Consider a less fundamental theory T and a more fundamental theory Tf. How do the explanatory capacities of Tf bear on whether T reduces to Tf?

Introduction

How do the explanatory capacities of Tf bear on whether T reduces to Tf? I suggest there are two relevant conditions about the explanatory capacities that Tf has towards T for its epistemic reduction to Tf. These are Event and Law Explanation,1 which attempts to show how T epistemically reduces to Tf. In developing these two conditions, I analyze how they relate to Fodor's discussion of metaphysical reduction. One upshot is that these conditions do not imply token physicalism. I then consider what fundamental might mean for this proposal, and suggest understanding it as supervenience. I conclude that EE and LE alone cannot determine whether Tf replaces T or T reduces to Tf, and offer some brief suggestions.

Event and Law Explanation

Fodor (1974) argues against the unity of science, the thesis that all scientific theories can/will ultimately reduce to physics. He does this by his famous multiple realizability argument. Reductionists, motivated by the generality of physics, classically proposed the following conditions for reduction.

Consider a law of a special science S (e.g., economics) of the form:

  1. S1 → S2

Where S1 and S2 are natural kind2 predicates in S. Standard reductionist strategies to reduce a special science to physics P propose bridge laws of the form:

  1. S1 ←→ P1
  2. S2 ←→ P2

(2) and (3) link the NK predicates of S to the NK predicates of P. The NK predicates of P themselves must be in a law-like relationship with each other:

  1. P1 → P2

Given that the bridge laws hold between the NK predicates of S and P, and that the reduced predicates enter into law-like relationships with one another, we have the necessary and sufficient conditions for S to reduce to P.

The short version of Fodor's objection to the reductionist's framework is that it is incredibly implausible that for any NK predicate in S that there is a corresponding NK predicate in P (Fodor, 1974). For example, economists have laws about the circulation of money. But the kind denoted by the predicate money is realized by many different physical forms (e.g., gold, silver, or paper), so it likely doesn't correspond one-to-one with any NK predicate in physics.3

Really, as Fodor argues, reductionists are too ambitious to suggest that each predicate of S can be reduced to a predicate of P. To respect the original intuition about the generality of physics we only need to maintain token physicalism: that all events in any special science S are physical events. As Fodor argues, token physicalism is a necessary condition on metaphysical reduction, but it is not sufficient.

Fodor discusses metaphysical reduction, but we should wonder what reduction has to do with explanatory capacities. We might think that theories might metaphysically reduce, but not epistemically reduce. So, it seems natural to suggest the following condition about how the explanatory capacities of P relate to S:

Event Explanation (EE): For all events E in S, P can give an explanation of E.

EE is distinct from token physicalism as it brings explanation into the equation. Furthermore, it is possible for physics to explain E in S without E being identical to any physical event, so EE does not imply token physicalism.4 However, it is consistent with token physicalism. We ought to maintain it as a plausible way in which explanation bears on epistemic reduction. If EE were false, then there is some E in S that P can't explain. But if some (or a part of) E in S goes beyond the explanatory reach of P, it doesn't seem that S epistemically reduces to P.

In what follows, if only for simplicity, I will be assuming and discussing a version of EE. Assuming a Deductive-Nomological (DN) theory of explanation, where an explanation of an explanandum requires that it be derivable from general laws plus auxiliary conditions, the explanda (Hempel & Oppenheim 1948). The explanandum is a sentence that describes the phenomena to be explained. Assuming this, we get a version of EE I'll call "DN-EE." Expressing it generally for any fundamental theory Tf and a less fundamental theory T:

DN-EE: For all events E in T, Tf can give a DN-explanation of E.

