THE SOURCES OF HIS PHILOSOPHY.
What is true of all men is true of philosophers, and of Leibniz
among them. Speaking generally, what they are unconsciously and
fundamentally, they are through absorption of their antecedents
and surroundings. What they are consciously and reflectively,
they are through their reaction upon the influence of heredity
and environment. But there is a spiritual line of descent and a
spiritual atmosphere; and in speaking of a philosopher, it is with this
intellectual heredity and environment, rather than with the physical,
that we are concerned. Leibniz was born into a period of intellectual
activity the most teeming with ideas, the most fruitful in results,
of any, perhaps, since the age of Pericles. We pride ourselves justly
upon the activity of our own century, and in diffusion of intellectual
action and wide-spread application of ideas the age of Leibniz
could not compare with it. But ours _is_ the age of diffusion and
application, while his was one of fermentation and birth.
Such a period in its earlier days is apt to be turbid and
unsettled. There is more heat of friction than calm light. And such had
been the case in the hundred years before Leibniz. But when he arrived
at intellectual maturity much of the crudity had disappeared. The
troubling of the waters of thought had ceased; they were becoming
clarified. Bacon, Hobbes, Descartes, each had crystallized something
out of that seething and chaotic mass of new ideas which had forced
itself into European consciousness. Men had been introduced into a
new world, and the natural result had been feelings of strangeness,
and the vagaries of intellectual wanderings. But by the day of Leibniz
the intellectual bearings had been made out anew, the new mental
orientation had been secured.
The marks of this "new spiritual picture of the universe" are
everywhere to be seen in Leibniz. His philosophy is the dawning
consciousness of the modern world. In it we see the very conception and
birth of the modern interpretation of the world. The history of thought
is one continuous testimony to the ease with which we become hardened
to ideas through custom. Ideas are constantly precipitating themselves
out of the realm of ideas into that of ways of thinking and of viewing
the universe. The problem of one century is the axiom of another. What
one generation stakes its activity upon investigating is quietly taken
for granted by the next. And so the highest reach of intellectual
inspiration in the sixteenth century is to-day the ordinary food of
thought, accepted without an inquiry as to its source, and almost
without a suspicion that it has a recent historic origin. We have to
go to Bacon or to Leibniz to see the genesis and growth of those ideas
which to-day have become materialized into axiomatic points of view
and into hard-and-fast categories of thought. In reading Leibniz the
idea comes over us in all its freshness that there was a time when
it was a discovery that the world is a universe, made after one plan
and of one stuff. The ideas of inter-relation, of the harmony of law,
of mutual dependence and correspondence, were not always the assumed
starting-points of thought; they were once the crowning discoveries
of a philosophy aglow and almost intoxicated with the splendor of its
far-reaching generalizations. I take these examples of the unity of
the world, the continuity and interdependence of all within it, because
these are the ideas which come to their conscious and delighted birth
in the philosophy of Leibniz. We do not put ourselves into the right
attitude for understanding his thought until we remember that these
ideas--the commonest tools of our thinking--were once new and fresh,
and in their novelty and transforming strangeness were the products
of a philosophic interpretation of experience. Except in that later
contemporary of Leibniz, the young and enthusiastic Irish idealist,
Berkeley, I know of no historic thinker in whom the birth-throes
(joyous, however) of a new conception of the world are so evident as
in Leibniz. But while in Berkeley what we see is the young man carried
away and astounded by the grandeur and simplicity of a "new way of
ideas" which he has discovered, what we see in Leibniz is the mature
man penetrated throughout his being with an idea which in its unity
answers to the unity of the world, and which in its complexity answers,
tone to tone, to the complex harmony of the world.
