Abstract
In Section III of his paper H. Putnam1 deals with Reichenbach’s attempt to interpret quantum mechanics on the basis of a three-valued logic, and he uses some arguments of his own in order to show that this attempt is “a move in the direction of simplifying the whole system of laws” (104). I believe that the Reichenbach-Putnam procedure cannot be defended and that it leads to undesirable consequences.
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Notes
‘Three-Valued Logic’, this volume, p. 99–107.
The following abbreviations will be used: PF for Philosophic Foundations of Quantum Mechanics; PA for The Principle of Anomaly in Quantum Mechanics’, Dialectica 7/8 (1948) 337; FL for ‘Les fondements logiques de la théorie des quanta’, in Applications Scientifiques de la Logique Mathématique, Paris, 1954, pp. 103ff.
This omits spin.
This is expressed by Reichenbach’s Principle of Anomaly (which he assumes to be independent of the uncertainty principle PF 44). It is worthwhile considering the transformations this principle undergoes in Reichenbach’s book. It is introduced as saying that “the class of descriptions of interphenomena contains no normal system” (PF 33) which means, when decoded, that the laws for quantum-mechanical objects cannot be formulated in such a way that they coincide with the laws governing the behavior of observable objects, viz. the classical laws (cf. PF 19). As it stands the principle is obviously refuted by the fact that formulations of quantum mechanics and of classical physics exist which are identical. We may, however, interpret the principle as saying that the laws (not their formulations) for quantum-mechanical objects are not the same as the laws governing the behavior of observed objects or, to use Reichenbach’s terminology (which is supposed to express “the quantum mechanical analogue of the distinction between observed and unobserved objects” (PF 21), that the laws of interphenomena are not the same as the laws of phenomena. In this case the truth of the principle follows from the definitions of ‘phenomenon’ and ‘interphenomenon’ provided by Reichenbach which say that the “phenomena are determinate in the same sense as the unobserved objects of classical physics” (PF 21) whereas the introduction “of interphenomena can only be given within the frame of quantum mechanical laws” (PF 21). For according to these definitions the principle of anomaly asserts that the laws of classical physics are different from the laws of quantum mechanics, which is of course true but does not justify the introduction of the principle as an independent assumption (see the beginning of this note). However, this is not the sense in which the principle is used at other places of the book where it is meant to say that “every exhaustive interpretation” (in the second sense) “leads to causal anomalies” (136 PF). Having introduced this latter sense of the principle and having announced that it will be proved later on the basis of the principles of quantum mechanics, Reichenbach swiftly returns to the first interpretation (in which, as we have seen, the principle follows trivially from the definitions given for its two main terms together with the fact that classical physics is not quantum mechanics) and derives from it that the idea of the uniformity of nature (same laws for observables and unobservables) must be given up (PF 39). These are only some of the confusions found in a book which demands that “the philosophy of physics should be as neat and clear as physics itself (PF vii).
Cf. especially Phys. Rev. 48 (1935), 696, and here especially the last paragraph, as well as Albert Einstein, Philosopher-Scientist, Evanston, 1949, especially pp. 231 ff.
Albert Einstein, p. 234.
Reichenbach and Putnam express in the ‘formal mode of speech’ a type of argument which has frequently been used by ‘traditional’ philosophers against the conceptions introduced through new theories: it was regarded as ‘unnatural’ to let simultaneity depend on the coordinate system chosen (and to assume that ‘Sim(xy)’ is not well formed and hence, meaningless); yet it had to be admitted that special relativity was more successful than prerelativistic physics. In order to solve this difficulty traditional philosophers usually adopted what we have called method 3 (Section II above; cf. Philipp Frank, Relativity, a Richer Truth). That is, they regarded relativity proper as a set of cognitively meaningless sentences which nevertheless could be used as parts (cogwheels, so to speak) of a good prediction machine. However objectionable this method may be, traditional philosophers took contradictions seriously and tried to remove them. It was left to Reichenbach (who argued against “speculative philosophy which must appear outmoded in the age of empiricism,” PF vii) to provide the above approach with two further methods, viz. the ‘method’ to call contradictions ‘anomalies’ and “to become accustomed to them” (his methods 1 and 2) and the ‘method’ to drop two-valued logic.
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© 1975 D. Reidel Publishing Company, Dordrecht, Holland
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Feyerabend, P. (1975). Reichenbach’s Interpretation of Quantum-Mechanics. In: Hooker, C.A. (eds) The Logico-Algebraic Approach to Quantum Mechanics. The University of Western Ontario Series in Philosophy of Science, vol 5a. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1795-4_6
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