Pure Inductive Logic

This contribution concerns recent developments in pure inductive logic (PIL), as conceived and initially developed by Rudolf Carnap and his coworkers during the 1940s to 1970s. The basic problem of PIL is how to select an initial probability function on sentences of a given logical language so that the values it assigns to sentences, as a whole, are rational, and such that the probabilistic updating on received information yields further probability functions which are also rational in view of what the conditioning sentences are. We explain the basic notions of PIL and discuss some principles of symmetry, relevance and irrelevance as well as the principle of language invariance, and we clarify the relationship between the strongest symmetry and irrelevance principles. We illustrate the effect of various principles on the behaviour of a hypothetical virtual agent who is assumed to possess exclusively the information that is spelled out, and no other, and who aspires to be rational.