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CLASSIFICATION OF
THE SCIENCES
The aim of every classification is to establish order in
things and in thought. When this operation is applied
in the sciences at a given time in their evolution, it
provides a faithful though provisional picture of the
scientific knowledge at that time. By enabling us to
take such an inventory of our knowledge, classification
provides a sort of spatiotemporal cross section of the
sphere of ideas and culture of a given period. The value
of classification, however, goes beyond a mere inven-
tory or “table of contents,” no matter how complete.
The very fact that classification appeals to logical
criteria which may possibly be subjective or objective
in nature gives us an initial idea of the obstacles con-
fronting the classifier, difficulties scarcely encountered
in the preparation of a catalogue, properly so called.
Consequently, a well conducted effort at surveying the
history of the classification of the sciences may be
valuable in leading us to discover the connections and
analogies existing among the different fields of knowl-
edge at a given time, and within the context of a
particular type of civilization. However, history of any
sort is not a static phenomenon, but follows an evolu-
tionary course. We are obliged therefore to study the
sciences and their classification considered essentially
as an historical process subject to continuous develop-
ment. We shall thus see the appearance of the great
currents of ideas which have sometimes dominated
many centuries and we can seek what is less apparent,
namely, the structure underlying these ideas.
We can already discern among the ancients this need
to classify and discover relationships and hidden con-
nections in order to obtain a total view of reality and
to explain the mechanism of the universe. Take
Pythagoras, for example, whose life was described by
Porphyry and Iamblichus, and whose teaching was
addressed primarily to those initiated in his circle.
According to Pythagoras, geometry, arithmetic (theory
of numbers), and music (acoustics) lead to the discovery
of the secrets of number and harmony; only the sage
by starting with these principles is able to reconstruct
reality (Stobaeus, Florilège, I, 62-63). Through Archy-
tas of Tarentum, Plato had been introduced to the
Pythagorean method, as can be seen in several places
in the Timaeus, the Platonic dialogue on which Proclus
wrote a commentary in four books.
Plato thought that ideas should be ordered according
to their extension (denotation) in inverse relationship
to their intension (comprehension): by starting from
general and vague ideas, one should end up with more
specific and clearer ideas. This dichotomy and progres-
sive division of each idea into those ideas immediately
below it, is expounded in the Republic. There is really
a hierarchy made up of genus (γένη) and species (εἴδη),
but for Plato, genus and species are inseparable. Be-
sides, Plato applies the term mathemata (μαθήματα)
not only to the exact sciences but also to the technical
and mechanical arts and to the liberal arts like music
and gymnastics, that is to say, to all the disciplines
capable of educating a man. However, among these
mathemata Plato bestows a privileged place on the
sciences properly called mathematical. We must re-
member that geometry, arithmetic, astrology (in the
   Page 463, Volume 1
sense of astronomy), and music belonged typically to
Hellenic culture. In the Laws, Plato returns to this
question in order to remind the reader that the first
three sciences must be acquired by every free man
(Laws VII, 817E).
It was not until Aristotle that we find the separation
between species and genus, which was to become the
basis of Aristotelian logic. The species is the specifica-
tion of the genus; both appear in deduction, induction,
and in the theory of definition (per genus proximum
et differentiam specificam
). We find this hierarchy again
in all the later types of classification, however, the
criterion of division by species and genus was later
shown to be inadequate; for example, according to the
theory of evolution zoological and botanical species
have no stability. We must therefore take into account
other criteria: such as the contrasting criteria of objec-
tivity and subjectivity, criteria varying with respect to
method, foundations, aims, and so forth. But, returning
to Aristotle, who is generally more systematic in his
ordering of the sciences, we note that for him there
exist only three large groups of sciences: (1) theoretical
sciences (physics and philosophy); (2) practical sciences
(ethics and politics); (3) poetic sciences (aesthetics).
