Friedman's "Prediction vs. Explanation"

Eliezer Yudkowsky

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

One of the commenters links to Overcoming Bias, but as of 11PM on Sep 28th, David's blog's time, no one has given the exact answer that I would have given. It's interesting that a question so basic has received so many answers.

David D. Friedman asks:

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

"One small nitpick: It could be more explicit that in Assumption 2, B1 and B2 range over actual observation, whereas in Assumption 1, B ranges over all possible observations. :)"

Actually, I implicitly was thinking of the "B" variables as ranging over actual observations (past, present, and future) in both assumptions. But you're right: I definitely should have made that explicit.

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Friedman's "Prediction vs. Explanation"

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Friedman's "Prediction vs. Explanation"

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