This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as example: the Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations (...) instead of committing us to additional elements of the ontology. The alternative theory strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology. (shrink)

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities (...) --qua part of a physical law-- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature. (shrink)

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered---and is thus susceptible to scientific progress---, the empirically successful structural features of the (...) framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space. (shrink)

We explore the significance of physical theories set in Euclidean spacetimes. In particular, we explore the use of these theories in contemporary physics at large, and the sense in which there can be a notion of temporal evolution in these theories. Having achieved these tasks, we proceed to reflect on the lessons that one can take from such theories for Knox’s ‘inertial frame’ version of spacetime functionalism, which seems to issue incorrect verdicts in the case of theories with Euclidean metrical (...) structure. (shrink)

Humeanism started life as a metaphysical program that could turn out to be false if our best physical theories were to postulate ontological features at odds with Humean ones. However, even if this has arguably already happened, Humeanism is still considered one of the strongest and most appealing metaphysical theories for describing the physical world. What is even more surprising is that a radical Humean thesis—Super-Humeanism—which posits an extremely parsimonious ontology including nothing more than propertyless matter points and their distance (...) relations, is said by its proponents to follow from an attentive reading of our best physical theories. Given its close relationship with physics, Super-Humeans argue that their doctrine conforms to Scientific Realism, offers the ontology that best explains physics’ empirical evidence, and is a naturalistic theory. This paper investigates the strategies that Super-Humeans have adopted to defend these three claims and, more generally, its alleged closeness to physics. I will show that, contrary to what advocates of Super-Humeanism claim, some of its commitments have inevitably created a gap between itself and physics that is difficult to overcome. While it is laudable that Super-Humeans have adopted various strategies to close this gap, no strategy has yet fully succeeded. (shrink)

In this paper, I discuss whether the results of loop quantum gravity (LQG) constitute a fatal blow to Humeanism. There is at least a prima facie reason for believing so: while Humeanism regards spatiotemporal relations as fundamental, LQG describes the fundamental layer of our reality in terms of spin networks, which are not in spacetime. However, the question should be tackled more carefully. After explaining the importance of the debate on the tenability of Humeanism in light of LQG, and having (...) presented the Humean doctrine, I review two cases which present serious threats to Humeanism, one concerning the fundamentality of vectorial quantities and the other concerning quantum entanglement. In particular, I recall the strategies that are usually employed in these two cases in order to save Humeanism: in the first case, the strategy consists in amending the characterization of the Humean mosaic; in the second case, it consists in adopting a realist or nomological interpretation of the wave function. These solutions will turn out to be helpful in my discussion of LQG where, after describing LQG, I show that Humeans might save their doctrine either by endorsing a realist interpretation of spin networks, or by giving them a nomological status and, at the same time, by revisiting the characterization of the Humean mosaic. However, I conclude that both solutions are wanting. (shrink)

According to the doctrine of Super-Humeanism, the world’s mosaic consists only of permanent matter points and changing spatial relations, while all the other entities and features figuring in scientific theories are nomological parameters, whose role is merely to build the best law system. In this paper, I develop an argument against Super-Humeanism by pointing out that it is vulnerable to and does not have the resources to solve the well-known problem of immanent comparisons. Firstly, I show that it cannot endorse (...) a fundamentalist solution à la Lewis, since its two pillars—a minimalist ontology and a best system account of lawhood—would generate, together, a tedious problem of internal coherence. Secondly, I consider anti-fundamentalist strategies, proposed within Humeanism, and find them inapplicable to the Super-Humean doctrine. The concern is that, since it is impossible to choose the best law system within Super-Humeanism, this doctrine may be charged with incoherence. (shrink)

The paper provides a critical discussion of the Super-Humean view of spacetime and the “minimalist ontology” in terms of Leibnizian relations and primitive matter points, recently developed by Esfeld et al. It investigates, in particular, the empirical adequacy of the proposed metaphysics, arguing that Super-Humeanism cannot provide a plausible account of space and time without committing to bona fide geometric structure in the fundamental relations. Against this backdrop, I propose a moderate version of Super-Humeanism and discuss its possible application to (...) Euclidean space and General Relativity. (shrink)

