Further Consequences for Justified Inference

Abstract

The models 𝔐 ^u _act , 𝔐 ^p _act , and 𝔐 ⁿ _act that we have referred to in section 7.1 of part II as models that satisfy universal conditionals, high probability conditionals, and normic conditionals, respectively, can now be characterized more clearly: 𝔐 ^u _act is a universal model 𝔐^u for the set W _act of propositional variable settings associated with the actual domain D _act of our cognitive agent’s sandbox area relative to the intended interpretation ℑ _act ; 𝔐 ^p _act may be presupposed to be one of the probabilistic models defined in section 9.2 for the actual probability measure Prob _act on ℘(W _act ); particularly, the infinitesimal _II semantics seems to match our pre-theoretical intuitions concerning the vague notion of “high” probability, while the noninfinitesimal semantics highlights the practical dimension of the high probability. 𝔐 ⁿ _act may be assumed to be one of the normality models defined in section 9.3 for the actual normality order ≺ _act of (states labelled by sets of) the worlds of W _act ; the preferential and the ranked model semantics are perhaps the most adequate ones.