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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


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