This paper seeks to answer the following question: What is a minimal set of entities that form an ontology of the natural world, given our well-established physical theories? The proposal is that the following two axioms are sufficient to obtain such a minimalist ontology: There are distance relations that individuate simple objects, namely matter points. The matter points are permanent, with the distances between them changing. I sketch out how one can obtain our well-established physical theories on the basis of (...) just these two axioms. The argument for minimalism in ontology then is that it yields all the explanations that one can reasonably demand in science and philosophy, while avoiding the drawbacks that come with a richer ontology. (shrink)

This paper seeks to answer the following question: What is a minimal set of entities that form an ontology of the natural world, given our well-established physical theories? The proposal is that the following two axioms are sufficient to obtain such a minimalist ontology: (1) There are distance relations that individuate simple objects, namely matter points. (2) The matter points are permanent, with the distances between them changing. I sketch out how one can obtain our well-established physical theories on the (...) basis of just these two axioms. The argument for minimalism in ontology then is that it yields all the explanations that one can reasonably demand in science and philosophy, while avoiding the drawbacks that come with a richer ontology. (shrink)

This workbook of "études" offers a collection of experimental texts for communal dialogue and discovery that crosses multiple academic disciplines, including: foundations of physics, metaphysics, theoretical biology, semiotics, cognitive science, linguistics, phenomenology, logic & mathematics, poetry and theology. Each étude probes limits, horizons and boundaries by implicitly bring into relation foundational issues that characterize different academic disciplines or systems of meaning formation. Some formal techniques are deployed the études. Most notable is the use of the “logic of three” to overcome (...) falsely totalizing images and inexorable dualities. This technique involves a particular kind of attunement to the “betweenness” of mediation that is not common in modern science. The attunement draws on the formal and precise movements of analysis in concert with the metaphoric and singular movements of synthesis. (shrink)

Triadic (systemical) logic can provide an interpretive paradigm for understanding how quantum indeterminacy is a consequence of the formal nature of light in relativity theory. This interpretive paradigm is coherent and constitutionally open to ethical and theological interests. -/- In this statement: -/- (1) Triadic logic refers to a formal pattern that describes systemic (collaborative) processes involving signs that mediate between interiority (individuation) and exteriority (generalized worldview or Umwelt). It is also called systemical logic or the logic of relatives. The (...) term "triadic logic" emphasizes that this logic involves mediation of dualities through an irreducibly triadic formalism. The term "systemical logic" emphasizes that this logic applies to systems in contrast to traditional binary logic which applies to classes. The term "logic of relatives" emphasizes that this logic is background independent (in the sense discussed by Smolin ). -/- (2) An interpretive paradigm refers to a way of thinking that generates an understanding through concepts, their inter-relationships and their connections with experience. -/- (3) Coherence refers to holistic integrity or continuity in the meaning of concepts that form an interpretation or understanding. -/- (4) Constitutionally open refers to an inherent dependence in principle of an interpretation or understanding on something outside of a specific discipline's discourse or domain of inquiry (epistemic system). Interpretations that are constitutionally open are incomplete in themselves and open to responsive, interdisciplinary discourse and collaborative learning. (shrink)

The paper argues for a metaphysics in the vein of the Canberra plan, namely to single out a minimal, basic set of entities and then to show how everything else is located in that set by being identical with something in that set and how the propositions that describe the basic entities entail all the other true propositions. The paper conceives the Canberra plan for the domain of the natural sciences as a naturalized metaphysics that is not committed to a (...) priori entailment. The proposal is that the minimal set of entities is defined by the following two axioms: There are distance relations that individuate simple objects, namely matter points. The matter points are permanent, with the distances between them changing. Finally, the paper explains how the Canberra plan sets a clear standard for ontological issues that go beyond the natural sciences. (shrink)