BOLZANO VERSUS KANT: MATHEMATICS AS A SCIENTIA UNIVERSALIS

Abstract. The paper will discuss some changes in Bolzano’s definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano’s works will be distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes will be interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence ot the overcome of Kant’s terminology, and of the radicalization of Bolzano’s anti-Kantianism. It will be argued that Bolzano’s evolution can be understood as a coherent move, if one compares the criticism expressed in the Beyträge on the notion of quantity with a different and larger notion of quantity that Bolzano developed already in 1816. This discussion is based on the discovery that two unknown texts mentioned by Bolzano can be identified with works by von Spaun and Vieth respectively. Bolzano’s evolution will be interpreted as a radicalization of the criticism of the Kantian definition of mathematics and as an effect of Bolzano’s unaltered interest in the Leibnizian notion of mathesis universalis. As a conclusion, it will be argued that Bolzano never abandoned his original idea of considering mathematics as a scientia universalis, i.e. as the science of quantities in general, and it will be suggested that the question of ideal elements in mathematics, which has been interpreted as a main reason for the development of a new logical theory, can also be considered as a main reason for developing a different definition of quantity. 1

Systematicity, knowledge, and bias. How systematicity made clinical medicine a science

This paper shows that the history of clinical medicine in the eighteenthcentury supports Paul Hoyningen-Huene’s thesis that there is a correlation between science and systematicity. For example, James Jurin’s assessment of the safety of variolation as a protection against smallpox adopted a systematic approach to the assessment of interventions in order to eliminate sources of cognitive bias that would compromise inquiry. Clinical medicine thereby became a science. I use this confirming instance to motivate a broader hypothesis, that systematicity is a distinctive featureof science because systematicity is required by processes of knowledge generation that go beyond our everyday cognitive capacities, and these processes are required to produce knowledge of the kinds that science aims at