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observable. Heisenberg affirmed the view that the physicist should consider only observable magnitudes, and for that reason he developed the matrix mechanics, which treats only of the frequencies and amplitudes associated with the lines in the spectrum of the atom. Heisenberg also stated that he was using the same philosophy that Einstein had used, when the latter had rejected the concept of absolute space and time in developing relativity theory.

      Einstein then replied that he no longer accepted the positivist view, because the physical theory decides what the physicist can observe. This idea that theory determines what is observed is philosophically very strategic, because it contradicts the underlying positivist assumption that there is a dichotomous distinction between the descriptive language about what is observable on the one hand, and the theoretical language about what is not observable on the other hand. When this dichotomy is denied, the positivist program of building science on firm foundations of observation is rendered untenable.

      In the chapter titled “Fresh Fields (1926-1927)” Heisenberg describes the arguments between Niels Bohr and Erwin Schrödinger concerning the issue of the wave verses the particle views in microphysics and of the statistical approach taken by 1954 Nobel-laureate Max Born in 1927. Born maintained that Schrödinger’s wave function can be construed as the measure of the probability of finding an electron at a given point in space and time. Heisenberg accepted Born’s probability interpretation, but there still remained a problem in Heisenberg’s mind: Born’s interpretation did not explain how the trajectory of an electron particle in the cloud chamber could be reconciled with the wave mechanics. Particle trajectories did not figure in the matrix mechanics, and wave mechanics could only be reconciled with the existence of a densely packed beam of matter if the beam spread over areas much larger than the diameter of an electron.

      With this problem in mind Heisenberg remembered his conversation with Einstein the previous year, specifically Einstein’s statement that it is the theory that decides what the physicist can observe. Einstein’s discussion with Heisenberg on the day in 1926, when Heisenberg had first presented his matrix mechanics in Berlin, led Heisenberg to recognize in 1927 that it was the classical theory that led him to think that the tracks in the Wilson cloud chamber represent the movement of a particle as having a definite position and velocity that defined its trajectory. Recognition of the interpenetration of theory and observation led Heisenberg to reconsider what is observed in the cloud chamber. He then rephrased his question about trajectories in terms of the quantum theory instead of the classical theory; he asked: Can the quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately at a given velocity?

      In answer to this new question he found that these approximations could be represented mathematically, and he called this mathematical representation the “uncertainty relations”, also known as the “indeterminacy principle”. On this principle the limit of accuracy with which both position and momentum can be known is defined in terms of Planck’s constant. In the view of Heisenberg and those who advocate the “Copenhagen interpretation” this necessary degree of approximation is not merely a measurement inaccuracy, but is imposed by the nature of the universal quantum of action. Einstein’s semantical principle, that theory decides what the physicist can observe, became one of the cornerstones of the post-positivist philosophy of science as articulated both by Karl Popper and by the contemporary pragmatists; it led the contemporary pragmatist philosophers to reject the positivist separation of theory and observation.

      Heisenberg also describes his thought processes in this discovery experience in his chapter on the history of quantum theory in his Physics and Philosophy (1958). There he says that he turned around a question: instead of asking how the known formalism of Newtonian physics could be used to express a given experimental situation, he asked whether or not only such experimental situations can arise in nature as can be expressed in the mathematical formalism of his matrix mechanics. This recounting of his thinking gives greater emphasis to the ontological commitment that characterizes the “indeterminacy principle”, according to which there does not simultaneously exist in reality both a determinate position and a determinate momentum for the electron. As it happens, Einstein was never willing to accept the ontology of the Copenhagen interpretation, even though Heisenberg attempted to do the same thing with his matrix mechanics that Einstein did with the Lorentz transformation, when the latter interpreted the Lorentz equation in non-Newtonian terms of actual time instead of apparent time and redefined the concept of simultaneity. Einstein maintained contrary to the Copenhagen interpretation that a more “complete” microphysical theory is needed, which would satisfy his own ontological criteria for physical reality. In imitating Einstein’s reinterpretation of the Lorentz transformation, Heisenberg was practicing scientific realism, i.e., ontological relativity according to which ontological commitment is extended to the most empirically adequate theory. The pragmatist philosophy of language implies this practice, in which it might be said that a carte blanche metaphysical realism is presumed, while the ontology describing reality is supplied by empirical science; it is a realism which is a blank check for which scientific theory specifies its cash value, and for which empirical criticism backs its negotiability.

      Heisenberg did not escape the influence of positivism, even though he had departed from it in a very fundamental way to develop the indeterminacy relations. Another influence upon his thinking was Bohr’s philosophy of knowledge. Bohr did not explicitly embrace positivism, but in his view classical physics is permanently valid and must serve as the language of observation, in which all accounts of evidence in physical science must be expressed. Heisenberg’s attempt to reconcile the contrary influences of Einstein and Bohr resulted in his developing his semantical thesis of “closed-off theories.” This is his attempt at a systematic philosophy of language for science. It is different from the logical positivist philosophy, but due to Bohr’s influence it is more like positivism than the contemporary pragmatism. Einstein and Heisenberg had made very insightful criticisms of positivism, but neither produced a new systematic philosophy of language adequate to their insights in physics, however portentous these insights have turned out to be. The portended contemporary pragmatist philosophy of language and science was as great an intellectual revolution in philosophy as the revolutions in physics.

      Comment and Conclusion

      This chapter examined two variations on positivism formulated by two turn-of-the-twentieth-century physicists, and previewed the story of positivism’s rejection by the physicists who made the two great scientific revolutions in twentieth-century physics. This latter story will be given in greater detail below in the BOOK describing Heisenberg’s philosophy of quantum theory. But to appreciate these developments more adequately, it is helpful firstly to have examined the development of the pragmatist philosophy of language.

      The next BOOK describes Carnap’s transformation of Mach’s positivism for his philosophy of semantical systems and then Quine’s transformation of Duhem’s positivist philosophy of mathematical physics into the contemporary pragmatism. Carnap and Quine were friends well known to one another, and both contributed insightfully to the linguistic-analysis tradition in philosophy. But Quine criticized Carnap’s positivism, and elaborated Duhem’s philosophy of mathematical physics beyond Carnap’s positivism into a new generalized philosophy of language now known as the Duhem-Quine thesis in contemporary pragmatism.

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