Abstract
According to Ernest Nagel, determinism is central to the scientific enterprise. Faced with the claim that determinism fails in quantum mechanics, Nagel proposed a notion of determinism which does not rely on a fundamental level of description, and can play a role in different scientific disciplines irrespective of their reducibility to physics. Nagel argues that determinism ultimately plays the role of a guiding principle in scientific research. In this way, Nagel argues that determinism has an enduring relevance in all domains of science, from quantum physics to the social sciences.
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Notes
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In a later paper, Nagel (1953) notes that in experimental practice, it is impossible to measure instantaneous values of position and momentum: there will always be some inaccuracy in the measurement, and in this way, statistic comes in. Nagel notes that some people have argued on this basis that classical mechanics is not deterministic, but argues that this confuses the issues of (1) the logical structure of the theory and (2) the relations of the theory with observations and experiments. Classical mechanics is deterministic because of its theoretical structure; that this determinism cannot be directly verified experimentally does not affect this property of the theory. “It is hardly more than a truism to maintain that classical mechanics is ‘indeterministic’ or statistical in nature, if the claim rests on no other grounds than that the experimental confirmation of classical mechanics involves the use of statistical procedures and that experiment confirms it only approximately. For any quantitatively formulated theory viewed from this standpoint is ‘indeterministic’ and statistical: the experimental measurement of physical magnitudes such as velocity always yields a ‘spread’ of values, and no law asserting a relation of dependence between continuous variables is in absolutely precise agreement with data of observation” (Nagel, 1953, p. 425).
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For more on Nagel’s interpretation of Heisenberg’s uncertainty relations, see Atkinson and Peijnenburg, in this volume.
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Within logical empiricism, there were extensive discussions about the question whether determinism, as a general principle, has empirical consequences or whether it is tautological (see Placek, 2014). Nagel’s claim that determinism is not empirically testable stands within this tradition. As Placek points out, in more recent literature, the question whether determinism in general is empirically testable is no longer asked: rather, determinism is taken to be an attribute of scientific theories, so one can merely ask whether specific theories are deterministic. This leads to the different question, posed by Werndl (2009), of whether deterministic and indeterministic theories are empiricially distinguishable.
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Causality and determinism can also come apart, especially since causality has more possible meanings than determinism: causality can e.g. also refer to conditions of locality, or to the presence of conservation laws (for an overview see Ben-Menahem, 2018). But as far as I have seen, Nagel uses ‘determinism’ and ‘causality’ synonymously.
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Mach argued, however, that also indeterminism plays a heuristic role in science: it is important to be aware of the limitations of scientific theories and pay attention to the unpredictable, since we can never be sure that our theories are fully accurate and complete; therefore, “also he who advocates an extreme determinism in theory must in practice remain an indeterminist, especially if he does not want to speculate away the most important discoveries” (Mach 1905, p. 278, my translation).
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“Quite clearly, then, a non-sequitur is involved in Laplace’s dictum that ‘nothing would be uncertain’ for an intelligence possessing a requisite knowledge of mechanical states and forces” (Nagel, 1953, p. 423).
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It does not really matter here at what moment this is done: say that from the mechanical state m1 at time t1, one can derive the mechanical state m2 at time t2. To arrive at the state at a higher level of description at time t2, one can use bridge principles to derive this state from m2. Alternatively, one could use bridge principles to connect the initial state m1, to a higher level state h1, and then derive the state h2 from h1—the latter would require having laws which determine the behavior of the system at the higher level of description.
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The equations of field theories and of hereditary mechanics typically yield well-posed problems, in the sense developed by Hadamard around 1900.
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The claim that quantum mechanics is deterministic because the wave function evolves deterministically is not unique to Nagel—it was already made by Planck in (1932). Also Earman (1986; 2007) makes this argument, and Earman (1986) in fact refers to Nagel in this connection. However, as also Earman admits, to argue that quantum mechanics is really deterministic on this basis is tricky, mainly because the issue of how to relate the theory of quantum mechanics to measurement outcomes remains unsolved.
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Nagel refers to von Neumann’s theorem which excludes the possibility of hidden variables, but argues that this theorem does not exclude the possibility that a hidden variable theory can be developed on a fundamentally different basis.
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As an anonymous referee points out, it does not hold in Bohmian mechanics either that there are no limits to the accuracy of predictions.
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For the details of Nagel’s views on the social sciences, see Matthias Neuber’s paper in this volume.
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“[I]t is impossible in the nature of the case to establish beyond question that any event is an absolute chance occurrence. For to show beyond all possible doubt that a given happening (e.g., the decomposition of an atom) is spontaneous and without determining circumstances, it would be necessary to show that there is nothing whatever upon which its occurrence depends. But this would be tantamount to showing that no satisfactory theory could ever be devised to explain what present theories already explain, and in addition account for the allegedly spontaneous event” (Nagel 1961, pp. 332–333).
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Nagel (1953) argues that the idea that indeterminism in quantum mechanics would also undermine determinism for macroscopic phenomena rests on the unwarranted assumption that if a complex is analyzable in terms of elements, then the elements are metaphysically prior and the complex can only have properties that can be attributed to the elements.
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van Strien, M. (2022). Ernest Nagel on Determinism as a Guiding Principle and Its Compatibility with Quantum Mechanics. In: Neuber, M., Tuboly, A.T. (eds) Ernest Nagel: Philosophy of Science and the Fight for Clarity. Logic, Epistemology, and the Unity of Science, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-81010-8_8
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