A Dappled World, Not a Broken One: Re-evaluating Anti-Realism in Science — Epoche B2
A Dappled World, Not a Broken One: Re-evaluating Anti-Realism in Science Scientific realism holds that our best theories are approximately true [1] , that the unobservable things they invoke exist, and that the laws they state hold everywhere [2] . Nancy Cartwright denies the last of these while accepting a great deal of the rest [3] , and the resulting position is easy to caricature as scepticism about science. It is not. Her claim in How the Laws of Physics Lie (1983) and The Dappled World (1999) is that the fundamental laws buy their generality by describing conditions that mostly do not obtain, and that the reliability of science comes from somewhere else: from the construction of arrangements in which those conditions do obtain. This essay takes the claim literally and checks it with numbers, because the debate is usually conducted with none, and the sizes of the discrepancies turn out to matter to who is right. The case Cartwright actually makes Take her central example. Two of the most secure laws in physics give the force between two bodies: $$ F_G = G\,\frac{m_1 m_2}{r^{2}}, \qquad F_C = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r^{2}}, $$ with $G = 6.674\times10^{-11}\ \mathrm{N\,m^{2}\,kg^{-2}}$ the gravitational constant, $\varepsilon_0$ the permittivity of free space, $m_i$ masses in kg, $q_i$ charges in coulombs and $r$ the separation in metres. Now consider two electrons, which have both mass and charge. What is the force between them? Neither law says. Newton's law, read as a statement about the force between two bodies, gives an answer that is wrong by a factor $$ \frac{F_C}{F_G} = \frac{e^{2}}{4\pi\varepsilon_0 G\,m_e^{2}} = \frac{2.31\times10^{-28}}{5.54\times10^{-71}} = 4.17\times10^{42}, $$ independent of separation, since both laws fall off as $r^{-2}$. Cartwright's point is not that physicists are confused about this [4] . It is that the correct reading of each law makes it not a description of any actual force: each states what the force would be if the other interaction were absent. Read literally, as the deductive account of explanation requires, the law of gravitation is false of every charged body in the universe, and by forty-two orders of magnitude in this case. The superposition reply, and why it does not close the question The standard realist reply is that the laws state component forces, which combine by vector addition: $$ \mathbf{F}_{\text{net}} = \mathbf{F}_C + \mathbf{F}_G . $$ Each component law is then strictly true of its component, and no falsehood arises. This is a good reply and it is not decisive, for two reasons that can both be stated quantitatively. First, the composition rule is an additional law, not a consequence of either of the two it combines. Nothing in Newton's inverse-square law entails that gravitational and electrostatic influences add as vectors rather than, say, the stronger suppressing the weaker; that they superpose is a separate empirical commitment, and one that fails in other domains — general relativity's field equations are nonlinear, so gravitational fields do not superpose, and in quantum electrodynamics photon–photon scattering makes even electromagnetism nonlinear in vacuum at high field strengths. Superposition holds in a regime, which is precisely Cartwright's thesis about laws generally. Second, a component that never appears alone is a strange thing to be a realist about. In the electron case the gravitational component is $F_G/F_C = 2.4\times10^{-43}$ of the resultant. No conceivable measurement on that system detects it; the claim that it is nonetheless there rests on the theory, not on the evidence, which is the very inference under dispute. The realist may still be right — but the argument for the component cannot be the predictive success of the resultant, because the resultant is what would be measured whether the component existed or not. A law that fails in the classroom Cartwright's examples are sometimes dismissed as exotic. They are not. Take Galileo's law of free fall, $v = gt$ with $g = 9.81\ \mathrm{m\,s^{-2}}$, and drop a table-tennis ball. Air resistance on a sphere at everyday speeds goes as the square of the velocity, so a limiting speed is reached at which drag balances weight: $$ v_t = \sqrt{\frac{2mg}{\rho\,C_d A}}, $$ where $m$ is the mass, $\rho = 1.2\ \mathrm{kg\,m^{-3}}$ the density of air, $C_d \approx 0.47$ the drag coefficient of a sphere and $A$ its cross-sectional area. For a regulation ball, $m = 2.7\,$g and diameter $40\,$mm, giving $A = 1.26\times10^{-3}\ \mathrm{m^{2}}$ and $v_t = 8.6\ \mathrm{m\,s^{-1}}$. The speed then follows $$ v(t) = v_t\tanh\!\left(\frac{g t}{v_t}\right), $$ which at $t = 1\,$s gives $8.6\tanh(1.13) = 7.0\ \mathrm{m\,s^{-1}}$ against the law's $9.8$. After one second of a fall anyone can perform, the fundamental law is $40\%$ wrong about the speed and $19\%$ wrong about the distance. Drop a solid lead sphere of the same diameter instead and the same law is right to $0.3\%$ at the same instant: $v_t$ scales as $\sqrt{m}$, the lead sphere is $140$ times heavier at $380\,$g, so its terminal speed is about twelve times larger at $103\ \mathrm{m\,s^{-1}}$ and nothing like it is approached in one second. The law is not approximately true of falling bodies. It is very nearly exactly true of some falling bodies and badly wrong about others, and which is which depends on a parameter the law does not mention. Case What the law states What happens Discrepancy Two electrons $F = Gm_e^2/r^2$ $F \approx q^2/4\pi\varepsilon_0 r^2$ factor $4\times10^{42}$ Table-tennis ball, $t=1\,$s $v = 9.8\ \mathrm{m\,s^{-1}}$ $v = 7.0\ \mathrm{m\,s^{-1}}$ $40\%$ Lead sphere, same size, $t=1\,$s $v = 9.81\ \mathrm{m\,s^{-1}}$ $v = 9.78\ \mathrm{m\,s^{-1}}$ $0.3\%$ The strongest objection: predictive success Against all anti-realism stands the no-miracles argument, given its canonical form by Hilary Putnam [5] : the success of science, and above all its success at predicting pheno