The familiarity of the ideas which we use hides their grandeur from
us. The unity of the world is a matter of course with us; the dependent
order of all within it a mere starting-point upon which to base
our investigations. But if we will put ourselves in the position of
Leibniz, and behold, not the new planet, but the new universe, so one,
so linked together, swimming into our ken, we shall feel something of
the same exultant thrill that Leibniz felt,--an exultation not indeed
personal in its nature, but which arises from the expansion of the
human mind face to face with an expanding world. The spirit which is at
the heart of the philosophy of Leibniz is the spirit which speaks in the
following words: "Quin imo qui unam partem materiæ comprehenderet, idem
comprehenderet totum universum ob eandem ~perichôrêsin~ quam dixi. Mea
principia talia sunt, ut vix a se invicem develli possint. Qui unum bene
novit, omnia novit." It is a spirit which feels that the secret of the
universe has been rendered up to it, and which breathes a buoyant
optimism. And if we of the nineteenth century have chosen to bewail
the complexity of the problem of life, and to run hither and thither
multiplying "insights" and points of view till this enthusiastic
confidence in reason seems to us the rashness of an ignorance which does
not comprehend the problem, and the unity in which Leibniz rested
appears cold and abstract beside the manifold richness of the world, we
should not forget that after all we have incorporated into our very
mental structure the fundamental thoughts of Leibniz,--the thoughts of
the rationality of the universe and of the "reign of law."
What was the origin of these ideas in the mind of Leibniz? What
influences in the philosophic succession of thinkers led him in this
direction? What agencies acting in the intellectual world about him
shaped his ideal reproduction of reality? Two causes above all others
stand out with prominence,--one, the discoveries and principles of
modern physical science; the other, that interpretation of experience
which centuries before had been formulated by Aristotle. Leibniz has a
double interest for those of to-day who reverence science and who hold
to the historical method. His philosophy was an attempt to set in order
the methods and principles of that growing science of nature which
even then was transforming the emotional and mental life of Europe;
and the attempt was guided everywhere by a profound and wide-reaching
knowledge of the history of philosophy. On the first point Leibniz
was certainly not alone. Bacon, Hobbes, Descartes, Spinoza, each felt
in his own way the fructifying touch of the new-springing science,
and had attempted under its guidance to interpret the facts of nature
and of man. But Leibniz stood alone in his interest in the history of
thought. He stands alone indeed till he is greeted by his compeers
of the nineteenth century. To Bacon previous philosophy--the Greek,
the scholastic--was an "eidol of the theatre." The human mind must be
freed from its benumbing influence. To Descartes it was useless rubbish
to be cleared away, that we might get a _tabula rasa_ upon which to
make a fresh start. And shall Locke and the empirical English school,
or Reid and the Scotch school, or even Kant, be the first to throw a
stone at Bacon and Descartes? It was reserved to Leibniz, with a genius
almost two centuries in advance of his times, to penetrate the meaning
of the previous development of reflective thought. It would be going
beyond our brief to claim that Leibniz was interested in this _as_ a
historical movement, or that he specially concerned himself with the
genetic lines which connected the various schools of thought. But we
should come short of our duty to Leibniz if we did not recognize his
conscious and largely successful attempt to apprehend the core of truth
in all systems, however alien to his own, and to incorporate it into
his own thinking.
Nothing could be more characteristic of Leibniz than his saying,
"I find that most systems are right in a good share of that which
they advance, but not so much in what they deny;" or than this other
statement of his, "We must not hastily believe that which the mass
of men, or even of authorities, advance, but each must demand for
himself the proofs of the thesis sustained. Yet long research generally
convinces that the old and received opinions are good, provided they
be interpreted justly." It is in the profound union in Leibniz of
the principles which these quotations image that his abiding worth
lies. Leibniz was interested in affirmations, not in denials. He was
interested in securing the union of the modern _method_, the spirit
of original research and independent judgment, with the conserved
_results_ of previous thought. Leibniz was a man of his times; that is
to say, he was a scientific man,--the contemporary, for example, of men
as different as Bernouilli, Swammerdam, Huygens, and Newton, and was
himself actively engaged in the prosecution of mathematics, mechanics,
geology, comparative philology, and jurisprudence. But he was also a
man of Aristotle's times,--that is to say, a philosopher, not satisfied
until the facts, principles, and methods of science had received an
interpretation which should explain and unify them.
