probabilities. See R. C. Jeffrey, ‘If’, The Journal of Philosophy 61 (1964), 702–703;

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  18. and E. W. Adams, ‘Probability and the Logic of Conditionals’, in J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, Amsterdam, 1966, pp. 265-316. I hope to present elsewhere my method of drawing the connection between the two notions, which differs from both of these.

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  19. J. R. Tolkien, ‘On Fairy Stories’, in The Tolkien Reader, New York, 1966, p. 3.

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Stalnaker, R.C. (1968). A Theory of Conditionals. In: Harper, W.L., Stalnaker, R., Pearce, G. (eds) IFS. The University of Western Ontario Series in Philosophy of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9117-0_2

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  • DOI: https://doi.org/10.1007/978-94-009-9117-0_2

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