A Note On An Impossibility Theorem of Gardenfors
Krister Segerberg · Noûs · 1989
Suppose that it makes sense to talk about theory addition: If a proposition A is added to a theory T the result is again a theory, T + A. While some philosophers may query the usefulness of a notion as abstract as that, logicians have already begun to ask what logical properties it might have; see [Alchourron, Girdenfors and Makinson 1985] and the references mentioned there. One noteworthy result in this area is an impossibility theorem due to Girdenfors [1986]. Assuming his underlying logic to be at least as strong as classical propositional logic, Girdenfors in effect proves that the following three conditions cannot be satisfied by any concept of theory addition: the Postulate of Addition Monotonicity,