A Two-Dimensional Continuum of a Priori Probability Distributions on Constituents

Hintikka has defined a one-dimensional continuum of a priori probability distributions on constituents and has built on it a two-dimensional continuum of inductive methods with the aid of Carnap’s λ-continuum ([1]), which plays also a fundamental role in his continuum of a priori distributions, and the formula of Bayes ([2]). Here a two-dimensional continuum of a priori probability distributions will be introduced. On its base a three-dimensional continuum of inductive methods can be constructed in the same way as Hintikka has done. The importance of the new continuum of a priori distributions, which is also based on Carnap’s λ-continuum but in a completely different way, is that it leaves room for almost all kinds of a priori considerations, whereas Hintikka’s continuum admits only considerations that lead to increasing probability for the constituents by increasing size.