(especially in the second half of the nineteenth century) for the
extension of _the method of the natural sciences_ to the sciences
of the spirit or moral sciences, the _orbis intellectualis,_ for a
naturalistic treatment of the productions of language and of art, or
of political, social, and religious life. Thus were originated or
prophesied a Psychology, an Æsthetic, an Ethic, a Sociology, _methodo
naturali demonstratae._ It was necessary to draw the attention of those
makers of programmes and advisers (apart from the evil philosophic
intentions, positivist or materialistic, which they nourished in their
bosoms) to the superfluity of their demand, and gently to reprove them
with the old phrase: _Quod petis in manu habes._ Since man was man and
constructed pseudoconcepts and empirical sciences, these naturalistic
classifications have never been limited to animals, plants, and
minerals, nor to physical, chemical, and biological phenomena, but
have been extended to all the manifestations of reality. Naturalistic
Logic, Psychology, Linguistic Sociology and Ethics have not awaited the
nineteenth century ere they should open to the sun. And (without going
too far back in time, or leaving Europe) they already bore flower and
fruit in the Sociology (Politics) of Aristotle, in the Grammatics of
the Alexandrians, in the Poetics and Rhetoric of Aristotle himself, or
of Hermagoras, of Cicero, or of Quintilian, and so on. The novelty of
the nineteenth century has principally consisted in giving the names
_social Physics,_ or the _physico-acoustic science of language_ to what
was once more simply, and perhaps in better taste, called otherwise.
But in saying this we do not wish to deny that certain naturalistic
work has been far more copious in the nineteenth century than in
Greece, and that naturalistic methods have not been applied with
singular acumen and exactitude in those fields of study. Linguistic
affords a case in point, with _its phonetic laws,_ by reason of which
it moves so proudly among its companions.
[Sidenote: _Historical basis of the natural sciences._]
The natural sciences and the empirical concepts which compose them
appear therefore like a tachygraphic transcription upon living and
mutable reality, capable of complete transcription only in terms of
individual representations. But upon what reality? Upon the reality of
the poet, or upon the clarified and existentialized reality of--the
historian? The constructions of the natural sciences take history
for their presupposition, just as judgments of classification take
individual judgments. Were this not so, their economic function would
have no way of expressing itself, from lack of matter whereon to work.
To employ the easy example already given, it would be of no use to the
zoologist to construct types and classes of animals that were certainly
conceivable, but non-existent. For while those types and classes would
distract the attention from the useful and urgent task of summarizing
reality historically given and known, they would not exhaust the
possibilities, which are infinite And if it appear that imaginary
animals are sometimes classified, as for example griffins centaurs,
Pegasi, and sirens, it is easy to see that this is not done in Zoology,
but in another naturalistic science,--comparative Mythology, in which
not animals but the imaginings of men are really classified. These
too are historical facts, because they are imaginings or fancies
historically given. They are not combinations of images which no people
has ever dreamed of, nor any poet represented, for such, as has already
been said, would be infinite in number and food for mere diversion.
[Sidenote: _The question as to whether history is the foundation or the
crown of thought._]
History, which has philosophy for its foundation, becomes in its
turn foundation in the natural sciences. This explains why, with the
controversy as to whether history be a science or an art, there has
always been inextricably connected the other question as to whether
history be the foundation of science or science the foundation of
history. The question finds a solution in the solution of the ambiguity
of the term "science," which is used indifferently, sometimes in the
sense of philosophy, sometimes in that of the natural sciences. If
science is understood as philosophy, history is not its foundation,
indeed philosophy is the foundation of history. Both mingle and are
identified in the sense already explained. If science is understood
as naturalistic science, then history is its necessary foundation or
precedent. Certainly, naturalistic classifications are also reflected
in historical narrative; but, as we have seen, they do not perform a
constitutive function in it; they are of merely subsidiary assistance.
