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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
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Continuity plays a major role in descriptive science,
mainly in geology and biology, but also in psychology.


Aristotle's Historia animalium has already a renowned
aphorism to this effect:

Nature passes little by little from things lifeless to animal
life, so that, by continuity, it is impossible to present the
exact lines of demarcation, or to determine to which of the
two groups intermediate forms belong

(588b 4-7).

Also, in Aristotle's system of psychology there may
have been a hierarchy of souls corresponding to the
hierarchy of living things (Tricot, pp. 492-93, note 2).
Altogether Aristotle already envisioned the so-called
Great Chain of Being, which reached a dominant posi-
tion in the thinking of Leibniz and of the Age of
Enlightenment (Lovejoy).

Leibniz took pains to expound that the Great Chain
is indeed “great” in the sense that

All the orders of natural beings form but a single chain
in which the various classes, like so many rings, are so
closely linked one to another that it is impossible for the
senses or the imagination to determine precisely the point
at which one ends and the next begins

(B. Glass, p. 37).

Also, in other contexts, Leibniz intensified, or diver-
sified, the adjective “great” by equating it variously
with “maximal,” “optimal,” “perfect,” “complete,”
“continuous,” etc.

Dr. Samuel Johnson, the redoubtable man of letters,
termed the Great Chain of Being the “Arabian Scale
of Existence,” and he made a very pertinent observa-
tion about its “greatness.” He compared this scale of
existence to the mathematical linear continuum, which
he probably knew from Aristotle's Physica, and he
pointed out that, notwithstanding a superficial similar-
ity, the two are very different from each other
(Lovejoy, pp. 253-54). In fact, as stated by Aristotle
in his Physica over and over again, the mathematical
linear continuum is “everywhere dense,” meaning that
between any two elements of it there are always some
other ones; in particular, no element of it is isolated.
However, in nature's Chain of Being, biological and
mineral, however great and complete it be, only a finite
number of Links can be discerned. Thus, even if the
Chain of Being has been made optimally great by
filling in all possible gaps in it, there still is only a
finite number of Links, all told. Because of that, each
individual member of the Chain is isolated; meaning
that there is a first neighbor that is hierarchically above
it, and another one that is hierarchically below it.

Leibniz must have been aware of this unbridgeable
difference between the Great Chain and the linear
continuum. He must have even been aware of the fact
that the linear continuum is not only “everywhere
dense,” as already known to Zeno of Elea and to
Aristotle, but also “complete,” in the sense that to any
bounded sequence of real numbers which is mono
tonely increasing or decreasing there corresponds a real
number which is a limit of the sequence. The com-
pleteness of the linear continuum was properly estab-
lished only in the nineteenth century by Dedekind and
Cantor; but Eudoxus and Archimedes had, more or less,
known it for their magnitudes, and Leibniz must have
half-known it for real numbers too.

But Leibniz pretended to be undeterred by such
differences. He desired to coalesce heterogeneous phe-
nomena from exact science, descriptive science, and
metaphysically oriented “moral” science into one
comprehensive law of continuity. The latter was ap-
parently also a law of optimality, and in this guise it
was closely allied to a principle of contradiction and
of sufficient reason. Yet, at other times Leibniz also
acknowledged that heterogeneity cannot be forcibly
overcome. Such an acknowledgment seems to be im-
plied in the following statement in which Leibniz
avows that his so-called labyrinth has two separate

There are two famous labyrinths where our reason very
often goes astray. One concerns the great question of the
Free and the Necessary, above all in the production and
the origin of Evil. The other consists in the discussion of
continuity, and of the indivisibles which appear to be the
elements thereof, and where the consideration of the infinite
must enter in

(Leibniz, Theodicy, p. 53).

In the nineteenth century, a quest for continuity was
particularly pronounced in geology and biology. As
already mentioned in section I, the hypothesis of con-
tinuity peculiar to geology is called uniformitarianism;
and its contrary was called catastrophism. Uniformi-
tarianism was introduced in 1795 in a treatise by James
Hutton (Gillispie, pp. 122-48; Albritton, chapter by
G. G. Simpson), and it became generally known
through a large-scale treatise of Charles Lyell, Princi-
ples of Geology,
whose first edition appeared in three
volumes, 1830-33.

