Jacopo Giraldo
University of Padova
This paper highlights the geometrically dimensional nature of spatial extension, as analyzed and applied in the literature, and argues that the concept of geometric dimension warrants metaphysical scrutiny, given its potential relevance to our understanding of the structure of reality. Attempts to define criteria for spatial extension trace back to classical debates, such as those concerning monads (see, e.g., Kant and Meerbote 1992). Today, questions about temporal persistence and the metaphysical possibility of extended simples or unextended complexes still revolve around what it means for something to be extended in time or space (see, e.g., Goodsell et al. 2020, Calosi 2022, Calosi 2025)—I will focus on space here). First, I argue that, despite the variety of definitions of spatial extension, each is extensionally equivalent to the condition that the spatial dimension of the region occupied by an entity is greater than zero. In other words, determining whether something is spatially extended in a given space boils down to determining whether its location is dimensionally positive within that space. Consequently, I propose the following notion of spatial extension:
Spatial Extension (SE): An entity is spatially extended in space S if and only if its location has a positive degree of spatial S-dimension.
The S-dimension is the type of dimension that is characteristic of space S.
The first implication of this proposal is that the metaphysical work to be done does not lie in developing new accounts of spatial extension depending on a specific space, but in understanding what dimension a space has. Indeed, according to SE, it is the positivity of the S-dimension of a region that determines whether it is spatially extended in S
A second, and perhaps more intriguing, implication lies in the metaphysical terrain itself: it prompts us to ask whether dimension is a fundamental feature of reality. Beyond the familiar mathematical spaces, which are typically used to model physical space, in what other spaces can dimension be meaningfully defined—and actually do metaphysical work? For instance, could we endow a modal space with a notion of dimension that captures the idea of modally extended entities, central to metaphysical theses such as five-dimensionalism, which argues for the existence of such entities? (see, e.g., Williamson 2016, Williamson 2017) These questions remain largely uncharted, and much work is still needed to explore the metaphysical scope of dimension.
References
Calosi, C. (2022), ‘Extended simples, unextended complexes’, Journal of Philosophical Logic pp. 1–26.
Calosi, C. (2024), ‘Regions, extensions, distances, diameters’, Philosophy and
Phenomenological Research.
Goodsell, Z., Duncan, M. and Miller, K. (2020), ‘What is an extended simple
region?’, Philosophy and Phenomenological Research 101(3).
Kant, I. and Meerbote, R. (1992), Showing that the existence of physical monads
is in agreement with geometry, The Cambridge Edition of the Works of Immanuel Kant, Cambridge University Press, p. 53–60.
Williamson, T. (2016), ‘Modal science’, Canadian Journal of Philosophy
46(4–5), 453–492.
Williamson, T. (2017), ‘Modality as a subject for science’, Res Philosophica
94(3), 415–436.
Chair: Satbhav Voleti
Time: 03 September, 16:00-16:30
Location: HS E.002
SOPhiA 2026 