The Interpretation of Probability in the Tractatus Logico-Philosophicus

Abstract

In this paper, I propose an assessment of the interpretation of the mathematical notion of probability that Wittgenstein presents in TLP (1963: 5.15 – 5.156). I start by presenting his definition of probability as a relation between propositions. I claim that this definition qualifies as a logical interpretation of probability, of the kind defended in the same years by J. M. Keynes. However, Wittgenstein’s interpretation seems prima facie to be safe from two standard objections moved to logical probability, i. e. the mystic nature of the postulated relation and the reliance on Laplace’s principle of indifference. I then proceed to evaluate Wittgenstein’s idea against three criteria for the adequacy of an interpretation of probability: admissibility, ascertainability, and applicability. If the interpretation is admissible on Kolmogorov’s classical axiomatisation, the problem of ascertainability brings up a difficult dilemma. Finally, I test the interpretation in the application to three main contexts of use of probabilities. While the application to frequencies rests ungrounded, the application to induction requires some elaboration, and the application to rational belief depends on ascertainability.