Introducton

Since ancient times, space has been studied in various fields of knowledge, from mathematics to physics. However, beyond its theoretical formulations, the nature of space poses a specifically philosophical problem: its ontological dimension is not immediately accessible to experience. Space is not an object that we can perceive directly or manipulate as a material entity; we do not "touch" it in the way we touch a physical body. Furthermore, precisely because we live entirely immersed in it, we cannot observe it "from the outside", as if it were one element among others in the world.

For this reason, our understanding of space depends largely on theoretical models, particularly mathematical and physical ones, which do not merely describe what immediately appears to the senses, but organize, structure, and interpret experience. Such models make intelligible phenomena that would otherwise remain opaque, allowing us to attribute to space properties that are not directly observable, but described by scientific theories.

Space, thus, becomes a central philosophical problem: it is unclear whether space should be established as an entity that exists independently of the objects it contains, or as something that depends entirely on the relationships between those objects. It is precisely this ambiguity that gives rise to one important debate between two conceptions: substantivalism and relationalism.

According to substantivalism, space is an ontologically autonomous reality: it exists independently of material bodies and is a kind of "container" in which objects are located and move. This conception finds a classic formulation in the physics of Isaac Newton, for whom, absolute space exists in itself, even in the absence of matter, and it has its own properties.

Relationalism, on the contrary, argues that space is not an independent entity, but emerges from the relationships between material objects. From this perspective, talking about space means talking about distances, positions, and mutual relationships between bodies; without objects, space would have no autonomous reality. This position is historically associated with Gottfried Wilhelm Leibniz and Ernst Mach, who criticized Newton's idea of absolute space.

This rises the need to address the question of space from three distinct but complementary perspectives, which also constitute the fundamental structure of the philosophical debate on the subject:

• Metaphysics: what is space? Is it a real and autonomous entity (substantialism) or a set of relationships between objects (relationalism)?
• Epistemology: how do we know space? Through sensory experience, through a prior conceptual structures, or through scientific theoretical models?
• Physics: what role does space play in the laws of physics? Is it a passive background or a dynamic structure that interacts with matter and energy?

The Philosophical Problem of Space

Metaphysical

The first question is whether space is a real and autonomous entity or whether it is instead something derived. In particular, the question arises whether space should be conceived as a "container" independent of the material bodies it contains, or whether it exists only as a system of relations between such bodies. In other words, the metaphysics of space seeks to clarify whether space exists in itself or whether it depends ontologically on matter, and whether it can be considered on the same level as physical objects or as something ontologically distinct.

Epistemological

Space is invisible and not directly perceptible, and this makes our knowledge of it problematic. This raises the question of whether knowledge of space derives primarily from sensory experience or from reason. Specifically, the question is whether the geometric structures we attribute to space are learned through observation of the physical world or whether they are instead the result of rational and theoretical activity. The epistemological problem, therefore, is to explain how it is possible to have reliable knowledge of space, despite its unobservability.

Physical

The main questions concern the relationship between space and matter. The question is whether space interacts, in some way, with matter or whether it simply serves as a passive background in which physical phenomena occur. Furthermore, a central issue is establishing which geometry correctly describes space: whether traditional Euclidean geometry is adequate or whether different geometries are necessary.

Substantivalism: Newton's Absolute Space

Isaac Newton's position represents the one of the most influential formulation of substantivalism. Newton developed his theory of classical mechanics by assuming the existence of absolute space and time, conceived as real entities independent of matter, with a three-dimensional Euclidean geometric structure. Space, for Newton, is an immutable container in which material bodies are placed, and relative to which, it is possible to define absolute position, velocity, and acceleration.

Newton's central argument is through the Inference to the Best Explanation (IBB). He observes that there are empirically detectable inertial effects: for example, the distinction between uniform and accelerated motion, which manifests itself through sensations and observable phenomena (such as being pushed backward in an accelerating vehicle or outward on a curve). These effects, according to Newton, cannot be explained by the relative motion of bodies alone. If all motions were purely relative, there would be no basis for physically distinguishing accelerated motion from uniform motion. The existence of inertial effects suggests, instead, that not all reference frames are equivalent, and that there must exist a privileged frame, provided by absolute space.

Relationalist criticisms, developed in particular by Gottfried Wilhelm Leibniz, challenge precisely this point. Leibniz argues that space is not an autonomous entity, but an order of coexistence between bodies, and therefore, speaking of absolute positions or velocities is lacking of empirical meaning. Through thought experiments such as static shift and kinematic shift, he argues that universes differing only by an absolute translation or velocity would be indistinguishable, thus violating the principle of sufficient reason and the principle of identity of indiscernibles.

