Quantification: Transcending Beyond Frege’s Boundaries

Aleksy Molczanow, Dr Habil. (1994) in General and Comparative Linguistics, Adam Mickiewicz University in Poznań, is Associate Professor of Logic and Methodology of Science at Rzeszow University, Poland. He has published extensively on linguistic, logical and philosophical aspects of quantification including Quantification and Inference (2002)..

All those interested in the history of philosophy, German idealism, Kant’s transcendental philosophy, philosophical logic, mathematical logic, semiotics, foundations of mathematics, as well as analytic philosophers, structural and generative linguists.

Preface

General Overview

The Transcendental Dialectic of Quantification

CHAPTER 1. The Favoured Distinction
1.1. Foundational Goals – Strategy and Tactics
1.2. Natural Language vs. “Formalised Language of Pure Thought”
1.3. Grammar vs. Language: The Quest for Basic Distinction
1.4. Extending Function Theory
1.5. The True Basis of Frege’s Logic: Function or Relation?
1.6. Frege’s New Way of Conferring Generality: Empty Placeholders in the Context of the Conditional
1.7. Schröder’s Objection Revisited
1.8. Frege’s Hidden Agenda
1.9. The Fregean Quantifier and the Philosophical Clarification of Generality: Frege’s Misjudgment and Heidegger’s Prophecy
1.10. GTS as Games with Tainted Strategies

CHAPTER 2. The Principle of Identity and its Instances
2.1. The Aboutness of Propositions
2.2. Frege, Euler, and Schröder’s Quaternio Terminorum
2.3. Ockham and Truth in Equation
2.4. Frege’s Improvement on Kant: Synthetic Statements as Kind of Analytic
2.5. The Burden of Proof

The Transcendental Analytic of Quantification

CHAPTER 3. Reference and Causality
3.1. ‘Hilfssprache’ vs. ‘Darlegungssprache
3.2. Frege’s Constant/Variable Distinction vs. Peirce’s Type/Token Distinction
3.3. The Generality of Reference and the Reference of Generality
3.4. Peirce’s Real Dyad and Causality
3.5. A Dual Perspective on Causality and Mind-Independence
3.6. Negation, Mind Independence, and the Tone/Token/Type Distinction

CHAPTER 4. Peirce’s Categories and the Transcendental Logic of Quantification
4.1. Degenerate Thirdness vs. Thirdness as Relationship
4.2. Vendler’s Query: ‘Each’ and ‘Every’, ‘Any’ and ‘All’
4.3. Further Keys to Addressing Quantification: Non-Partitive vs. Partitive Use of Quantifiers
4.4. Earlier Proposals for Quantifiers
4.5. Jackendoff’s Query Revisited: The Purloined Pronoun
4.6. Jackendoff’s Query Revisited: The Hidden Identity

CHAPTER 5. Gödel’s Incompleteness Theorem and the Downfall of Rationalism: Vindication of Kant’s Synthetic A Priori
5.1. Chomsky’s Understanding Understanding and Gödel’s First Incompleteness Theorem
5.2. Gödel, Chomsky, and the Synthetic Base of Mathematics. Part I
5.3. Gödel, Chomsky, and the Synthetic Base of Mathematics. Part II
5.4. Are There Absolutely Unsolvable Problems? Gödel’s Dilemma
5.5. Gödel’s Dichotomy: The Third Alternative

Conclusion

References

Index of Names

Subject Index