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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


Russell's Account of Classes

Michael Potter

in Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

Published in print:
2002
Published Online:
May 2007
ISBN:
9780199252619
eISBN:
9780191712647
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199252619.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

Russell discovered his paradox while writing The Principles of Mathematics. When this book appeared in 1903, it contained a discussion of his paradox but no more than a sketch of a solution. He then ... More


The Freedom of the Will

J. R. Lucas

Published in print:
1970
Published Online:
October 2011
ISBN:
9780198243434
eISBN:
9780191680687
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198243434.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, Moral Philosophy

The three great problems of philosophy, according to Kant, are God, freedom, and immortality. Of these, freedom, that is, the Freedom of the Will, is the one most accessible to reason, and has ... More


Gottlob Frege and the Interplay between Logic and Mathematics

Christian Thiel

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/9780195137316.003.0020
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter explores Gottlob Frege's contribution to logic. Frege has been called the greatest logician since Aristotle, but he failed to gain influence on the mathematical community of his time and ... More


Reverse Mathematics: Proofs from the Inside Out

John Stillwell

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691196411
eISBN:
9781400889037
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691196411.001.0001
Subject:
Mathematics, History of Mathematics

Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. Reverse mathematics began as a technical field of mathematical logic, but its main ideas have ... More


Freedom and Philosophy

J. R. Lucas

in The Freedom of the Will

Published in print:
1970
Published Online:
October 2011
ISBN:
9780198243434
eISBN:
9780191680687
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198243434.003.0001
Subject:
Philosophy, Metaphysics/Epistemology, Moral Philosophy

This chapter begins with a brief discussion of the concept of freedom of the will. It then sets out the purpose of the book, which is to reformulate an argument about freedom of will by drawing on a ... More


The Longest Journey: Bertrand Russell

Bas C. van Fraassen

in Scientific Representation: Paradoxes of Perspective

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199278220
eISBN:
9780191707926
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278220.003.00010
Subject:
Philosophy, Philosophy of Mind, Philosophy of Science

The first sustained, rigorous development of a structuralist view of science appeared in the writings of Bertrand Russell, where the philosophical motivation precedes a precise formulation drawing on ... More


The Philosophy of Mathematics: Privation and Representation in Gershom Scholem’s Negative Aesthetics

Matthew Handelman

in The Mathematical Imagination: On the Origins and Promise of Critical Theory

Published in print:
2019
Published Online:
January 2020
ISBN:
9780823283835
eISBN:
9780823286270
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823283835.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

Chapter 2 investigates the moment in 1917 when the philosophy of mathematics revealed to Gershom Scholem the symbolic potential of privation. Mathematics—in particular, the translation of logic into ... More


Introduction and Overview

Kumaraswamy Velupillai

in Computable Economics: The Arne Ryde Memorial Lectures

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198295273
eISBN:
9780191596988
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198295278.003.0001
Subject:
Economics and Finance, Macro- and Monetary Economics

The first chapter gives a summary of the methodological and epistemological underpinnings of computable economics. There are, in addition, concise chapter summaries and a brief excursion into a ... More


Mathematics and Language

Danielle Macbeth

in Realizing Reason: A Narrative of Truth and Knowing

Published in print:
2014
Published Online:
May 2014
ISBN:
9780198704751
eISBN:
9780191774232
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198704751.003.0007
Subject:
Philosophy, History of Philosophy

This chapter considers the twentieth century response to the developments in mathematical practice in the nineteenth century. This response, we see, is essentially Kantian. Although Kant’s account of ... More


The Trouble with Logical Positivism: Max Horkheimer, Theodor W. Adorno, and the Origins of Critical Theory

Matthew Handelman

in The Mathematical Imagination: On the Origins and Promise of Critical Theory

Published in print:
2019
Published Online:
January 2020
ISBN:
9780823283835
eISBN:
9780823286270
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823283835.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

How did critical theory, at least as it was first envisioned by Max Horkheimer and Theodor W. Adorno, come to be so opposed to mathematics? Chapter 1 examines the transformation of Horkheimer, ... More


Mathematical legacy

Francine F. Abeles

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/9780198817000.003.0007
Subject:
Mathematics, History of Mathematics

This chapter re-examines Dodgson’s achievements during his lifetime, and how some of them resurfaced in the 20th century. The chapter is divided into subject areas: geometry (including his ... More


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

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


Mathematics and the Unity of Sensibility

Waxman Wayne

in Kant's Anatomy of the Intelligent Mind

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199328314
eISBN:
9780199369348
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199328314.003.0007
Subject:
Philosophy, History of Philosophy

This chapter focuses on Kant’s account of the possibility of mathematics in relation to the transcendental expositions of space and time in the Transcendental Aesthetic, that is, the role of ... 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 Logical Study of Language

Scott Soames

in Philosophy of Language

Published in print:
2010
Published Online:
October 2017
ISBN:
9780691138664
eISBN:
9781400833931
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691138664.003.0002
Subject:
Philosophy, History of Philosophy

This chapter discusses the foundations of philosophical semantics, covering the work of Gottlob Frege and Bertrand Russell. Frege, along with Russell, did more than anyone else to create the subject. ... 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


Introducing Turing’s mathematics

Robin Whitty and Robin Wilson

in The Turing Guide

Published in print:
2017
Published Online:
November 2020
ISBN:
9780198747826
eISBN:
9780191916946
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198747826.003.0048
Subject:
Computer Science, History of Computer Science

Alan Turing’s mathematical interests were deep and wide-ranging. From the beginning of his career in Cambridge he was involved with probability theory, ... More


Turing’s mentor, Max Newman

Ivor Grattan-Guinness

in The Turing Guide

Published in print:
2017
Published Online:
November 2020
ISBN:
9780198747826
eISBN:
9780191916946
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198747826.003.0052
Subject:
Computer Science, History of Computer Science

The interaction between mathematicians and mathematical logicians has always been much slighter than one might imagine. This chapter examines the case of ... More


Recursive generation in language

David J. Lobina

in Recursion: A Computational Investigation into the Representation and Processing of Language

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198785156
eISBN:
9780191827235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198785156.003.0003
Subject:
Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics, Syntax and Morphology

The introduction of recursion into linguistics was the result of applying some of the results of mathematical logic to the study of language. In particular, recursion was introduced in the 1950s as a ... More


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