Abstract

The primary focus of this project is Peirce's theory of mathematical reasoning and its application to his philosophy of religion, after 1890. The central thesis is that Peirce carries Kant's critique of pure reason to its next logical step by incorporating a role for a non-empirical, inner "experience" into mathematics. Necessary reasoning is thus grounded in human experience, carefully understood. The key to Peirce's contribution is his phenomenological examination of mathematical proof, in light of his three categories of reality. Imaginative reasoning with diagrams is found to be intimately tied with Peirce's metaphysics: we "experience" our mathematical diagrams not only cognitively, but sensuously, in virtue of their iconicity and percussivity . Mathematical reasoning with diagrams is found, by Peirce, to be essentially creative; and it is the backbone of his view of how we reason toward a belief in God in his "Neglected Argument for the Reality of God." ;Our starting point for discussion is the claim that Peirce makes an important distinction between mathematics and logic. In contrast to the philosophical "tradition" stemming from Frege, Russell, et. al., we find that Peircean mathematics is a pre-logical reasoning practice which does not require a theoretical foundation in logic. Peirce's view of mathematical reasoning emerges, we suggest, from Kant's First Critique where the mathematician is said to make an intuitive, not discursive, use of reason by means of the construction of concepts. This method becomes a model for reasoning with diagrams, in which the thinker is not reduced to reasoning upon a rule or definition, but may create new concepts and ideas based on inner observations. ;Musement in Peirce's N. A. is read as an exploration of how we reason about God through reasoning about infinite sets, by applying Cantorian set theory to Peirce's three categories. A direct perception of God is understood as the experience of creatively reasoning with diagrams about the interrelations of the three categories. ;Peirce is situated in the history of the philosophy of mathematics, in relation to Plato, Aristotle, Lully, Leibniz, Descartes, Kant, Mill and key twentieth-century thinkers. We discuss his rejection of mechanistic views of reasoning, including Babbage's reasoning machine