*Jan von Plato*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174174
- eISBN:
- 9781400885039
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174174.003.0004
- Subject:
- History, History of Science, Technology, and Medicine

This chapter explores how algebraic logic began in 1847 when George Boole presented his “calculus of deductive reasoning” in a short book titled The Mathematical Analysis of Logic. His calculus ...
More

This chapter explores how algebraic logic began in 1847 when George Boole presented his “calculus of deductive reasoning” in a short book titled The Mathematical Analysis of Logic. His calculus reduced known ways of logical reasoning into the solution of algebraic equations. The known ways of logical reasoning were not just accounted for but were extended to full classical propositional logic. Boole reduced Aristotelian syllogistic reasoning to calculation, which was a wonderful achievement. Encouraged by the success, he wrote a book with the bold title An Investigation of the Laws of Thought (1854). However, his logic was not able to treat relations but just one-place predicates.Less

This chapter explores how algebraic logic began in 1847 when George Boole presented his “calculus of deductive reasoning” in a short book titled *The Mathematical Analysis of Logic*. His calculus reduced known ways of logical reasoning into the solution of algebraic equations. The known ways of logical reasoning were not just accounted for but were extended to full classical propositional logic. Boole reduced Aristotelian syllogistic reasoning to calculation, which was a wonderful achievement. Encouraged by the success, he wrote a book with the bold title *An Investigation of the Laws of Thought* (1854). However, his logic was not able to treat relations but just one-place predicates.

*Jan von Plato*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174174
- eISBN:
- 9781400885039
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174174.001.0001
- Subject:
- History, History of Science, Technology, and Medicine

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. This book draws on original sources and rare ...
More

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. This book draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. The book examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. The book shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. The book describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, this book is essential reading for students and researchers in logic, mathematics, and computer science.Less

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. This book draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. The book examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. The book shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. The book describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, this book is essential reading for students and researchers in logic, mathematics, and computer science.

*Brendan Dooley (ed.)*

- Published in print:
- 2018
- Published Online:
- September 2019
- ISBN:
- 9780262535007
- eISBN:
- 9780262345576
- Item type:
- book

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262535007.001.0001
- Subject:
- History, History of Science, Technology, and Medicine

George Boole (1815–1864), remembered by history as the developer of an eponymous form of algebraic logic, can be considered a pioneer of the information age not only because of the application of ...
More

George Boole (1815–1864), remembered by history as the developer of an eponymous form of algebraic logic, can be considered a pioneer of the information age not only because of the application of Boolean logic to the design of switching circuits but also because of his contributions to the mass distribution of knowledge. In the classroom and the lecture hall, Boole interpreted recent discoveries and debates in a wide range of fields for a general audience. This collection of lectures, many never before published, offers insights into the early thinking of an innovative mathematician and intellectual polymath. Bertrand Russell claimed that “pure mathematics was discovered by Boole,” but before Boole joined a university faculty as professor of mathematics in 1849, advocacy for science and education occupied much of his time. He was deeply committed to the Victorian ideals of social improvement and cooperation, arguing that “the continued exercise of reason” joined all disciplines in a common endeavor. In these talks, Boole discusses the genius of Isaac Newton; ancient mythologies and forms of worship; the possibility of other inhabited planets in the universe; the virtues of free and open access to knowledge; the benefits of leisure; the quality of education; the origin of scientific knowledge; and the fellowship of intellectual culture. The lectures are accompanied by a substantive introduction that supplies biographical and historical context.Less

George Boole (1815–1864), remembered by history as the developer of an eponymous form of algebraic logic, can be considered a pioneer of the information age not only because of the application of Boolean logic to the design of switching circuits but also because of his contributions to the mass distribution of knowledge. In the classroom and the lecture hall, Boole interpreted recent discoveries and debates in a wide range of fields for a general audience. This collection of lectures, many never before published, offers insights into the early thinking of an innovative mathematician and intellectual polymath. Bertrand Russell claimed that “pure mathematics was discovered by Boole,” but before Boole joined a university faculty as professor of mathematics in 1849, advocacy for science and education occupied much of his time. He was deeply committed to the Victorian ideals of social improvement and cooperation, arguing that “the continued exercise of reason” joined all disciplines in a common endeavor. In these talks, Boole discusses the genius of Isaac Newton; ancient mythologies and forms of worship; the possibility of other inhabited planets in the universe; the virtues of free and open access to knowledge; the benefits of leisure; the quality of education; the origin of scientific knowledge; and the fellowship of intellectual culture. The lectures are accompanied by a substantive introduction that supplies biographical and historical context.

*Brendan Dooley (ed.)*

- Published in print:
- 2018
- Published Online:
- September 2019
- ISBN:
- 9780262535007
- eISBN:
- 9780262345576
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262535007.003.0001
- Subject:
- History, History of Science, Technology, and Medicine

This introductory chapter provides an overview of the life and work of George Boole. Boole is known for developing the system of algebraic logic, which eventually found an unexpected engineering ...
More

This introductory chapter provides an overview of the life and work of George Boole. Boole is known for developing the system of algebraic logic, which eventually found an unexpected engineering application in the design of switching circuits. He was also an early advocate of the mass distribution of knowledge, using the methods at his disposal in early Victorian times. In the classroom and lecture hall, he interpreted the results of recent discoveries and debates originating among specialists in numerous fields—history, psychology, ethnography, and much else—and communicated them to a broad audience. Less known and therefore less appreciated is Boole's role in the history of the making and organization of knowledge. A better understanding of this feature, may eventually provoke a more thoroughgoing reappraisal of the whole figure.Less

This introductory chapter provides an overview of the life and work of George Boole. Boole is known for developing the system of algebraic logic, which eventually found an unexpected engineering application in the design of switching circuits. He was also an early advocate of the mass distribution of knowledge, using the methods at his disposal in early Victorian times. In the classroom and lecture hall, he interpreted the results of recent discoveries and debates originating among specialists in numerous fields—history, psychology, ethnography, and much else—and communicated them to a broad audience. Less known and therefore less appreciated is Boole's role in the history of the making and organization of knowledge. A better understanding of this feature, may eventually provoke a more thoroughgoing reappraisal of the whole figure.