We also note that for him all reality is knowable
only through classification, but we must not forget also
that for Aristotle all sciences have to be subordinate
to philosophy. It is true that Aristotle's Physics comes
exactly between mathematics and theology and is pre-
ceded by Logic, which is the structure of science and
also the science of structure. Physics is followed by
Aristotle's treatises On the Heavens (De caelo), and
Meterology. This plan is in conformity with the prin-
ciples of classification which appear in several places
of his work. We note three in particular. In Aristotle's
Topics we read that science “is indeed called specula-
tive, practical, and poetic, the differences depending
on how each is related respectively to the theory, the
production, and the action of something” (Topics VI,
6, 145a 15). In the Nicomachean Ethics (VI, 3-5) there
is a brief passage concerning art (technē), science
(epistemē), wisdom (phronēsis), philosophy (sophia), and
intelligence (nous). There are longer passages in the
Metaphysics.
“Physics is the theoretical science of material objects
in motion...; mathematics is a contemplative sci-
ence, though certain mathematical entities are station-
ary” (VI, 1026a). Then farther on: “Theoretical sci-
ences come before the practical ones and philosophy
before the theoretical sciences...; motion exists only
in relation to quantity, quality, and place” (XI, 7
passim; XI, 12, 1068b).
Among Aristotle's pupils, Demetrius of Phalerum
was a great encyclopedic mind and one of the orga
nizers of the library in Alexandria, the center of scien-
tists and philosophers. He deserves mention here for
having introduced divisions and subdivisions of knowl-
edge with the aim of permitting specialization in a
given field of study. In the second century B.C., there
was Posidonius of Apamea, the Stoic and polymath;
he was later in Rome and Cadiz; his work also included
all fields of learning, though unfortunately only some
few fragments of his work are extant.
In the following century, in Rome, Marcus Terentius
Varro expounded a whole program of studies extending
from grammar to architecture (Varro was contem-
porary with Vitruvius), the program answering certain
practical needs without being devoid, however, of a
certain idealism. In Varro's Disciplinarum (ca. 50 B.C.),
which may be regarded as the first illustrated encyclo-
pedia, we find the following classification: grammar,
dialectic, rhetoric, geometry, arithmetic, astrology,
music, medicine, and architecture. It reflects perfectly
the genius of his time and especially of his people;
it owes nothing, in any case, to Aristotelian ideas. With
respect to special disciplines, mention must be made
of the works of the physician A. Cornelius Celsus and
the Natural History of Pliny the Elder in 37 books,
completed in A.D. 77, a true testament of ancient sci-
ence and a model of classification within a branch
of science. Pliny's work has come down to us in its
entirety.
We know that the Arabs preserved Creek science,
that they translated the works of the ancients, added
commentaries, and not only left the imprint of their
genius on these commentaries, but made some original
contributions in every field of knowledge. Greek sci-
ence, enriched by the Arabs' contribution, was intro-
duced by the Moors into Spain, and then proceeded
to penetrate other European countries. Within Islam
there appeared during the seventh century the first
seeds of the new sciences which were essentially reli-
gious; then a distinction was made between Arabic
sciences (such as poetry and the art of oratory) and
foreign sciences (astronomy, medicine, mathematics).
Most of the “foreign sciences” came from the Greek
heritage, thanks to the Syrian translations; there were
also works translated from the Sanskrit via the Pali.
A very distinct effort at classification is discernible
among the Arabs, for example, in Al Farabi and
Avicenna (Ibn Sina), an effort which had been preceded
by the work of systematization. To be remembered are
the names of Djahiz (`Amr Ibn Bahr Jahiz), an Iraquian
scientist (died 868), author of a bestiary, or Book of
Animals
in seven volumes, in which we meet subjects
going beyond the scope of the title. His contemporary
Ibn Qutaibah wrote a treatise, Adab al Katib, contain-
ing an essay on classification (in the introduction).
   Page 464, Volume 1
In China and in India throughout the centuries, there
are examples of classification in encyclopedic works.