[Sidenote: _Naturalists and historical research._]
But since history is the foundation of the natural sciences, and the
special treatment of perceptive material or historical data by these
sciences does not possess theoretic value, but is valuable merely as
a convenient classification, it is clear that the whole content of
truth of the natural sciences (the measure of truth and reality that at
bottom they contribute) is history. Therefore it is not without reason
that the natural sciences or some of them have been called in the
past _natural history._ History is the hot and fluid mass, which the
naturalist cools and solidifies by pouring it into formal classes and
types. Previous to this manipulation, the naturalist must have thought
as a historian. The matter thus cooled and solidified for preservation
and for transport has no theoretic value, save in so far as it can
again be rendered hot and fluid. Similarly, on the other hand, it is
necessary to revise continually the classifications adopted, returning
to the observation of facts, to simple intuitions and perceptions, to
the historical consideration of reality. The _naturalist_ who makes a
discovery, in so far as he is a discoverer of truth, is a _historical_
discoverer; and revolutions in the natural sciences represent progress
in historical knowledge. Lamarckianism and Darwinism may serve as an
example of this. Naturalists (and we use the word in its ordinary
meaning, applying it to those who explore this "fair family of plants
and animals," and what is called in general the physical world)
feel themselves somewhat humiliated when described as classifiers
careless of truth. But if such classification is exactly what the
natural sciences accomplish from the gnoseological point of view, yet
naturalists as individuals and as corporations of students exercise a
far more substantial and fruitful function. The historical foundation
of the life of the natural sciences is also found in the fact that
a change of historical conditions sometimes renders, if not wholly
useless, at least less useful, certain classifications made with the
object of controlling conditions of life remote from us, or perceptions
concerning life that have now been abandoned. This has occurred
with regard to the classifications of alchemy and of astrology, and
also (passing on to examples from other empirical sciences) to the
descriptive and casuistic portions of feudal law. When the book is no
longer read, the _index_ also falls into disuse.
[Sidenote: _The prejudice as to the non-historicity of nature._]
The strangest of statements, that _nature has no history,_ comes from
forgetting the historical foundation of the natural sciences, from
ignorance that it constitutes their sole truth, and from attributing
theoretic importance to classifications which have merely practical
importance. In this case, nature signifies that reality, from man
downwards, which is empirically called inferior reality. But how, if
it is reality, is it without history? How, if it is reality, is it
not becoming? And further, the thesis is confuted by all the most
attentive studies of so-called inferior reality. To limit ourselves
to the animal kingdom, a century before Darwin the acute intellect
of the Abbé Galiani shook itself free of this prejudice as to the
immobility of animals. He remarks in certain places about cats:
"_A-t-on des naturalistes bien exacts qui nous disent que les chats, il
y a trois mille ans, prenaient les souris, préservaient leurs petits,
connaissaient la vertu médicinale de quelques herbes, ou, pour mieux
dire, de l'herbe, comme ils font à présent? ... Mes recherches sur
les mœurs des chattes m'ont donné des soupçons très forts qu'elles
sont perfectibles; mais au bout d'une longue traînée de siècles,
je crois que tous que les cliats savent est l'ouvrage de quarante à
cinquante mille ans. Nous n'avons que quelques siècles d'histoire
naturelle: ainsi le changement qu'ils auront subi dans ce temps,
est imperceptible."_[3] This slight perceptibility of the relative
changes of what is called nature or inferior reality has contributed
to that prejudice (not to mention the confusion between the fixity
that belongs to naturalistic classifications and reality, which is
always in motion). Nature appears to be motionless, just because of
the slight interest that we take in the shadings of its phenomena and
in their continuous variation. But not only is nature not motionless,
but it is not even true that it proceeds (as the poet says) "with
steps so slow that it seems to stand still." The movement of nature or
inferior reality is fast or slow, neither in less nor greater degree
than human reality, according to the various arbitrary constructions of
empirical concepts which are adopted, and according to the variable and
arbitrary standards of measurement which are applied to them. We watch
with vigilant eye every social movement that can cause a variation in
the price of grain or the value of Stock Exchange securities; but we
do not surprise with equally vigilant eye the revolutions that are
prepared in the bosom of the earth or among the green-clad herbs of the
field.
[Sidenote: _The philosophic foundation of the natural sciences, and the
efficacy of the philosophy that they contain._]
But if history is the foundation of the natural sciences, it follows
from this that those sciences are always based upon a philosophy. This
is indubitable, for the naturalist, however much he be a naturalist, is
above all things a man, and a man without a philosophy (or what comes
to the same thing, without a religion) has not yet been found. This
does not mean that the natural sciences are philosophy. Their special
task is classification, and here they are just as independent and
autonomous as philosophy is incompetent. But philosophy is competent
in philosophy, and so we see that those naturalists who possess
philosophic culture avoid the prejudices, errors, and absurdities
that spring from bad philosophies, and to which other naturalists are
prone. For instance, if the chemist Professor Ostwald had possessed a
better philosophy, he would not have abandoned his good chemistry for
that doubtful mixture of things--his _Philosophy of Nature._ And had
Ernest Haeckel made an elementary study of philosophy, he would never
have given up his researches upon micro-organisms, in order to solve
the riddles of the universe and to falsify the natural sciences. Let
us limit ourselves to these instances, for our life of to-day supplies
innumerable examples of philosophizing men of science, who are as
pernicious to science as they are to philosophy and to culture. The
antithesis between science and philosophy, of which so many speak, is
a dream. The antithesis is between philosophy and philosophy, between
true philosophy and that which is very imperfect and yet very arrogant,
and manifestly active in the brains of many scientists, though it
has nothing to do with the discoveries made in laboratories and
observatories.
