Reductive explanations in the sciences are as ubiquitous as they are illuminating. As a gloss, a reductive explanation gives an account of the nature or behaviour of a complex system in terms of the properties of its parts and their interactions. This then allows us to make predictions about the system, and to understand how it might change if things were slightly different.
Probably one of the first scientific reductive explanations you were exposed to as a child was the answer to ‘why is the sky blue?’. Whether you fully understood or not (I definitely didn’t), you might have been told that the sky is blue because light is scattered off molecules in the air that act like prisms, and the colour scattered most is blue because it has a short wavelength.
By reducing the colour to facts about properties of the sky’s constituents and light, one can go on to explain and predict what would happen if the sun hits the molecules at a different angle (as they do at sunset) or if different types or configurations of molecules are present (as they are in clouds).
Richard Corry’s Power and Influence: The Metaphysics of Reductive Explanation advocates a modification of a standard ontology of causal powers, to better understand and analyse what it takes for a reductive explanation to succeed, and highlights potential failures of the reductive method.
The book makes three key arguments. First, it argues that the current powers approach is insufficient to support the success of reductive explanations. Second, it aims to show that its ontology of power and influence is well suited to the role of supporting reductive explanation, through explicating the reductive method and its assumptions, and through showing that its position satisfies them. Finally, in order to demonstrate its explanatory power of its framework, the book addresses outstanding problems in debates concerning laws of nature, causation, emergence, and morality.
Corry argues that it is a necessary presupposition of a successful reductive method that there is some constant element, but that commonly used concepts such as behaviours, laws, dispositions, and powers cannot satisfactorily play this part. Instead, Corry’s key contribution is to introduce the notion of a ‘causal influence’ to the powers ontology: an extra element that allows us to explain how and why the reductive method works.
First, we have powers, which are the capacities or dispositions of objects to effect a certain change. Corry argues that powers alone are insufficient to provide the relevant invariance, since on a powers view dispositions are still identifiable by conditionals involving a stimulus condition and a manifestation. Thus, powers alone aren’t useful for predictions regarding situations other than the one specified, which is a key element of reductive explanation. Second, we have outcomes: the actual events that occur due to the exercise of a power. Third, influences link powers and outcomes: influences are the outcomes that powers would exert in isolation. These influences provide the invariance necessary for reductive explanation.
Corry points out that the possibility of a three-part ontology has been noticed by Molnar (), Cartwright (), and Marmodoro (), but that no one gives it significant enough explication. In sum, powers are dispositions to exert particular invariant causal influences toward a certain outcome, which combine with other influences in the context to produce the overall outcome.
The bulk of the book is spent on the second argument, that Corry’s ontology of power and influence is well suited to reductive explanation. A key part of the argument involves examining the process and assumptions necessary to make the reductive method work with a power and influence ontology.
The first step in this process is the decomposition of a complex system by positing a set of component entities and attributing causal powers to them. This involves the first assumption: the supervenience of the relevant properties of the complex system on the relevant properties of the basic objects that compose it.
The second step is identifying relevant powers and their associated subsystems, which involves identifying the set of basic powers. All influences that are relevant to the phenomenon being reduced will then be manifestations of powers in this set.
Each power has a rank, defined by the number of objects contained in the smallest system of basic objects, N, such that the influence of the power on some outcome is invariant. The associated second assumption is limited rank: when performing a reductive explanation, we must choose a value of N such that the explanatory basis for a phenomenon in the system does not include any powers that have a rank greater than N.
The third step is to calculate the basic influences: each basic influence is manifested by a single basic power, each of which are associated with certain subsystems. Thus, the influences are determined by the state of the subsystem, and this allows us to calculate the influences generated within each subsystem. This is advantageous to the reductive method in that we can identify such subsystems in larger, unfamiliar contexts and know how they behave and compose.
Finally, we combine the influences by figuring out the combined effect of the influences acting simultaneously. This involves the third assumption, that any change in a property of a basic object is determined by the set of all and only the relevant basic influences, meaning that they are each individually directed towards changes in the property at that time.
