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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


The Development of Modern Logic

Leila Haaparanta (ed.)

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195137316
eISBN:
9780199867912
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195137316.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This book presents a history of modern logic from the Middle Ages through the end of the 20th century. In addition to a history of symbolic logic, the book also examines developments in the ... More


Introduction

Leila Haaparanta

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/9780195137316.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

This introductory chapter begins with a discussion of the concept of logic, focusing on Aristotelian logic and symbolic logic. It then discusses the concept of modern logic, and the uses of the terms ... More


Reasoning and Belief in Victorian Mathematics

Daniel J. Cohen

in The Organisation of Knowledge in Victorian Britain

Published in print:
2005
Published Online:
January 2012
ISBN:
9780197263266
eISBN:
9780191734854
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197263266.003.0006
Subject:
History, British and Irish Modern History

This chapter focuses on the progress of mathematics in the nineteenth century. British mathematicians of this period showed interest in the formal aspects of mathematics, particularly in symbolic ... More


Logic and Intuition

Michael Heim

in The Metaphysics of Virtual Reality

Published in print:
1994
Published Online:
October 2011
ISBN:
9780195092585
eISBN:
9780199852987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195092585.003.0002
Subject:
Philosophy, Metaphysics/Epistemology

Infomania does not merely place additional tools at the tip of a man's fingertips; it builds a new environment and alters his psychic framework. The chapter argues that thinking in front of a ... More


Logic

Amirouche Moktefi

in The Mathematical World of Charles L. Dodgson (Lewis Carroll)

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198817000
eISBN:
9780191858697
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198817000.003.0004
Subject:
Mathematics, History of Mathematics

This chapter discusses Dodgson’s work on syllogisms (a topic that can be traced back to Aristotle and Ancient Greece) and how to solve them systematically using a marked board and some counters. His ... More


The Syntax of Modal Sentential Calculi

Nino B. Cocchiarella and Max A. Freund

in Modal Logic: An Introduction to its Syntax and Semantics

Published in print:
2008
Published Online:
October 2011
ISBN:
9780195366587
eISBN:
9780199851898
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195366587.003.0002
Subject:
Philosophy, Philosophy of Language

The authors construct different modal calculi in this chapter. These cover all the well-known systems, S1–S5, of Lewis and Langford's 1932 classic Symbolic Logic. These systems are constructed first ... 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 Erotic Ontology of Cyberspace

Michael Heim

in The Metaphysics of Virtual Reality

Published in print:
1994
Published Online:
October 2011
ISBN:
9780195092585
eISBN:
9780199852987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195092585.003.0007
Subject:
Philosophy, Metaphysics/Epistemology

How does the metaphysical laboratory fit into human inquiry as a whole? What status do electronic worlds have within the entire range of human experience? What perils haunt the metaphysical origins ... More


Symbolic Logic on the Social Plane of Alice’s Adventures in Wonderland

Anna Kornbluh

in The Order of Forms: Realism, Formalism, and Social Space

Published in print:
2019
Published Online:
September 2020
ISBN:
9780226653204
eISBN:
9780226653488
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226653488.003.0005
Subject:
Literature, Criticism/Theory

This chapter asks what a nonsense novel reveals about realism. It shows that Wonderland’s overarching concerns with sovereignty, execution, and social ordering cohere with its commitment to nonsense, ... More


Intelligent Systems

William B. Rouse

in Computing Possible Futures

Published in print:
2019
Published Online:
September 2019
ISBN:
9780198846420
eISBN:
9780191881589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198846420.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter addresses the ways in which human intelligence in routine and partly routine jobs can be augmented rather than replaced. The design of aids should begin with defining the user ... 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


Algebraic Art: Mathematical Formalism and Victorian Culture

Andrea Henderson

Published in print:
2018
Published Online:
May 2018
ISBN:
9780198809982
eISBN:
9780191860140
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198809982.001.0001
Subject:
Literature, 19th-century Literature and Romanticism

Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth ... More


The Peculiar Codex Jerusalem 22

in All the Names of the Lord: Lists, Mysticism, and Magic

Published in print:
2008
Published Online:
March 2013
ISBN:
9780226388700
eISBN:
9780226388724
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226388724.003.0009
Subject:
Religion, History of Christianity

This chapter explores Horus Apollo's Book on the Hieroglyphics. The subject is the symbolic logic behind the Egyptian script. The passage itself introduces the peculiar cultural association between ... More


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