Reliability via synthetic a priori: Reichenbach's doctoral thesis on probability

Hans Reichenbach is well known for his limiting frequency view of probability, with his most thorough account given in The Theory of Probability in 1935/49. Perhaps less known are Reichenbach's early views on probability and its epistemology. In his doctoral thesis from 1915, Reichenbach espouses a Kantian view of probability, where the convergence limit of an empirical frequency distribution is guaranteed to exist thanks to the synthetic a priori principle of lawful distribution. Reichenbach claims to have given a purely objective account of probability, while integrating the concept into a more general philosophical and epistemological framework. A brief synopsis of Reichenbach's thesis and a critical analysis of the problematic steps of his argument will show that the roots of many of his most influential insights on probability and causality can be found in this early work. 3 1. Historical Background Hans Reichenbach wrote his thesis Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit (The Concept of Probability in the Mathematical Representation of Reality) largely independently in 1914. It was accepted in March 1915 by Paul Hensel and Max Noether at the University of Erlangen. Unlike his later views, the thesis was deeply influenced by the Kantian view dominant in philosophy and epistemology at the time. Reichenbach took synthetic a priori principles to form the foundation of empirical knowledge, and transcendental arguments to be the appropriate method to support such principles. Reichenbach had studied with Ernst Cassirer, and had hoped (unsuccessfully) to write his dissertation with the neo-Kantian Paul Natorp. In 1914 the mathematics of probability was already reasonably well developed but there was not yet an agreed upon axiomatization. First proposals were around (e.g. Bohlmann, 1901), but Andrey Kolmogorov only published the now standard set of axioms in 1933, while Reichenbach published his own (structurally, but not semantically similar) axiomatization in a paper in 1932. In 1914 the discussion surrounding the formal definition of randomness (involving R. A. Wald etc.), which is generally regarded as one of the main impediments in the early development of an axiomatization of probability, had not yet started. Emile Borel had published a few papers on this topic, but Reichenbach does not appear to have been familiar with them at the time. Without an axiomatization or any other widely accepted 4 foundation, probability claims and their corresponding inferences supplied successful heuristics, but were without any epistemological grounding. 2. Thesis Synopsis Reichenbach's thesis set …