Leibniz's acquaintance with the higher forms of mathematics was
due, as we have seen, to his acquaintance with Huygens. As he made
the acquaintance of the latter at the same time that he made the
acquaintance of the followers of Descartes, it is likely that he
received his introduction to the higher developments of the scientific
interpretation of nature and of the philosophic interpretation of
science at about the same time. For a while, then, Leibniz was a
Cartesian; and he never ceased to call the doctrine of Descartes
the antechamber of truth. What were the ideas which he received from
Descartes? Fundamentally they were two,--one about the method of truth,
the other about the substance of truth. He received the idea that the
method of philosophy consists in the analysis of any complex group of
ideas down to simple ideas which shall be perfectly clear and distinct;
that all such clear and distinct ideas are true, and may then be used
for the synthetic reconstruction of any body of truth. Concerning
the substance of philosophic truth, he learned that nature is to be
interpreted mechanically, and that the instrument of this mechanical
interpretation is mathematics. I have used the term "received" in
speaking of the relation of Leibniz to these ideas. Yet long before
this time we might see him giving himself up to dreams about a vast
art of combination which should reduce all the ideas concerned in
any science to their simplest elements, and then combine them to any
degree of complexity. We have already seen him giving us a picture
of a boy of fifteen gravely disputing with himself whether he shall
accept the doctrine of forms and final causes, or of physical causes,
and as gravely deciding that he shall side with the "moderns;" and
that boy was himself. In these facts we have renewed confirmation of
the truth that one mind never receives from another anything excepting
the stimulus, the reflex, the development of ideas which have already
possessed it. But when Leibniz, with his isolated and somewhat
ill-digested thoughts, came in contact with that systematized and
connected body of doctrines which the Cartesians presented to him in
Paris, his ideas were quickened, and he felt the necessity--that final
mark of the philosophic mind--of putting them in order.
About the method of Descartes, which Leibniz adopted from him, or
rather formulated for himself under the influence of Descartes,
not much need be said. It was the method of Continental thought
till the time of Kant. It was the mother of the philosophic systems
of Descartes, Leibniz, and Spinoza. It was equally the mother of
the German _Aufklärung_ and the French _éclaircissement_. Its
fundamental idea is the thought upon which Rationalism everywhere bases
itself. It says: Reduce everything to simple notions. Get clearness;
get distinctness. Analyze the complex. Shun the obscure. Discover
axioms; employ these axioms in connection with the simple notions,
and build up from them. Whatever can be treated in this way is capable
of proof, and only this. Leibniz, I repeat, possessed this method in
common with Descartes and Spinoza. The certainty and demonstrativeness
of mathematics stood out in the clearest contrast to the uncertainty,
the obscurity, of all other knowledge. And to them, as to all before
the days of Kant, it seemed beyond doubt that the method of mathematics
consists in the analysis of notions, and in their synthesis through the
medium of axioms, which are true because identical statements; while
the notions are true because clear and distinct.
And yet the method led Leibniz in a very different direction. One of
the fundamental doctrines, for example, of Leibniz is the existence
everywhere of minute and obscure perceptions,--which are of the
greatest importance, but of which we, at least, can never have
distinct consciousness. How is this factor of his thought, which
almost approaches mysticism, to be reconciled with the statements just
made? It is found in the different application which is made of the
method. The object of Descartes is the _erection of a new structure
of truth_ upon a _tabula rasa_ of all former doctrines. The object of
Leibniz is the _interpretation of an old body of truth_ by a method
which shall reveal it in its clearest light. Descartes and Spinoza
are "rationalists" both in their method and results. Leibniz is a
"rationalist" in his method; but his application of the method is
everywhere controlled by historic considerations. It is, I think,
impossible to over-emphasize this fact. Descartes was profoundly
convinced that past thought had gone wrong, and that its results were
worthless. Leibniz was as profoundly convinced that its instincts had
been right, and that the general idea of the world which it gave was
correct. Leibniz would have given the heartiest assent to Goethe's
saying, "Das Wahre war schon längst gefunden." It was out of the
question, then, that he should use the new method in any other than an
interpreting way to bring out in a connected system and unity the true
meaning of the subject-matter.
