The mathematicization of nature
This thesis defends the Quine-Putnam indispensability argument for mathematical realism and introduces a new indispensability argument for a substantial conception of truth. Chapters 1 and 2 formulate the main components of the Quine-Putnam argument, namely that virtually all scientific laws quantify over mathematical entities and thus logically presuppose the existence thereof. Chapter 2 contains a detailed discussion of the logical structure of some scientific theories that incorporate or apply mathematics. Chapter 3 then reconstructs the central assumptions of Quine's argument, concluding (provocatively) that ~science entails platonism~. Chapter 4 contains a brief discussion of some major theories of truth, including deflationary views (redundancy, disquotation). Chapter 5 introduces a new argument against such deflationary views, based on certain logical properties of truth theories. Chapter 6 contains a further discussion of mathematical truth. In particular, non-standard conceptions of mathematical truth such as ~if-thenism~ and ~hermeneuticism~. Chapter 7 introduces the programmes of reconstrual and reconstruction proposed by recent nominalism. Chapters 8 discusses modal nominalism, concluding that
Ketland, Jeffrey John
Quine-Putnam; Mathematical realism; Truth
The mathematicization of nature. This thesis defends the Quine-Putnam indispensability argument for mathematical realism and introduces a new indispensability argument for a substantial conception of truth. Chapters 1 and 2 formulate the main components of the Quine-Putnam argument, namely that virtually all scientific laws quantify over mathematical entities and thus logically presuppose the existence thereof. Chapter 2 contains a detailed discussion of the logical structure of some scientific theories that incorporate or apply mathematics. Chapter 3 then reconstructs the central assumptions of Quine's argument, concluding (provocatively) that ~science entails platonism~. Chapter 4 contains a brief discussion of some major theories of truth, including deflationary views (redundancy, disquotation). Chapter 5 introduces a new argument against such deflationary views, based on certain logical properties of truth theories. Chapter 6 contains a further discussion of mathematical truth. In particular, non-standard conceptions of mathematical truth such as ~if-thenism~ and ~hermeneuticism~. Chapter 7 introduces the programmes of reconstrual and reconstruction proposed by recent nominalism. Chapters 8 discusses modal nominalism, concluding that
nature defends quine putnam argument mathematical realism introduce_new argument substantial conception truth formulate main_component quine putnam argument namely virtually scientific law quantify mathematical entity thus logically presuppose existence thereof contains detailed_discussion logical_structure scientific_theory incorporate apply mathematics reconstructs central assumption quine argument conclude science entail platonism contains brief_discussion major theory_truth include deflationary view redundancy introduces new argument deflationary view base certain logical property truth theory contains discussion mathematical truth particular non_standard conception mathematical truth introduces programmes reconstruction propose recent discus modal conclude