A Case for Underdetermination: Consequences of Opposing the Distinction between Quantum Mechanics and Bohmian Mechanics

1 Introduction

In his article Must Evidence Underdetermine Theory? John D. Norton attempts to refute a certain version of the underdetermination thesis. He attacks the idea that all evidence necessarily underdetermines any scientific theory. In the first part of this paper, I want to call into question part of his argument in some general terms and then focus on a particular case of possible underdetermination, namely Quantum mechanics (QM) and Bohmian mechanics (BM), in order to strengthen my criticism of Norton. Norton himself does not take sides in the debate over the question whether or not QM and BM are essentially the same theory, but says the possibility that they are cannot be ruled out. I will show that Norton, both in his general argument as well as in his judgment in the ‘QM/BM case’, takes a certain notion of theory for granted that his opponents would not agree with. In addition, I will investigate further consequences resulting from his position. This part makes up the bulk of my paper. In a second part I attempt to refute Norton on his own grounds. That is, on the basis of his idea of what a theory is, I will show that one can preclude the possibility that QM and BM are the same theory. To be clear: This paper is not a defense of the underdetermination thesis, but rather a critique of Norton’s attack.

Part I

2 Norton’s line of argument and my criticism thereof

In this section, I will take a closer look at the part of Norton’s paper that is supposed to show how the display of observationally equivalent theories is a self-defeating strategy for establishing the underdetermination thesis. Norton attacks a form of induction to underdetermination by showing that two observationally indistinguishable theories are likely to also be theoretically indistinguishable.^[1] This is supposed be a refutation of the underdetermination thesis, because his argument casts enough doubt on the difference of observationally indistinguishable theories that the inference to underdetermination does not work. He argues that differences between two theories that are not interconvertible represent additional structure in one of the two theories.^[2] Since it is assumed that both theories have identical observational consequences, the additional structure is a strong candidate for being superfluous.^[3] The conclusion of Norton’s argument that “[…] pairs of theories that can be demonstrated to be observationally equivalent are very strong candidates for being variant formulations of the same theory”^[4] can only be adhered to on the basis of a notion of theory that excludes the so-called ontological structure of a theory as part of what constitutes a theory. Theories may drastically differ in how they describe the world, according to Norton’s argument those differences by themselves do not matter – as long as they are observationally indistinguishable. Because his opponents cannot be assumed to share his notion of theory, his argumentation is weakened by this implicit assumption. What the exclusion of ontological differences amounts to in the case of QM and BM will be analyzed in the next section.

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^[1] Norton, John D. “Must Evidence Underdetermine Theory?” (Prepared for the First Notre Dame-Bielefeld Interdisciplinary Conference on Science and Values Zentrum für Interdisziplinäre Forschung, Universität Bielefeld, July 9-12, 2003), 21.

^[2] Ibid., 22.

^[3] Ibid.

^[4] Ibid.