Between Theories: The Limits of Theory

这个项目将考察物理理论之间的关系，既使用非常技术性的数学检查，也使用对这些数学关系的含义进行更哲学的思考。这项研究的目的是对物理理论的本质达成新的哲学理解，并对理论之间的关系，如还原和解释，发展新的见解。为了做到这一点，PI将使用渐近展开数学中的最新进展来检查将物理理论描述为理论的基本参数(例如，普朗克常数)接近极限值的函数的性质。因为通常情况下，一个物理理论代表另一个物理理论的极限情况--一种理论间的还原--这种检验将为理论之间的还原关系的含义提供新的见解。从所有这些技术分析中，PI将对在科学哲学中具有普遍实用价值的理论的性质和它们的关系做出推断。

This project will examine the relationships between physical theories, using both a very technical examination of the mathematics and a more philosophic reflection on the implications of those mathematical relationships. The purpose of this investiagtion is to reach new philosophic understandings about the nature of physical theories and to develop new insights into relationships between theories, such as reduction and explanation. To do this the PI will use recent advances in the mathematics of asymptotic expansions to examine the properties of functions that describe physical theories as a fundamental parameter of the theory (say, Planck's constant) approaches a limiting value. Since it is often the case that one physical theory represents the limiting case of another--a kind of intertheoretic reduction--this examination will offer new insights into the meaning of reductive relationships between theories. From all this technical analysis the PI will then draw inferences about the nature of theories and their relationship that have general utility in the philosophy of science.