Bolzano as logician

Abstract

Bernard Bolzano stands out with Frege as one of the great logicians of the nineteenth century. His approach to logic, set out in the Theory of Science of 1837, marks a fundamental reorientation of the subject on many fronts, one that is as radical as any in the history of the field. In sharp contrast to many of his contemporaries, Bolzano insisted upon a rigorous separation of logic from psychology. It should be possible, he thought, to characterize propositions, ideas, inferences, and the axiomatic organization of sciences without reference to a thinking subject. Consistently pursuing this approach to logic and methodology, Bolzano developed important accounts of formal semantics and formal axiomatics. A talented mathematician, Bolzano developed his logic in conjunction with his mathematical research. Among the first to work on the foundations of mathematics in the modern sense of the term, he made a number of key discoveries in analysis, topology, and set theory and had a significant influence on the development of mathematics in the nineteenth century. This chapter discusses Bolzano's logic along with some of his work in the foundations of mathematics that has some bearing on logic.