There are two further assumptions (the fourth and fifth) regarding the development and justification of a reductive explanation, termed the reductive method. The fourth assumption is that the explanation must obey the algebra of composition for influences, consisting of closure, commutativity, and associativity, and a two-place operator. The fifth and final assumption is that causal influences are uniquely characterized by the effect they would bring about if acting in isolation.
While Corry’s account provides a conceptually rich and promising explanation of why the reductive method works, I was troubled by an element of vagueness at its core, concerning his definition of the ‘same type’ of power. Let me explain.
I assume that given the functional model of powers, for two powers to be of the same type, their domain and range must be the same. This is given in Chapter 3 as the set of possible stimuli and the set of influences, respectively. In Chapter 5, we see this cashed out: both the state-spaces of the power’s associated subsystems are the same, and the influences each of these states manifests are directed towards a change in the same property.
We are told that the state-space is the space of all possible values for all the ‘relevant’ properties of the system, where I suppose the relevant properties of the system are those related to the input of the function, the possible stimuli. So for two powers to be of the same type, they must have the same possible stimuli.
However, in the following chapter, Corry considers adding two powers of the ‘same type’, and claims that the two related influence functions need not have the same domain. It is then unclear to me how to make sense of the ‘same type’ of power.
The lack of clarity surrounding this is detrimental to its force, since a key element of the account rests on it. Powers being of the ‘same type’ directly affects the projectability of explanations using powers. A key selling point of Corry’s account is that it is modular: once we understand what’s going on in one system, we can explain other systems of the same type; if we don’t understand what the ‘same type’ of power means, we can’t apply them to other systems and the account loses this key feature.
In Chapter 6, Corry rounds out his framework of power and influence by showing how this would apply to macroscopic systems. The core idea here is that since causal influences can be composed of more fundamental causal influences, so causal powers can be composed of more fundamental causal powers.
This allows the power and influence model to perform reductive explanations at anything other than the most fundamental level, which is essential to the majority of scientific explanations that involve reduction.
This chapter poses two issues for Corry’s account. First, it claims that forces can compose to form influences that are not themselves forces. There is no discussion of non-force influences composing to other non-force influences at higher levels, and it is unclear what this would look like or if it is possible.
Second, a discussion of the possibility of composite entities having non-composite, high-rank powers is promised for Chapter 10; unfortunately, I did not find this discussion. Instead, the example of a high-rank power is given in terms of a three-particle system. This was not particularly illuminating for, nor relevant to, understanding the nature of the kind of macroscopic powers that Corry discusses in Chapter 6. This is a significant limitation of the account, since such high-rank powers are an important part of his notion of emergence.
The final argument focuses on the application of the framework to laws of nature, causation, emergence, and morality.
Corry discusses laws of nature in Chapter 7, drawing on (Bird ). He explores the fit between his ontology of power and influence, and dispositional essentialism, the view that the laws of nature are those universal generalizations that are made true by the dispositional essences of the properties involved. The aim is to satisfy the non-Humean desire for explanation of regularities while avoiding the Humean concern that laws should not necessitate events. He argues that we need modal fixity to explain rather than just describe universal generalizations, and dispositional essentialism can give us this.
Corry also defends against a challenge from Cartwright (), that the laws are in fact ceteris paribus—they are only obeyed all other things being equal—and so don’t provide the kind of regularity we are looking for. He claims that there are fundamental powers immune to finks and antidotes and so are invariant, and many non-fundamental powers will be sufficiently invariant in the appropriate context and so can serve in reductive explanation.
In Chapters 8 and 9, Corry applies his framework to causation, noting a deep connection between causal and reductive explanations through explaining the world in terms of localized parts. He distinguishes two concepts of causation: production and dependence (following Hall ). He argues in Chapter 8 for a weaker relation between productive causation and causal influence than identity or reduction, namely, that our causal claims are grounded in the set of causal influences and causal powers.
