THE RAMSEY TEST FOR BELIEF

This remark of Frank Ramsey appears only as a footnote to his paper ‘General Propositions and Causality’, but it has sufficed to lend his name to a hypothesis that has figured prominently in contemporary debate in both the semantics and pragmatics of conditionals. This interest in the Ramsey Test hypothesis, as it is usually called, is fuelled by widespread dissatisfaction with the material conditional as a rendition of the semantic content of ordinary language conditionals. Discontent is focused on two points: the fact that the material conditional interpretation appears to support fallacious reasoning and the fact that reasonable belief in conditionals appears to diverge from that demanded by the material conditional interpretation of them.

On the material conditional construal of conditionals, α → β is logically equivalent to ￢α ∨αβ. Hence, for example, ￢(α→β) implies that α. But the inference from ‘It is not the case that if it snows tomorrow then the government will fall’ to ‘It will snow tomorrow’ is clearly not valid, because denying that the weather will have an impact on the government's fortunes does not commit one to any particular meteorological prognosis. Likewise, disbelieving that the government will fall if it snows does not mean believing that it will snow (and, in summer, should not).

Nor does the material conditional do any better as an interpretation of counterfactuals – indeed, if anything, it does worse. On a material conditional interpretation, the claim expressed by the sentence ‘If George Bush had been concerned to protect the environment, then he would have lowered the tax on fuel’ should be highly credible, because of the improbability of its antecedent (this follows from the fact that this view implies that P(α → β) = P(￢α) + P(αβ)). But intuitively the claim is implausible because environmentalists typically believe that fuel taxes should be raised.