What counts as a Newtonian system? The view from Norton’s dome

Abstract

If the force on a particle fails to satisfy a Lipschitz condition at a point, it relaxes one of the conditions necessary for a locally unique solution to the particle's equation of motion. I examine the most discussed example of this failure of determinism in classical mechanics-that of Norton's dome-and the range of current objections against it. Finding there are many different conceptions of classical mechanics appropriate and useful for different purposes, I argue that no single conception is preferred. Instead of arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one usefully and legitimately to adopt one conception over another in which determinism may or may not hold.

Conceptual fragmentation and the rise of eliminativism

“…SCIENTIFIC THEORY (pluralism concerning individual theories) -e.g. Fletcher (2012), partly drawing on Malament (2008) and Wilson (2009);Vickers (2013Vickers ( , 2014.…”

“…Fletcher (2012) writes as follows: Bthere are many different conceptions of classical mechanics appropriate and useful for different purposes( p.275). He continues: BIn practice, the choice of a particular formulation of classical mechanics will depend largely on pragmatic factors like what one is trying to do with the theory^(p.277).…”

Determinism and Indeterminism

“…While there is much that has been learned from this debate, I would agree with Fletcher (2012) that the question "Is Newtonian mechanics indeterministic" is too simplistic. The answer to this question depends on what one takes Newtonian mechanics to be, and there is no unequivocal answer to this question (cf.…”

“…On the contrary, the analysis of the various indeterministic systems and the detailed investigations into the reasons why determinism obtains or fails has been highly insightful. To provide a few examples, we have learned that the violation of Lipschitz continuity is benign in the sense that the force on a ball rolling off the table is not Lipschitz at the point where it looses contact (Fletcher, 2012). Zinkernagel's (2010) analysis has shown us that are two different understandings of Newton's first law (one where it is required that every force has a first "cause" and one where this is not the case) and that some cases of indeterminism can be avoided by requiring that every force has a first "cause".…”

“…Zinkernagel's (2010) analysis has shown us that are two different understandings of Newton's first law (one where it is required that every force has a first "cause" and one where this is not the case) and that some cases of indeterminism can be avoided by requiring that every force has a first "cause". Furthermore, we have learned that trying to exclude the indeterministic examples by forbidding certain kinds of idealizations is unlikely to succeed as virtually all of the idealizations are used elsewhere without any complaint (Fletcher 2012;Wilson 2009). …”