## 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