Wednesday, August 11, 2010

A modification to the Deductive-Nomological account of explanation

there is a deficiency in the standard formulation of the deductive-nomological (D-N) model of explanation. On the standard model, one explains by citing laws and initial conditions that jointly explain the explanandum. But in fact the explanans not only should state the laws but also that they are laws or at least consequences of laws. For suppose I wish to explain why Mappy liked one of my buttons. I cite three facts: Mappy is a magpie, all my buttons are shiny and all magpies like shiny things, and on the D-N model I am done. But knowing these three facts and justifiably believing that they explain why Mappy liked one of my buttons is not sufficient for my knowing why Mappy liked one of my buttons. For to know why Mappy liked one of my buttons, I need to know that it is a law or a consequence of a law that magpies like shiny things. Unless I know this, I do not know why Mappy liked one of my buttons. Imagine, after all, someone who knows all the three facts cited but who incorrectly justifiably believes that (a) it is a mere accidental generalization that magpies like shiny things and (b) it is a law of nature that all my buttons are shiny. Such a person knows each of the three facts, but does not know why Mappy liked one of my buttons. Therefore, we should take it as part of the explanans that it is a law that magpies like shiny things.

8 comments:

Mike Almeida said...

Matters might be worse for DN. Suppose it is a law that (x)(Fx -> Gx), make it necessarily true if you like. It will entail (x)(Fx & p -> Gx), for any p. Suppose p is true (or necessarily true, if you like). It follows that anything that is explained by Gx is explained by Gx and p. But of course p won't be doing any explaining at all. This is too obvious not to have been noticed.

John said...

That's not so bad, Mike. Suppose Gx is explained by either Fx or Fx & p. We only need to have recourse to the principle that the simplest sufficient explanation is the correct one. From that, we can infer that Fx, rather than Fx & p, is the correct explanation.

Mike Almeida said...

Well, it seems simple enough to fix, but it isn't. Specifying the criteria of simplicity is a mess. Worse, you now have worries abouit begging the question. There is nothing in the DN model of explanation that tells us that complex explanations do not explain as well as simpler ones. Explanation is largely a matter of entailment alone. Nor will it do to say that we cannot strengthen the antecedent in laws, since every DN explanation needs auxilliary hypotheses, and there is always a valid corresponding conditional for the proof where we simply strengthening antecedents in laws.

Alexander R Pruss said...

Mike:

But (x)(Fx & p → Gx) may not be a law. It may only be an entailment of a law. I don't remember if Hempel and Oppenheim thought laws were closed under entailment. If they did, this is a problem. If they didn't, then maybe they don't need to make any modification to accommodate your example.

But if laws aren't closed under entailment, we'll need simplicity to figure out which nomically necessary statements are in fact laws. And that gets to the simplicity stuff. But we probably can't do without simplicity anyway in looking at scientific practice. So that's not so bad.

Alexander R Pruss said...

Here's a different counterexample to DN. I have a billiard table, and I shoot a ball at a bunch of balls on the table, whereupon they do something interesting, call it J. I videotape the whole thing. I am puzzled why they did J. Now, along come Hempel and Oppenheim and tell me this:
1. We have very good reason to think that the dynamics of billiard balls are to a very good approximation governed by a deterministic Newtonian physics with laws L1, L2, ..., Ln (Newton's laws, supplemented with some stuff about frictional forces, etc.)
2. Based on the video-tape, the initial conditions were I.
3. By (1) and (2), I have very good a posteriori reason to think that L1 & ... & Ln & I entails J.
4. Therefore, L1 & ... & Ln & I explains J.

But if I knew as much Newtonian physics as they did, and if I knew the initial conditions, the explanation in (4) told me nothing I didn't already know. I already knew that the initial conditions and these laws entailed the puzzling phenomenon J. But J was still puzzling, because I didn't know how they entailed J.

I don't know if this is a serious objection to DN. Maybe it's not: maybe the thing to say is that L1 & ... & Ln & I explains J, but there is a further question for mathematical, not physical, explanation: why do L1 & ... & Ln & I entail J.

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David said...

"On the standard model, one explains by citing laws and initial conditions that jointly explain the explanandum."

Why is your Mappy case a counterexample to this? If it isn't a law or consequence of a law that magpies like shiny things, then the example doesn't meet the D-N requirements that you have stated. The last sentence of your post isn't a correction of D-N, but simply a reiteration of it. Also, so long as one does cite a law, why is it necessary to state that it is a law as a premise in the explanation?

Alexander R Pruss said...

If p explains q, and I know that p explains q, then I know why q.

Now, let q = Mappy liked one of my buttons.
Let p = Mappy is a magpie and all my buttons are shiny and all magpies like shiny things.

If p explains q, I can know that p explains q, without knowing why Mappy liked one of my buttons. For I only know why Mappy liked one of my buttons if I know which of the conjuncts in p are laws.