University of Virginia Library

I. INTRODUCTION

Continuity is a key conception in the history of ideas
in many fields. A form of continuity, under one name
or another, is frequently attributed to processes or
developments in mathematics, science, philosophy,
history, and theology. In mathematics proper and its
direct applications, especially to “exact” science, con-
tinuity is nowadays rigorously defined and unequivo-
cally fixed. Also, in mathematical contexts continuity
is sharply distinguished from neighboring concepts like
uniformity, steadiness, constancy, etc., all of which
have, in mathematical contexts, definitions of their
own. But, by reason of its general nature, continuity
is a sprawling concept. Outside of mathematics, it is
ambiguously conceived and loosely applied, and merg-
ers and fusions with neighboring concepts are really
unavoidable.

Thus, the historical books of the Old Testament are
a vast dissertation on the Lord's unceasing concern for
his “Chosen People”; and a theologian may pronounce
with almost no difference of meaning that the Lord
perseveres in this concern with “continuity,” or
“steadiness,” “constancy,” “uniformity,” etc.

In general history and theology imprecisions as to
the meaning of continuity may be enriching rather than
disturbing, but in descriptive science, in which impre-
cisions also occur, they may become outright embar-
rassing. A leading instance of such an embarrassment
is the case of the hypothesis of uniformitarianism. The
hypothesis asserts, for geology and biology, that there
has been a certain continuity of evolution since the
formation of the earth. But no satisfactory definition
of this would-be continuity has been agreed upon, or
is in sight. (See section V.)

Imprecisions as to the meaning of continuity may
border on the very threshold of “exact science.” A
notable case is Isaac Newton's description of his abso-
lute time, which runs as follows:

[F. Cajori trans., p. 6].

Newton makes it clear that this pronouncement,
which is made in an elucidating scholium only, is not
meant to be a primary operational definition of abso-
lute time but only a supplementary background de-
scription of it. The decisive ingredient of this descrip-
tion is the word “equably” (which does not occur in
the immediately following description of “absolute
space”), and it is meant to suggest that the flow of
time is somehow intrinsically continuous and uniform.
But this suggestion is tenuous and fugacious, and
Newton's sentence about the nature of his time cannot
be made into a truly informative definition.

Two thousand years before the Principia, Aristotle,
in his great essay on time (Physica, Book 4, Chs. 10-14),

performed much better than Newton. Aristotle's time
is hierarchically anterior to events in it and even to
our awareness of it; and Aristotle is much more per-
suasive than Newton in his expostulations that time
is intrinsically continuous, and that this continuity is
a preexistent standard by which to assess, for any
“movement”—which, in Aristotle, stands for a general
process in nature, more or less—whether it is continu-
ous, discrete, or constant (Bochner, Ch. 4). Further-
more, already many centuries before Aristotle, a lin-
guistic bond between time and continuity had been
clearly present in Homer, and we are going to describe
it briefly.

The Greek word for our “abstract” noun “continu-
ity,” as standardized by Aristotle, is the adverbial form
to synechés (τὸ συνεχές), and the cognate verb syn-
echein means literally “to hang, or hold together.” It
so happens that the Latin root of the English word
continuity also means literally “hanging, or holding
together”; but works on Indo-European linguistics do
not assert that the Greek and Latin stem words for
continuity had a common root in Sanskrit.

Now, the verb synechein and the adverb synechés
occur already in Homer, but on different levels of
abstraction. The verb occurs in Iliad 4, 133, in the
expression: “The golden clasps of the belt were held
together,” in which its meaning is quite concrete. But
the adverb, which is used twice, is both times used
in a semi-abstract meaning, namely in the meaning of:
continually (in time). The first occurrence is in Iliad
12, 25-26, thus: “Zeus made it rain continually”; and
the second occurrence is in Odyssey 9, 74, thus: “There
for two nights and two days we lay continually.” Also,
in the second passage the adverb synechés is reinforced,
seemingly redundantly, by the adverb aiei (αἰεί) which
means: always, ever, eternally. The Odyssey thus
adumbrated a tripartite bond between continuity, time,
and eternity, and this bond has been variously contem-
plated and exalted in general philosophy and theology
since. This bond is nowhere stronger than in the Old
Testament, but the extant canon of the Old Testament
does not have a word whose functions would corre-
spond to those of synechés.

Post-Hellenistically, this bond is also verified by the
order in which the cognates of our English word con-
tinuity have come into use. According to the entries
in the Oxford English Dictionary, our word continual
(in time) was the first to emerge. It occurs already
around A.D. 1340, in the phrase: “great exercise of body
and continual travail of the spirit,” in one of the so-
called English Prose Treatises of the hermit Richard
Rolle of Hampole (1290-1349). But for all other cog-
nates of continuity the same dictionary quotes only
from Chaucer, who wrote about half a century after
Hampole, or from later sources, even much later ones.
Thus, according to this dictionary, our adjective con-
tinuous gained currency in the seventeenth century
only.

Continuity has many shadings of meaning and
therefore also many antonyms. The leading antonym
to “continuous” is “discrete”; other ones are: saltatory,
sudden, intermittent, indivisible, atomic, particulate,
and even monadic. A monad however, being a kind
of synonym for unity and one-ness, may suggest both
continuity and discreteness, at one and the same time.
The monad of Leibniz, as presented in his Monadology,
is apparently of such a kind; that is, it also suggests
continuity, even if it is an irreducible ultimate unit,
not only of physical structure but also of consciousness,
cognition, and metaphysical coherence. In the thinking
of Leibniz this simultaneousness is grounded in the
all-pervading lex continui, which maintains that “all”
basic constituents of the universe are somehow contin-
uous, be they physical or metaphysical, elemental or
rational.

Long before Leibniz, the outlines of a lex continui,
and an involvement of unity with continuity, were
already present in the great ontological poem of Par-
menides (sixth century B.C.) from which we quote two
passages (L. Tarán, p. 85).

(frag.
8, lines 22-26).

In sum, the Parmenidean “Being” is one, yet contin-
uous; homogeneous, that is continuously distributed,
yet indivisible; ungenerated, and imperishable, and
atemporal. Such bold accumulations of divers attributes
in one have been occurring in Western philosophy ever
since. And Western science has been harboring self-
dualities and near-inconsistencies, many of which affect
continuity, from early Pythagoreans until our very day.

Our present-day intellectual discomfort, if any, over
the contrast between the continuous and the discrete
is an inheritance from the nineteenth century. Through
the length of the nineteenth century there was a wide-
spread predilection for continuity in all areas of
knowledge, in mathematics, physics, earth-and-life sci-
ence, general philosophy, and even in historiography.
This predilection manifested itself in a tendency to
subsume and subordinate the discrete under the con-
tinuous, even when the presence of the discrete was
freely and fully acknowledged. In the twentieth cen-

tury the Victorian outlooks on continuity have been
modified and reoriented, some gradually and some
vehemently; and the discrete has come into its rightful
own, reaching a high-point in quantum mechanics.