Paul Rusnock

This edition provides the first complete English translation of Bernard Bolzano's four-volume Wissenschaftslehre or Theory of Science, a masterwork of theoretical philosophy. First published in 1837, the Wissenschaftslehre is a monumental, wholly original study in logic, epistemology, heuristics, and scientific methodology. Unlike most logical studies of the period, it is not concerned with the "psychological self-consciousness of the thinking mind." Instead, it develops logic as the science of "propositions in themselves" and their parts, especially the relations between these entities. It offers, for the first time in the history of logic, a viable definition of consequence (or deducibility), and a novel view of probability. Giving constant attention to Bolzano's predecessors and contemporaries, with particular emphasis on Kant, this richly documented work is also a valuable source for the history of logic and philosophy.

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences. We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later

In the works of Kant and his followers, the notion of form plays an important role in explaining the apriority, necessity and certainty of logic. Bernard Bolzano (1781–1848), an important early critic of Kant, found the Kantians' definitions of form imprecise and their explanations of the special status of logic deeply unsatisfying. Proposing his own conception of form, Bolzano developed radically different views on logic, truth in virtue of form, and other matters. This essay presents Bolzano's views in the light of his criticisms of the Kantian logicians