Inferring, Updating, and a Plausible Principle of Hypothetical Reasoning

SPEAKER

Peter Milne

ABSTRACT

Certain common patterns of reasoning, if taken to instantiate valid inference forms, would when taken in combination with widely accepted inference forms pretty much compel us to treat indicative conditionals as material conditionals. Under the probabilistic semantics for conditionals advocated by Ernest Adams and Dorothy Edgington, these common patterns of reasoning are invalid. They can be explained as the result of updating: coming to believe a minor premise with certainty. From there, we turn to a very general principle of hypothetical reasoning that is sound under the Adams-Edgington semantics and sound under a naïve reading of the most general possible-world semantics for conditionals, the Routley-Meyer ternary relation semantics. A common understanding of negation together with the principle yields the negative paradox of material implication: ¬P |- P -> Q. The probability semantics rejects the common understanding of negation (although it is compatible with a formulation of probability for intuitionist logic). Relevantists are forced to a sophisticated reading of the Routley-Meyer semantics (and rejection of the principle), drawing a distinction between possible and impossible worlds; we briefly look at two ways of doing this.