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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
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Continuity enters into all parts of philosophy. A
measure of continuity is involved in any conception
or philosopheme of Plato's, be it about man or God,
body or soul, memory or ideas, mathematics or morals,
poetry or artisanship, state or citizen. Without an
awareness of continuity there would have been no City
of God
or Confessions of Saint Augustine; no medieval
problems about particulars and universals, creation and
eternity, fate and free will, Faith and Reason. And yet,
only in the philosophy of nature and of mathematics


is the presence of continuity immediate and tangible;
in other areas of philosophy the degree of its presence
is not easy to verify and the importance of its role
is not easy to determine.

Thus, Aristotle's Physica is full of concern for conti-
nuity, directly and emphatically, and it is easy to iden-
tify its presence in related treatises like De caelo and
De generatione et corruptione. But there is, directly,
very little about continuity in the Metaphysica, and
almost nothing indirectly to stir one's imagination.
Thus, at the beginning of Book 10 of the Metaphysica,
continuity is mentioned, directly, as one of several
meanings of Unity, but the context is philosophically
indifferent and little known. And even the continuity
in Physica deals, for the most part, only with the linear
of mathematics, which, from our retrospect,
is a rather circumscribed topic, in a sense.

The first Western philosopher on record who tried
to visualize the problem of continuity in its entirety,
that is for philosophy in general, was G. W. Leibniz.
He set out to spread his lex continui over the vastnesses
of the theories of cognition, metaphysics, and sciences.
He even asserted that the mission of the Law of Conti-
nuity is to affirm that “the present is always pregnant
with the future,” and he also implied that to deny the
law would amount to denying the Principle of Suffi-
cient Reason, whatever that be (Leibniz Selections, p.
185). Yet, whenever Leibniz attempts to be specific and
to adduce some particular application of his general
Law of Continuity, the application usually becomes
a specific assertion within mathematics, or within nat-
ural philosophy, or within philosophy of mathematics.
It is true that in his mathematical allusions Leibniz
sometimes reaches out far into the future, but it is a
future of professional mathematics and not of extra-
mathematical philosophy.

After Leibniz, the eighteenth century contributed
nothing notable to the comprehension of continuity in
philosophy. This fully applies even to Immanuel Kant.
To judge by the entries “Kontinuität,” and “Stetigkeit”
in a recent Kant dictionary (R. Eisler, Kant-Lexikon),
Kant made no pronouncements on continuity that
contributed anything new to what had been said by
philosophers from Aristotle to Leibniz.

In the nineteenth century, in general philosophy,
most pronouncements on continuity were likewise
monotonous and uninspiring (R. Eisler, Wörterbuch).
But a few philosophers did try to break out of the
monotony; and by an odd coincidence, or perhaps
concurrence, they designated continuity in philosophy
not by names that are cognates to the Latin verb
continere, but by names which they coined from the
Greek verb synechein.

Thus, Johann Friedrich Herbart (1776-1841) has a
section on “Synechology” in his Metaphysics. Next,
Gustav Theodor Fechner (1801-87), co-founder of the
famed Weber-Fechner law of quantitative psychology
(intensity of sensation varies as the logarithm of the
stimulus), the first of its kind, has, in an impenetrably
obscure book of his, a section on the “synechological
outlook versus the monadological outlook” (Fechner,
p. 204). Finally, and most importantly, the American
philosopher Charles S. Peirce (1839-1914), the leading
architect of the algebra of relations in symbolic logic,
denotes by “synechism” what, from a certain retro-
spect, was a revival of Leibniz' Law of Continuity.
But Peirce made the lex continui genuinely universal,
and he updated it in its scope and intent, so as to make
it measure up to the exigencies of the late Victorian
and Edwardian eras.

Herbart's synechology is a peculiar philosophical
compound of realism and psychology. As a realist
Herbart finds that data from natural philosophy like
space, time, and matter exist outside ourselves. As a
psychologist however he finds that all attributes of such
data, continuity among them, are created by the psy-
chological process which operates on the intuition
through which such data reveal themselves to us. These
two findings seem to be divergent, but Herbart some-
how reconciles them.

In connection with this we wish to point out that
a passage in Aristotle's De anima apparently argues
against identifying the continuity of the process of
thought with the continuity of data conceived by

But the thinking mind is one and continuous in the same
sense as the process of thinking. Now thinking consists of
thoughts. But the unity of these thoughts is a matter of
succession, that is the unity of a number, and not the unity
of a magnitude. This being so, neither is mind continuous
in the latter sense, but either it is without parts, or it is
continuous in a different sense from an extended magnitude

(407a 6-11).

