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Title: Indicative Conditionals: Probabilities and Relevance

Abstract: Adams’ Thesis claims that the acceptability of a simple indicative conditional equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional ‘If Ï•, then ψ’ to the extent that (i) the conditional probability p(ψ|Ï•) is high, provided that (ii) Ï• is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. We propose a formal framework giving acceptability and logical closure conditions for simple indicatives: its probabilistic component (i) uses Popper functions; its relevance component (ii) is given via an algebraic structure of topics. We then present the resulting logic. We argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals.