Carnap, Tarski, and Quine at Harvard: Conversations on Logic, Mathematics, and Science

272 Pages·2013·3.23 MB·English

by  Greg Frost-Arnold

Carnap, Tarski, and Quine at Harvard

PublicationsoftheArchiveofScientificPhilosophy
HillmanLibrary,UniversityofPittsburgh
Steve Awodey, Editor
EDITORIALBOARD
John Norton
University of Pittsburgh
Richard Creath John Earman
Arizona State University University of Pittsburgh
Michael Friedman Gottfried Gabriel
Stanford University University of Jena
James Lennox Dana Scott
University of Pittsburgh Carnegie Mellon University
Wilfried Sieg Mark Wilson
Carnegie Mellon University University of Pittsburgh
Gereon Wolters
University of Constance
PublicationsoftheArchiveofScientificPhilosophy
HillmanLibrary,UniversityofPittsburgh
Volume 1.
Frege’s Lectures on Logic: Carnap’s Student Notes, 1910–1914,
edited by Erich H. Reck and Steve Awodey
Volume 2.
Carnap Brought Home: The View From Jena, edited by Steve
Awodey and Carsten Klein
Volume 3.
The Concept of Probability in the Mathematical Representation of
Reality, by Hans Reichenbach, translated and edited by
Frederick Eberhardt and Clark Glymour
Volume 4.
Empiricism at the Crossroads: The Vienna Circle’s Protocol-Sentence
Debate, by Thomas Uebel
Volume 5.
Carnap, Tarski, and Quine at Harvard: Conversations on Logic,
Mathematics, and Science, by Greg Frost-Arnold
C arnap, Tarski, and
Quine at H arvard
Conversations on Logic,
Mathematics, and Science
Greg Frost-Arnold
Open Court
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Contents
Preface xiii
1 OverviewandHistoricalBackground 1
1.1. Introduction:SettingtheHistoricalStage 1
1.2. TheMainProject:A‘Finitist-Nominalist’LanguageofScience 3
1.3. MathematicsinaFinitist-NominalistLanguage 11
1.4. Pre-historyofthe1941Finitist-NominalistProject 15
2 JustificationsfortheFinitist-NominalistConditions 27
2.1. FirstJustification:Verständlichkeit 27
2.2. SecondJustification:OvercomingMetaphysics 37
2.3. ThirdJustification:InferentialSafety 43
2.4. FourthJustification:NaturalScience 45
2.5. CurrentJustificationsforNominalism 47
3 ObjectionstotheFinitist-NominalistProject 51
3.1. WhyDoesCarnapParticipate,GivenHisReservations? 51
3.2. HigherMathematicsIsMeaningful 54
3.3. AreAnyInfinitiesCompatiblewiththeFNProject? 61
3.4. AttackingtheFNConditions 65
3.5. AnObjectionNotintheNotes 71
4 TheFinitist-NominalistProjectandAnalyticity 73
4.1. UnderaFinitist-NominalistRegime,ArithmeticIsSynthetic 74
4.2. RadicalizationofQuine’sCritiqueofAnalyticity 81
5 DirectDiscussionsofAnalyticTruthin1940-41 89
5.1. WhatIsAnalyticity,circa1940? 90
5.2. Tarski’sObjectionstoAnalyticity 94
5.3. Quine’sDisagreementswithCarnapcirca1940 102
6 OvercomingMetaphysicsthroughtheUnityofScience 117
6.1. UnityofLanguage,NotLaws 118
ix