Lowe on Conditional Probability

The concept of conditional probability has been employed for hundreds of years. Thomas Bayes used the expression "the probability that [B] on the supposition that [A]" in the statement of a basic law (1763, p. 378). Frank Ramsey, developing the application of probability to uncertain epistemic attitudes, the "logic of partial belief (1926, p. 166), wrote of your "degree of belief in [B] given [A]": there are degrees of belief (degrees of closeness to certainty); and there are degrees of belief-under-a-supposition. Ramsey suggested that the latter illuminate conditional judgements—judgements expressed using "if: we add the antecedent hypothetically to our stock of beliefs, and assess the consequent on that basis (1929, p. 247). The idea is attractive. Will I recover if I have the operation? Trying to answer questions like that can leave you more or less uncertain. "On the supposition that", "given", and " i f are prima facie interchangeable. Especially since Ernest Adams's work (1965), many (I think most) philosophers who have a working knowledge of probability theory, a sympathy for its application to uncertain epistemic attitudes, and an interest in the theory of conditionals, have recognized a promising connection here. According to E. J. Lowe (1996) they are rather obviously mistaken: on its "standard definition" conditional probability throws no light on conditionals (pp. 604-6); the same is true on Lowe's preferred definition of conditional probability (pp. 608—9), for it presupposes an understanding of a conditional judgement (p. 609); and anyway, conditional probability is an incorrect measure of the degree to which a conditional judgement is acceptable (pp. 611-4).