So far, DN-EE seems to be a necessary condition for epistemic reduction. However, it is clearly not sufficient. To see why, let's turn to why Fodor argues the special sciences are autonomous from physics. Due to the implausibility of NK predicates in S corresponding one to one with NK predicates in P, Fodor suggests loosening the restriction on bridge laws (such as (2) and (3)) so that they are not necessarily laws, but rather true generalizations. This allows room for special sciences to employ distinct ceteris paribus laws from those in physics. The classical reductionist framework required laws with correspondence between NK predicates, and assuming that the laws of physics must be exceptionless, it is unclear how reductionists could account for ceteris paribus laws in the special sciences. However, it is widely known that the special sciences employ ceteris paribus laws and that these laws are useful (and perhaps indispensable) in making special science generalizations.

So the laws of special sciences cannot be metaphysically reduced to laws of physics, and therefore the special sciences enjoy an autonomy from physics. In a DN model, laws do the explanatory work in a science, so S is free to give explanations with its own set of laws distinct from those in P. This suggests the following condition:

DN-LE: For all laws L in T, Tf can give a DN-explanation of L.5

This is the epistemological correlate to the metaphysical reducibility of the laws in a less fundamental theory. The guiding idea is that if Tf can explain all the laws employed in T, there are no laws in T "over and above" Tf and it is therefore not autonomous. While DN-EE was merely consistent with Fodor's token physicalism, if Fodor's suggestion that the laws of S are irreducible to P is true, then it implies DN-LE is false. This is because if a law is metaphysically distinct from physical laws, it certainly cannot be logically derived from physical laws. And in this case blocking derivation blocks explanation.

Furthermore, there is no special problem for Tf giving a DN-explanation of a law as opposed to an event (Woodward & Ross, 2021). The explanandum of a DN-explanation is a sentence. Laws can be considered universal generalizations, and a universal generalization may be derived from others. So it also seems if DN-LE is true, then the laws of T cannot be metaphysically distinct. Because the laws can be derived entirely from Tf, there doesn't seem to be any laws "over and above" in T. To give a concrete example, consider that Tf is physics and T is chemistry. At first glance it is plausible that all the laws of chemistry may be derived from physics,6 while it is far less plausible that the laws of economics can be. If this is true, chemistry reduces whereas psychology does not.

The suggestion thus far is that DN-LE and DN-EE are jointly sufficient for T epistemically reducing to Tf. They seem to capture how there is no explanatory power in T beyond Tf. How does this relate to metaphysical reduction of T to Tf? DN-LE itself forces the metaphysical reduction of laws, whereas DN-EE is more open-ended, merely being consistent with token physicalism. Nor does the combination of the conditions imply token physicalism.7 So it is consistent to hold both conditions without endorsing type physicalism, if (ala Fodor) type physicalism implies token physicalism. These conditions are compatible with a flexible metaphysical package.

Summing up: If T and Tf fail DN-LE, like economics and physics do, then T is autonomous and doesn't reduce. If T and Tf fail DN-EE, then T doesn't epistemically reduce either. So this is the following proposal: that T epistemically reduces to Tf iff DN-EE and DN-LE.

A Gripe and an Objection

The gripe is that the proposal includes a notion like "fundamental," and that this notion is too obscure. By "more fundamental," we might mean something like "a subset of the domain of." This could capture the generality of the fundamental theory, as the generality of physics motivated this discussion in the first place (Fodor, 1974). So perhaps by "fundamental," we just mean something like EE–that all the events in T can be explained by Tf–or something about token physicalism–where all events in T are identical to events in Tf. But this clearly won't work. Neuroscience is presumably more fundamental than psychology, yet it is plausible that psychological states can be realized by non-neural brains. If so, then neuroscience events cannot be identical with psychological events, nor can neuroscience laws explain psychological events.

I think the best course of action is to hold that fundamentality is related to supervenience. A supervenes on (a "base") B iff some difference in B is required for a change in A. It is an asymmetrical relation, and seems to capture fundamentality in that if there's a physical change there might not be an economic change; but if there's an economic event change, there must be a physical change. Supervenience also explains why EE and token physicalism weren't enough to capture fundamentality. The supervenience base of all psychological events does include neuroscience events, but neuroscience is merely part of the base. All of psychology rests upon neuroscience and the hypothetical silicon-science, which could be jointly considered its supervenience base.

