Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |

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Dictionary of the History of Ideas | ||

*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

iae.

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

lutionibus orbium coelestium.

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

docta ignorantia

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-

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.

Dictionary of the History of Ideas | ||