Frege's Conception of Logic by Patricia A. BlanchetteFrege's Conception of Logic by Patricia A. Blanchette

Frege's Conception of Logic

byPatricia A. Blanchette

Hardcover | April 11, 2012

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In Frege's Conception of Logic Patricia 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 conceptionand 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, wecan 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 significantlyfrom 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 completenessof 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 systemsand their properties in the treatment of fundamental logical properties and relations.
Patricia A. Blanchette is Associate Professor of Philosophy at the University of Notre Dame.
Title:Frege's Conception of LogicFormat:HardcoverDimensions:256 pages, 9.25 × 6.12 × 0.98 inPublished:April 11, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199891613

ISBN - 13:9780199891610

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Table of Contents

AcknowledgementsIntroduction1. Logicism and Conceptual Analysis1.1 Introduction to Analysis and Proof1.2 Analysis and Proof in 18791.2.1 Derivation, Proof and Definition1.2.2 Conceptual Analysis1.3 Analysis in 18811.4. Analysis in 18841.5 Grundgesetze1.6. The General Picture2. Thoughts2.1 Thoughts and Language2.2 Sense and Reference2.3 The Structure of Sense2.4 Thoughts and Language Again2.5 Where we are3. Thoughts and Sharp Boundaries3.1 The Issue3.2. The Texts3.3 Piecemeal Definition and New Objects3.4 Ordinary Discourse3.5 Caesar3.6 Quantification3.7 Conclusion4. The Analysis of Arithmetic4.1 - The Issue4.2 Analysis as Thought-Preserving?4.3 Reference-Preservation and Analysis4.4 Dummett on What's Preserved4.5 What's Preserved4.5.i The Case of Directions4.5.ii. Numbers4.5.iii - Arithmetic4.5.iv Alternative Reductions4.6 Conclusions5. Analysis and Consistency: The Case of Geometry5.1 Introduction5.2 Frege-Hilbert5.3 Hilbert's Method5.4 Frege's Objections5.5 Consistency and Concepts5.6 Analysis and Consistency5.7 The 1906 Passage5.8 Ultimate Analyses5.9 Concluding Remarks6. Frege and Models6.1 Models and Consistency6.2 Models and Entailment6.3 Implications6.4 Summing Up7. Metatheory7.1 Frege's Metatheory7.2 Universalism and Metatheory7.2.i - The Issue7.2.ii - Internal Tensions7.3 - Soundness, Completeness, and Consistency7.4 Categoricity7.5 Conclusion8. ConclusionBibliography