Peirce and the Logic of Diagrams

Abstract

Peirce’s insistence that logic and mathematics are prior to, and independent of, the natural sciences faces serious objections. First, his claim that all knowledge is scientific seems to imply that any justification of the principles of scientific method presupposes the legitimacy of those principles and thus is circular. Second, his claim that truths of logic and mathematics hold independently of facts about the actual world seems hard to square with his insistence that they are established by observation using the experimental method. Finally, his view that logic and mathematics are sciences on the same epistemological footing as any other science seems at odds with his view that results in mathematics and logic are more secure than those of the natural sciences. I argue that Peirce’s answers to these objections rest on his theory of icons. If this is right, his theory of icons is central to his epistemology and issues in a view of mathematics and logic that is original and has been largely overlooked.