Herbart has been lauded for the saying: “Continuity
is union in separation, and separation in union”
(Mauxion, p. 107). The saying is interesting enough,
but there are plenty of similar statements in Aristotle.
Also, after Herbart, in Fechner, there is a counterpart
to Herbart's saying which seems more original. We
translate it thus:

What is psychically uniform and simple comes out of physi-
cal variety; and physical variety contracts into something
that is psychically uniform, and simple, or, at any rate,

(Fechner, p. 247).

Following this, Fechner asserts in a very difficult
sentence of his that this “contraction” leads to a kind
of “synechological” equidistribution in the world,


which Fechner opposes to a “monadological” concen-
tration at points, and, Fechner continues, of this equi-
distribution we have a divinely inspired awareness.

C. S. Peirce, finally, being a master of mathematical
logic and also of philosophy of mathematics, knew
about the importance of continuity for mathematics
in considerable detail; he also knew how the concep-
tion of continuity, when fanning out from mathematics,
was reaching into large areas of cognition. Being thus
equipped, Peirce was elaborating aspects of continuity
which are recognizably mathematical, and he was also
endeavoring to establish a presence of continuity,
under the name of “synechism,” in most of philosophy.

It is however not clear from the statements in Peirce,
and it may have never become clear to himself,
whether synechism is indeed effectively present outside
of areas of philosophy of mathematics, or whether,
conversely, philosophy of mathematics extends into
every precinct of metaphysics in which the presence
of synechism is detectable. Peirce was one of the first
of a species of philosophers who by trend, intent, or
circumstances had been blurring the several demarca-
tions between mathematics, mathematical logic, phi-
losophy of mathematics, and general philosophy.

Being a logician by intellectual faculty, Peirce con-
ceived his synechism within a logical setting. Peirce
established a certain triad of metaphysical constructs
which he called categories, in which he placed “Syne-
chism” along with “Tychism” and “Agapism.”

Peirce called his three categories “cenopythago-
rean”: “Firstness, Secondness, Thirdness,” and they
recognizably corresponded to the triads in Kant's table
of twelve categories, but also resembled the stages of
Hegel's phenomenology of mind (Peirce, pp. 384ff.).

Now, “syn-thesis” means literally “putting-
together,” and in analogy to this, Peirce associated
various aspects of Thirdness with “synechism,” which
means literally “hanging-together.” And Peirce's aim
becomes clear if one contemplates the actual content
of his Thirdness, which a commentator of his has de-
scribed thus.

Thirdness is mediation, generality, order, interpretation,
meaning, purpose. The Third is the medium or bond which
connects the absolute first and last, and brings them into
relationship. Every process involves Continuity, and Conti-
nuity represents Thirdness to perfection

(Freeman, p. 19).

Thus Peirce's design for his Synechism was even
more ambitious than Leibniz' design for his lex con-
but Peirce was even less successful than Leibniz
in carrying out his plans. Even friendly critics of Peirce,
like Morris R. Cohen, were complaining that Pierce
had been promising a vast philosophical system, but
had never been able to erect it. And a recent critic
puts it thus:

The grand design was never fulfilled. The reason is that
Peirce was never able to find a way to utilize the continuum
concept effectively. The magnificant synthesis which the
theory of continuity seemed to promise somehow always
eluded him, and the shining vision of the great system
always remained a castle in the air

(Murphey, p. 407).

This harsh verdict against Peirce is true as to fact;
and yet it can be mellowed by the fact that Peirce
was reaching out for the impossible and stumbled over
his own genius when attempting this. Peirce wanted
a conception of continuity that would be philo-
sophically as all-pervasive as Leibniz had envisioned
it, and, at the same time, logically as rigorous as math-
ematics of his own day was capable of making it. But
Peirce was striving after an impossibility. Mathematics
cannot be thus fused with philosophy in entirety, and
mathematics is in no justifiable sense sufficient to de-
termine philosophy in its general scope. If a conception
from general philosophy has been made mathe-
matically rigorous, then it can wear the vestments of
mathematical rigor to advantage only when moving
about in areas of mathematics proper, or, at best, in
border areas which mathematics is in the process of
penetrating, but certainly not when moving about in
areas which are well outside of mathematics' sphere
of influence. There are differences between mathe-
matics and philosophy which cannot be winked at with
impunity. A. N. Whitehead and Bertrand Russell were
frequently musing that it ought to be possible to tres-
pass on philosophy proper with conceptions from
mathematics. But they were prudent enough, especially
Whitehead, not to become entangled in difficulties into
which Peirce was stepping only too boldly.