Trevor Teitel’s paper explores the philosophical foundations of spacetime substantivalism, a position in the philosophy of physics that asserts spacetime points (or regions) exist as independent entities, not just as relations between material objects. His focus is on a technical issue involving modal questions—questions about what is metaphysically possible or necessary regarding spacetime and its relationship to the physical universe. The paper examines how substantivalists should think about these possibilities, arguing that current approaches have significant problems and suggesting the need for new ways of framing the debate.

Key Terms and Ideas in the Paper

1. Spacetime Substantivalism: The view that spacetime is a “substance,” meaning that it exists independently of objects or matter. For example, the points of empty spacetime are still real, even if there’s no matter or energy in the universe.

2. Modal Arbitrariness: This term refers to the problem of why certain possibilities about spacetime are treated as legitimate while others are excluded. Teitel argues that the consensus view creates arbitrary distinctions between these possibilities without providing a satisfactory explanation.

3. Cheap Determinism: This critique suggests that the consensus view of spacetime substantivalism makes the relationship between spacetime and the physical world overly simple. It implies that spacetime deterministically “chooses” certain physical outcomes in a way that doesn’t sufficiently account for the complexity of possibilities.

4. Plenitudinous Substantivalism: An alternative view Teitel explores, which holds that all possible spacetime configurations exist in some sense. This avoids arbitrariness but introduces other issues, like “modal vagueness,” which Teitel finds problematic.

The Structure of the Paper

Teitel critiques the current mainstream view held by substantivalists about how spacetime relates to metaphysical possibility. He highlights two key issues:

1. The arbitrariness problem: If spacetime points exist independently, what determines which possible configurations of those points are metaphysically allowed? Teitel argues that substantivalists don’t provide a satisfactory answer, and their distinctions between possibilities often feel arbitrary.

2. The determinism problem: Substantivalists often claim that spacetime points play a deterministic role in how the physical universe unfolds. Teitel critiques this view as overly simplistic and argues that it fails to account for deeper metaphysical complexities.

He then evaluates potential alternatives, including plenitudinous substantivalism, but ultimately finds them lacking. In his view, substantivalists need to reconsider their assumptions about how spacetime relates to metaphysical possibility and physical reality.

Expanded Critique and Analysis

Teitel raises valid concerns, but his conclusions and framework can be critiqued on several fronts. Let us now explore these critiques in depth, starting with the concept of modal arbitrariness.

1. Modal Arbitrariness and the Problem of Justification

Teitel claims that substantivalists fail to justify why certain spacetime configurations are possible while others are not. This critique assumes that every modal distinction requires a clear justification grounded in metaphysical principles. However, this demand might itself be unwarranted.

Substantivalists could argue that spacetime’s modal structure arises from its intrinsic nature, independent of our ability to justify it. For instance, the physical properties of spacetime (as described by general relativity) could constrain its modal landscape in ways that are not reducible to external principles. Teitel’s critique presupposes a form of modal realism (the idea that all possibilities must be treated equally unless explicitly ruled out), but many substantivalists operate within frameworks that reject this assumption.

Additionally, some approaches in physics—such as loop quantum gravity or string theory—suggest that spacetime might have a more fundamental structure than classical substantivalism assumes. These theories could naturally limit the range of possible spacetime configurations, addressing the arbitrariness problem without requiring additional metaphysical commitments.

2. Plenitudinous Substantivalism and Modal Vagueness

Teitel critiques plenitudinous substantivalism for introducing “modal vagueness,” where it becomes unclear which possibilities should count as legitimate. However, this critique conflates epistemic vagueness (our inability to precisely describe possibilities) with ontological vagueness (the idea that the world itself is indeterminate).

Substantivalists could defend plenitudinous views by appealing to epistemic humility: our limited knowledge about the true nature of spacetime doesn’t imply that spacetime itself is vague. Alternatively, they could embrace a many-worlds interpretation, where all possible spacetime configurations coexist, each realized in a distinct physical or metaphysical context. While Teitel dismisses this approach as overly extravagant, it might provide the most consistent resolution to the issues he raises.

3. Cheap Determinism and Its Alternatives

Teitel’s critique of “cheap determinism” hinges on the idea that substantivalists oversimplify the relationship between spacetime and physical possibility. However, this critique overlooks more nuanced versions of determinism that could avoid his objections. For example:

• Relational determinism: Instead of tying determinism to individual spacetime points, this approach grounds determinism in the global structure of spacetime, such as its geometry or topology. This view aligns with modern physics, where global constraints often play a more fundamental role than local properties.

• Probabilistic determinism: Substantivalists could adopt a probabilistic framework, where spacetime influences physical outcomes by constraining probabilities rather than dictating fixed results. This view is compatible with quantum mechanics and avoids the oversimplifications Teitel critiques.

4. Teitel’s Theoretical Costs

One of the biggest problems with Teitel’s critique is that it introduces significant theoretical costs without offering clear benefits. Abandoning the consensus view forces substantivalists to adopt more complex ontological or modal frameworks, such as plenitudinous substantivalism or radical modal revisions. These alternatives are not only harder to defend but also risk undermining the explanatory power of spacetime substantivalism.

Teitel’s critique also fails to engage with broader metaphysical debates about the nature of modality. For example, actualists (who deny the reality of unactualized possibilities) might reject the premise that modal arbitrariness is a problem at all, as they would deny the existence of “arbitrary” possibilities in the first place. Similarly, structural realists might argue that spacetime’s modal structure is grounded in its relational properties, bypassing the need for independent justification.

Conclusion

Trevor Teitel’s paper raises important questions about the relationship between spacetime substantivalism and metaphysical possibility. However, his critiques rely on contentious assumptions about modal justification and determinism that are not universally accepted. By failing to engage with alternative frameworks—such as relational or probabilistic approaches to spacetime determinism—Teitel risks overstating the problems with the consensus view.

Substantivalists have multiple ways to address the issues he raises without abandoning their core commitments. These include grounding modal structure in the physical properties of spacetime, embracing epistemic humility about our understanding of possibility, or adopting probabilistic or relational determinism. Ultimately, Teitel’s paper highlights the need for further philosophical exploration but falls short of providing a compelling reason to abandon the consensus view of spacetime substantivalism.

References

Teitel, Trevor. “How to Be a Spacetime Substantivalist.” Philosophy of Science Archive, 2021. Available at: https://philsci-archive.pitt.edu/19545/