This book aims to develop certain aspects of Gottlob Frege's theory of meaning, especially those relevant to intentional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege.
This book aims to develop certain aspects of Gottlob Frege's theory of meaning, especially those relevant to intentional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege.
PREFACE ABBREVIATIONS 1. THE NEED FOR A LOGICAL CALCULUS FOR THE THEORY OF SINN AND BEDEUTUNG Introduction Frege's Project: Logicism and the Notion of Begriffsschrift The Theory of Sinn and Bedeutung The Limitations of the Begriffsschrift Filling the Gap 2. THE LOGIC OF THE GRUNDGESETZE Logical Language and the Content of Logic Functionality and Predication Quantifiers and Gothic Letters Roman Letters: An Alternative Notation for Generality Value-Ranges and Extensions of Concepts The Syntactic Rules of the Begriffsschrift The Axiomatization of Frege's System Responses to the Paradox 3. SINNE AND GEDANKEN The Nature of Sinne Generally The Sinne of Incomplete Expressions and the Composition of Gedanken Context Principle Priority Thesis and Multiple Analyses: Challenges to Compositionality The Identity Conditions of Sinne and Gedanken 4. CHURCH'S LOGIC OF SENSE AND DENOTATION Overview The Method of Transparent Intensional Logic Alternatives (0) (1) and (2) and Synonymous Isomorphism The Formulation of the Systems Problems in Church's Logic of Sense and Denotation The UnFregean Elements of Church's Logic of Sense and Denotation 5. A LOGICAL CALCULUS FOR THE THEORY OF SINN AND BEDEUTUNG Basic Features Names and Variables for Sinne The New Constants of the Expanded Language Syntactic Rules of the Expanded Language Axioms and Inference Rules of the Expanded Calculi Inferences Involving Propositional Attitudes and Quantifying In Difficulties with the Expanded Calculi 6. COMPARISON WITH RUSSELL AND OTHER THINKERS Solatium miseris socios habuisse malorum. Russell's Ontology of Propositions Russell and the Principles of Mathematics Appendix B Paradox Frege and the Principles of Mathematics Appendix B Paradox Lessons Learned from Russell Other Systems of Intensional Logic 7. POSSIBLE REVISIONS TO FREGE'S PHILOSOPHY Adequate versus Ad Hoc Solutions A Cantorian Analysis of the Difficulties Dropping Classes and/or Concepts Reducing the Number of Sinne and Gedanken Ramification as a Solution to the Paradoxes The Justification of Ramification Conclusion APPENDIX: SUMMARY OF DEFINITIONS AXIOMS AND INFERENCE RULES BIBLIOGRAPHY INDEX
PREFACE ABBREVIATIONS 1. THE NEED FOR A LOGICAL CALCULUS FOR THE THEORY OF SINN AND BEDEUTUNG Introduction Frege's Project: Logicism and the Notion of Begriffsschrift The Theory of Sinn and Bedeutung The Limitations of the Begriffsschrift Filling the Gap 2. THE LOGIC OF THE GRUNDGESETZE Logical Language and the Content of Logic Functionality and Predication Quantifiers and Gothic Letters Roman Letters: An Alternative Notation for Generality Value-Ranges and Extensions of Concepts The Syntactic Rules of the Begriffsschrift The Axiomatization of Frege's System Responses to the Paradox 3. SINNE AND GEDANKEN The Nature of Sinne Generally The Sinne of Incomplete Expressions and the Composition of Gedanken Context Principle Priority Thesis and Multiple Analyses: Challenges to Compositionality The Identity Conditions of Sinne and Gedanken 4. CHURCH'S LOGIC OF SENSE AND DENOTATION Overview The Method of Transparent Intensional Logic Alternatives (0) (1) and (2) and Synonymous Isomorphism The Formulation of the Systems Problems in Church's Logic of Sense and Denotation The UnFregean Elements of Church's Logic of Sense and Denotation 5. A LOGICAL CALCULUS FOR THE THEORY OF SINN AND BEDEUTUNG Basic Features Names and Variables for Sinne The New Constants of the Expanded Language Syntactic Rules of the Expanded Language Axioms and Inference Rules of the Expanded Calculi Inferences Involving Propositional Attitudes and Quantifying In Difficulties with the Expanded Calculi 6. COMPARISON WITH RUSSELL AND OTHER THINKERS Solatium miseris socios habuisse malorum. Russell's Ontology of Propositions Russell and the Principles of Mathematics Appendix B Paradox Frege and the Principles of Mathematics Appendix B Paradox Lessons Learned from Russell Other Systems of Intensional Logic 7. POSSIBLE REVISIONS TO FREGE'S PHILOSOPHY Adequate versus Ad Hoc Solutions A Cantorian Analysis of the Difficulties Dropping Classes and/or Concepts Reducing the Number of Sinne and Gedanken Ramification as a Solution to the Paradoxes The Justification of Ramification Conclusion APPENDIX: SUMMARY OF DEFINITIONS AXIOMS AND INFERENCE RULES BIBLIOGRAPHY INDEX
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