The Metaphysics of Forces

This paper defends the view that Newtonian forces are real symmetrical and noncausal relations. In the first part, I argue that Newtonian forces are real; in the second part, that they are relations; in the third part, that they are symmetrical relations; in the fourth part, that they are not causal relations, (but causal relata) by which I mean that they are not species of causation. The overall picture is anti-humean to the extent that it defends the existence of forces, irreducible to spatio-temporal relations, but is still compatible with humean approaches to causation (and others) since it denies that forces are species of causation. I shall defend the view that Newtonian forces are real symmetrical and non-causal relations. I first defend the reality of forces, by arguing that a realist view of component forces is the best way to make sense of the cases in which bodies change their disposition to move without changing their actual kinematical behaviours. It is then argued that those real forces cannot be monadic properties for there is no way for a monadic property to have a direction akin to the direction commonly ascribed to forces. In the third part, I claim that force-relations have to be symmetrical relations, on the ground that it is the best metaphysical reading of Newton’s Third Law. The last part is devoted to distinguishing forces from causation: forces have causal powers, but are not instances of causal relations, one reason for that being that they are symmetrical. 1. Forces are real: a truthmaker argument Are forces real? Following a long tradition, which has been recently revived by J. Wilson (2007), I want to argue that Newtonian forces are real, by which is meant that forces exist independently of our thinking about them and are irreducible to other same-level properties (such as mass or acceleration for instance). Before deciding whether Newtonian forces are real or not, we need first to make clear why the ontology of Newtonian Mechanics still matters today, and second to spell out what kind of ontological candidates forces are. 1.1. The ontology of Newtonian mechanics Newtonian Mechanics (NM) may seem to be of little interest for contemporary metaphysics since it has been superseded by better physical theories (quantum mechanics, the theory of general relativity). Is the ontology of NM of more than historical importance? J. Wilson (2007) has argued for a positive answer. According to her, Newtonian mechanics should be treated in the same way as the special sciences. The ontologies of thermodynamics, biology, psychology, botany or geology are still of some metaphysical importance, despite their inapplicability to the quantum world. According to Wilson, the fact that certain structurally complex entities or aggregates exhibit enough stability, independent of the details of the behaviour of their constituents, constitutes one important rationale for special sciences. The same may be true of Newtonian mechanics: though it cannot handle quantum indeterminacy, it is still close to the truth concerning the behaviour of the medium-sized world. This may be understood in two different ways: first, one may think that microphysicalism is false, and that the world is irreducibly layered. If so, Newtonian mechanics could be seen as describing and explaining sui generis emergent properties or episodes. Second, one may think that microphysicalism is true and that all the entities assumed by special sciences are reducible to microphysical ones. Even so, it is still true that the ontologies of special sciences matter: they give us candidates for reduction. If we are going to carry out a reduction of a special science, or to evaluate whether this reduction has been achieved, we need to understand its ontology. Microphysical reductionism is not eliminativism: though both agree on the ontology, reductionism holds the reduction of the entities posited by the special sciences to be an important task to achieve, contrary to eliminativism. I shall only assume that eliminativism about Newtonian mechanics is wrong. I will not decide between anti-reductionism and reductionism concerning Newtonian entities. In both cases, the ontology of Newtonian mechanics matters for contemporary metaphysics. 1.2. What do forces purport to be? I shall focus on the question of the ontology of Newtonian forces as they are referred to in the three fundamental laws of NM (Newton, 1999): First law: “Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.” Second Law: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.” Third Law: “To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction.” Before deciding whether forces are real or not it is worth spelling out what kind of ontological candidates they are. One suggestion is that the definition of forces is to be found in the Second Law. This sounds odd since prima facie Newton’s formulation does not look like a definition. Nevertheless, such a proposal is more easily understood when one considers not Newton’s own formulation of the law, but its usual mathematical translation, which states that the force exerted on a body equals the product of the mass of the body and the acceleration induced in that body: