4. Apeiron. The generic meaning of apeiron
(ἄπειρον) is Infinity without a direct suggestion of space.
But the term has many connotations, and late tradition
makes it likely that Anaximander, the younger com-
patriot of Thales, denoted by it a generative substance
of the universe (Kirk and Raven, Ch. 3). If this was
so, then, in Anaximander's imagery, apeiron may have
also been a part-synonym for space, since matter and
space were probably proximate notions to him.
A token of this proximity is woven into the fabric
of Aristotle's Physica. Book 4 of this treatise is made
up of three essays, on place (Chs. 1-5), on void (Chs.
6-9), and on time (Chs. 10-14). Now, immediately
preceding these essays (Book 3, Chs. 4-8) is an essay
on apeiron, as if to indicate that there is a close link
between infinity and space (and void).
In the seventeenth century, Baruch Spinoza went
philosophically much farther, when, in his Ethics he
imparted infinity to Extension, that is, to space and
to other attributes of his God (Wolfson, 1, 154).
Before that, in the sixteenth century, Giordano Bruno
ecstatically fused space and infinity in an unbridled
vision of infinitely many worlds regularly distributed
over a wide-open all-infinite Euclidean space (D. W.
Singer, pp. 50-61). The cosmological facts were not
entirely new (ibid.), nor were they presented in ade-
quate detail to become meaningful as such, nor were
Bruno's insights greatly welcomed by his contem-
poraries. But somehow Bruno's outpourings made an
impression, and they created and fashioned, or only
activated, a philosopher's yearning for the infinitude
of space, which played a leading part on the stage of
philosophy until well into the twentieth century. In
a broad sense, the English philosophers Henry More
(1614-1687) and Richard Bentley (1662-1742) were
followers of Bruno (Koyré, Chs. 6-10), and so were
virtually all representatives of German idealism begin-
ning with Immanuel Kant, or even earlier.
Oswald Spengler advanced the thesis (Decline of the
West, Vol. 1, Ch. 5 and elsewhere), which probably
was not quite new either, that this hankering after the
infinitude of space, especially in its extra-rational
aspects, was a characteristic trait and a propellant of
Western European civilization since the early Middle
Ages, and he somehow also interpreted the emergence
of Gothic art and architecture as a response to this
hankering. This thesis, whatever its overall validity,
does not properly apply to leading scientists (Bochner,
Eclosion and Synthesis, Ch. 14). Most scientists, even
when adopting some features of Bruno's cosmology,
were circumspect and restrained. In scientific cos-
mology today, the Kinematic Relativity (J. D. North,
Ch. 8) of Edward Arthur Milne (1896-1950) seems
more compatible with Bruno's suggestions than other
viable theories; but even in Milne the physical presence
of infinity is considerably more restrained than in
Bruno's paradigm.
