Part VI: Explanation & Laws

Aristotle recognized four kinds of causes (material, formal, efficient, final) and held that scientific knowledge is knowledge of causes. Modern science has narrowed this to efficient causes — the mechanisms and processes that bring about effects — but the impulse remains the same. To explain a phenomenon is to make it intelligible by showing why it had to happen, or why it was to be expected, given certain conditions.

The philosophical study of explanation was transformed in 1948 by Carl Hempel and Paul Oppenheim’s landmark paper “Studies in the Logic of Explanation.” Their deductive-nomological (D-N) model provided the first rigorous account of what a scientific explanation is: a deductive argument in which the conclusion (the explanandum — the phenomenon to be explained) follows logically from premises that include at least one law of nature and a set of initial conditions.

The D-N model dominated for decades, but it faced powerful counterexamples that exposed its limitations. These criticisms spurred the development of alternative accounts — causal models, unificationist models, mechanistic models — each capturing different aspects of explanatory practice. Understanding these models and their limitations is essential to understanding how science works.

The concept of explanation connects to many other central topics in the philosophy of science:

Many philosophers believe that to explain is fundamentally to cite causes. We explain why the window broke by citing the rock that struck it; we explain why the patient died by citing the disease that killed her; we explain why the bridge collapsed by citing the structural flaw that gave way. On this view, explanation is essentially causal, and understanding explanation requires understanding causation.

But causation itself is philosophically problematic. David Hume’s devastating analysis showed that we never directly observe causal connections — we observe only regular successions of events. If Hume is right, how can we justify causal claims? Philosophers have proposed regularity theories, counterfactual theories, interventionist theories, and mechanistic theories of causation, each with distinctive strengths and weaknesses.

The mechanistic turn in recent philosophy of science has been especially fruitful. Rather than analyzing causation in terms of abstract philosophical categories (regularities, counterfactuals), the mechanistic approach focuses on the organized entities and activities that produce, underlie, or maintain phenomena. This approach resonates with actual scientific practice, particularly in biology, neuroscience, and medicine.

Different sciences explain phenomena in distinctive ways, raising the question of whether there is a single, unified model of explanation or irreducibly different explanatory practices:

The diversity of explanatory practices across sciences has led many philosophers to embrace explanatory pluralism — the view that different domains require different types of explanation, and no single model captures them all.

Laws of nature occupy a peculiar position in philosophy. On the one hand, they seem central to science: Newton’s laws of motion, the laws of thermodynamics, Mendel’s laws of inheritance, the law of supply and demand. On the other hand, it is remarkably difficult to say what a law of nature is — what distinguishes a genuine law from a mere accidental regularity.

Consider two true generalizations: “All gold spheres are less than one mile in diameter” and “All uranium-235 spheres are less than one mile in diameter.” Both are true. But the first is merely accidental (it just happens that no one has made a gold sphere that large), while the second is lawlike (a uranium sphere that large would undergo nuclear fission and could not maintain its structure). The difference matters for explanation, prediction, and counterfactual reasoning — but articulating it precisely has proved surprisingly difficult.

Nancy Cartwright has raised a further challenge: “the laws of physics lie.” Fundamental laws describe idealized situations that never actually obtain. No real pendulum swings without friction; no real gas is perfectly ideal; no real population mates randomly. The laws that are strictly true are the complex, messy, ceteris paribus laws of application — and these seem to lack the universality and necessity we associate with genuine laws.

Not all scientific explanations work in the same way. Philosophers have identified several distinct types:

A key question is whether these are genuinely different types of explanation or different descriptions of the same underlying explanatory relation. Pluralists hold that there are irreducibly different modes of explanation; monists seek a single account that captures what all explanations have in common.

A growing body of work explores the possibility of genuinely non-causal scientific explanation. Mathematical explanations provide particularly clear examples. Why is it impossible to cross all seven bridges of Königsberg exactly once? Not because of any causal factor, but because of the mathematical structure of the bridge network (it has more than two nodes with an odd number of edges). Why do honeybees build hexagonal cells? Partly because hexagons provide the most efficient partition of a plane into equal areas — a mathematical fact that constrains the range of possible solutions, regardless of the specific causal mechanism.

Marc Lange has developed an account of “distinctively mathematical explanations” in science — explanations where the explanatory work is done by mathematical necessity rather than causal processes. These pose a challenge to purely causal accounts of explanation and suggest that the philosophy of explanation must accommodate a broader range of explanatory structures than causal theorists typically recognize.

Similarly, structural explanations in physics — such as explaining conservation laws by appeal to symmetries (Noether’s theorem) — seem to work by citing structural or mathematical features of the world rather than causes in any straightforward sense. These examples suggest that an adequate theory of explanation must go beyond the causal and embrace structural, mathematical, and perhaps other modes of making phenomena intelligible.

The three topics of this part — explanation, causation, and laws — are deeply interconnected. Understanding these connections is essential to grasping the overall picture:

The choice of how to understand these interconnections has far-reaching consequences for one’s philosophy of science. A Humean will see laws as the most fundamental concept, with causation and explanation derived from laws. A causal realist will see causation as fundamental, with laws and explanations grounded in causal relations. A mechanist will see mechanisms as the primary explanatory units, with laws and causation as aspects of mechanistic organization.

Why do the tides rise and fall? This seemingly simple question reveals the depth and complexity of scientific explanation. Consider several possible answers:

Each answer captures something genuine about why the tides rise and fall, yet they differ in what they emphasize and how they make the phenomenon intelligible. The philosophy of explanation asks which of these (if any) is the “correct” form of explanation, and what the relationship between them is.

The philosophy of explanation has evolved through several distinct phases:

Each phase has contributed lasting insights. Aristotle taught us that explanation involves understanding why things are as they are. Hume taught us that causation is philosophically problematic. Hempel taught us that explanation should be rigorous and subject to formal analysis. Salmon taught us that causation and statistical relevance are central. And the mechanists taught us that explanation in practice involves describing organized systems of entities and activities.

The philosophy of explanation connects directly to the realism/anti-realism debate examined in Part V. The scientific realist relies heavily on inference to the best explanation (IBE) — the principle that we should believe the hypothesis that best explains the evidence. If IBE is a legitimate form of inference, it supports realism: the best explanation of science’s success is that our theories are approximately true.

But whether IBE is truth-conducive depends on what we mean by “best explanation.” If explanation is purely pragmatic (as van Fraassen argues), then the “best” explanation is merely the most useful, not the most likely to be true. If explanation is fundamentally causal or mechanistic, then IBE may be more truth-conducive, since citing real causes and mechanisms tracks something objective about the world. The philosophy of explanation thus provides crucial resources for — and constraints on — the realism debate.