In biology of today, the hypothesis of continuity is
specifically the hypothesis of “transformism,” that is
the hypothesis that there is in operation an organic
evolution of life which proceeds by a transformation
of one species into another; the direct contrary to it
would be the doctrine of “fixed species” which the
French call “fixism” (P. Ostoya). Transformism as a
biological hypothesis fully began with Lamarck, and
evolution was assumed by him to come about by
adaptation. Charles Darwin presented an impressive
plea that evolution comes about by natural selection;
and, “popularly,” transformism is associated with this
kind of evolution only. Yet in present-day biology,
adaptation is not entirely ruled out, even if Natural
Selection remains the prime cause.


Geologists nowadays greatly favor uniformitarianism
over catastrophism, but it is easier to say what catas-
trophism asserts than what uniformitarianism actually
is. Catastrophism maintains that manifest discon-
tinuities in geological stratifications of mineral deposits
and imbedded fossils are due to discontinuities in the
physical processes which brought about the stratifica-
tions and perhaps even abrupt changes in the physi-
cal laws which produce the processes (Toulmin, Ch.
7). Uniformitarianism however wants to be a true con-
trary to catastrophism and not only a negation of it.
A mere negation would only demand that important
basic data and phenomena be continuous in time, and
nothing more; there would be no need for anything
to be a constant in time, say. Thus, the gravitational
force need not have at all times the same Newtonian
value 1/r2, but it might be a positive function of dis-
tance and time, provided that the dependence on all
its variables is a continuous one. This however is not
what uniformitarianism really wants to be. Its real aim
is to avow that there is “uniformity” in nature; and
this seems to imply that certain basic causes and laws
are not only continuous in time, but also constant in
time, and perhaps constant in some other parameters
too. By the prevalent interpretations of uniformitari-
anism, certain leading attributes of nature are recog-
nizably always the same, so that the “present deter-
mines the past” and, of course, the future.

It appears that our perception of “uniformity” and
of “continuity”—in whatever form these concepts
appear—is inseparable from our rational awareness of
the flow of time. The awareness of time, in its turn,
has come about by the presence of cyclical and recur-
rent phenomena in nature, although by cognitive
structure time is rectilinear and, in fact, a mathematical
linear continuum. It also appears that within our
Western civilization man's capacity for specific rigor-
ous knowledge has been awakened and shaped under
the impact of lunar, sidereal, and planetary events in
the external world which are recurring periodically (O.
Neugebauer, Ch. 1).

Apparently in keeping with these basic ingredients
of our rationality, the demand of uniformitarianism is
a compound of constancy, continuity, and cyclicity;
and the relative magnitude of these three components
varies with the approach to the conception.

In the first half of the nineteenth century, in the
thinking of Charles Lyell at any rate, the component
of constancy was predominant; so much so that when
Lyell was extending uniformitarianism from geological
to organic matter, he had to give preference to fixed
species over evolving ones. But in the second half of
the nineteenth century, continuity proper was ever
more outweighing constancy; and there was a rising
consensus that, contrary to the view of Lyell, uniform-
itarianism and transformism mutually condition and
justify each other (Glass, pp. 367ff.). To Lyell, the
transition from one species to a next following one,
however short the distance, was a “catastrophe,” and
thus not admissible (de Beer, p. 104). To affirmers of
general continuity however, a sufficiently close transi-
tion from species to species ceased to be a “catas-
trophe,” that is a disquieting discontinuity, and became
“progress,” which bespoke the kind of continuity that
arises in the optical merger of rapidly succeeding visual
tableaus. (In the motion picture industry, “continuity”
refers to the coherence of the scenario, and not to the
flow of the optical illusion).

In the twentieth century, the continuity aspect of
organic evolution has been somewhat beclouded by the
fact that, genetically, evolutionary transition comes
about by a so-called mutation of the chromosomic
apparatus and that “the basis of spontaneous mutation
remains one of the great unsolved problems of genet-
ics” (McGraw-Hill Encyclopedia of Science and Tech-
“Mutation”). Nevertheless, the fact that every-
thing proceeds by mutations is no more damaging to
the overall continuity in evolution than atomic and
quantum spontaneities in basic physics are prejudicial
to overall continuities in the foundations of modern
physics and related science.

Strictly speaking, every event in nature is probably
discrete, or a union of discrete subevents; that is, most
likely, no one event actually proceeds as mapped on
the mathematical continuum in its conceptual purity.
But the “fiction” that most events are best described
by continuous functions seems to be an operational
necessity, and there is nothing to suggest that it will
ever be possible to abandon it entirely. For instance,
the principles of our engineering mechanics, as taught
in engineering schools all over the world, were laid
down in Victorian and Edwardian treatises, and it
would be most cumbersome and inappropriate to make
this entire mechanics, in all its parts, nuclearly discon-
tinuous in accordance with some quantum field, or solid
state theory of our day.