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The Mathematical Origins of Nineteenth-Century Algebra of Logic

Volker Peckhaus

in The Development of Modern Logic

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195137316
eISBN:
9780199867912
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195137316.003.0018
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical ... More


George Boole and Claude Shannon: Two Mini-Biographies

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0003
Subject:
Mathematics, History of Mathematics

This chapter presents brief biographical sketches of George Boole and Claude Shannon. George was born in Lincoln, a town in the north of England, on November 2, 1815. His father John, while simple ... More


Introduction

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

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


The Difficulty about Corroboration and Convergence

L. Jonathan Cohen

in The Probable and The Provable

Published in print:
1977
Published Online:
October 2011
ISBN:
9780198244127
eISBN:
9780191680748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198244127.003.0011
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

This chapter examines the difficulty about corroboration and convergence. It begins by addressing the common structure of testimonial corroboration and circumstantial convergence. The chapter also ... More


The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Paul J. Nahin

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.001.0001
Subject:
Mathematics, History of Mathematics

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics ... More


Boolean Algebra

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0004
Subject:
Mathematics, History of Mathematics

This chapter discusses how Boole cast logic into algebraic form. Boole was interested in symbolic analysis years before he wrote his Laws of Thought. In fact, others before him—in particular, the ... More


Algebra: Symbolic Logic and the Logic of Symbolism

Andrea Henderson

in Algebraic Art: Mathematical Formalism and Victorian Culture

Published in print:
2018
Published Online:
May 2018
ISBN:
9780198809982
eISBN:
9780191860140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198809982.003.0003
Subject:
Literature, 19th-century Literature and Romanticism

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean ... More


The Continued Exercise of Reason: Public Addresses by George Boole

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


Philosophic Prophecy

Eric Schliesser

in Philosophy and Its History: Aims and Methods in the Study of Early Modern Philosophy

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199857142
eISBN:
9780199345427
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199857142.003.0011
Subject:
Philosophy, History of Philosophy

This paper argues that historians of philosophy must coin concepts that disclose the near or distant past and create a shared horizon for our philosophical future. Two concepts are introduced: ... More


Boole, Shannon, and Probability

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0006
Subject:
Mathematics, History of Mathematics

George Boole and Claude Shannon shared a deep interest in the mathematics of probability. Boole's interest was, of course, not related to the theory of computation—he was a century too early for ... More


The Algebraic Tradition of Logic

Jan von Plato

in The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age

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


Introduction

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0002
Subject:
Mathematics, History of Mathematics

This introductory chapter considers the work of mathematician George Boole (1815–1864), whose book An Investigation of the Laws of Thought (1854) would have a huge impact on humanity. Boole's ... More


Beyond Boole and Shannon

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0010
Subject:
Mathematics, History of Mathematics

Boole and Shannon never studied the physics of computation. Obviously Boole simply could not have, as none of the required physics was even known in his day, and Shannon was nearing the end of his ... More


Charles Sanders Peirce: An Overview

Vincent G. Potter

in Peirce's Philosophical Perspectives

Published in print:
1996
Published Online:
May 2019
ISBN:
9780823216154
eISBN:
9780823284832
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823216154.003.0001
Subject:
Philosophy, American Philosophy

This chapter provides an overview of the life of Charles Sander Peirce—philosopher, logician, scientist, and father of American pragmatism. This man, unappreciated in his lifetime, virtually ignored ... More


The Claims of Science

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

Published in print:
2018
Published Online:
September 2019
ISBN:
9780262535007
eISBN:
9780262345576
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262535007.003.0008
Subject:
History, History of Science, Technology, and Medicine

This chapter presents George Boole's lecture on the claims of the pursuit of science, He says that like all other claims with which we are concerned, these must ultimately rest upon some intrinsic ... More


The Social Aspect of Intellectual Culture

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

Published in print:
2018
Published Online:
September 2019
ISBN:
9780262535007
eISBN:
9780262345576
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262535007.003.0009
Subject:
History, History of Science, Technology, and Medicine

This chapter presents George Boole's lecture on the social aspect of intellectual culture. He says that within proper limits and under proper conditions, intellectual tastes are not only compatible ... More


On the Character and Origin of the Ancient Mythologies

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

Published in print:
2018
Published Online:
September 2019
ISBN:
9780262535007
eISBN:
9780262345576
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262535007.003.0003
Subject:
History, History of Science, Technology, and Medicine

This chapter presents George Boole's lecture on the origin of ancient mythologies. Very few ancient writers agree in the representations on this subject despite living in the country whose opinions ... More


On the Question: Are the Planets Inhabited?

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

Published in print:
2018
Published Online:
September 2019
ISBN:
9780262535007
eISBN:
9780262345576
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262535007.003.0004
Subject:
History, History of Science, Technology, and Medicine

This chapter presents George Boole's lecture on whether the planets are inhabited. He first considers the general conditions to which life here has manifested; second, the adaptations of the earth as ... More


The Right Use of Leisure

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

Published in print:
2018
Published Online:
September 2019
ISBN:
9780262535007
eISBN:
9780262345576
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262535007.003.0006
Subject:
History, History of Science, Technology, and Medicine

This chapter presents George Boole's lecture on the right use of leisure. He says that every right involves a responsibility. The greater our freedom from external restrictions, the more we become ... More


On Education

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

Published in print:
2018
Published Online:
September 2019
ISBN:
9780262535007
eISBN:
9780262345576
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262535007.003.0007
Subject:
History, History of Science, Technology, and Medicine

This chapter presents George Boole's lecture on education. He identifies three things to which the attention of the teacher must be chiefly directed: the imparting of knowledge, the production of a ... More


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