So much of generality for the method of Leibniz. The positive substance
of doctrine which he developed under scientific influence affords
matter for more discussion. Of the three influences which meet us here,
two are still Cartesian; the third is from the new science of biology,
although not yet answering to that name. These three influences are, in
order: the idea that nature is to be explained mechanically; that this
is to be brought about through the application of mathematics; and,
from biology, the idea that all change is of the nature of continuous
growth or unfolding. Let us consider each in this order.
What is meant by the mechanical explanation of nature? To answer a
question thus baldly put, we must recall the kind of explanations which
had satisfied the scholastic men of science. They had been explanations
which, however true, Leibniz says, as general principles, do not touch
the details of the matter. The explanations of natural facts had been
found in general principles, in substantial forces, in occult essences,
in native faculties. Now, the first contention of the founders of the
modern scientific movement was that such general considerations are
not verifiable, and that if they are, they are entirely aside from the
point,--they fail to explain any given fact. Explanation must always
consist in discovering an immediate connection between some fact and
some co-existing or preceding fact. Explanation does not consist in
referring a fact to a general power, it consists in referring it to an
antecedent whose existence is its necessary condition. It was not left
till the times of Mr. Huxley to poke fun at those who would explain
some concrete phenomenon by reference to an abstract principle ending
in --ity. Leibniz has his word to say about those who would account for
the movements of a watch by reference to a principle of horologity, and
of mill-stones by a fractive principle.
Mechanical explanation consists, accordingly, in making out an actual
connection between two existing facts. But this does not say very
much. A connection of what kind? In the first place, a connection of
the same order as the facts observed. If we are explaining corporeal
phenomena, we must find a corporeal link; if we are explaining
phenomena of motion, we must find a connection of motion. In one of his
first philosophical works Leibniz, in taking the mechanical position,
states what he means by it. In the "Confession of Nature against the
Atheists" he says that it must be confessed to those who have revived
the corpuscular theory of Democritus and Epicurus, to Galileo, Bacon,
Gassendi, Hobbes, and Descartes, that in explaining material phenomena
recourse is to be had neither to God nor to any other incorporeal
thing, form, or quality, but that all things are to be explained
from the nature of matter and its qualities, especially from their
magnitude, figure, and motion. The physics of Descartes, to which was
especially due the spread of mechanical notions, virtually postulated
the problem: given a homogeneous quantity of matter, endowed only with
extension and mobility, to account for all material phenomena. Leibniz
accepts this mechanical view without reserve.
What has been said suggests the bearing of mathematics in this
connection. Extension and mobility may be treated by mathematics. It is
indeed the business of the geometer to give us an analysis of figured
space, to set before us all possible combinations which can arise,
assuming extension only. The higher analysis sets before us the results
which inevitably follow if we suppose a moving point or any system of
movements. Mathematics is thus the essential tool for treating physical
phenomena as just defined. But it is more. The mechanical explanation
of Nature not only requires such a development of mathematics as will
make it applicable to the interpretation of physical facts, but the
employment of mathematics is necessary for the very discovery of these
facts. Exact observation was the necessity of the growing physical
science; and exact observation means such as will answer the question,
_How much?_ Knowledge of nature depends upon our ability to _measure_
her processes,--that is, to reduce distinctions of quality to those of
quantity. The only assurance that we can finally have that two facts
are connected in such a way as to fulfil the requirements of scientific
research, is that there is a complete quantitative connection between
them, so that one can be regarded as the other transformed. The advance
of physical science from the days of Copernicus to the present has
consisted, therefore, on one hand, in a development of mathematics
which has made it possible to apply it in greater and greater measure
to the discussion and formulation of the results of experiment, and to
deduce laws which, when interpreted physically, will give new knowledge
of fact; and, on the other, to multiply, sharpen, and make precise all
sorts of devices by which the processes of nature may be measured. The
explanation of nature by natural processes; the complete application
of mathematics to nature,--these are the two thoughts which, so far,
we have seen to be fundamental to the development of the philosophy
of Leibniz.
