It is often said that biology, chemistry and other high-level sciences cannot be reduced to physics, e.g. laws governing evolution are irreducible to anything on offer in physics. On the other hand one often reads in descriptions of what a deterministic world would look like something akin to this: If one has a complete description (of every particle) of the universe at time t and knows all the physical laws that govern it, then one could at least in principle deduce the state of affairs obtaining at another time t2, where t2 could either be a future or past point in time. Since causation is a debated concept, I take it that that the main aim of scientific theories is prediction rather that (causal) explanation. But how can we reconcile the fact (?) that higher-level sciences cannot be reduced to physics and with this common description of determinism.

I think the way to sort this out is to be careful about some relevant distinctions.

A theory is a certain sort of construction that we use for prediction/explanation etc. Theories are at different levels. A biological theory or a psychological theory is at a quite different level than a theory of subatomic particles. Furthermore the laws or generalizations we use in biological or psychological explanation will by and large not appeal to the concepts we use in our physics. If we try to define biological or psychological concepts in the vocabulary of physics, we're not likely to succeed, and even if we did, it's not likely that this would be a useful way to do biology or psychology.

So theories in biology and psychology don't reduce to theories in physics if by "reduce" we have in mind deriving the higher-level laws from physical laws and facts, couched in the language of physics (together with so-called "bridge principles" to connect the two vocabularies.) That said...

It may still be that biological and psychological phenomena supervene on physical facts and laws. This would mean that there can't be a biological difference between two cases unless there's also some physical difference or other, whether or not we can say what that difference amounts to. Put another way: on this view, once the physical facts are set (whether anyone knows the details or not) so are the biological and psychological and economic and geological... facts. But this isn't a claim about deductive relationships among theories. It's a claim about "ontological" relationships among bits of the world.

As for determinism, the world can be deterministic whether or not our theories represent it that way. It's a question of whether the things themselves hang together in a certain way that our theories might or might not capture. The physical level could be deterministic, and the biological facts or psychological facts or... could supervene on the physical facts even if there's no way to deduce our biological theories or psychological theories or... from our physical theories. In that case, what happens at the biological or psychological level would ultimately be fixed by what goes on at the physical level. But from our point of view as macroscopic creatures, trying to replace biology or psychology with physics would be utterly impracticable, even if God could pull off the trick, so to speak.

This is an old-fashioned answer and there are more recent variations on it. But the distinction to keep in mind is between the way things are and the theoretical tools we use to try to capture that.

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