Quantification: Transcending Beyond Frege’s Boundaries

A Case Study In Transcendental-Metaphysical Logic

Series:

In his attempt to give an answer to the question of what constitutes real knowledge, Kant steers a middle course between empiricism and rationalism. True knowledge refers to a given empirical reality, but true knowledge has to be understood as necessary as well, and so consequently, must be a priori. Both demands can only be reconciled if synthetic a priori judgments are possible. To ground this possibility, Kant develops his transcendental logic.
In Frege’s program of providing a logicistic basis for true knowledge the same problem is at issue: his logicist solution places the quantifier into the position of the basic element connected to the truth of a proposition. As the basic element of a theory of logic, it refers at the same time to something in reality.
Mołczanow argues that Frege’s program fails because it does not pay sufficient attention to Kant’s transcendental logic. Frege interprets synthetic a priori judgments as ultimately analytic, and thus falls back onto a Leibnizian rationalism, thereby ignoring Kant’s middle course.
Under the title of the transcendental analytic of quantification Mołczanow discusses Frege’s concept of quantification. For Frege, the proper analysis of number words and the categories of quantity raises problems which can only be solved, according to Mołczanow, with the help of Kant’s transcendental logic. Mołczanow’s book thus deserves its places in the series Critical Studies in German Idealism because it provides a further elaboration of Kant’s transcendental logic by bringing it into conversation with contemporary logic. The result is a new conception of the nature of quantification which speaks to our time.
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Biographical Note

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)..

Table of contents

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

Readership

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.

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