In China such works always enjoyed, more than else-
where, an important role in education and in prepara-
tion for taking examinations for official positions. In
the Han dynasty (second century B.C.) appeared a
dictionary entitled Erh-ya; it was probably composed
earlier. This work is divided into nineteen categories:
explanation of definitions, definitions of concepts, ex-
planation of words, degrees of affinity; then come the
art of construction, tools, music, heaven, earth, hills,
mountains, water, fields, forests, insects, fish, birds,
quadrupeds, and domestic animals. Notice that this
series is not devoid of a certain structure. During the
same period there also appeared a classification in the
dictionary of Liu Hsi (or Liu Hsieh), the Shih-ming
or interpretation of concepts. The criterion applied is
the way of passing from heaven to earth and from earth
to man; it includes twenty-seven divisions. In the Ming
era, which marked the first commercial contacts with
the Occident, the number of schools and candidates
taking examinations increased rapidly; in 1615, Mei
Ying-tsu published the Tzu-hui, a dictionary which
revolutionized the arrangement of words by ordering
them on the basis of graphic analogies. A century later,
by taking the Tzu-hui as a model, a new dictionary
was published, the K'ang-hsi tzu-tien, (dictionary of
the era of “splendid peace”) which serves as the basis
of modern Chinese encyclopedias.
In India, works embracing the whole of knowledge
or bearing on a particular field have been traditional
since ancient times. The language used in the beginning
was nearly always Sanskrit. In the first centuries A.D.
there were the Dharmaśāstra (Treatises of the Correct
Order) in which there are ideas on cosmology, social
rules, human functions, and law. In the eleventh cen-
tury, the encyclopedic work of the Sanskrit author
from Kashmir, Abinavagupta, and in the twelfth cen-
tury Somadeva's work on the arts and techniques are
worthy of notice. At the beginning of the nineteenth
century, encyclopedic works multiplied constantly, at
first in Sanskrit, then in the majority of the languages
of India: Hindi (the government's language), Bengali,
Marath, Gujrāti, Tamil, Malayālam, Telugu, Kannada.
Returning to the Occident, more precisely to the
medieval Christian Occident, we find that for many
centuries the regular study of the Quadrivium (arith-
metic, music, geometry, and astronomy) was a required
preliminary to the study of philosophy and theology.
This rule, followed in Paris as well as in Oxford, had
been the practice in Constantinople where a new
branch of science was added to the list, namely, the
art of “horse-matters” or veterinary art. In Paris,
among the first masters of the Abbey of Saint-Victor,
which was one of the famous Parisian schools of the
twelfth century, was the important scholar, Hugh of
Saint-Victor. His chief work, the Didascalicon, contains
a classification of the sciences and is a typical example
of the cultural level of the high Middle Ages. The
following are its main divisions, resulting from philos-
ophy's encompassing all knowledge. Philosophy is sub-
divided into: (1) theoretical sciences (mathematics,
physics, theology); (2) practical sciences (private or
public); (3) mechanical sciences (navigation, agricul-
ture, hunting, medicine, theater); (4) logic, including
grammar and rhetoric. There is obviously a certain
arbitrariness in the system proposed here, but nautical
knowledge emerges as a new branch of science. Fur-
thermore, cartography is soon to make its appearance—
well before the era of great sea voyages and discoveries.
As for Hugh of Saint-Victor, a curious mind and good
pedagogue, he gave his readers the following advice:
learn everything, you will see later that nothing is
superfluous (omnia disce, videbis postea nihil esse
superfluum
).
In the thirteenth century, we see how Roger Bacon,
continuing the work of Robert Grosseteste, placed
mathematics at the base of the sciences of nature. His
classification contains four large classes: (1) grammar
and logic; (2) mathematics; (3) philosophy of nature;
and (4) metaphysics and ethics.
We must now observe that the essays on classification
mentioned above, though they provide us with a fairly
faithful picture of the knowledge of an era and in a
given country, have yet failed to yield any satisfactory
connection among the scientific disciplines; they fail
even more to furnish a theory of knowledge internal
to the sciences which would enable us to take into
account the great currents of thought in the sciences.
It was not until the time of the Renaissance, more
specifically, the end of the Renaissance, that a system
of classification appeared which for the first time is
logical, organic, and firmly structured with respect to
aims, objects, and different groups of phenomena. It
was the system proposed by Francis Bacon in his work
on the worth and advancement of the sciences (De
dignitate et augmentis scientiarum
). The author applied
psychological criteria, namely, Memory, Imagination,
and Reason: history is constructed by memory, and may
be either Civil History or Natural History; poetry flows
from the fancy or imagination, and may be narrative,
dramatic, or parabolic; finally, philosophy, which re-
sults from the use of reason, is divided into the sciences
of the divine, of nature, and of man. The system of
the classification of the sciences and arts by Francis
Bacon was adopted, with a few modifications, by
d'Alembert in the Discours préliminaire des éditeurs
de l'Encyclopédie.
