Restricted composition and laws of nature Ted Sider famously argues for the universality of composition on the grounds that: If composition is not universal, then one can find a continuous series of cases from a case of no composition to a case of composition. Given such a continuous series, there won’t be any abrupt cut-off in composition. But composition is never vague, so there would have to be an abrupt cut-off. Consider this argument that every velocity is an escape velocity: If it’s not the case that every velocity is an escape velocity from a spherically symmetric body of some fixed size and mass, then one can find a continuous series of cases from a case of insufficiency to escape to a case of sufficiency to escape. Given such a continuous series, there won’t be any abrupt cut-off in escape velocity. But escape velocity is never vague, so there would have to be an abrupt cut-off. It’s obvious that we should deny (5). There is an abrupt cut-off in escape velocity, and there is a precise formula for what it is: (2GM/r)1/2 where G is the gravitational constant, M is the mass of the spherical body, and r is its radius. As the velocity of a projectile gets closer and closer to the (2GM/r)1/2, the projectile goes further and further before turning back. When the velocity reaches (2GM/r)1/2, the projectile goes out forever. There is no paradox here. Why think that composition is different from escape velocity? Why not think that just as the laws of nature precisely specify when the projectile can escape gravity, they also precisely specify when a bunch of objects compose a whole? My suspicion is that the reason for thinking the two are different is thinking that composition is something like a “logical” or maybe “metaphysical” matter, while escape is a “causal” matter. Now, universalists like David Lewis do tend to think that the whole is a free lunch, nothing but the “sum of the parts”, in which case it makes sense to think that composition is not something for the laws of nature to specify. But if we are not universalists, then it seems to me that it is very natural to think of composition in a causal way: when the xs are arranged a certain way, they cause the existence of a new entity y that stands in a composed-by relation to the xs, just as when a projectile has a certain velocity, that causes the projectile to escape to infinity. Some may be bothered by the fact that laws of nature are often taken to be contingent, and so there would be a world with the same parts as ours but different wholes. That would bother one if one thinks that wholes are a free lunch. But if we take wholes seriously, it should no more bother us than a world where particles behave the same way up to time t1, and then behave differently after t1 because the laws are different. David Lewis probably has a good reason to reject the above view, though. If the laws of composition are to match our intuitions about composition, they are likely to be extremely complex, and perhaps too complex to be part of the best system defining the laws on a Humean account of laws. But if we are not Humeans about laws, and think the simplicity of laws is merely an epistemic virtue, the explanatory power of laws of composition might make it reasonable to accept very complex such laws. (I don’t endorse the view described above. I prefer, but still do not endorse, an Aristotelian alternative: when y is in a certain condition, it causes the existence of xs related to it in a composing way.) https://alexanderpruss.blogspot.com/2024/10/restricted-composition-and-laws-of.html