On the other hand, Chapter 9 focuses on causation as dependence. Corry turns his attention to causal models as a way of developing the relation of causal dependence, claiming that they are particularly amenable to his power and influence ontology. For him, it is basic that the dependence relations are connections of causal influences, so various counterfactual and probabilistic dependencies can be grounded in them.
Chapter 10 then focuses on the concept of emergence, which it defines as the failure of reduction. This, in my opinion, is the most interesting part of the book, where we start to see the payoff from the framework that Corry has built and substantiated.
Corry defends the possibility of ontological emergence: the idea that there can be genuinely novel properties that nevertheless supervene on the properties of and relationships between an object’s parts. This is opposed to mere epistemological emergence, which is the unpredictability of some supervenient property even to the ideal knower.
He identifies ways that this could occur, each relating to the failure of a different assumption of the reduction account that I outlined above. He dismisses the rejection of the first assumption (supervenience) out of hand, since this would go against the definition of ontological emergence. He also dismisses the rejection of the third assumption, since this is essential to his power and influence framework.
Thus, the discussion really begins with the second assumption: limited rank. To violate this assumption, there must be basic powers of high rank in the system. However, this depends on the value of N we choose: Corry notes that a reductive explanation is still possible when N is less than the number of entities involved in the reduction.
He uses this idea to respond to Kim’s objections (for example, Kim , , ), which essentially argue that such emergence is logically impossible due to the impossibility of reconciling effective downward causation with physical closure. Corry claims that his power and influence framework reconciles this tension by showing that the problem arises in confusing a power with the influence it manifests. Kim has no problem with powers as causes, Corry claims, only influences; and since influences are not causes but the grounds of the connections between cause and effect, the problem dissolves.
Corry argues the failure of the fourth assumption regarding composition could count as ontological emergence if the correct composition function depends on the statistical properties of the entire set of resultant influences. Thus, it cannot be expressed pairwise and is, in a sense, more than the sum of its parts.
One possibility I would have liked to have seen explored, related to the failure of the fourth assumption, was the possibility of the emergence of laws at higher levels. In Chapter 6 Corry argues for the existence of non-fundamental powers and influences, and in Chapter 7 he argues that when properly specified they can give rise to regularities that can approximately be described as laws of nature. He does not discuss this as a relevant sense of emergence in Chapter 10, presumably because he claims that these higher-level laws can always be expressed as composed from more fundamental powers.
However, if the fourth assumption fails at higher levels, this may not be so. An example from physics is the second law of thermodynamics, which is explained via a statistical postulate. This is a good candidate for a law whose correct composition function depends on the statistical properties of the whole set of resultant influences. Investigating this link would have tied in nicely to his claims at the end of Chapter 6 regarding the different sciences having different explanatory bases, and failing to do so indicates that there may be some important phenomena that Corry’s account does not apply to.
Finally, in Chapter 11, Corry applies the power and influence framework to moral theory, claiming it to be a middle ground between deontology and consequentialism. Though this is an intriguing concept, it felt a little out of place in a book focused on reduction in science, and I feel the discussion might have been better had elsewhere.
In sum, Power and Influence: The Metaphysics of Reductive Explanation is a well-developed approach to an important topic, and provides many important considerations not only for those interested in reduction, powers, and metaphysical explanation, but also for those working in the areas of causation and emergence to which Corry applies his framework.
Anaïs Rebecca White
University College London
Bird, A. : Nature’s Metaphysics: Laws and Properties, Oxford: Oxford University Press.
Cartwright, N. : ‘Causal laws, policy predictions and the need for genuine powers’, in T. Handfield (ed.), Dispositions and Causes, Oxford: Oxford University Press, pp. 127–57.
Hall, N. : ‘Two Concepts of Causation’, in J. Collins, N. Hall and L. Paul (eds), Causation and Counterfactuals, Cambridge, MA: MIT Press, pp. 225–76.
Kim, J. : ‘“Downward Causation” in Emergentism and Non-reductive Physicalism’, in A. Beckermann, H. Flohr and J. Kim (eds), Emergence or Reduction? Essays on the Prospects of Nonreductive Physicalism, Berlin: Walter de Gruyter.