He argues that causality is important in all the sciences except for fundamental physics, where it is not because of the following chain of reasoning:
* The equations of fundamental physics have a time reversal symmetry.
* Microscopic physics obeys those equations, and hence has no arrow of time.
* Entropy has an arrow of time, but that is classical physics, and hence not fundamental.
* Without a fundamental arrow of time, there is no way to say one thing causes another.
This is just wrong on every level. The equations of physics do have time reversal asymmetries. Even system with time reversal symmetric equations have physics showing an arrow of time. Entropy increases on both the quantum and classical levels, and is as fundamental as anything. The soft sciences prove causality often, without using any arrow of time.
As commenter Coel explains, quantum mechanics is an irreversible theory. Every observation is irreversible. Decoherence is irreversible. CP violating weak interactions are irreversible.
MP quotes Eddington and the Wikipedia Arrow of Time
Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.This statement is artfully misleading, as there is also an obvious direction of time at the microscopic level.
You might see a neutron decay into a proton, electron, and (anti-)neutrino. You never see a proton, electron, and anti-neutrino all coming together to make a neutron. Likewise, other nuclear reaction have an obvious direction of time.
Wave equations often have time reversal symmetries, but the observed waves do not. Waves go forward in time from initial conditions, and this is often obvious by looking at the wave.
All of this does not really have much to do with causality. A medical paper might have data showing that smoking causing lung cancer, but it does not need an arrow of time to reach the conclusion. There would be causality even if all the laws of physics were time symmetric.
I am not just blaming MP here, as he says he is just reciting conventional wisdom among philosophers. If so, then philosophers do not know the first things about physics.