In our previous lesson, we explored Inference to the Best Explanation (IBE) as a cornerstone of scientific reasoning. We treated the notion of "explanation" as intuitively understood, focusing on how we might infer the truth of the "best" one. But this naturally begs the question: what exactly is a scientific explanation? What is the structure of this thing we are supposedly inferring?
This lesson delves into that very question. We will move from using "explanation" as a tool to placing it under the philosophical microscope. Our goal is to distinguish between three major families of models that philosophers have proposed to capture the essence of scientific explanation:
- The Deductive-Nomological (D-N) model, which sees explanation as a logical deduction from laws of nature.
- Causal models, which argue that to explain something is to lay bare its underlying causal mechanisms.
- Unificationist models, which equate explanation with fitting phenomena into a single, cohesive theoretical framework.
By dissecting these models, we can begin to appreciate the formal structures that might underpin the explanatory virtues—like scope, precision, and mechanism—that we discussed in the context of IBE.
1. The Classic View: Explanation as Logical Argument
The first systematic and highly influential model of scientific explanation was developed by the logical empiricist philosopher Carl Hempel. His Deductive-Nomological (D-N) model, often called the "covering law" model, proposes a simple yet powerful idea: to explain a phenomenon is to show that it was to be expected by demonstrating that its description can be logically deduced from a set of general laws and specific initial conditions.
Let's break down the components of this model with the help of a video that lays out Hempel's project.
Scientific Explanation 1 - The Deductive-Nomological Model
This video, "Scientific Explanation 1 - The Deductive-Nomological Model" by Kane B, provides a clear and thorough introduction to Hempel's theory, its philosophical motivations, and its structure.
Please watch the following segments to understand the core of the D-N model: The D-N Model's Structure: This section introduces the key terms explanandum (the phenomenon to be explained) and explanans (the statements that do the explaining). Pay close attention to the structure: Laws of Nature (e.g., All metals expand when heated) Initial Conditions (e.g., This piece of mercury is a metal and was heated) Explanandum (e.g., This piece of mercury expanded) The relationship must be a valid deductive argument. What is a Law?: The model hinges on the concept of a "law of nature." This part explores the distinction between true, law-like regularities and merely "accidental" regularities, introducing the idea that laws support counterfactual conditionals. Further Requirements and Examples: Hempel adds that the premises of the explanans must be empirically testable and true. The video provides an excellent example from physics using Newton's second law, F=ma, which should be very familiar. The Symmetry Thesis: This is a crucial consequence of the D-N model. It claims that explanation and prediction are two sides of the same coin; they have the exact same logical structure, differing only in whether the explanandum is known before or after the fact.
The D-N model's appeal lies in its logical clarity and its alignment with many paradigmatic examples from physics. Explaining the trajectory of a projectile using Newtonian mechanics is a perfect D-N explanation: from the laws of motion and gravity (the nomological part) and initial conditions like mass, initial velocity, and launch angle, you can deduce the subsequent path. As Hempel puts it, the explanation shows that the phenomenon was to be expected.
Problems with the D-N Model
Despite its initial appeal, the D-N model was quickly shown to suffer from significant counterexamples. The very elegance of the Symmetry Thesis turns out to be its downfall, as it fails to capture two crucial features of explanation: asymmetry and relevance.
The Asymmetry Problem
We often think of explanation as having a direction. Causes explain effects, but effects don't explain causes. The D-N model, being based on logical deduction, struggles with this. The classic example is the flagpole and its shadow.
Using the height of the flagpole (), the angle of the sun (), and the laws of trigonometry and the rectilinear propagation of light, we can deduce the length of the shadow (). This fits the D-N model perfectly and seems like a good explanation.
However, we can also perform the reverse deduction. From the length of the shadow (), the angle of the sun (), and the same laws, we can deduce the height of the flagpole (). This derivation also perfectly fits the D-N model. Yet, intuitively, it is not an explanation. The length of the shadow does not explain the height of the flagpole; rather, the height of the flagpole explains the length of the shadow. The D-N model cannot account for this explanatory asymmetry.
