Quantification : transcending beyond Frege's boundaries : a case study in transcendental-metaphysical logic
著者
書誌事項
Quantification : transcending beyond Frege's boundaries : a case study in transcendental-metaphysical logic
（Critical studies in German idealism, v. 5）
Brill, 2012
- : hardback
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注記
Includes bibliographical references (p. [223]-227) and index
内容説明・目次
内容説明
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.
Molczanow 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 Molczanow 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 Molczanow, with the help of Kant's transcendental logic. Molczanow'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.
目次
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. Schroeder'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 Schroeder'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. Goedel's Incompleteness Theorem and the Downfall of Rationalism: Vindication of Kant's Synthetic A Priori
5.1. Chomsky's Understanding Understanding and Goedel's First Incompleteness Theorem
5.2. Goedel, Chomsky, and the Synthetic Base of Mathematics. Part I
5.3. Goedel, Chomsky, and the Synthetic Base of Mathematics. Part II
5.4. Are There Absolutely Unsolvable Problems? Goedel's Dilemma
5.5. Goedel's Dichotomy: The Third Alternative
Conclusion
References
Index of Names
Subject Index
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