From metaphysical principles to dynamical laws

My thesis in this paper is: the modern concept of laws of motion—qua dynamical laws—emerges in 18th-century mechanics. The driving factor for it was the need to extend mechanics beyond the centroid theories of the late-1600s. The enabling result behind it was the rise of differential equations. In consequence, by the mid-1700s we see a deep shift in the form and status of laws of motion. The shift is among the critical inflection points where early modern mechanics turns into classical mechanics as we know it. Previously, laws of motion had been channels for truth and reference into mechanics. By 1750, the laws lose these features. Instead, now they just assert equalities between functions; and serve just to entail (differential) equations of motion for particular mechanical setups. This creates two philosophical problems. First, it’s unclear what counts as evidence for the laws of motion in the Enlightenment. Second, it’s a mystery whether these laws retain any notion of causality. That subverts the early-modern dictum that physics is a science of causes

Dynamic Semantics of Plurals DPLQ⊛

AbstractThis paper proposes a dynamic semantics of plurals, DPL⊛Q, that is an extension of DPL [8] by adding binary generalized quantifiers, plural terms with join-operators as in Link [17]'s semilattice semantics of plurals, dynamic selectors, dynamic distributors and division functions. DPL⊛Q provides a formalism for handling dependent plurals, bound plurals, generic plurals, and ambiguity of collective/distributive/cumulative interpretation of plurals