**Space** is the undefined and unbounded entity that contains all material things. These, having an extension, occupy a part of it and assume a position in space, which is defined quantitatively according to the principles of geometry, and qualitatively, according to relationships of proximity (distance) and size (smallness).

Real physical space is believed to be three-dimensional, although in modern physics such three-dimensional space is considered to be part of a four-dimensional continuum called space-time, which also includes time. In mathematics they can be defined as “spaces” with even more than four dimensions, and with complex underlying structures. Experimental observations so far confirm the hypothesis of a three-dimensional space up to subatomic dimensions. High energy physics, and in particular the experiments at the Large Hadron Collider at CERN, search for possible manifestations of extradimensions on subatomic scales.

The concept of space is considered of fundamental importance for understanding the physical universe, and the properties attributed to it are related to everyday observations and experiences of objects around us. However, there is ongoing disagreement among philosophers as to whether it is itself an entity, a relation between entities, or part of a conceptual framework.

Our own biological constitution has led us to a representation of the Universe that makes it natural for us to consider space and the bodies in it separately. This concept of space allows a convenient description of many properties of objects, such as the length of a segment, the distance of two points, the area of a surface, the volume enclosed by a surface, angles, the position of a point with respect to another, etc. All these geometric properties of objects can be transferred to space as its properties, independent of the objects. All these geometric properties of objects can be transferred into space as its own properties, independent of the specific objects, and a precise description of what is called three-dimensional or Euclidean is achieved.

As the common concept of three-dimensional space, i.e. of the ordinary, is foreign to a born blind, so it proves inadequate when studying phenomena that occur on a scale immensely larger than human scale, such as the space where collisions of galaxies occur, or immensely smaller, as in atomic physics, nuclear physics or physics of fundamental particles. On the one hand, in the description of phenomena in the immensely large, Einstein’s theory of relativity criticizes and abandons the concept of Euclidean space; on the other hand, quantum mechanics puts limits to our ability to describe phenomena on atomic and subatomic scale and introduces concepts different from the classical ones. For example, the space considered in the theory of relativity is called Minkowski space-time, or chronotope, or four-dimensional.

## Philosophy of space

In the history of thought and science, the concept of space is fundamental and has been analyzed in different ways and with different methods in different disciplines: the consideration of space is in fact central to mathematics as to geometry, to physics as to philosophy.

In philosophy, the concept of space was analyzed by the first Greek research in a realistic line, which saw space as a property of matter and entities: among the pre-Socratics – from the Pythagoreans to the Eleates, to the atomists – dominates the problem of the finite (Parmenides) or infinite (Melissus, Leucippus, Democritus), divisible or indivisible (Zeno) extension of space; up to Plato, from whose dialogues results a substantial identification between space and that initial formless chaos that then, by the action of the Demiurge, in imitation of the Ideas, takes shape and structure, thus generating all the things of the sensible world.

According to the Platonic concept, therefore, it turns out that space is in itself formless and distinct from the forms gradually assumed: not directly perceptible, but such as to make perceptible the things that live and move in it, as a universal “background” of becoming.

Aristotle in his Physics defines space as a “place” where different bodies move, enter and leave: something absolutely existing and invariable, as well as all spatial determinations of high and low, forward and backward; so that, in space, elements and bodies of different nature move each towards its “natural” place (fire goes up, heavy bodies go down).

The three-dimensionality of space, which according to Aristotle’s conception contains all bodies and objects, does not, however, require that space itself be considered corporeal in nature, precisely because, if it were corporeal, it would in turn have to refer to another space that included it. In addition, the Aristotelian conception of space excludes both infinity and emptiness: space, because the place of all worldly entities, is delimited by the sky; emptiness, because in it is not given the possibility of those local determinations which are for Aristotle of an absolute nature and essential to the concept of space; in late Greek times, there was a return to positions close to those of the pre-Socratics; in the period of Scholasticism, with the sole exception of William of Occam, here as elsewhere an anticipator of Renaissance thought, the Aristotelian conception dominated unchallenged.

Throughout the Renaissance, from N. Cusano to Giordano Bruno – fundamental in this regard his work De l’infinito, universo e mondi (On the Infinite, Universe and Worlds) – dominated instead the idea of a space without boundaries, infinite as the Universe itself, completely devoid of fixed limits; conception also accepted by G. Galilei. R. Descartes, who sees in the extension the essential property of matter, rejected the idea of an empty space and reaffirmed the divisibility to infinity.

With I. Newton and his school prevailed the idea of an absolute space, motionless, immutable; G. Leibniz, on the contrary, considered space as the order of the coexistence of bodies; Spinoza identified it with the extension.

With J. Locke and the other empiricists, space is an idea derived from experience, without any absolute nature and determinable on metaphysical grounds: space is not for Locke of the Essay on the Human Intellect a positive reality, absolute and independent of our ideas, but is rather precisely an idea born from the perception of the relationships between things.

Against these theses of the empiricists – taken up with greater strength by G. Berkeley and D. Hume, I. Kant claimed the accuracy of scientific knowledge: space is not something absolutely existing and external to the knowing subject, but it is actually a form that the subject itself imposes to the data of sensitivity: it is the form of the external sense (as the time of the internal sense); a pure a priori intuition, on which only it is possible to base universally valid scientific judgments.

After Kant, in the nineteenth century, the enormous development of geometry and mathematics, together with the abandonment of the assumption of the unique and exclusive character of Euclidean geometry (G. Riemann, N. Lobačevskij, H. von Helmholtz above all), led to the abandonment of the philosophical assumption of the intuition of space and the fixed and stable structure of our cognitive intuition (so, then, also A. Einstein).

On a more strictly philosophical level, there are several solutions in contemporary thought, especially with the phenomenology of E. Husserl and with existentialism: M. Heidegger – in Sein, Seinrichtung, and Husserl’s Sein. Heidegger – in Sein und Zeit – has developed, from his particular point of view, the rare Husserlian ideas and has defined the characteristic spatiality of man as being-in-the-world and therefore in a relationship of distance-vicinity-use with the “intramundane” entities; not an absolute dimension in which there are world and “subject”, but a space that is such only in relation to Dasein and that is, in the end, only for it and because it exists. Merleau-Ponty, always in a phenomenological-existentialist perspective, space is not to be conceived as a place or environment in which things are located, but the “means” by which their placing and positioning becomes possible.