Newton implicitly responds by insisting that, even if absolute space is not directly observable, it is necessary to explain observable phenomena, such as inertial effects. For him, therefore, the metaphysical cost of substantivalism is justified by its explanatory power, while relationism fails to explain fundamental aspects of dynamics. In conclusion, Newton's position defends absolute space as an indispensable condition for a coherent theory of motion and inertia.

Relativism: Leibniz and Mach

Gottfried Wilhelm Leibniz and Ernst Mach developed two important versions of the relational conception of space, both in opposition to Newton's theory of absolute space. While they shared a rejection of substantivalism, their arguments were based on different philosophical assumptions: rationalist in Leibniz, empiricist and anti-metaphysical in Mach.

For Leibniz, space is neither a real substance nor an independent container, but an order of coexistence or a set of bodies with respect to one another. It exists only as a set of spatial relations between material objects. Consequently, there is no privileged frame of reference: each body can define a valid frame of reference. Concepts such as absolute position and velocity are, therefore, meaningless.

One of Leibniz's main criticisms of substantivalism is based on the Principle of Sufficient Reason (PSR). If absolute space existed, then universes identical in all relations between bodies but located in different absolute positions would be distinct. However, there would be no sufficient reason why the world should be in one position rather than another. Hence, Leibniz supports this argument with the Principle of Identity of Indiscernibles (PII): two states of the universe that are indistinguishable in all observable and relational respects cannot correspond to distinct physical states. He uses the static and kinematic shift thought experiments to show that absolute space creates metaphysical distinctions without any corresponding physical differences.

However, the problem of inertial effects remains, which Newton interprets as evidence for the existence of absolute accelerations. Leibniz responds by observing that, although acceleration is physically detectable, absolute position and velocity are not.

The critique of substantivalism is further radicalized by Mach. From an empiricist perspective, Mach rejects any unobservable entity, such as absolute space, assuming that, it lacked of scientific meaning. For him, the only relevant facts of mechanics are the relative motions of material bodies. In a universe without of other objects, the very notion of motion would be meaningless.

Mach, therefore, proposes a relational explanation of inertial effects: they depend on the overall distribution of matter in the universe, particularly distant stars. In this way, Mach eliminates the reference to space as an autonomous entity and attributes the entire explanatory role to matter.

In conclusion, Leibniz and Mach reject substantivalism because it introduces superfluous metaphysical entities. Leibniz criticizes it for rational and metaphysical reasons, Mach for empirical and epistemological reasons. Both defend relationism as a more effective conception of space, while acknowledging the difficulty of fully explaining inertial effects without resorting to an absolute space.

Personal View

Personally, I closely relate space to the universe, to the point of considering them equally: space is the universe itself, as the totality of everything that exists in a physical sense. However, this identification immediately clashes with our everyday intuitions. We are, in fact, led to attribute familiar characteristics to space: a finite volume, well-defined boundaries, as if it were a room or a delimited container. The universe, however, is probably the least intuitive object we can imagine.

The very question of its finitude is problematic. What we actually observe is not the universe in its entirety, but only a portion of it, called the observable universe: the region from which light has had time to reach us from the Big Bang to the present. This limit does not depend on a lack of instruments, but on a fundamental physical constraint (the speed of light).

Modern cosmology has indeed shown that the universe is expanding faster than light. On large scales, space itself expands, and some regions recede from us at a rate faster than light. This does not violate the laws of relativity, because it is not objects moving through space faster than light, but space itself that is expanding faster than light. Consequently, the light emitted from certain regions has never been able to reach us, and in some cases, it will never be able to do so.

For this reason, we can only observe a finite portion of the universe, while beyond it we are unable to gather any empirical information. However, this does not mean that the universe as a whole is finite: the only possible assumption we can make is that the observable universe is finite or infinite, while the overall structure of the universe remains an open question.

If we assume that the universe is finite, a further difficulty immediately arises: does it have boundaries? Here too, a common intuition misleads us. Talking about boundaries only makes sense if we imagine something "outside", but if the universe coincides with space itself, the idea of an "outside" loses meaning. There is no outside of the universe in the same sense that there is an outside of a room or a building, because the universe is not contained within a larger space: it is space itself.

For this reason, some cosmological models hypothesize a universe that is finite but without boundaries, analogous to the surface of a sphere: it is finite, but has no edges, and has no "outside" within the geometry of the surface itself. Other models, however, admit a spatially infinite universe. In both cases, however, our assertions remain tied to theoretical models, that go beyond what we can directly observe.

These considerations show how the concept of space, while central to physics, is profoundly abstract in nature and not immediately accessible to experience. We live immersed in space and cannot observe it from the outside; we can only infer its properties through indirect observations and mathematical structures. Consequently, seemingly simple questions like "is the universe finite or infinite?" or "does it have boundaries?" reveal the epistemic limits of our knowledge and highlight the delicate balance between intuition, theory, and observation in the scientific understanding of the universe.