[Sidenote: _Action of the natural sciences upon philosophy, and errors
in conceiving such relation._]
The action of philosophy upon the natural sciences is not constitutive
of them, but preparatory. The action of the natural sciences upon
philosophy is not even preparatory, but merely incidental and
subsidiary, having for its end simplicity of exposition and of
memorizing, just as in history. A very common error, derived from a too
hasty analysis of the forms of spiritual life, is that of looking upon
the empirical and natural sciences as a _preparation_ for philosophy.
But in the achievement of the natural sciences, philosophy has been
cold-shouldered, and to recover it we must seek pure intuition, which
is the necessary and only precedent of logical thought.
Still worse is it, when the natural sciences are considered, not
only as preparation, but just as a first sketch, or a chiselling of
the marble block, from which philosophy will carve the statue. For
this view denies without being aware of it, either the autonomy of
the natural sciences, or that of philosophy, according as either the
philosophic method or the naturalistic method is held to be the method
of truth.
Indeed, in the first case, if the natural sciences be of a philosophic
nature and represent a first approximation to philosophy, they must
disappear when philosophy is evolved, as the provisional disappears
before the definite, as the proof before the printed book. This would
mean that natural sciences as such do not exist and that what really
exists is philosophy. In the second case, if philosophy have the same
nature as the natural sciences, the further development of the first
sketch will always be the work of the naturalistic method, however
refined and however increased in power we may please to imagine it.
Thus, what would really exist would never be philosophy, but always the
natural sciences. This erroneous conception therefore reduces itself
to a denial, either of the natural sciences or of philosophy; either
of the pseudoconcepts or of the pure concepts; a negation that need
not be confuted, because the whole of our exposition of Logic is its
explicit confutation.
[Sidenote: _Motive of these errors: naturalistic philosophy._]
The genesis of such a psychological illusion resides in the fact that
the natural sciences seem to be tormented with the thirst for full and
real truth, and philosophy, on the other hand, to be intent solely
upon correcting the perversions and inexactitudes of the empirical and
natural sciences. But it is a question of likeness or appearance only,
because the thirst for truth belongs not to the natural sciences, but
to philosophy, which lives in all men, and also in the naturalist.
And the philosophic perversions and inexactitudes which have to be
corrected do not form part of the natural sciences (which as such
affirm neither the true nor the false), but to that philosophy which
the naturalist forms and into which he introduces the prejudices
derived from his special business.
[Sidenote: _Philosophy as destroyer of naturalistic philosophy, but not
of the natural sciences. Autonomy of these._]
The proof of the theory here maintained is that even when philosophy
engages in strife with naturalistic prejudices, it dissolves those
prejudices, but does not and could not dissolve the sciences which had
suggested them. Indeed, a philosopher becoming again a naturalist,
cultivates those sciences successfully, just as his philosophizing
does not forbid his going into the garden and there scenting and
pruning the plants. The naturalistic sciences of language and of art,
of morality, of rights and of economics (to take instances from the
intellectual world, which seem to have closer contact with philosophy),
are not only what is called the _empirical stage_ of the corresponding
philosophic disciplines, but persist and will persist side by side with
them, because they render services which cannot be replaced. Thus there
is no philosophy of language and of art which can expel from their
proper spheres, even if it does expel them from its own, empirical
Linguistic, Grammar, Phonetics, Morphology, Syntax, and Metric, with
their empirical categories, which are useful to memory. Nor can they
eliminate the classifications of artistic and literary kinds, and
those of the arts according to what are called means of expression,
by means of which it is possible to arrange books on shelves, statues
and pictures in museums, and our knowledge of artistic-literary
history in our memories. Psychology, an empirical and natural science,
certainly does not make us understand the activity of the spirit;
but it permits us to summarize and to remember very many effective
manifestations of the spirit, by classifying as well as may be the
species or classes of facts of representation (sensations, intuitions,
perceptions, imaginings, illusions, concepts, judgments, arguments,
poems, histories, systems, etc.), facts of sentiment, and volitional
facts (pleasure, pain, attraction, repulsion, mixed feelings, desires,
inclinations, nostalgias, will, morality, duties, virtue, family,
judicial, economic, political, religious life, etc.), or by classifying
these same facts according to groups of individuals (the Psychology
of animals, of children, of savages, of criminals, and of man, both
in his normal and abnormal conditions). This wholly extrinsic mode of
consideration, which is now prevalent in Psychology, is the source of
the remark that it has risen (or has sunk?) _to the level_ of a natural
science, and that its method is mechanical, determinist, positive,
antiteleological. Sociology, understood not as a philosophic science
(--there is no such thing--), but as an empirical science, classifies
as well as may be the forms of family and the forms of production, the
forms of religion, of science and of art, political and social forms,
and constructs series of classifications to summarize the principal
forms which human history has assumed in the course of its development.
