Indicative conditionals: probabilities and relevance

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative 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$$\varphi \rightarrow \psi$$φ→ψto the extent that (i) the conditional probability$$\mathrm{p}(\psi |\varphi )$$p(ψ|φ)is high, provided that (ii)$$\varphi$$φis relevant for$$\psi$$ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals.