"A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth- and early twentieth-century probability theory, mathematics and logic

This dissertation provides a contribution to a new history of exact thought in which the existence of a break between "non-modern" and "modern" abstraction is put forward to account for the possibility of the "modernization" of probability theory, mathematics and logic during the 19th- and early 20th-century. The articles that make up the dissertation are all concerned not with the "modern" idea of a formal axiomatic system as such, but with what allowed it to become conceivable and they understand the way in which this came about not from the perspective of the "modern" but from that of the "non-modern".
The articles can be read on four different levels - the first two of which form the main body of the text. Firstly, as detailed historical studies of the work of "non-modern" probabilists, mathematicians and logicians (ca. 1830-1930). Secondly, as an elaboration of a general view of "non-modern" conceptions of probability theory, mathematics and logic - a negative characterization which suggests that the later modifications of some of the ideas of "non-moderns" were unthinkable for them given the foundations of their position. Thirdly, as a contribution to a post-Kuhnian history of "modernization" in these realms of exact thought which evokes, fourthly, a theoretization of the philosophical "break" in abstraction that underlies the "modernist transformation."