Abstract

Charles Sanders Peirce (1839–1914) argued for a specific conception of the scientific method, according to which scientific knowledge is fallible and hypothetical. It is grounded in experience through observation and experimentation. Scientific reasoning, for Peirce, involves the systematic operation with signs of different kinds and is carried out through three modes of inference: abduction, deduction, and induction. Moreover, the scientific method is guided by what he called the pragmatic maxim. Peirce also argued for the general application of this scientific method across all sciences, including mathematics. Thus, the features of the scientific method should also be present in mathematical knowledge, leading to a conception of mathematics that was both idiosyncratic and heterodox for his time. In this presentation, I aim to show how these features are instantiated in mathematics. I will emphasize the importance of Peirce’s theory of signs and his view of mathematical proof, which, in his account, cannot be reduced solely to deductive reasoning. Finally, I will discuss the viability of Peirce’s approach in light of mathematical practice.

Coffee/tea, cake and fruit will be served @ 2pm.