Conditional Probabilities and Symmetric Grounding

Abstract

I present new counterexamples to the asymmetry of grounding: we have prima facie reason to think that some conditional probabilities partially ground their inverse conditional probabilities, and vice versa. These new counterexamples may require that we reject the asymmetry of grounding, or alternatively may require that we reject one or more of the assumptions (regarding, e.g., the correct interpretation of probability) which enable the counterexamples. Either way, by reflecting on these purported counterexamples to grounding asymmetry we learn something important, either about the formal properties of grounding, or about the nature of probability (or both).