   Page 465, Volume 1
Locke and Leibniz make a clear distinction between
natural sciences (of bodies and of the mind) and moral
sciences (history and ethics). Locke introduced Semi-
otic or the science of language, and Leibniz gave logic
a preponderant place. From the eighteenth century on,
most philosophers and scientists who dealt with clas-
sification divided the sciences into two fundamental
kinds: sciences of nature and sciences of the mind.
Towards the middle of the nineteenth century there
appeared the system of Auguste Comte, which is based
on a series of decreasing generality and increasing
complexity of subject matter in the following order:
mathematics, astronomy, physics, chemistry, biology,
sociology. The order of the classes is inherently linear,
and has several weak points. Comte pictured in it a
“natural logic” which has nothing to do with the mod-
ern idea of axiomatic logic. He excluded the study of
a spiritual or purely mental subject (it is true that he
later added morals and introspective data); he included
among the abstract sciences the concrete science of
astronomy. His system was reshaped by T. Whittaker
who separated the two orders of objective (physical)
and subjective (psychological) sciences; unfortunately,
this separation fails to take account of the historical
development of the sciences.
It was the great physicist A. M. Ampère who pro-
posed to make a comprehensive table of all the fields
of science. In his first table, Ampère separated all
knowledge into two domains and divided each domain
into subdomains and branches; the first domain com-
prised the cosmological sciences and the second the
sciences of the mind. In his second table, each branch
is divided into sub-branches and into the primary sci-
ences. In a third and final classification, he divided each
science of the first order into sciences of the second
and third orders, thus producing a sort of binary system
which provided a total of 27 = 128 names of disci-
plines. Ampère's system based on the content of the
sciences, possesses a very dynamic internal structure;
it takes into account the historical relations among
different domains and it remains the most complete
inventory of scientific knowledge for the mid-
nineteenth century.
In 1851, A. A. Cournot worked out a system which
introduced a separation between structural laws and
historical criteria in all their forms by employing three
great series of sciences, a theoretical, an historical, and
a practical series, each composed of the following kinds
of science: mathematical, physical, biological, mental
or symbolical, and political. Every branch of science
has its place in one of the three times five boxes in
columns. This is clearly an advance on Comte's system
in particular, even though, here again, logic remains
a difficult science to place satisfactorily. (The question
can again be raised whether each science does not have
its own axiomatic structure or whether there might not
be a common axiomatic structure underlying all the
sciences.)
Not long after Cournot, Herbert Spencer started
from the assumption that all knowledge varies with
the object, and he classified the sciences according to
their degree of abstraction in relation to the object.
He thus obtained a linear series going from the abstract
to the concrete, in which series there is the following
order of succession: the abstract sciences, like logic and
mathematics which are concerned with the form in
which phenomena appear; the abstract-concrete sci-
ences, like mechanics, physics, and chemistry which
investigate the causes of these phenomena; and, finally,
the concrete sciences which are interested only in
results. There is a striking similarity between this divi-
sion and the one in the passage from Aristotle's Topics
quoted above.
It is in the Manuel du libraire et de l'amateur de
livres
(“Bookseller's and Book-Lover's Manual”) of
Jacques-Charles Brunet, and exactly in the introduction
to Volume 6 (5th ed. 1865), that we find the first insight
into a historical classification. The author examines
many systems, including Konrad Gesner's, that of the
Parisian publishers at the time of the Revolution, and
Ampère's.
Several German and British philosophers and scien-
tists dealt with the same problem of classification.
