The Many Foundations of Newtonian Dynami

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

SES 0211011 The Many Foundations of Newtonian Dynamics Lawrence Sklar, University of Michigan From its earliest days Newtonian dynamics has been formulated in terms of a variety of foundational principles. The initial varied foundations proliferated in the 18th and 19th centuries, and this variety of possible foundational versions of the theory was augmented by a number of important additional reconstructions of the theory's first principles in the 20th century. Some of these alternative foundations of the theory were motivated by considerations of mathematical simplicity or elegance, or were generated primarily out of the desire to find versions of the theory particularly suitable for problem solving in novel ranges of applications of the theory. But a number of the alternative foundations were strongly motivated by the desire to provide resources that would help resolve long-standing interpretive issues with the theory. This project provides some discussion of the historical development of the panoply of alternative foundations for the theory. The primary goal of the research, however, is to explore a number of philosophical, methodological and interpretive issues that reveal how the possibility of alternative reconstructions of the theory plays its role in ongoing interpretive debates. The PI focuses on a number of foundational structures for the theory, including contemporary axiomatizations, contemporary Machian versions of the theory, and versions of the theory that rely on using spacetime concepts from relativistic theories, to reconstruct Newtonian dynamics and gravitational theory, and contemporary foundations based on extremal principles. Three specific issues are to be treated. First, exponents of alternative axiomatizations of Newtonian dynamics have taken deeply opposed attitudes toward the concept of "force" in the theory. Is force an uneliminable component of the ontology required by the theory, or can its place be given a completely representationalist account? How do the new axiomatic reconstructions play into the (very old) debate? Second, three separate foundational reconstructions can play important roles in the famous debates about the nature of space and time, debates reaching back to the controversy between Leibniz and Newton at the very beginnings of the theory. Structuralist axiomatizations provide a newly coherent approach to a representationalist version of the theory that can be used both by substantivalists and relationists to back up their claims. Third, the spacetime versions of the theory relying on apparatus retro-fitted to the theory from special and general relativity provide a new context in which the old ontological debate can gain new insights. Contemporary Machianism provides, perhaps, the version of the theory most suited to the relationist. But its nature and its relation to the orthodox theory opens up many interesting questions about what it is to iointerpretli a foundational theory. Contemporary formalizations of the theory that ground it in an extremal principle allow us new insights into the question of the legitimacy of such modes of explanation as fundamental to a theory, rather than as mere derivatives from a causal mode of explanation.