Some philosophers say that explanations involve an entailment relation, that is if X explains Y then that means that X entails Y. Is this a valid way of understanding explanations? If not, what does it mean for X to explain Y? Further reading on this would be greatly appreciated, thanks!

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    Smoking explains cancer, but it does not entail it. Swimming involves water, but it is not water. Explanations are complicated. For philosophical theories see IEP, Theories of Explanation and SEP, Scientific Explanation, Metaphysical Explanation
    – Conifold
    Commented Jun 11 at 23:50
  • @Conifold I've heard a response which goes something like this: suppose that there was a 60% chance I would develop cancer from smoking. This could just mean that the probability that smoking entailed my cancer was 60% or that I developed cancer as opposed to not developing cancer was just a brute fact.
    – Bob
    Commented Jun 12 at 1:08
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    Reverse it. Having cancer increases probability that you are a smoker, but it does nothing to explain your smoking. Lightning increases probability that thunder is coming, but even if the correlation was 100% neither would explain the other. There is clearly more to the explanatory relation than entailment, whether strict or probabilistic.
    – Conifold
    Commented Jun 12 at 1:14
  • @Conifold Why would we reverse it? Cancer is the explanandum and smoking is invoked as the explanans.
    – Bob
    Commented Jun 12 at 1:20
  • Because entailment goes both ways, hence cannot "be" explanation.
    – Conifold
    Commented Jun 12 at 1:37

5 Answers 5


If you are talking at such a very general level, then an explanation is just any more or less valid or reasonable response to a "why" or "how" question. If we generalize over all situations in which explanations are asked for, guessed, suggested, accepted and rejected, then I believe it's false to claim that all explanations contain entailments. If we restrict ourselves to scientific discourse, for instance, in physics, I believe it's also false.

"But why did Alice hit me, mommy?" "Because you took her dragon away, Bobby."

In teleological and intentional explanations there is usually some form of entailment. Perhaps not explicit entailment, but we may want to construe the explanation as if there was one. Alice became mad and wanted to punish Bobby, therefore ...

The deep blue of the sky - Is that it's true color? Or is it (caused by) of its endless depth? [Zhuang-zi]

As far as I know, Zhuang-zi was the first philosopher who asked why the sky is blue. He offered two guesses (the second one must have been exhilarating to even consider in his days!). We had to wait until modern times to find out that both guesses are wrong. The current, causal explanation is that the blue color of the sky is caused by the dispersal of light in the earth atmosphere. This in essence gives a "formal cause" (in Aristotelian speak), not an "efficient cause". In other words, it's another description of a given phenomenon, but on a different level: The fact that blue light is scattered more strongly than other colors is not something that triggers or precedes or somehow causes (in the sense of efficient cause) or entails the fact that the sky is blue. There is no "if this (explanandum)(at time t), then that (explanans)(at time t+n)" here. It is the very same fact (set of facts), described in two different ways, where one description is deeper, more precise, more powerful than the other.

Ok, now you can say: "Well, you now have two what you call "descriptions" of a given process, doesn't this require that the "explanatory" description still "entails" the other, original one?" I think that then quickly devolves into a purely semantic discussion. I'd say: "Sure, if you want to call that 'entailment', go ahead. But it's a trivial entailment. Similar to how the inference 'p then p' is trivial. It's more fruitful to think of this not as entailment between descriptions, but as a kind of equivalence of descriptions."

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    +1 "teleological and intentional explanations" And oh, how intentions and goals are often irrational.
    – J D
    Commented Jun 13 at 15:59

Explanations are not entailments. For example - “Wind blows because fan is running.” Why wind is blowing can be explained by the fan’s motion but blowing wind does not necessarily entail a fan.


You ask:

Are explanations entailments?

No, but may involve them. We can look to an explanation offered by W.H. Newton-Smith of why explanation may rely on entailment, but is not entailment itself.

In his article Explanation in the book A Companion to the Philosophy of Science, Newton-Smith opens up with an exploration of the deductive-nomological model offered by Hempel as a non-statistical formalization of scientific explanation. The model simply tries to take a set of conditions (in the spirit of Carnapian facts) and a set of laws to describe a limited thing, an event: the deductive argument would be an explanation. But even Hempel understood that entailment is only part of explanation, and was at best an ideal. Newton-Smith writes:

[e]ven when restricted to the explanation of paricular events, [DN] met insurmountable objections. Explanation is asymmetric... No model of explanation can be acceptable unless it meets this consideration.

He goes on to an example of the use of the DN model: the position of the sun and the height of the flagpole explain the length of the shadow cast by the pole. Deductive calculations get us there. But likewise, the mathematics allows us to use the model to go in the other direction. Given the length of the shadow and the position of the sun, we can calculate the height of the flagpole. But the latter fact cannot be an explanation. Lengths of shadows don't explain heights of flagpoles. Thus, entailment is a feature of explanation, but it is not explanation itself.

Thus, explanation requires things that go above and beyond entailment. Newton-Smith spends the rest of the article offering some clues. For instance, he cites Michael Scriven arguing that complete explanations can be provided without any appeal to laws, the mechanisms of entailment, at all, for instance, relying on descriptions of intention of action. Or, explanations might be modeled with causal relevancy which requires normative application or they might not because some explanations are not about causes at all. He notes explanation is linked to understanding, which is a measure of the state of mind. He ends the article with this note about the failure of science to produce an adequate model of explanation:

The current situation is an embarrassment for the philosophy of science. Indeed one might go so far as to say that it is the sort of scandal to philosophy of science that Kant thought skepticism was to epistemology.

See also:


I would say that explanation involves consideration of entailment, absolutely, but that does not mean that one system (X) entails another (Y), as in, if you have X, then you have Y, necessarily.

(If am I understanding your question correctly)

You could consider an "explanation" to be a "model" of a system, where the entailment pattern in one system is matched by the entailment pattern of another system.

A classic example would be the modeling of causal entailment in natural systems by the inferential entailment of a formal system, e.g. calculus describing the flight of a cannonball, arithmetic describing the behavior of your bank balance etc.

I've always found Robert Rosen's notion of the Modeling Relation to be insightful, where he describes a modeling relation as existing when there is a "congruence of entailment structures" between two different systems. enter image description here


An explanation definitely is an argument i.e. the explanans (that which is explained) is entailed by the explanandum (that which explains). The difference between an explanation and an argument is the nature of the conclusion (which is the explanandum for an explanation). There is little/no doubt as to the truth of the explanandum, whereas an argument's conclusion is controversial.

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