The Irrelevance Problem
An argument can satisfy all the D-N criteria and still be a terrible explanation because the premises are irrelevant to the conclusion, even if they are part of a valid deduction.
Scientific Explanation - Stanford Encyclopedia of Philosophy
The Stanford Encyclopedia of Philosophy (SEP) entry on "Scientific Explanation" provides concise summaries of the classic counterexamples.
Please read the subsection on counterexamples to sufficiency, beginning with Explanatory Irrelevancies. This covers both the flagpole example and the famous "explanatory irrelevancies" example involving a man taking birth control pills.
As the reading shows, you can construct a D-N argument to "explain" why a man, John Jones, did not get pregnant by citing the "law" that all males who take birth control pills fail to get pregnant, and the initial condition that John Jones took the pills. The argument is deductively sound, but the explanans is completely irrelevant. Mr. Jones's ingestion of birth control pills has nothing to do with his non-pregnancy.
These problems suggest that nomic expectability—showing that an event was to be expected based on laws—is not sufficient for explanation. Something crucial seems to be missing: causation.
2. The Causal-Mechanical Model
The failures of the D-N model led many philosophers, most notably Wesley Salmon, to argue that explanation is not about logical arguments but about tracing causal connections. To explain an event is to show how it fits into the causal structure of the world—to expose the physical mechanisms that brought it about.
Salmon's view evolved over time, but his mature theory is known as the Causal-Mechanical (C-M) model. It is built on two key concepts: causal processes and causal interactions.
Scientific Explanation 3 - The Causal-Mechanical Model
This video, "Scientific Explanation 3 - The Causal-Mechanical Model," provides an excellent overview of Salmon's theory.
Please watch the following segments: Introduction to the Causal Model: This briefly introduces the motivation for turning to causation. Statistical Relevance and Screening Off: This covers Salmon's earlier ideas. The key concept here is "screening off": if a factor C is the common cause of A and B, then knowing C makes A and B statistically independent. For example, the drop in a barometer (A) is correlated with a storm (B), but both are caused by a drop in atmospheric pressure (C). Given the drop in atmospheric pressure, the barometer reading provides no additional information about the storm. This helps distinguish correlation from causation. Causal Processes and Interactions: This is the heart of the C-M model. A causal process is a process capable of transmitting a "mark" (a local modification). A moving billiard ball is a causal process; its shadow is a pseudo-process. A causal interaction is an intersection of causal processes that modifies both. Explanation as Exposing Mechanisms: This section summarizes the model. To explain an event is to trace the web of causal processes and interactions leading to it. This provides understanding by showing how the world works, not just by showing that an outcome was expectable.
The C-M model directly solves the problems of the D-N model.
- Asymmetry: The flagpole causes the shadow, but the shadow does not cause the flagpole. The causal relationship is asymmetric, so the explanation is too.
- Irrelevance: Taking birth control pills does not initiate any causal process that results in a male's non-pregnancy. Therefore, it is explanatorily irrelevant.
The C-M model offers a "bottom-up" view of explanation. We start with a specific event and trace the causal chains and mechanisms backwards, uncovering the nitty-gritty details of how it came to be.
Problems with the C-M Model
While intuitive, the C-M model faces its own challenges.
- Explanations without Spatio-Temporal Mechanisms: Some explanations don't seem to involve the transmission of a mark or energy. Explanations by omission (e.g., "The plant died because I didn't water it") are one category. More relevant to your background, some explanations in fundamental physics seem to appeal to structural features of the world rather than mechanisms. For instance, explaining a particle's trajectory by appealing to the geometric structure of spacetime in General Relativity might be seen as a non-causal, structural explanation.
- The Problem of Causal Relevance: Just as the D-N model struggled with explanatory relevance, the C-M model struggles to distinguish which features of a causal process are relevant. When a cue ball hits an eight ball, it transmits a mark (e.g., a bit of blue chalk) and it also transmits momentum. Both are transmitted by a causal process. But only the momentum is explanatorily relevant to the eight ball's subsequent motion. The C-M model, based simply on the ability to transmit any mark, doesn't automatically give us the tools to distinguish the relevant marks from the irrelevant ones.
