We have now (1) sketched the life of Aristotle as a reader and a writer
from early manhood; (2) have watched him as a Platonist, partly
imitating but gradually emancipating himself from his master to form a
philosophy of his own; (3) have traced the gradual composition of his
writings from Plato's time onwards; (4) have distinguished earlier, more
Platonic and rudimentary, from later, more independent and mature,
writings; (5) have founded the real order of his writings, not on
chronology, nor on tradition, but on his classification of science and
learning. It remains to answer the final question:--What is the
Aristotelian philosophy, which its author gradually formed with so much
labour? Here we have only room for its spirit, which we shall try to
give as if he were himself speaking to us, as head of the Peripatetic
school at Athens, and holding no longer the early views of his
dialogues, or the immature views of such treatises as the _Categories_,
but only his mature views, such as he expresses in the _Metaphysics_.
Aristotle was primarily a metaphysician, a philosopher of things, who
uses the objective method of proceeding from being to thinking. We shall
begin therefore with that primary philosophy which is the real basis of
his philosophy, and proceed in the order of his classification of
science to give his chief doctrines on:--
(1) Speculative philosophy, metaphysical and physical, including his
psychology, and with it his logic.
(2) Practical philosophy, ethics and politics.
(3) Productive science, or art.
_Things are substances_ ([Greek: ousiai]), each of which is a separate
individual ([Greek: choriston tode ti, kath ekaston]) and is variously
affected as quantified, qualified, related, active, passive and so
forth, in categories of things which are attributes ([Greek:
sumbebaekota]), different from the category of substance, but real only
as predicates belonging to some substance, and are in fact only the
substance itself affected ([Greek: auto peponthos]). The essence of each
substance, being what it is ([Greek: to tiest, to ti aen einai]), is
that substance; e.g. this rational animal, Socrates. Substances are so
similar that the individuals of a species are even the same in essence
or substance, e.g. Callias and Socrates differ in matter but are the
same in essence, as rational animals. The universal ([Greek: to
katholoy]) is real only as one predicate belonging to many individual
substances: it is therefore not a substance. There are then no separate
universal forms, as Plato supposed. There are attributes and universals,
real as belonging to individual substances, whose being is their being.
The mind, especially in mathematics, abstracts numbers, motions,
relations, causes, essences, ends, kinds; and it over-abstracts things
mentally separate into things really separate. But reality consists only
of individual substances, numerous, moving, related, active as efficient
causes, passive as material causes, essences as formal causes, ends as
final causes, and in classes which are real universals only as real
predicates of individual substances. Such is Aristotle's realism of
individuals and universals, contained in his primary philosophy, as
expressed in the _Metaphysics_, especially in Book Z, his authoritative
pronouncement on being and substance.
The individual substances, of which the universe is composed, fall into
three great irreducible kinds: nature, God, man.
I. Nature.--The obvious substances are natural substances or bodies
([Greek: physikai ousiai, somata]), e.g. animals, plants, water, earth,
moon, sun, stars. Each natural substance is a compound ([Greek:
syntheton, synthetae, ousia]) of essence and matter; its essence
([Greek: eldos, morphae, to ti esti, to ti aen einai]) being its actual
substance, its matter ([Greek: ulae]) not; its essence being
determinate, its matter not; its essence being immateriate, its matter
conjoined with the essence; its essence being one in all individuals of
a species, its matter different in each individual; its essence being
cause of uniformity, its matter cause of accident. At the same time,
matter is not nothing, but something, which, though not substance, is
potentially substance; and it is either proximate to the substance, or
primary; proximate, as a substance which is potentially different, e.g.
