Theories in fundamental physics are unlikely to be ontologically neutral, yet they may nonetheless fail to offer decisive empirical support for or against particular metaphysical positions. I illustrate this point by close examination of a particular objection raised by Wolfgang Pauli against Hermann Weyl. The exchange reveals that both parties to the dispute appeal to broader epistemological principles to defend their preferred metaphysical starting points. I suggest that this should make us hesitant to assume that in deriving metaphysical conclusions from physical theories we place our metaphysical theories on a purely empirical foundation. The metaphysics within a particular physical theory may well be the result of a priori assumptions in the background, not particular empirical findings.
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This view has perhaps been most forcefully articulated by , but somewhat less polemical versions of this idea appear to be wide-spread among philosophers of physics, as well as some metaphysicians.
The first edition appeared in 1918. Weyl continued to revise his arguments considerably in subsequent editions, largely in response to Einstein’s objections. For a detailed reconstruction of the arguments leading to this revision process, see .
For details of the objection, and how Weyl successively dealt with it, see .
For operational definitions of meaning, as well as the physical inspiration for the view, see .
Mach, notoriously, remained highly skeptical about the existence of atoms for most of his life.
We should not be surprised to find that  objects to field-theoretic conceptions of matter in general, on the grounds that something over and above the continuous field needs to be added in order to account for matter.  suggests that this, more than any technical problems, was seen as a problem for pure field-theoretic physics.
Strictly speaking, Weyl does not actually want to measure the field strength ‘in the interior of the electron’. As we saw above, Weyl first re-conceptualizes the meaning of electron: it is not to be understood as a body, but as a region of the field. Accordingly, measuring the field strength in the interior of the electron really just means measuring the field strength in a very small region of the field, where those values are extremely high.
Indeed, Weyl’s argument for treating apparently particulate matter in this fashion draws heuristically on the treatment of matter in theories like hydrodynamics. “In phenomenological theories in which we abstract from the particulate structure of matter, we think of the energy stored in electrons, atoms and so forth as continuously distributed across the body; we only have to take it into account by introducing the energy-momentum tensor—relative to a coordinate system—as energy density into the rest mass \(\mu _0\).” (, p. 174) My translation.
On the different strands of philosophy, their engagement with physics, and with each other, see .
In the literature on Kant, Anschauung and anschaulich are more commonly translated as intuition and intuitive. While those terms are suitable as translations of Kant’s notions, I nonetheless prefer to translate Anschaulichkeit as visualizability for the purposes of this paper, since within the debate I’m looking at, the term is not used exclusively in its Kantian sense.
For a detailed reconstruction of Weyl’s approach, as well as its Husserlian roots, see once again , especially chapters five and six.
“The conception of the process [of experienced temporal development] as consisting of points, and hence as disintegrating into points, turns out to be mistaken. We are missing precisely what makes for continuity, [namely] the flow from point to point.” (, pp. 69–70; mytranslation).
In Kant’s own work, these epistemic notions of course have semantic companions: intuitions and concepts as two distinct types of representations. I do not mean to invoke this semantic distinction here, and I do not think it mirrors the metaphysical distinction between the continuous and the discrete in a straightforward way.
This should of course not suggest that epistemic constraints have no role to play in theorizing, either in physics or philosophy. As the Weyl-Pauli exchange shows, they have important heuristic functions.
I have in mind here, for example, the debate between defenders of Lagrangian QFT and axiomatic QFT, for discussion see .
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Wolff, J. Observability, Visualizability and the Question of Metaphysical Neutrality. Found Phys 45, 1046–1062 (2015). https://doi.org/10.1007/s10701-015-9904-7
- Interpreting physics
- Field concept