The philosopher expels these classifications from philosophy, as
extraneous elements causing pathological processes; but that same
philosopher, in so far as he is a complete man, and in so far as
he provides for the economy of his internal life and for more easy
communication with his fellows, must fashion and avail himself of the
empirical. Having ideally destroyed the adjective and the adverb, the
epic and the tragic kinds, the virtues of courage and of prudence, the
monogamous and the polygamous family, the dog and the wolf, he must yet
speak when necessary of adjectives and adverbs, of epics and tragedies,
of courage and of prudence, of families formed in this or that way, of
the species "dog," as though it were clearly distinguished from the
species "wolf."
Thus is confirmed the autonomy and the peculiar nature of the empirical
or natural sciences, indestructible by philosophy as philosophy is
indestructible by them.
[Footnote 1: _Nov. Org._ I. §§ 81, 116; and II. in fine.]
[Footnote 2: See _The Philosophy of the Practical,_ pt. i. sect. i.]
[Footnote 3: Letter to d'Epinay, October 12, 1776.]
VI
MATHEMATICS AND THE MATHEMATICAL SCIENCE OF NATURE
[Sidenote: _The idea of a mathematical science of nature._]
The conception of a _mathematical science of nature_ is at variance
with the thesis that recognizes the ineliminable historical foundation
of the natural sciences and the consequences which follow from it. It
is claimed that this mathematical science, in expressing the ideal and
end of the natural sciences, would express also their true nature,
which is not empirical but abstract, not synthetic but analytic, not
inductive but deductive. The mathematical conception of the natural
sciences would imply perfect mechanism, the reduction of all phenomena
to quantity without quality, the representation of each phenomenon
by means of a mathematical formula, which should be its adequate
definition.
[Sidenote: _Various definitions of mathematics._]
But the nature of mathematics cannot be considered a mystery in our
time. Mathematics (as has lately been said with a subtlety equal to
its truth) is a science "in which it can never be known _what_ we
are talking about, nor whether what we are talking about be _true_"
These affirmations are made one after the other by all mathematicians
who are conscious of their own methods. In what sense can a process
that merits such a description be called a science? A science that
states no sort of truth does not belong to the theoretic spirit,
since it is not even poetry; and a science which is not related to
anything is not even an empirical science, which is always related
to a definite group of representations. For this reason, others
incline to consider mathematics sometimes as _language,_ sometimes as
_logic._ But mathematics is neither language in general nor any special
language; it is not language in the universal sense, co-extensive with
expression and with art; nor is it a historically given language,
which would be a contingent fact; nor a class of languages (phonetic,
pictorial, or musical language, etc.), which would be an approximate
and empirical definition, inapplicable in a function like mathematics,
which expresses its own original nature. It is not logic, because
there is only one logic, and thought thinks always as thought. If it
is maintained, on the other hand, that the human spirit has also a
special logic, which is that of mathematicizing, a return is made to
the problem to be solved, namely, what is mathematicizing? that is to
say, this logic, which is not the logic of thought, because it does not
give truth, and is not the logic of the empirical sciences, because it
does not depend upon representations.
[Sidenote: _Mathematical process._]
Any sort of arithmetical operation can serve as an example of
mathematical process. Let us take the multiplication: 4×4 = 16. The
sign = (equals) indicates identity: 4×4 is identical with 16, as it
is identical with an infinite number of such formulæ, since there
can be infinite definitions of every number. What do we learn from
such an equivalence concerning the reality, phenomenal or absolute,
to which the human mind aspires? Nothing at all. But we learn how to
substitute 16 for 8×2, for 9+7, for 21-5, for 32÷2, for 4², for √256,
and so on. One or the other substitution is of service, according to
circumstances. When, for instance, some one promises to pay us 4 lire
daily, and we wish to know the total amount of lire, that is to say,
the object that we shall have at our disposal after four days, we shall
carry out the operation 4×4=16. Again, when we have 32 lire to divide
into equal parts between ourselves and another, we shall have recourse
to the formula: 32÷2 = 16. Mathematics as Mathematics does not know,
but establishes formulæ of equality; it does not subserve knowing, but
counting and calculating what is already known.
[Sidenote: _Apriority of mathematical principles._]