Patrick Maher Probabilities for Multiple Properties: the Models of Hesse and Carnap and Kemeny

In 1959 Carnap published a probability model that was meant to allow for reasoning by analogy involving two independent properties. Maher (2000) derived a generalized version of this model axiomatically and defended the model’s adequacy. It is thus natural to now consider how the model might be extended to the case of more than two properties. A simple extension was published by Hesse (1964); this paper argues that it is inadequate. A more sophisticated one was developed jointly by Carnap and Kemeny in the early 1950s but never published; this paper gives the first published description of Carnap and Kemeny’s model and argues that it too is inadequate. Since no other way of extending the two-property model is currently known, the conclusion of this paper is that a satisfactory extension to multiple properties requires some new approach.