The third factor, and that which brings Leibniz nearer, perhaps, our
own day than either of the others, is the growth of physiological
science. Swammerdam, Malpighi, Leewenhoek,--these are names which
occur and recur in the pages of Leibniz. Indeed, he appears to be the
first of that now long line of modern philosophers to be profoundly
influenced by the conception of life and the categories of organic
growth. Descartes concerned himself indeed with physiological problems,
but it was only with a view to applying mechanical principles. The
idea of the vital unity of all organs of the body might seem to
be attractive to one filled with the notion of the unity of all in
God, and yet Spinoza shows no traces of the influence of the organic
conception. Not until Kant's famous definition of organism do we see
another philosopher moved by an attempt to comprehend the categories of
living structure.
But it is the idea of organism, of life, which is radical to the
thought of Leibniz. I do not think, however, that it can truly be said
that he was led to the idea simply from the state of physiological
investigation at that time. Rather, he had already learned to think of
the world as organic through and through, and found in the results of
biology confirmations, apt illustrations of a truth of which he was
already thoroughly convinced. His writings show that there were two
aspects of biological science which especially interested him. One
was the simple fact of organism itself,--the fact of the various
activities of different organs occurring in complete harmony for one
end. This presented three notions very dear to the mind of Leibniz,
or rather three moments of the same idea,--the factors of activity,
of unity brought about by co-ordinated action, and of an end which
reveals the meaning of the activity and is the ideal expression of
the unity. The physiologists of that day were also occupied with the
problem of growth. The generalization that all is developed _ab ovo_
was just receiving universal attention. The question which thrust
itself upon science for solution was the mode by which ova, apparently
homogeneous in structure, developed into the various forms of the
organic kingdom. The answer given was "evolution." But evolution had
not the meaning which the term has to-day. By evolution was meant
that the whole complex structure of man, for example, was virtually
contained in the germ, and that the apparent phenomenon of growth was
not the addition of anything from without, but simply the unfolding
and magnifying of that already existing. It was the doctrine which
afterwards gave way to the epigenesis theory of Wolff, according to
which growth is not mere unfolding or unwrapping, but progressive
differentiation. The "evolution" theory was the scientific theory of
the times, however, and was warmly espoused by Leibniz. To him, as we
shall see hereafter, it seemed to give a key which would unlock one of
the problems of the universe.
Such, then, were the three chief generalizations which Leibniz found
current, and which most deeply affected him. But what use did he make
of them? He did not become a philosopher by letting them lie dormant in
his mind, nor by surrendering himself passively to them till he could
mechanically apply them everywhere. He was a philosopher only in virtue
of the active attitude which his mind took towards them. He could not
simply accept them at their face-value; he must ask after the source of
their value, the royal stamp of meaning which made them a circulatory
medium. That is to say, he had to interpret these ideas, to see what
they mean, and what is the basis of their validity.
Not many men have been so conscious of just the bearings of their
own ideas and of their source as was he. He often allows us a direct
glimpse into the method of his thinking, and nowhere more than when
he says: "Those who give themselves up to the details of science
usually despise abstract and general researches. Those who go into
universal principles rarely care for particular facts. But I equally
esteem both." Leibniz, in other words, was equally interested in the
application of scientific principles to the explanation of the details
of natural phenomena, and in the bearing and meaning of the principles
themselves,--a rare combination, indeed, but one, which existing,
stamps the genuine philosopher. Leibniz substantially repeats this
idea when he says: "Particular effects must be explained mechanically;
but the general principles of physics and mathematics depend upon
metaphysics." And again: "All occurs mechanically; but the mechanical
principle is not to be explained from material and mathematical
considerations, but it flows from a higher and a metaphysical source."
