Abstract
There is good reason to suppose that our best physical theories, quantum mechanics and special relativity, are false if taken together and literally. If they are in fact false, then how should they count as providing knowledge of the physical world? One might imagine that, while strictly false, our best physical theories are nevertheless in some sense probably approximately true. This paper presents a notion of local probable approximate truth in terms of descriptive nesting relations between current and subsequent theories. This notion helps explain how false physical theories might nevertheless provide physical knowledge of a variety that is particularly salient to diachronic empirical inquiry.
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Notes
Hillary Putnam echoes this sentiment in his characterization of scientific realism: when a realistically minded scientist accepts a theory “he accepts it as true (or probably true, or approximately-true, or probably approximately-true)” (Putnam 1979, 210).
See Barrett (2003) for a discussion of this point.
That particular physical laws, theories, and models must be considered false is a recurring theme in the philosophy of science. See Cartwright (1999), Sklar (2003), Barrett (2003), Teller (2004), and Frisch (2004) for recent examples. The reasons for judging a particular law, theory, or model to be false vary. The relativistic quantum measurement problem is particularly troubling insofar as one is committed to both relativity and quantum mechanics eventually providing the basis for a unified description of the physical world at some level.
Both GRW and Bohmian mechanics have dynamical laws that presuppose a preferred inertial frame. For GRW this is the frame in which the collapse occurs; and for Bohmian mechanics this is the frame used to characterize the (3N-dimensional) N particle configuration space. See Albert (1992) for a description of GRW and Bohmian mechanics and Barrett (2005) for a discussion of the sort of descriptive sacrifices one would have to make in order to construct a relativistic hidden-variable theory.
See Barrett (2003) for a discussion of this point.
This approach to approximate truth and the discussion of guiding principles later in the paper fit well with a pragmatic account of truth akin to that of C. S. Peirce. On such an account, truth is descriptive of the world and is approached through diachronic inquiry by the elimination of error from our current best descriptions. That there are objective matters of fact can be thought of here as a precondition for the possibility of our current descriptions being in error and as the ground for a commitment to methodological fallibilism. Similarly, that error can be remedied through inquiry can be thought of as a precondition for the possibly of inquiry. Guiding principles represent higher-order commitments concerning how to make local progress in inquiry (e.g. Peirce 1877 and 1878).
I take this to be a demand that is negotiated together with the desire for increased descriptive precision and the elimination of descriptive error in the next generation of theories. If no such descriptive nesting were satisfied, then it would be impossible to recognize the next generation of theories as providing a refined description of the world that remedies error. Rather, they would look like an abrupt change in subject.
While descriptive nesting between subsequent theories typically involves all three aspects of description, one of the three is sometimes better preserved than the others in a particular historical case. I take this to be why would-be positivists (instrumentalists, and such), entity realists, and structural realists can always find historical examples that they take to support their own views and to undermine the views of their opponents in the other camps.
See Malament (2006, 40).
This is a consequence of the Trautman-Malament geometrization theorem. See Malament (2006, 40–41).
This is a consequence of the Trautman-Malament recovery theorem. See Malament (2006, 42–43).
That there be some sort of descriptive nesting is a standing demand, but the sort of nesting that obtains is negotiated in theory construction and selection with the aim of eliminating descriptive error. This process is less a cost-benefit analysis between competing ready-made theories and more a negotiation within the activity of constructing theories to construct those that can be recognized as refinements of current theories that eliminate descriptive error. Toward this end, theories are constructed that satisfy a descriptive nesting relation while eliminating descriptive error.
See Barrett (2000) for a discussion of the sense in which momentum is and is not conserved in Bohmian mechanics.
I would like to thank David Malament and Kyle Stanford for discussions on the topics addressed in this paper and Martha Barrett for editorial suggestions. I would also like to thank the two anonymous referees for helpful comments on an earlier version of this paper.
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Barrett, J.A. Approximate Truth and Descriptive Nesting. Erkenn 68, 213–224 (2008). https://doi.org/10.1007/s10670-007-9086-6
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DOI: https://doi.org/10.1007/s10670-007-9086-6