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Introduction The Principle of Composition A Role for HPS HPS and Realism Questions of Reality Gone Wrong: The Philosophical Importance of Force Composition Corey Dethier University of Notre Dame Philosophy Department corey.dethier@gmail.com September 19, 2017 Get Real!: Realism as a goal for the sciences and for HPS

Introduction The Principle of Composition A Role for HPS HPS and Realism Introduction

Introduction The Principle of Composition A Role for HPS HPS and Realism Introduction Question: How should the realist determine what to believe in? Brief Outline: ‚ Metaphysical debates about the principle of composition ‚ What does this debate look like from an HPS perspective? ‚ How did Newtonians determine which forces were real? ‚ Why HPS-style inquiry is useful for realism

Introduction The Principle of Composition A Role for HPS HPS and Realism The Principle of Composition

Introduction The Principle of Composition A Role for HPS HPS and Realism The Principle of Composition The effects of forces on a body combine linearly—meaning we can use vector addition to represent the net effect. A typical statement: “If two forces from different directions act simultaneously on a body, the forces are equivalent to a unique force capable of imparting to this body the same velocity that the two forces acting individually would have imparted to it.” (Lagrange 1811/1997, 17)

Introduction The Principle of Composition A Role for HPS HPS and Realism A problem for realism? Which are real: components or resultants? ‚ “should both component and resultant forces exist in conjoined circumstances, this would lead to an unacceptable overdetermination of effects.” (J. Wilson 2009, 538) ‚ “does particle A accelerate because of these many component forces, does it accelerate because of a singular resultant force, or does it accelerate because of both the component forces and the resultant force?” (Moore 2012, 360) ‚ “most philosophers in the field believe that the composition of forces is a mere fiction—for its truth would entail that both component forces and resultant forces are real, a view that even realists about forces widely reject.” (Massin forthcoming)

Introduction The Principle of Composition A Role for HPS HPS and Realism The technicalities of composition 1 Example: the solar system Given: bodies ( i ), masses ( m i ), a system ( S ), and the distance between each pair of bodies ( r ij ), Newtonian physics gives us: F ij “ G m i m j Ý Ñ z j ´ i y “ ´Ý Ñ p r ij q 2 x ˆ x j ´ i , ˆ y j ´ i , ˆ F ji (1) where Ý Ñ F ij should be read as the the force from j on i .

Introduction The Principle of Composition A Role for HPS HPS and Realism The technicalities of composition 2 From these forces, we can determine a unique force, Ý Ñ F i , such that: Ý Ñ Ý Ñ ÿ F i “ F ij (2) j P S Or the force in each direction: G m i m j Ý Ñ Ý Ñ ÿ ÿ F x i “ F x ij “ p r ij q 2 x ˆ x j ´ i , 0 , 0 y (3) j P S j P S G m i m j Ý Ñ Ý Ñ ÿ ÿ F y i “ F y ij “ p r ij q 2 x 0 , ˆ y j ´ i , 0 y (4) j P S j P S G m i m j Ý Ñ Ý Ñ ÿ ÿ F z i “ F z ij “ p r ij q 2 x 0 , 0 , ˆ z j ´ i y (5) j P S j P S

Introduction The Principle of Composition A Role for HPS HPS and Realism Upshot: nothing special about the distinction The upshot is that there’s nothing special about the “component”-“resultant” distinction as understood in the metaphysical debate. A useful way of describing transformations between models that make equivalent predictions regarding the motion of a single body. But not something we can found a metaphysical distinction on.

Introduction The Principle of Composition A Role for HPS HPS and Realism A Role for HPS

Introduction The Principle of Composition A Role for HPS HPS and Realism The limits of composition A very simple system: a b c We observe b accelerate to the right, caused either by an attraction or an impulse: a b Ý Ñ c vs. a Ý Ñ b c Then apply the third law: a b Ð Ñ c vs. a Ð Ñ b c This difference is empirically testable.

Introduction The Principle of Composition A Role for HPS HPS and Realism Upshot: a way of distinguishing between models The “very simple system” illustrates that not all models unified by the principle of composition are equivalent; even if they predict the same motion for one object, they can differ in the predictions they make about other parts of the system. Some of the models will simply have empirically falsifiable results. Not the only way that such models were constrained, however.

Introduction The Principle of Composition A Role for HPS HPS and Realism How did Newtonians determine which forces really exist? In practice, astronomers constrain their models by assigning forces only where there are (a) identifiable masses that (b) interact with every other massive body in the system according to the law of gravity. E.g., no assigning forces to (empty) points in space—have to be able to detect a massive body to vindicate any assignment.

Introduction The Principle of Composition A Role for HPS HPS and Realism How did Newtonians determine which forces really exist? This constraint allows for iterative testing procedures that narrow down the space of possible models. Allows Newcomb to argue that the forces that the Vulcan hypothesis requires are impossible as no planet or group of planets “could exist and produce the observed effect without disturbing the secular motions of the node of Mercury and Venus” (Newcomb 1882, 475).

Introduction The Principle of Composition A Role for HPS HPS and Realism The metaphysical conclusion If we take the applications of the models seriously, the real forces are those that can be attributed to physical causes like massive bodies. This might be what some of the philosophers mean by “component” forces, but avoids the incorrect implication that such forces are to be identified by being added together. Instead, identified with interactions of (robustly) detectable objects (Smith 2014)—e.g., objects whose existence can be confirmed absent the theory.

Introduction The Principle of Composition A Role for HPS HPS and Realism HPS and Realism

Introduction The Principle of Composition A Role for HPS HPS and Realism HPS and realism Some takeaways: ‚ Natural metaphysical readings of science are not always technically or historically accurate. ‚ HPS-style inquiry is (therefore) useful to determining how we should read the science. ‚ For realists—or anyone with realist inclinations—HPS-style inquiry is essential for figuring out what we ought to believe.