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case reversals over

, if it is as good as the second (in the sense just defined) and the second is

not as good as it (in that sense). Then the ascending reversal sequences of the Ockham method

are all duplicated by the violator (due to nature’s winning strategy to force all convergent

methods to produce all such sequences), but the violator’s reversal sequence (3, 1) is never

matched by the Ockham method.

v

This is just a simplified, informal gloss, and there remains a great deal to be said. For example,

the order is a pre-order in general, but is a partial order if the theories are locally closed (in the

topological sense) with respect to the topology induced by possible information states. When

answers are not locally closed, we recommend shifting the question until they are. That is the

beginning of a normative theory of how to pose scientific questions.

vi

This discussion of the Copernican revolution follows Kuhn (1957).

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