Scientific Explanation

Gig Φ Philosophy: Published April, 2026

🤷 What exactly is a scientific explanation?

We know that science describes the world, but describing that something happens is very different from explaining why it happens. In the 20th century, a group of scientifically-minded philosophers known as the Logical Positivists (or the Vienna Circle) set out to rigorously define the logical structure of a genuine scientific explanation.

🔬 Banishing the "Spooky"

Philosophers like Rudolf Carnap wanted to purge science of "metaphysical" or pseudo-explanations. For example, the biologist Hans Driesch tried to explain how organisms develop and regenerate by claiming they possess an "entelechy" (a nonphysical, unobservable life force or internal purpose).

Carnap and the positivists called foul. Because the entelechy theory doesn't appeal to any testable empirical laws, and it doesn't allow us to make any predictions, it fails to truly explain anything. To be a genuine scientific explanation, an account must include at least one empirical law, and it must be capable of predicting the event it explains.

Logical Positivists

FREE PRIMARY READINGS

Hempel "Two Basic Types of Scientific Explanation"

"Commentary - Scientific Explanation"

📐 The D-N Model: Covering Things in Laws

Building on Carnap's ideas, Carl Hempel developed the most famous framework for this: the Deductive-Nomological (D-N) Model (also known as the Covering Law Model).

Deductive: The explanation takes the form of a deductively valid logical argument where the conclusion follows with necessity from the premises.
Nomological: It involves universal general laws of nature (from the Greek nomos, meaning law).

In the D-N model, an explanation has two parts.

The Explanans (the facts doing the explaining) consists of a set of initial conditions and at least one general law.
These logically imply the Explanandum (the event, law, or fact to be explained).

If you want to explain why a soap bubble expands and recedes when you put a hot glass upside down on a wet plate, you list the initial conditions (the temperatures of the glass and the trapped air) and apply the ideal gas laws. The expansion of the bubble is the necessary, logical consequence.

🎲 The I-S Model: Playing the Odds

But what happens when our laws aren't absolute universal rules, but instead deal in probabilities, like in genetics or quantum mechanics? Hempel expanded his theory to include the Inductive-Statistical (I-S) Model.

Here, the explanation is an inductive argument rather than a deductive one. Instead of a universal law, we have a statistical probability based on past observations. Because it's statistical, the Explanans doesn't guarantee the Explanandum with 100% certainty; it just confers a high probability upon it. If you take 8 milligrams of a specific antihistamine, and the statistical law says this drug brings relief 95% of the time, that serves as a highly probable inductive explanation for why your allergy attack subsided.

🥊 The Problems: Flagpoles and Birth Control

Hempel championed the Thesis of Structural Identity (or Symmetry Thesis): every good explanation is a potential prediction, and every good prediction is a potential explanation. But philosophers quickly found massive logical loopholes in this idea.

The Flagpole Problem (Asymmetry): If you know the height of a flagpole and the laws of optics, you can predict and deduce the length of its shadow. This perfectly fits the D-N model and intuitively explains the shadow. But, using the exact same laws, you can logically deduce the height of the flagpole from the length of the shadow. Is the shadow's length the explanation for why the flagpole is tall? Of course not!
The Syphilitic Mayor (Explanation without Prediction): Philosopher Michael Scriven pointed out that paresis (a form of paralysis) is only caused by untreated syphilis, but only about 10% of syphilis patients ever develop paresis. Because 10% is not a "high probability", we can't predict paresis using the I-S model. Yet, if the town mayor develops paresis, we accept that his untreated syphilis perfectly explains it. We have explanation without predictability.
Irrelevant Causes: What if Edward (a biological male) takes his wife's birth control pills every day? Can we explain why Edward didn't get pregnant by pointing to the "fact" that he took the pills, combined with the probabilistic law that birth control prevents pregnancy? It fits the logical structure of an explanation perfectly, but taking the pills is completely irrelevant to the actual cause of him not getting pregnant!

🧠 Food for Thought

Hempel’s models beautifully capture the logical rigor we want from science, but his critics highlight a glaring omission: causality.

Can we really reduce scientific explanation to a logical argument, or does a true explanation fundamentally require us to trace the physical cause-and-effect mechanisms of the messy real world?

The next time you ask "why" something happened, ask yourself if you're looking for a logical deduction, or if you're looking for the cause.