Certain considerations from cosmology (Ellis, in: arXiv preprint, 2006. arXiv:astro-ph/0602280; Stud Hist Philos Mod Phys 46:5–23, 2014) and other areas of physics (Sklar, in: PSA Proceedings of the biennial meeting of the philosophy of science association, pp. 551–564, 1990; Frisch, in: Philos Sci 71:696–706, 2004) pose challenges to the traditional distinction between laws and initial conditions, indicating the need for a more nuanced understanding of physical modality. A solution to these challenges is provided by presenting a conceptual framework according to which laws and fundamental lawlike assumptions within a theory’s nomic structure determine what is physically necessary and what is physically contingent from a physical theory’s point of view. Initial conditions are defined within this framework in terms of the possible configurations of a physical system allowed by the laws and other lawlike assumptions of a theory. The proposed deflationary framework of physical modality offers an alternative way of understanding the distinction between laws and initial conditions and allows the question of the modal status of the initial conditions of the Universe to be asked in a meaningful way.

Of the many ways of getting at the core of the weirdnesses in quantum mechanics, there’s one which traces back to Schrödinger’s seminal 1935 paper, and has to do with the apparent fuzzy nature of the reality described by the formalism through the wavefunction ψ. This issue, which I will be calling the Determinacy Problem, is distinct from the standard measurement problem of quantum mechanics, despite Schrödinger himself ends up conflating the two. I will argue that the Determinacy Problem is an exquisitely philosophical problem, for as it is standard when facing any phenomenon which appears to have indeterminate or fuzzy characteristics, the solutions available are to either blame the deficiencies of our language, or our lack of knowledge, or to blame the world itself. These three attitudes can already be found in the literature on quantum mechanics, either explicitly or implicitly, and they appear to motivate three very distinct research programs: high-dimensional realism, primitive ontology, and quantum indeterminacy.

There is solid consensus among physicists and philosophers that, in gauge field theory, for a quantity to be physically meaningful or real, it must be gauge-invariant. Yet, every “elementary” field in the Standard Model of particle physics is actually gauge-variant. This has led a number of researchers to insist that new manifestly gauge-invariant approaches must be established. Indeed, in the foundational literature, dissatisfaction with standard methods for reducing gauge symmetries has been expressed: Spontaneous symmetry breaking is deemed conceptually dubious, while gauge fixing suffers the same limitations and is subject to the same criticisms as coordinate choices in General Relativity. An alternative gauge-invariant proposal was recently introduced in the literature, the so-called “dressing field method” (DFM). It is a mathematically subtle tool, and unfortunately prone to be confused with simple gauge transformations, hence with standard gauge fixings. As a matter of fact, in the physics literature the two are often conflated, and in the philosophy community some doubts have been raised about whether there is any substantial difference between them. Clarifying this issue is of special significance for anyone interested in both the foundational issues of gauge theories and their invariant formulation. It is thus our objective to establish as precisely as possible the technical and conceptual distinctions between the DFM and gauge fixing.

The paper presents an extension of the metaphysics of self-subsisting structures set out in a companion paper to the realm of non-relativistic quantum physics. The discussion is centered around a Pure Shape Dynamics model representing a relational implementation of a de Broglie-Bohm N-body system. An interpretation of this model in terms of self-subsisting structures is proposed and assessed against the background of the debate on the metaphysics of quantum physics, with a particular emphasis on the nature of the wave function. The analysis shows that elaborating an appropriate Leibnizian/Machian metaphysics of the quantum world requires a substantial revision of the notion of world-building relation.