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A Review on Charles S. Peirce's Mathematical Logic (1839-1914)

Charles S. Peirce, Scientist and Philosopher

This chapter provides an overview of Charles S. Peirce's life and contributions to various fields, including mathematics, linguistics, psychology, and history. Peirce's broad spectrum of interests is highlighted, and his role as a pioneer in the development of mathematical logic is discussed. The chapter also touches on Peirce's contributions to the philosophy of science, including his development of the theory of the scientific method and his revision of Kant's phenomenological categories.

Peirce's Contributions to Mathematical Logic

This chapter focuses specifically on Peirce's contributions to mathematical logic. It proposes a classification of Peirce's works based on their incorporation into the mathematical corpus and briefly reviews some of his key works in this area. The chapter also highlights some of the open research problems in Peirce's mathematical logic.

Peirce's Legacy in Mathematics

This chapter discusses Peirce's legacy in mathematics, including his influence on the development of mathematical logic and his contributions to the measurement of gravity and the study of the Earth's ellipticity. The chapter also touches on Peirce's proposal to establish the measure of the meter in terms of the wavelength of light, as well as his work in linguistics and the history of science.

Conclusion

This chapter provides a brief summary of the text and emphasizes the importance of Charles S. Peirce's contributions to various fields, particularly his role as a pioneer in the development of mathematical logic. The chapter concludes by noting the ongoing efforts to recover, systematize, and apply Peirce's thought.

Introduction

The text discusses the lesser-known aspect of Charles S. Peirce's legacy as a mathematician. Despite being primarily known as a philosopher and logician, Peirce had a deep understanding and knowledge of mathematics. His father, Benjamin Peirce, was a renowned mathematician and philosopher, and his influence played a significant role in Charles's education. Peirce had contact with many contemporary American and European mathematicians and kept up with the latest developments in the field.

Peirce's Contributions to Mathematics

Peirce's work in mathematics can be divided into two main areas: the logic of relatives and the logic of the continuum. In the logic of relatives, Peirce aimed to generalize the works of Boole and De Morgan by defining a variety of operations between logical propositions and studying their properties. He also developed the theory of quantification, which is still used in mathematics today. Peirce's work in the logic of the continuum focused on the study of the general continuum, which he believed was a type of generality. He proposed that the continuum was supermultitudinous, reflexive, inextensible, modal, and plastic, which went beyond the continuum of Cantor.

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