Besides Schopenhauer, who distinguished between
empirical (a posteriori) sciences and pure (a priori)
sciences, there were Hegel, Helmholtz, Wilhelm
Dilthey, Hugo Münsterberg, and later the psychologists
Alfred Adler and Wilhelm Wundt. Wundt drew a sharp
contrast between the sciences of the real and formal
sciences. The chemist and Nobel laureate Wilhelm
Ostwald divided the sciences into formal, physical, and
biological. Paul Tillich considered three kinds: sciences
of thought or the ideal, of being or the real, and of
the mind or normative sciences. Among the British
writers, classifications were made by Jeremy Bentham,
John Stuart Mill, Karl Pearson, and Franklin H. Gid-
dings. The American scientist and philosopher Charles
S. Peirce (son of the mathematician and astronomer
Benjamin Peirce) classified the sciences after investi-
gating and writing on logic, psychology, mathematics,
astronomy, optics, chemistry, and even technology.
Peirce emphasized methods of inquiry in two essays
“The Fixation of Belief” and “How To Make Our Ideas
Clear” (Popular Science Monthly, 1877-78), which
mark the beginning of American pragmatism, though
he later preferred the term “pragmaticism” (as ex-
plained in the article “Pragmatism” in this Dictionary).
Peirce's trichotomous classification placed Sciences of
   Page 466, Volume 1
Discovery first, followed by Sciences of Review and
Practical Sciences in a descending order of importance.
Sciences of Discovery included Mathematics (of logic,
of discrete series, of continua and pseudo-continua),
Philosophy (phenomenology, normative science, meta-
physics), and Idioscopy (physical and psychical sci-
ences). Peirce had a low opinion of Comte's and Spen-
cer's attempts at synthesis which fell under Sciences
of Review, and had even a lower opinion of the Practi-
cal Sciences which included a motley array of items
such as etiquette, paper-making, wine tasting, etc.
(Peirce, I, 77-137).
In 1920, Adrien Naville's Classification des sciences
appeared, based not on nomenclature, strictly speaking,
but on the leading ideas of the principal groups of
sciences and their interrelations. Naville separated
three great classes of science: Theorematics, science of
laws; History, science of facts; and Canonics, science
of normative rules. These three classes provide answers
to three questions, respectively: What is possible?
What is real? What is good? To Naville the science
of laws (nomology) is fundamental. A law is a condi-
tionally necessary relationship; law exists wherever
resemblance dominates the scene. Hence, science must
be concerned with general facts, thus recalling the
statement of Marcelin Berthelot (1827-1907) in the
Preface to the Grande Encyclopédie (p. v): “The classi-
fication of general facts is the classification of the
sciences.”
In the first class considered by Naville, following
nomology are mathematics, physics, chemistry, somatic
biology, psychology, and sociology. Natural history, the
theory of evolution, and human geography belong to
the second class. The sciences of normative rules are
the work of the arts and of everything concerned with
the beautiful, the true, and the useful for society as
well as for the individual.
Among recent thinkers preoccupied with the prob-
lem of classification is the Soviet writer Bonifatii M.
Kedrov whose system is a closed, cyclical, and tight
structure based on principles of objectivity, subordi-
nation, and transition from lower to higher forms. The
psychologist Jean Piaget has on several occasions in-
vestigated classification, its history, and its importance
for the theory of knowledge. He has emphasized the
increasing interpenetration of all the branches of
knowledge, the role of linguistic structuralism, and the
operational theory of intelligence. The system which
he has proposed is not circular or closed, and even
less a linear one, but rather takes the form of a con-
stantly growing spiral. According to Piaget, the
subject-object opposition and dualism must be elimi-
nated, for there is a constant interaction and mutual
exchange between the two.
The object is known only through actions of the subject
and the subject is known only through the relations it has
to objects, from which the twofold consequence is that in
order to ground logic and mathematics we must really go
back in one form or another to the subject, and in order
to construct a science of the subject we must go back to
biology, hence also to physics and mathematics
(Piaget, p.
1159).
Lately a leading role has been assigned to language,
to its mathematical structure, its axiomatic logic of
grammatical categories, and to the logic of binary
relations in linguistics. The linguistic problem is tied
to the automatic (computerized) treatment of “infor-
mation,” which is a matter of interest not only to
philologists, philosophers, and psychologists but
equally as much to mathematicians, cybernetic theo-
rists, and engineers. Logic, which has only with great
difficulty found its place in the classification of the
sciences, is not the sole basis of structural linguistics,
for the latter depends on the psychology of form
(Gestalttheorie) and on topology and graphs. Starting
with language everything seems to converge on the
unity of knowledge. This advance towards unity should
perhaps be, after all, the primary aim of a new scien-
tific humanism. A classification of the sciences which
is free from the subject-object dualism and from an
enslaving chainwork of values, and which takes into
account the profound, intimate, and reciprocal rela-
tionships among all disciplines, would be the only
classification fit to instruct us about the present state
of our scientific knowledge.
