## Visual Thinking in Mathematics

*Marcus Giaquinto*

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199285945
- eISBN:
- 9780191713811
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199285945.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Visual thinking — visual imagination or perception of diagrams and symbol arrays, and mental operations on them — is omnipresent in mathematics. Is this visual thinking merely a psychological aid, ... More

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

*Michael Potter*

- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. It reassesses the brilliant ... More

## Grounding Concepts: An Empirical Basis for Arithmetical Knowledge

*C. S. Jenkins*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199231577
- eISBN:
- 9780191716102
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199231577.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book is a philosophical discussion of arithmetical knowledge. No extant account, it seems, is able to respect simultaneously these three strong pre-theoretic intuitions: (a) that arithmetic is ... More

## Set Theory and its Philosophy: A Critical Introduction

*Michael Potter*

- Published in print:
- 2004
- Published Online:
- September 2011
- ISBN:
- 9780199269730
- eISBN:
- 9780191699443
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269730.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book presents a philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. The book offers an ... More

## Frege’s Conception of Logic

*Patricia A. Blanchette*

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199891610
- eISBN:
- 9780199933211
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199891610.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Frege’s Coneption of Logic explores the relationship between Frege’s understanding of conceptual analysis and his understanding of logic. It is argued that the fruitfulness of Frege’s ... More

## Dreaming Connects. The Dreaming End of the Continuum Is Hyper-connective

*Ernest Hartmann*

### in The Nature and Functions of Dreaming

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199751778
- eISBN:
- 9780199863419
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199751778.003.0006
- Subject:
- Psychology, Cognitive Psychology, Clinical Psychology

This chapter shows that dreaming is hyper-connective. At the dreaming end of the continuum connections are made more easily than in waking, and connections are made more broadly and loosely. Dreaming ... More

## Arithmetic Certainty

*José Ferreirós*

### in Mathematical Knowledge and the Interplay of Practices

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167510
- eISBN:
- 9781400874002
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.003.0007
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter considers the idea that we have certainty in our basic arithmetic knowledge. The claim that arithmetical knowledge enjoys certainty cannot be extended to a similar claim about number ... More

## Inconsistent Arithmetic

*Graham Priest*

### in In Contradiction

- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0018
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The study of formal inconsistent arithmetics has already occasioned a number of interesting technical results, as well as philosophical spin-offs. This chapter looks at some of these. It shows how ... More

## Hilbert's Programme

*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/9780199252619.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

By the time Hilbert's first series of published research on the foundations of mathematics came to an end around 1904, he had formulated but not solved the problem of finding — for a formal system of ... More

## Conclusion: William Petty's Political Science

*Ted McCormick*

### in William Petty: And the Ambitions of Political Arithmetic

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199547890
- eISBN:
- 9780191720529
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199547890.003.0010
- Subject:
- History, British and Irish Early Modern History, Economic History

The conclusion draws together several of the main themes of the book, arguing that political arithmetic can only be understood properly from the manuscripts he circulated in his lifetime, and in the ... More

## The Rise of Scientific Method

*A. H. Halsey*

### in A History of Sociology in Britain: Science, Literature, and Society

- Published in print:
- 2004
- Published Online:
- April 2004
- ISBN:
- 9780199266609
- eISBN:
- 9780191601019
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199266603.003.0003
- Subject:
- Political Science, UK Politics

The history of the search for a science of society is traced back to the political arithmeticians of the seventeenth century. Social survey is defined. What is right and what is wrong with sociology ... More

## Logic and Revisability

*Graham Priest*

### in Doubt Truth to be a Liar

- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter argues that logic is a theory, and can be revised as any other scientific theory. The comparison with geometry is helpful in this regard. It also discusses Quine’s views on the matter, ... More

## The Vocabulary of the Liberal Arts

*Philip Burton*

### in Language in the Confessions of Augustine

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199266227
- eISBN:
- 9780191709098
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199266227.003.0003
- Subject:
- Religion, Early Christian Studies

This chapter considers Augustine's use of Greek and Latin terminology in the technical register of the Seven Liberal Arts (grammar, rhetoric, dialect, arithmetic, geometry, music, and philosophy). It ... More

## Geometric Means and Lognormal Distributions

*Rein Taagepera*

### in Making Social Sciences More Scientific: The Need for Predictive Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199534661
- eISBN:
- 9780191715921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534661.003.0009
- Subject:
- Political Science, Comparative Politics, Political Economy

Geometric means are often more meaningful than arithmetic means, because they are closer to the central figure (median). When x and y can conceptually take only positive values, their distributions ... More

## Mathematics for Humans

*Robert Hanna*

### in Kant, Science, and Human Nature

- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199285549
- eISBN:
- 9780191713965
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199285549.003.0007
- Subject:
- Philosophy, History of Philosophy

This chapter examines Kant's much-criticized views on mathematics in general and arithmetic in particular. It makes a case for the claim that Kant's theory of arithmetic is not subject to the most ... More

## BASICS

*Roman Kossak and James H. Schmerl*

### in The Structure of Models of Peano Arithmetic

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This introductory chapter covers a wide range of topics, from basic notational conventions and coding in arithmetic to important classical results. The well-known theorems, such as Gaifman's ... More

## Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

*Mark Green, Phillip A. Griffiths, and Matt Kerr*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154244
- eISBN:
- 9781400842735
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154244.001.0001
- Subject:
- Mathematics, Analysis

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive ... More

## Meaning Constitution and Epistemic Rationality

*Paul Horwich*

### in Reflections on Meaning

- Published in print:
- 2005
- Published Online:
- September 2006
- ISBN:
- 9780199251247
- eISBN:
- 9780191603983
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019925124X.003.0006
- Subject:
- Philosophy, Philosophy of Language

Our beliefs and inferential transitions are subject to evaluation as rational or irrational by reference to general epistemic norms. But what could determine certain norms as the correct ones? This ... More

## Introduction

*Marcus Giaquinto*

### in Visual Thinking in Mathematics

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199285945
- eISBN:
- 9780191713811
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199285945.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This introductory chapter outlines the main themes of the book. It then describes visual thinking in mathematics during the 19th century. An overview of the chapters in the book is presented.

## Visual Aspects of Calculation

*Marcus Giaquinto*

### in Visual Thinking in Mathematics

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199285945
- eISBN:
- 9780191713811
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199285945.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter describes the roles of visual thinking in calculation, with the aim of showing that in many cases it is not peripheral. It does this by setting the visual aspects of calculation within ... More