Frege's Conception of Logic

by Blanchette, Patricia A.

• ISBN13: 9780199891610
• ISBN10: 0199891613
• Format: Hardcover
• Copyright: 2012-04-30
• Publisher: Oxford University Press

Summary

InFrege's Conception of LogicPatricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.

Author Biography

Patricia A. Blanchette is Associate Professor of Philosophy, University of Notre Dame

Table of Contents

Acknowledgments	p. xi
Note on the Cover	p. xiii
A Note on Citations	p. xv
Introduction	p. 3
Logidsm and Conceptual Analysis	p. 7
Introduction to Analysis and Proof	p. 7
Analysis and Proof in 1879	p. 12
Derivation, Proof, and Definition	p. 12
Conceptual Analysis	p. 13
Analysis in 1881	p. 18
Analysis in 1884	p. 19
Grundgesetze	p. 22
The General Picture	p. 23
Thoughts	p. 28
Thoughts and Language	p. 28
Sense and Reference	p. 37
The Structure of Sense	p. 39
Thoughts and Language Again	p. 45
Where we are	p. 50
Thoughts and Sharp Boundaries	p. 55
The Issue	p. 55
The Texts	p. 56
Piecemeal Definition and New Objects	p. 62
Ordinary Discourse	p. 68
Caesar	p. 70
Quantification	p. 72
Conclusion	p. 75
The Analysis of Arithmetic	p. 77
The Issue	p. 77
ANalysis as Thought-Preserving?	p. 79
Reference-Preservation and Analysis	p. 82
Dummett on What's Preserved	p. 87
What's Preserved	p. 89
The Case of Directions	p. 89
Numbers	p. 92
Arithmetic	p. 95
Alternative Reductions	p. 101
Conclusions	p. 102
Analysis and Consistency: The Case of Geometry	p. 108
Introduction	p. 108
Frege-Hilbert	p. 109
Hilbert's Method	p. 110
Frege's Objections	p. 112
Consistency And Concepts	p. 121
Analysis and Consistency	p. 123
The 1906 Passage	p. 125
Ultimate Analyses?	p. 128
Concluding Remarks	p. 130
Frege and Models	p. 135
Models and Consistency	p. 135
Models and Entailment	p. 137
Implications	p. 144
Summing Up	p. 146
Metatheory	p. 149
Frege's Metatheory	p. 149
Universalism and Metatheory	p. 156
The Issue	p. 156
Internal Tensions	p. 162
Soundness, Completeness, and Consistency	p. 165
Categoricity	p. 167
Conclusion	p. 170
Conclusion	p. 175
Bibliography	p. 183
Index	p. 189
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