As a man of science, Leibniz might have stopped short with the
ideas of mechanical law, of the application of mathematics, and of
the continuity of development. As a philosopher he could not. There
are some scientific men to whom it always seems a perversion of their
principles to attempt to carry them any beyond their application to the
details of the subject. They look on in a bewildered and protesting
attitude when there is suggested the necessity of any further
inquiry. Or perhaps they dogmatically deny the possibility of any such
investigation, and as dogmatically assume the sufficiency of their
principles for the decision of all possible problems. But bewildered
fear and dogmatic assertion are equally impotent to fix arbitrary
limits to human thought. Wherever there is a subject that has meaning,
there is a field which appeals to mind, and the mind will not cease
its endeavors till it has made out what that meaning is, and has made
it out in its entirety. So the three principles already spoken of were
but the starting-points, the stepping-stones of Leibniz's philosophic
thought. While to physical science they are solutions, to philosophy
they are problems; and as such Leibniz recognized them. What solution
did he give?
So far as the principle of mechanical explanation is concerned,
the clew is given by considering the factor upon which he laid
most emphasis, namely, motion. Descartes had said that the essence
of the physical world is extension. "Not so," replied Leibniz;
"It is motion." These answers mark two typical ways of regarding
nature. According to one, nature is something essentially rigid
and static; whatever change in it occurs, is a change of form,
of arrangement, an external modification. According to the other,
nature is something essentially dynamic and active. Change according
to law is its very essence. Form, arrangement are only the results
of this internal principle. And so to Leibniz, extension and the
spatial aspects of physical existence were only secondary, they were
phenomenal. The primary, the real fact was motion.
The considerations which led him to this conclusion are simple
enough. It is the fact already mentioned, that explanation always
consists in reducing phenomena to a law of motion which connects
them. Descartes himself had not succeeded in writing his physics
without everywhere using the conception of motion. But motion cannot
be got out of the idea of extension. Geometry will not give us
activity. What is this, except virtually to admit the insufficiency
of purely statical conceptions? Leibniz found himself confirmed in
this position by the fact that the more logical of the followers
of Descartes had recognized that motion is a superfluous intruder,
if extension be indeed the essence of matter, and therefore had been
obliged to have recourse to the immediate activity of God as the cause
of all changes. But this, as Leibniz said, was simply to give up the
very idea of mechanical explanation, and to fall back into the purely
general explanations of scholasticism.
This is not the place for a detailed exposition of the ideas of Leibniz
regarding matter, motion, and extension. We need here only recognize
that he saw in motion the final reality of the physical universe. But
what about motion? To many, perhaps the majority, of minds to-day it
seems useless or absurd, or both, to ask any question about motion. It
is simply an ultimate _fact_, to which all other facts are to be
reduced. We are so familiar with it as a solution of all physical
problems that we are confused, and fail to recognize it when it appears
in the guise of a problem. But, I repeat, philosophy cannot stop with
facts, however ultimate. It must also know something about the meaning,
the significance, in short the ideal bearing, of facts. From the point
of view of philosophy, motion has a certain function in the economy of
the universe; it is, as Aristotle saw, something ideal.
The name of Aristotle suggests the principles which guided Leibniz
in his interpretation of the fact of motion. The thought of Aristotle
moves about the two poles of potentiality and actuality. Potentiality
is not _mere_ capacity; it is being in an undeveloped, imperfect
stage. Actuality is, as the word suggests, activity. Anything is
potential in so far as it does not manifest itself in action; it is
actual so far as it does thus show forth its being. Now, movement, or
change in its most general sense, is that by which the potential comes
to the realization of its nature, and functions as an activity. Motion,
then, is not an ultimate fact, but is subordinate. It exists for an
end. It is that by which existence realizes its idea; that is, its
proper type of action.
