Diversity in “Cause”

This chapter applies the diagnostic lessons of the previous chapter to familiar philosophical controversies with respect to causation, in which the word “cause” appears to highlight different forms of physical circumstance depending upon the context in which it is employed. By examining the modeling of billiard ball behavior from a multiscalar point of view, it becomes easy to appreciate why “cause” must naturally adapt its referential attachments in a variable manner, for essentially the same “division in linguistic labor” reasons that lead the word “force” to distinct forms of applicational attachment. Often we fail to notice the tacit structural safeguards that render such context-sensitive patterns of usage effective within our everyday employments. This chapter then argues that conceptual analyses of this “division of labor” character supply better answers to many of the standard “small metaphysics” issues that arise whenever a natural language gradually increases it applicational scope. From this perspective, the standards of “ersatz rigor” associated with theory T conceptions of philosophical analysis rest upon a faulty diagnosis of how the conceptual tensions of everyday life should be remedied, in a manner analogous to Hertz’s mistaken embrace of single-leveled axiomatics.

Collision of two coins on a horizontal surface

Oblique angle collisions of two penny coins on a smooth, horizontal surface were filmed with a video camera to investigate the physics of the collision process. If one of the coins is initially at rest, then the two coins emerge approximately at right angles, as commonly observed in billiard ball collisions and in puck collisions on an air table. The coins actually emerged at an angle less than 90 degrees due to friction between the coins, which also resulted in both coins rotating after the collision. At glancing angles, the friction force was due to sliding friction. At other angles of incidence the coins gripped each other and the friction force was then due to static friction.

Facts and Values

This chapter introduces the first of the four main subjects of the book, Philippa Foot, as well as sketching the philosophical outlook against which all four would argue in later years. A young Foot, recently returned to Oxford, confronts for the first time the horrors of the Nazi regime, through a newsreel exposing conditions in the concentration camps. For Foot, this moment encapsulated a major failing of philosophical ethics in the mid-twentieth century: its inability to grapple with real evil. The contemporary philosophy against which Foot and her friends would revolt depended on a background picture, the “billiard-ball” picture of the universe as nothing but inert, value-free matter. A fact–value dichotomy was grounded in this picture, positing that no ethical propositions can validly derive from fact statements; these together led to what Lipscomb calls the “Dawkins sublime”—the Romantic view that adults must bravely face this harsh and denuded world.

Computational Study of the Dynamics of an Asymmetric Wedge Billiard

We introduce the asymmetric wedge billiard as a generalization of the wedge billiard first studied by Lehtihet and Miller in 1986. This is a billiard system in which the billiard ball moves under the influence of a constant gravitational field, colliding elastically with two wedge walls with the collisions obeying the reflection law. Collision maps are given from which derivatives and area-preservation (or lack thereof) were determined. Expressions for the fixed points of the collision maps were also calculated and discussed. Long-term dynamics were determined computationally from which we observed integrable, quasi-periodic and chaotic behavior which were all dependent on the wedge angles.