 In his autobiography, Feyerabend acknowledged Niels Bohr’s direct influence on the development of his notion of incommensurability in the 1950s. Feyerabend recalled a conversation in which Bohr had talked about the discovery that the square root of two cannot be an integer or a fraction. According to Feyerabend, Bohr presented the event as having led to the extension of a concept of number that retained some properties of integers and fractions, but changed others; and claimed that the transition from classical to quantum mechanics was carried out in accordance with precisely this principle (1995, 78). Feyerabend also used the notion of incommensurability in a publication on Bohr’s complementarity thesis, where Feyerabend argued that Bohr’s complementarity thesis is an example of an unjustified conceptual conservativism, taking issue with Bohr’s contention that all quantum mechanical evidence will always necessarily be expressed in classical terms (Feyerabend 1958b). He presented Bohr’s defence of the principle of complementarity as based on the conviction that every experience must necessarily make its appearance within the frame of our customary points of view, which is currently that of classical physics. However, according to Feyerabend, even though classical concepts have been successful in the past, and even though at the moment it may be difficult, or even impossible, for us to imagine how to replace them, it does not follow that the classical framework could not one day be superseded by an incommensurable rival. Consequently, it does not follow that all our future microscopic theories will have to take the notion of complementarity as fundamental. Instead, according to Feyerabend, a theory may be found whose conceptual apparatus, when applied to the domain of validity of classical physics, would be just as comprehensive and useful as the classical apparatus, without coinciding with it. He claimed that such a situation is by no means uncommon, and he used the transition from Newtonian to relativistic physics to bolster his point. According to Feyerabend, while the concepts of relativity theory are sufficiently rich to state all of the facts captured by Newtonian physics, the two sets of concepts are “completely different” and bear “no logical relations” to each other (1958b, 83; 1961, 388; 1962, 88–89). This is clearly an early version of his incommensurability thesis. On Feyerabend’s fallibilist view of empirical knowledge, no element of our knowledge can be held to be necessary or absolutely certain. In our search for satisfactory explanations, we are at liberty to change any parts of our existing knowledge, however fundamental they may seem, including the concepts of classical physics.