Critical Thinking Note 9: Explanation


We often ask students to explain one thing or another. Judging from the single sentence or sentence fragment responses we often get, it seems to me that our students all too often don’t really understand what is being asked of them. The nature of scientific explanation has been a big topic in the philosophy of science for a century or so, and that inquiry could offer a couple of useful models. Here is an excerpt from my open source Introduction to Philosophy that addresses one helpful model of explanation:

According to the Deductive Nomological model of explanation developed by the Logical Positivist Carl Hempel, a scientific explanation has the form of a deductively valid argument. The difference between an argument and an explanation consists only their respective purposes. Formally they look just the same. But the purpose of an explanation is to shed light on something we accept as factual, while the purpose of an argument is to establish something as factual. Given this difference in purpose, we call the claim that occupies the place of the conclusion in an explanation the explanandum (it’s the fact to be explained), and the claims that occupy the place of the premises the explanans (these are the claims that, taken together, provide the explanation). In a scientific explanation, the explanans will consist of statements of laws and factual claims. The factual claims in conjunction with the laws will deductively entail the explanandum. For example, consider this explanation for why a rock falls to the earth:

  1. F = G*m1m2/r2 – Newton’s law of universal gravitation which tells us that massive bodies experience a force of mutual attraction that is proportionate to their mass and inversely proportionate to the distance between them.
  2. F=ma  – The force law, which tells us that force equals mass times acceleration.
  3. The rock has mass of 1 Kg.
  4. The earth has a mass of 5.97219 × 1024
  5. The rock was released within the gravitational field of the earth.
  6. No forces prevented the rock from falling to the earth.
  7. The rock fell to the earth.

Recall that according to the Logical Positivists, deductive logic is part of every theory, every explanatory framework. The first two claims in this explanation are statements of law from Newtonian physics. The remaining four are statements of fact. Taken together, these six claims deductively entail the explanadum, that the rock fell to the earth. This should illustrate how theories function as explanatory frameworks (as opposed to merely marking a whistle stop between educated guess and complete certainty).

One very useful thing Hempel’s account of explanation does is alert us to the argument-like structure of explanations. The basic idea here is that a complete explanation should include all of the facts involved in making the fact to be explained true. These will include both particular facts relevant to the specific circumstances of the case and general principles that belong to a broader framework for explanation, laws in the case of scientific explanations.

Hempel’s account of explanation faced a number of problems that have helped to refine our understanding of scientific explanation. We won’t address them here except to mention one because it’s amusing. Consider this explanation:

  1. Men who take birth control pills do not get pregnant.
  2. Bruce is a man and he takes birth control pills.
  3. Bruce is not pregnant.

This seems to meet all of the positivist’s criteria for being an explanation. But aside from being silly, it’s at least not a very good explanation for why Bruce isn’t pregnant.

There is a more general lesson I’d like you to take from the Logical Positivist’s account of explanation. For your entire career as a student you’ve been asked to explain things, but odds are nobody has ever really explained what it means to explain something. Personally, I don’t think I had ever given a thought to what an explanation was until I encountered the Deductive Nomological account in a Philosophy of Science class. But now you’ve been introduced to a developed model of explanation. You may not find it fully applicable to every academic situation you encounter. But if you try to make use of it by thinking of explanations as having a developed argument-like structure, you might expect your grades on future assignments in many of your classes to improve significantly.

Russ Payne

February 4, 2014

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