3. The Unificationist Model
A third major approach takes a completely different tack. Instead of focusing on deduction from laws or tracing causal mechanisms, unificationist models propose that the essence of explanation is organizing and systematizing our knowledge. Scientific understanding increases when we reduce the number of independent phenomena we must accept as brute facts. An explanation is good to the extent that it demonstrates how a particular phenomenon fits into a general, unified picture of the world.
This "top-down" view was developed by Michael Friedman and refined by Philip Kitcher. For Kitcher, science explains by repeatedly using a small number of stringent argument patterns to derive a large number of conclusions.
salmon-scientific-explanation.pdf
This paper by Wesley Salmon himself provides a remarkably clear and fair-minded overview of the different traditions and argues for their reconciliation.
First, read the section "Explanation as Unification". This introduces the core idea from Friedman and Kitcher: increasing understanding by reducing the number of independently acceptable assumptions. Next, read these three sections together: "Some New Perspectives" "Rapprochement?" "Two Concepts of Explanation" In these sections, Salmon masterfully contrasts the "bottom-up" causal view with the "top-down" unificationist view. He then uses compelling examples from physics and biology to argue that these are not competing but complementary approaches to explanation.
Salmon's first physics example is perfect for you.
- The Balloon in the Accelerating Plane: Why does a helium balloon move forward when a plane accelerates for takeoff?
- Causal/Mechanical Explanation (Bottom-Up): When the plane accelerates, the air molecules are pushed towards the back, creating a pressure gradient from rear to front. The buoyant force pushes the less-dense balloon in the direction of lower pressure, i.e., forward. This is a story about forces and local interactions.
- Unificationist Explanation (Top-Down): We invoke Einstein's Principle of Equivalence, which states that a uniform acceleration is equivalent to a gravitational field. The forward acceleration of the plane creates a "gravitational field" pointing towards the rear. A helium balloon rises against gravity. Therefore, it will "rise" against this new field, moving forward. This explanation works by showing how this surprising phenomenon is just another instance of a deep, fundamental principle of physics.
As Salmon argues, both are perfectly good explanations. The causal one tells us how the mechanism works, while the unificationist one shows us how the phenomenon fits into our broader physical worldview. Neither seems intrinsically superior; their appropriateness might depend on the context and the audience.
Conclusion: A Dualist View of Explanation
We began by seeing how IBE requires a concept of "explanation," and we have now explored three major attempts to define it.
- The D-N Model proposed that explanation is nomic expectability via deductive argument. It established the field but ultimately failed because it could not handle asymmetry and irrelevance.
- The Causal-Mechanical Model proposes that explanation is the exposition of underlying mechanisms. This "bottom-up" approach tells us how things work.
- The Unificationist Model proposes that explanation is the systematization of knowledge under a minimal set of general principles. This "top-down" approach shows us why things fit into a coherent worldview.
Rather than seeing the causal and unificationist models as rivals in a zero-sum game, we can follow Salmon's suggestion and view them as two complementary aspects of scientific understanding. The world is a complex web of causal processes, and science seeks to uncover them. The world is also governed by a few deep regularities, and science seeks to discover them and use them to unify our knowledge. A complete scientific understanding likely involves both: knowing the nitty-gritty mechanisms and seeing how those mechanisms are manifestations of fundamental, unifying principles.
Preview of the Next Lesson:
Our discussion has touched upon how scientists explain phenomena in biology (evolution), classical mechanics (forces), and general relativity (spacetime structure). Much of your own work involves another crucial scientific tool: computational models and simulations. In our next lesson, we will investigate the role and epistemic status of these models. Are they just complex calculators, or can they provide genuine scientific explanations in their own right? This will allow you to directly connect these philosophical debates to your own research experience in simulating bubble rafts and barchan dunes.