Introduction. Space is a conception of many aspects,
and it has arisen—under various names, appellations,
and descriptions—in different areas of cognition and
knowledge: in cosmology, physics, mathematics, phi-
losophy, psychology, and theology.
There are stirring philosophemes about space in the
Timaeus of Plato and the Physica of Aristotle, and they
foreshadow our present-day space, or spaces, of labo-
ratory and cosmos, of mechanics and physics, of worlds
that are everlasting and stationary, and of universes
that are born and grow, and perhaps even age and
collapse. But, as a rule, Greek thoughts about space
were only about space in cosmology and physics, and
perhaps also theology; and seldom, if ever, did Greeks
compose a statement, or even an aphorism, about space
in any other area of insight.
Thus, the Greeks did not create a space of logical,
ontological, or psychological perception. There is
almost nothing about space in Plato's Meno,
Theaetetus, Sophistes, or Parmenides, or in Aristotle's
De anima, or Metaphysica. In Aristotle's collection of
several treatises in logic, the so-called Organon, there
is mention of space only once, in Chapter 6 of Categor-
iae. It is not a “research” conception of space, but an
indifferent schoolbook description of it, and Aristotle
had no occasion ever to recall it.
In modern philosophy, that is since 1600, any doc-
trine of perception since John Locke has dealt with
space as a matter of course; and, within this general
approach, a monumental construction, which kept the
nineteenth century enthralled, was the famed a priori
space of Immanuel Kant. In contrast, Greek philosophy
knew absolutely nothing about an a priori space (and
time) of pure intuition as expounded by Kant in the
“Transcendental Aesthetics” of his Critique of Pure
Reason (1781). It is true (see sec. 13, below) that in
psychology of the twentieth century the role of space,
as a primary datum, has greatly shrunk. But this
shrinkage affected space in experimental psychology
rather than in metaphysical perception, and a marked
difference between ancient and modern attitudes re-
mains.
More conspicuous, and almost fate-sealing, was the
absence from Greek thought of a general conception
of space for geometry and geometrically oriented
analysis. Greek mathematics did not conceive an over-
all space to serve as a “background space” for geo-
metrical figures and loci. There is no such background
space for the configurations and constructs in the
mathematical works of Euclid, Archimedes, or Apol-
lonius, or even in the astronomical work Almagest of
Ptolemy. When Ptolemy designs a path of a celestial
body, it lies in the astronomical universe of Ptolemy;
but as a geometrical object of mathematical design and
purpose, it does not lie anywhere. In Archimedes, who,
in some respects was second only to Isaac Newton, the
mathematical constructs were placed in some kind of
metaphysical “Nowhere” from which there was “No
Exit” into a mathematical “Future.”
Such a background space was rather slow in coming.
Thus, Nicholas Copernicus did not have it yet. He was
an innovator in astronomical interpretation, and not
in mathematical operation. His mathematics was still
largely Ptolemaic, and only a bare outline of a mathe-
matical background space is discernible in his De revo-
lutionibus orbium coelestium. Nevertheless, already a
century before Copernicus, Nicholas of Cusa, church-
man, theologian, mystic, and gifted mathematician, in
Book II of his leading work Of Learned Ignorance (De
docta ignorantia), adumbrated an overall space of
mathematics by way of an overall mathematical
framework for the space of the universe. But the lead-
ing statements of the metaphysics of Cusa were
enveloped in theology and mysticism and not very
comprehensible to his contemporaries and to others
after him.
On the other hand, soon after the death of Coperni-
cus, in the second half of the sixteenth century, some
mathematicians began to grope for projective and
descriptive geometry, and this was bound to lead to
a background space. It did, but only after two hundred
years. In the meantime, in the first half of the seven-
teenth century a background space for geometry was
created, for all to see, in La Géométrie (1637) of René
Descartes. Half a century later, Isaac Newton in his
Principia (1687), created an ambitiously conceived
absolute space which was intended to be a background
space for mathematics, for terrestial and celestial me-
chanics, and for any space-seeking metaphysics.
Newton even made it into a “Sensorium of God,”
whatever that might be, and this aroused philosophical
passions which are still smoldering. A resulting corre-
spondence between Gottfried Wilhelm Leibniz and Dr.
Samuel Clarke (for a spirited account see Koyré,
[1957], Ch. XI) is much prized for what it reveals about
the philosophy of Leibniz. But it is less significant for
what it reveals about the role of space in science.
Beginning in the late eighteenth century, and
through the length of the nineteenth century, mathe-
matics developed a duality or polarity between space
and (geometrical) structure, by which, at long last—
two and a half millennia after Thales of Miletus—
mathematics became an artificer of space and spaces.
In the twentieth century this dualism of space and
structure greatly affected all of theoretical physics. For
instance, there would be no General Theory of Rela-
tivity without it. In this theory, space is gravitational
space; it is “curved,” and thus endowed with “form.”
This form is affected by the presence of gravitational
matter, which is the only kind of matter known to this
theory. In this way, the theory establishes a novel
intimacy between matter and space and between mat-
ter and form. An enthusiast might even declare that,
in this theory, matter is space (or form) and space is
matter.
In quantum theory, the de Broglie dualism of parti-
cles and waves offers a different version of the dualism
of matter and space, since matter is built of elementary
particles and waves are space-filling. Also, in quantum
“field” theory, the field is highly mathematical through
its conceptual provenance; and if mathematics is
equated with form, then a new version of the dualism
of matter and form emerges.
In the sections to follow we will have many other
assertions and details. Each section will be headed
either by a name for space, or by a formulaic descrip-
tion of space or of something resembling space. These
appellations will be introduced roughly in the chrono-
logical order in which they have arisen, and each
appellation will be then followed up in its develop-
ment. Our first appellation will be a Hebrew term from
the Old Testament, which seems to be the earliest on
record; and there is hardly another case from natural
philosophy in which the Old Testament fashioned a
“technical” term ahead of the Greeks.
