Probabilities of Conditionals and Conditional Probabilities
Lewis (David)
Source: The Philosophical Review, Vol. 85, No. 3 (Jul., 1976), pp. 297-315
Paper - Abstract

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Author’s Introduction

1. The truthful speaker wants not to assert falsehoods, wherefore he is willing to assert only what he takes to be very probably true. He deems it permissible to assert that A only if P(A) is sufficiently close to 1, where P is the probability function that represents his system of degrees of belief at the time. Assertability goes by subjective probability. At least, it does in most cases. But Ernest Adams has pointed out an apparent exception. In the case of ordinary indicative conditionals, it seems that assertability goes instead by the conditional subjective probability of the consequent, given the antecedent.
2. […]
3. Alas, this most pleasing explanation cannot be right. We shall see that there is no way to interpret a conditional connective so that, with sufficient generality, the probabilities of conditionals will equal the appropriate conditional probabilities. If there were, probabilities of conditionals could serve as links to establish relationships between the probabilities of non-conditionals, but the relationships thus established turn out to be incorrect. The quest for a probability conditional is futile, and we must admit that assertability does not go by absolute probability in the case of indicative conditionals.

Philosophers Index Abstract
1. Ernest Adams has noted that the assertability of indicative conditionals is measured by the conditional subjective probability of the consequent relative to the antecedent.
2. I refute the suggestion that there is a way to interpret the conditional so that this conditional probability always equals the probability of the conditional itself.
3. I discuss the question of why the assertability of a conditional is not measured by its probability.

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