## Tuesday, February 8, 2011

### A recipe for counterexamples to the Hume-Edwards-Campbell Principle

The Hume-Edwards-Campbell (HEC) principle says that if you have a bunch of items, and each one is explained, then the whole bunch might be explained. In particular, any infinite regress might be a complete explanation. The Hume-Edwards principle replaces the "might" with "is". I've published counterexamples to the HEC before, but here is a cool recipe for generating counterexamples.

Let p1,p2,... be an explanatory regress of propositions, so p2 explains p1, p3 explains p2, and so on. Suppose (as might easily be the case) that there is some proposition q such that (a) q couldn't be self-explanatory, and (b) the pi are all clearly completely explanatorily irrelevant to q. Now, let qi=pi&q. Then q1,q2,... are an infinite explanatory regress. But if q couldn't be self-explanatory, this regress can't be completely explanatory as it does nothing to advance the explanation of q.

I might have got the basic idea here from Dan Johnson. I can't remember. The counterexamples depend on the idea that if A explains B and Q is irrelevant, then A&Q explains B&Q. I am a bit less sure of that than when I started writing this post (which was quite a while ago).

Mr Veale said...

Dr Pruss
I've tried to come up with a counter-example to HEC that my students can grasp (they're 14- 16) but I feel like I'm missing the point. I'll try posting it here, and hopefully someone can tell me what I'm ding wrong. (popularisation ain't as easy as it looks)

Mr Veale said...

To take another example from the life of a teacher, suppose we have a layabout student who is perpetually underachieving. Call him Jim. Now one day Jim presents a piece of examination work that is flawless. Not a single mistake has been made. Perhaps our teaching has brought Jim’s intellect to life.
But anyone who knows us will tell you that it is much more likely that Jim cheated. So when we check we find that he has copied his work from another student, John. So we’ve explained Jim’s answers…but then discover a bigger problem.

When we mark all the papers it transpires that every student who sat the test achieved a perfect score! Now this is practically impossible unless cheating took place. We’ll need to explain to the external examiner how this occurred.
When we investigate it transpires that John has copied of a brighter student, Jill. And it doesn’t stop there. Jill copied off Susan, Susan off Gillian, Gillian off Mike and so on. We can find out how and why each act of copying took place. In principle we could have an infinitely long list of students all copying off each other (if we taught in large enough classrooms). But even if we can explain how each act of copying took place we still have not explained why every student has achieved the perfect score.
We won’t have an explanation for Jim’s perfect score if we discover and list every act of cheating. We won’t have our explanation until we answer a fundamental question. Who sat down and worked out the perfect answer in the first place? Until we know how that perfect answer was created and made its way to our students we have not explained why every student has a perfect score. But once we have that explanation we have reached a stopping point. Nothing more need be said.

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