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