The paper explores a particular line of objection against wave-function realism. This view, advocated by Bell (1987) and presently defended by Albert (1996), North (2013) and Ney (2016), claims that the quantum wave function is a high-dimensional physical field. Normally, wave-function realism has been criticized for its ontological commitments, which are regarded as empirically unsupportable in principle and as violating empirical coherence. In this paper, I investigate whether there are any methodological arguments for endorsing such an ontology and whether they are sound. In particular, I home in on and discuss three arguments that may be used to support wave-function realism: (i) the argument from laws; (ii) the argument from the complete information of the system; (iii) the argument from explanation. My conclusion is that these arguments do not provide any good methodological grounds for inferring the existence of a high-dimensional physical field from quantum theory.
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