Peirce, fallibilism, and the science of mathematics

In this paper, it will be shown that Peirce was of two minds about whether his scientific fallibilism, the recognition of the possibility of error in our beliefs, applied to mathematics. It will be argued that Peirce can and should hold a theory of fallibilism within mathematics, and that this position is more consistent with his overall pragmatic theory of inquiry and his general commitment to the growth of knowledge. But to make the argument for fallibilism in mathematics, Peirce's theory of fallibilism must be reconceived to incorporate two different kinds of fallibilism, which correspond to two different kinds of truth claims.