Now Leibniz does not formally build upon these distinctions; and
yet he is not very far removed from Aristotle. Motion, he is never
weary of repeating, means force, means energy, means activity. To
say that the essence of nature is motion, is to say that the natural
world finally introduces us to the supremacy of action. Reality is
activity. _Substance c'est l'action._ That is the key-note and the
battle-cry of the Leibnizian philosophy. Motion is that by which being
expresses its nature, fulfils its purpose, reveals its idea. In short,
the specific scientific conception of motion is by Leibniz transformed
into the philosophic conception of force, of activity. In motion he
sees evidence of the fact that the universe is radically dynamic.
In the applicability of mathematics to the interpretation of nature
Leibniz finds witness to the continuity and order of the world. We
have become so accustomed to the fact that mathematics may be directly
employed for the discussion and formulation of physical investigations
that we forget what is implied in it. It involves the huge assumption
that the world answers to reason; so that whatever the mind finds to be
ideally true may be taken for granted to be physically true also. But
in those days, when the correlation of the laws of the world and the
laws of mathematical reasoning was a fresh discovery, this aspect of
the case could not be easily lost sight of.
In fact it was this correlation which filled the _Zeitgeist_ of
the sixteenth century with the idea that it had a new organ for the
penetration of nature, a new sense for learning its meaning. Descartes
gives the following as the origin of his philosophy: "The long chains
of simple and easy reasons which geometers employ, even in their
most complex demonstrations, made me fancy that all things which are
the objects of human knowledge are _similarly interdependent_." To
Leibniz also mathematics seemed to give a clew to the order, the
interdependence, the harmonious relations, of the world.
In this respect the feeling of Plato that God geometrizes found
an echoing response in Leibniz. But the latter would hardly have
expressed it in the same way. He would have preferred to say that God
everywhere uses the infinitesimal calculus. In the applicability of the
calculus to the discussion of physical facts, Leibniz saw two truths
reflected,--that everything that occurs has its reason, its dependent
connection upon something else, and that all is continuous and without
breaks. While the formal principles of his logic are those of identity
and contradiction, his real principles are those of sufficient reason
and of continuity. Nature never makes leaps; everything in nature has
a sufficient reason why it is as it is: these are the philosophic
generalizations which Leibniz finds hidden in the applicability
of mathematics to physical science. Reason finds itself everywhere
expressed in nature; and the law of reason is unity in diversity,
continuity.
Let us say, in a word, that the correlation between the laws of
mathematics and of physics is the evidence of the rational character
of nature. Nature may be reduced to motions; and motions can be
understood only as force, activity. But the laws which connect motions
are fundamentally mathematical laws,--laws of reason. Hence force,
activity, can be understood only as rational, as spiritual. Nature
is thus seen to mean Activity, and Activity is seen to mean
Intelligence. Furthermore, as the fundamental law of intelligence is
the production of difference in unity, the primary law of physical
change must be the manifestation of this unity in difference,--or,
as Leibniz interpreted it, continuity. In nature there are no breaks,
neither of quantity nor of quality nor of relationship. The full force
of this law we shall see later.
Such an idea can hardly be distinguished from the idea of growth or
development; one passes naturally into the other. Thus it is equally
proper to say that the third scientific influence, the conception of
organism and growth, is dominant in the Leibnizian thought, or that
this is swallowed up and absorbed in the grand idea of continuity. The
law of animal and vegetable life and the law of the universe are
identified. The substance of the universe is activity; the law of
the universe is interdependence. What is this but to say that the
universe is an organic whole? Its activity is the manifestation of
life,--nay, it is life. The laws of its activity reveal that continuity
of development, that harmony of inter-relation, which are everywhere
the marks of life. The final and fundamental notion, therefore, by
which Leibniz interprets the laws of physics and mathematics is that of
Life. This is his regnant category. It is "that higher and metaphysical
source" from which the very existence and principles of mechanism
flow. The perpetual and ubiquitous presence of motion reveals the
pulsations of Life; the correlation, the rationality, of these motions
indicate the guiding presence of Life. This idea is the alpha and omega
of his philosophy.