A more pressing question is whether DN-EE and DN-LE can determine whether Tf replaces T or T reduces to Tf. Consider phlogiston theory, which was eventually beaten out by oxygen theory. Do we wish to say that phlogiston theory was epistemically reduced to oxygen theory, or that it was replaced by oxygen theory? For a historical case, Maxwell's electromagnetic theory reduced physical optic theory by deriving all the laws of optics from Maxwell's equations, so it seems to fulfill both DN-EE and DN-LE (Ney, 2008). So perhaps oxygen theory replaced phlogiston despite never deriving the laws of phlogiston theory from oxygen theory. The present suggestion could be that theory replacement fails DN-LE whereas reduction fulfills it.

But there are two problems. First, it doesn't seem that DN-LE must fail for theory replacement. For all I've said, it is possible that oxygen theory could derive the laws of phlogiston theory, even if this wasn't the impetus for its replacing phlogiston. Oxygen theory replaced it only because it explained all events in phlogiston theory, in addition to events that phlogiston theory sought to explain. Secondly, even assuming that DN-LE fails for theory replacement, it is difficult to distinguish when a theory is replaced versus when it is a bona fide autonomous theory, such as economics. Both autonomous and replaced theories fail DN-LE, so we must determine how to distinguish them.

Continuing down this second line, we might think to involve the notion of fundamentality as supervenience to distinguish autonomous from replaced theories. It was never suggested that oxygen was more fundamental than phlogiston, or that phlogiston really supervened on oxygen. This involves a metaphysical notion to demarcate the two, but this seems acceptable–and perhaps the only way to make sense of replacement. Assuming that they have similar explanatory power, there doesn't seem to be an in principle epistemic difference between the two. Nor is one theory having more explanatory power sufficient for replacement: chemistry can perhaps be entirely explained by physics and not be replaced (because it is, evidently, still here). The discussion suggests that to make sense of replacement, it can't just be epistemic. This should make sense: theory replacement might be thought of as "throwing out" an old framework, or, for one theory to replace another, perhaps both theories must be talking about events in the same domain.

Bibliography

Fodor, Jerry A. (1974). Special sciences (or: The disunity of science as a working hypothesis). Synthese 28 (2): 97–115.

Hempel, Carl Gustav & Oppenheim, Paul (1948). Studies in the logic of explanation. Philosophy of Science 15 (2): 135–175.

Ney, Alyssa (2008). Reductionism. Internet Encyclopedia of Philosophy.

Sober, Elliott (1999). The multiple realizability argument against reductionism. Philosophy of Science 66 (4): 542–564.

Woodward, James & Ross, Lauren (2021). Scientific Explanation. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Summer 2021 Edition).

Notes

1 "Natural kind" will henceforth be abbreviated "NK."

2 Underlying this argument is an assumption that NKs cannot be "wildly disjunctive," but it isn't quite relevant for our purposes.

3 Given some plausible reductionist assumptions, does EE imply token physicalism? Assume P explains E in P terms, and that E is in S, but that E is not token identical to any physical event. So, consider that E either (1) emerges from or (2) supervenes on a physical event. (1) obviously runs counter to reductionist proclivities. (2) is much more complicated, even if we only include properties and events kosher to reductionists and exclude phenomena like emergence. Recall that Fodor is discussing contingent identity between events. But does supervenience, plus plausible reductionist assumptions, imply contingent token physicalism? No. Perhaps the window glass shattering supervenes on my throwing a ball. But my throwing the ball isn't event identical to the shattering, as they are clearly different events! Token physicalism is certainly consistent with EE, but more should be said about the metaphysics of events.

4 Without assuming DN, we would just have LE, which is open ended about what kind of explanation is involved.

5 This is probably very controversial.

6 This is because DN-LE implies nothing about the metaphysics of events, which is exactly the issue.

7 Nor does the combination of the conditions imply token physicalism.