The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.

We cannot know something unless it is true. The things that we know, therefore, must be logically consistent. Moreover, we cannot know something unless we are justified in believing it. But it does not obviously follow that the things that we are justified in believing must be consistent with each other. For we can be justified in believing something that turns out to be false. Knowledge entails truth and hence consistency. Rationally justified belief does not entail truth and it may (...) not entail consistency.Knowledge, however, requires especially good justification. We can have reason to believe something that happens to be true, even good reason, without our belief being so well-grounded that we know it to be true. (shrink)

(1980). The development of attitudes to the wave-particle duality of light and quantum theory, 1900–1920. Annals of Science: Vol. 37, No. 1, pp. 59-79.