Kathleen A. Hull

The founder of both American pragmatism and semiotics, Charles Sanders Peirce is widely regarded as an enormously important and pioneering theorist. In this book, scholars from around the world examine the nature and significance of Peirce’s work on perception, iconicity, and diagrammatic thinking. Abjuring any strict dichotomy between presentational and representational mental activity, Peirce’s theories transform the Aristotelian, Humean, and Kantian paradigms that continue to hold sway today and, in so doing, forge a new path for understanding the centrality of visual thinking in science, education, art, and communication. The essays in this collection cover a wide range of issues related to Peirce’s theories, including the perception of generality; the legacy of ideas being copies of impressions; imagination and its contribution to knowledge; logical graphs, diagrams, and the question of whether their iconicity distinguishes them from other sorts of symbolic notation; how images and diagrams contribute to scientific discovery and make it possible to perceive formal relations; and the importance and danger of using diagrams to convey scientific ideas. This book is a key resource for scholars interested in Perice’s philosophy and its relation to contemporary issues in mathematics, philosophy of mind, philosophy of perception, semiotics, logic, visual thinking, and cognitive science.

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