Charles Sanders Peirce is generally regarded as the founder of pragmatism, and one of the greatest ever American philosophers. Peirce is also widely known for his work on truth, his foundational work in mathematical logic, and an influential theory of signs, or semiotics. Albert Atkin introduces the full spectrum of Peirce’s thought for those coming to his work for the first time. The book begins with an overview of Peirce’s life and work, considering his early and long-standing interest in logic (...) and science, and highlighting important views on the structure of philosophical thought. Atkin then explains Peirce’s accounts of pragmatism and truth examining important later developments to these theories. He then introduces Peirce’s full accounts of semiotics, examines his foundational work on formal and graphical logic, and introduces Peirce’s account of metaphysics, the least understood aspect of his philosophy. The final chapter considers Peirce’s legacy and influence on the thought of philosophers such as John Dewey and Richard Rorty, as well as highlighting areas where Peirce’s ideas could still provide important insights for contemporary philosophers. Including chapter summaries, suggestions for further reading and a glossary, this invaluable introduction and guide to Peirce’s philosophy is essential reading for those new to his work. (shrink)

Two different concepts of iconicity compete in Peirce's diagrammatical logic. One is articulated in his general reflections on the role of diagrams in thought, in what could be termed his diagrammatology — the other is articulated in his construction of Existential Graphs as an iconic system for representing logic. One is operational and defines iconicity in terms of which information may be derived from a given diagram or diagram system — the other has stronger demands on iconicity, adding to the (...) operational criterion a demand for as high a degree of similarity as possible and may be termed optimal iconicity. Peirce himself does not clearly distinguish these two iconicity notions, a fact that has caused some confusion. By isolating them, we get a clearer and more refined conceptual apparatus for analyzing iconic signs, from pictures to logic. (shrink)

Covers first-order language in method appropriate for first and second courses in logic. CD-ROM consists of a new book, 3 programs,and an Internet-based grading service.

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does (...) exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”. (shrink)

The paper gives a detailed reconstruction and discussion of Peirce’s doctrine of propositions, so-called Dicisigns, developed in the years around 1900. The special features different from the logical mainstream are highlighted: the functional definition not dependent upon conscious stances nor human language, the semiotic characterization extending propositions and quasi-propositions to cover prelinguistic and prehuman occurrences of signs, the relations of Dicisigns to the conception of facts, of diagrammatical reasoning, of icons and indices, of meanings, of objects, of syntax in Peirce’s (...) logic-as-semiotics. (shrink)

The evolution of Euler diagrams is examined from Euler's original system through the modifications made by Venn and Peirce. It is shown that these modifications were motivated by an attempt to increase the expressivity of the diagrams, but that a side effect of these modifications was a loss of the visual clarity of Euler's original system. Euler's original system is reconstructed from a modern, logical point of view. Formal semantics and rules of inference are provided for this reconstruction of Euler's (...) system, and basic logical properties are proved. (shrink)

1 INTRODUCTION Above the other titles he might justly have claimed, Charles S. Peirce prized the title 'logician'. He expressed in several places his ...

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...) constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular. (shrink)