BIBLIOGRAPHY
A.-M. Ampère, Essai sur la philosophie des sciences, ou
Exposition analytique d'une classification de toutes les
connaissances humaines
(Paris, 1834). F. Bacon, De dignitate
et augmentis scientiarum
(London, 1623); Advancement of
Learning
(1605), Novum organum (1620); rev. English ed.
with Introduction by J. E. Creighton (London and New
York, 1900). R. Bacon, The Opus Majus of Roger Bacon, ed.
J. H. Bridge, Vols. I and II (Oxford, 1897), Vol. III with
revisions (London, 1900); idem, The Opus Majus of Roger
Bacon,
trans. R. B. Burke (Philadelphia, 1928). L. Baur, ed.,
“Die philosophischen Werke des Robert Grosseteste,
Bischofs von Lincoln,” in Beiträge zur Geschichte der Philos-
ophie des Mittelalters
(Münster, 1912). J. Bentham, “Essay
on the Nomenclature and Classification of Arts and Sci-
ences,” in Works, 11 vols. (New York, 1962), VIII, 63-128.
A. Comte, Cours de philosophie positive (Paris, 1830-42).
A.-A. Cournot, Essai sur les fondements de nos connaissances
(Paris, 1851); idem, Des méthodes dans les sciences de rai-
sonnement
(Paris, 1865). Jean le Rond d'Alembert, Discours
préliminaire de l'Encyclopédie
(Paris, 1751). Stewart C.
Easton, Roger Bacon and His Search for a Universal Science
(New York, 1952), has an extensive bibliography. G. Goblot,
   Page 467, Volume 1
Essai sur la classification des sciences (Paris, 1898); idem,
Le système des sciences (Paris, 1922). H. von Helmholtz,
Über das Verhältnis der Naturwissenschaften zur Gesamtheit
der Wissenschaften
(Brunswick, 1862). A. Hill, Introduction
to Science
(London, 1911). B. M. Kedrov, “La classification
des sciences,” Actes du IIe Congrès de philosophie scien-
tifique
(Zurich, 1954). G. W. Leibniz, Nouveaux essais sur
l'entendement humain,
Book IV, Ch. XXI, “De la division
des sciences,” in Oeuvres philosophiques... (Amsterdam
and Leipzig, 1765), pp. 489-96. A. O. Lovejoy, “The Unity
of Science,” University of Missouri Bulletin (1912). R. P.
McKeon, Selections from Medieval Philosophers, 2 vols.
(New York, 1929), I, 259-314, contains excerpts from Gros-
seteste. A. Naville, Classification des sciences (Paris, 1920).
K. Pearson, The Grammar of Science (London, 1911).
C. S. Peirce, Collected Papers, ed. C. Hartshorne and P.
Weiss, 6 vols. (Cambridge, Mass., 1935), I, 77-137. J. Piaget,
“Classification des sciences et principaux courants épisté-
mologiques contemporains,” Logique et connaissance scien-
tifique
(Paris, 1967), esp. pp. 1149-1271. E. C. Richardson,
Classification, Theoretical and Practical (New York, 1901).
H. Spencer, The Classification of the Sciences (London,
1864). Paul Tillich, Das System der Wissenschaften nach
Gegenständen und Methoden
(Göttingen, 1923). UNESCO,
Cahiers d'histoire mondiale (Journal of World History), 9,
3 (1965); this number is devoted to encyclopedias from
antiquity to the present in Europe and in other parts of
the world. W. Whewell, The Philosophy of the Inductive
Sciences
(London, 1847). T. Whittaker, The Metaphysics of
Evolution, with other essays
(London, 1926).
PIERRE SPEZIALI
[See also Axiomatization v1-24  ; Classification of the Arts v1-56  ; Linguistics v3-08  ; Pragmatism v3-70  ; Unity of Science. v4-58  ]