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Shadows of syntax revitalizing logical and mathematical conventionalism
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| 자료유형 | 단행본 |
|---|---|
| 서명/저자사항 | Shadows of syntax : revitalizing logical and mathematical conventionalism/ Jared Warren. |
| 개인저자 | Warren, Jared,author. |
| 형태사항 | 1 online resource (xx, 385 pages): illustrations. |
| 기타형태 저록 | Print version: Warren, Jared. Shadows of syntax New York, NY, United States of America : Oxford University Press, [2020] 9780190086152 |
| ISBN | 9780190086183 0190086181 9780190086176 0190086173 9780190086169 0190086165 |
| 서지주기 | Includes bibliographical references and indexes. |
| 내용주기 | PART I THE PHILOSOPHICAL BACKGROUND -- 1. What Is Conventionalism? 3 -- 2. Linguistic Conventions 21 -- PART II REVITALIZING LOGICAL CONVENTIONALISM -- 3. Unrestricted Logical Inferentialism 55 -- 4. Logical Conventionalism 95 -- 5. Alternative Conventions, Alternative Logics 125 -- 6. The Epistemology of Logic 153 -- 7. The Very Idea of Truth by Convention 171 -- PART III REVITALIZING MATHEMATICAL CONVENTIONALISM 8. From Logic to Mathematics 197 -- 9. Metaontology, Existence, and Reference 209 -- 10. Mathematical Determinacy 239 -- 11. Truth, Paradoxes, Freedom, Applications, and Knowledge 276 -- 12. Metamathematics versus Conventionalism 301 -- PART IV REFLECTIONS -- 13. Old Slogans, New Dogmas 321 -- 14. The Facts of the Matter. |
| 요약 | "What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first booklength treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax"-- |
| 해제 | Provided by publisher. |
| 일반주제명 | Convention (Philosophy) Logic. Mathematics --Philosophy. Pluralism. Convention (Philosophy) Logic. Mathematics --Philosophy. Pluralism. |
| 언어 | 영어 |
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