wood potentially a table; primary, as an indeterminate something which
is a substratum capable of becoming natural substances, of which it is
always one; and it is primarily the matter of earth, water, air, fire,
the four simple bodies ([Greek: apla somata]) with natural rectilineal
motions in the terrestrial world (_De Gen. et Cor_. ii. I seq.); while
aether ([Greek: aithaer]) is a fifth simple body, with natural circular
motion, being the element of the stars ([Greek: to ton astron
stoicheion]) in the celestial world. Each natural substance is a formal
cause, as being what it is; a material cause, as having passive power to
be changed; an efficient cause, as having active power to change, by
communicating the selfsame essence into different matter so as to
produce therein a homogeneous effect in the same species; and a final
cause, as an end to be realized. Moreover, though each natural substance
is corruptible ([Greek: phtharton]), species is eternal ([Greek:
aidion]), because there was always some individual of it to continue its
original essence (expressed by the imperfect tense in [Greek: to ti aen
einai]), which is ungenerated and incorruptible; the natural world
therefore is eternal; and nature is for ever aiming at an eternal
propagation, by efficient acting on matter, of essence as end. For even
nature does nothing in vain, but aims at final causes, which she
uniformly realizes, except so far as matter by its spontaneity ([Greek:
apo tou automatou]) causes accidental effects; and the ends of nature
are no form of good, nor even the good of man, but the essences of
natural substances themselves, and, above them all, the good God
Himself. Such is Aristotle's natural realism, pervading his metaphysical
and physical writings.
II. _God._--Nature is but one kind of being ([Greek: en gar ti genos tou
ontos ae physis], _Met._ [Gamma] 3, 1005 a 34). Above all natural
substances, the objects of natural science, there stands a supernatural
substance, the object of metaphysics as theology. Nature's boundary is
the outer sphere of the fixed stars, which is eternally moved day after
day in a uniform circle round the earth. Now, an actual cause is
required for an actual effect. Therefore, there must be a prime mover of
that prime movable, and equally eternal and uniform. That prime mover is
God, who is not the creator, but the mover directly of the heavens, and
indirectly through the planets of sublunary substances. But God is no
mechanical mover. He moves as motive ([Greek: kinei de os eromenon],
_Met._ [Lambda] 7, 1072 b 3); He is the efficient only as the final
cause of nature. For God is a living being, eternal, very good ([Greek:
zoov aision ariston], _ib._ 1072 b 29). While nature aims at Him as
design, as an end, a motive, a final cause, God's occupation ([Greek:
diagogae]) is intelligence ([Greek: noaesis]); and since essence, not
indeed in all being, but in being understood, becomes identical with
intelligence, God in understanding essence is understanding Himself; and
in short, God's intelligence is at once intelligence of Himself, of
essence and of intelligence,--[Greek: kai estin ae noaesis noaeseos
noaesis] (_Met._ [Lambda] 7, 1074 b 34). But at the same time the
essence of good exists not only in God and God's intelligence on the one
hand, but also on the other hand on a declining scale in nature, as both
in a general and in his army; but rather in God, and more in some parts
of nature than in others. Thus even God is a substance, a separate
individual, whose differentiating essence is to be a living being,
eternal and very good; He is however the only substance whose essence is
entirely without matter and unconjoined with matter; and therefore He is
a substance, not because He has or is a substratum beneath attributes,
but wholly because He is a separate individual, different both from
nature and men, yet the final good of the whole universe. Such is
Aristotle's theological realism without materialism and the origin of
all spiritualistic realism, contained in his _Metaphysics_ ([Lambda]
6-end).
III. _Man._--There is a third kind of substance, combining something
both of the natural and of the divine: we men are that privileged
species. Each man is a substance, like any other, only because he is a
separate individual. Like any natural substance, he is composed of
matter and immateriate essence. But natural substances are inorganic and
organic; and a man is an organic substance composed of an organic body
([Greek: organikon soma]) as matter, and a soul ([Greek: psychae]) as
essence, which is the primary actuality of an organic body capable of
life ([Greek: zoae]). Still a man is not the only organism; and every
organism has a soul, whose immediate organ is the spirit ([Greek:
pneuma]), a body which--analogous to a body diviner than the four
so-called elements, namely the aether, the element of the stars--gives
to the organism its non-terrestrial vital heat, whether it be a plant or
an animal. In an ascending scale, a plant is an organism with a
nutritive soul; an animal is a higher organism with a nutritive,
sensitive, orectic and locomotive soul; a man is the highest organism
with a nutritive, sensitive, orectic, locomotive and rational soul. What
differentiates man from other natural and organic substances, and
approximates him to a supernatural substance, God, is reason ([Greek:
logos]), or intellect ([Greek: nous]). Now, though only one of the
powers of the soul, intellect alone of these powers has no bodily organ;
it alone is immortal: it alone is divine. While the soul is propagated,
like any other essence, by the efficient, which is the seed, to the
matter, which is the germ, of the embryo man, intellect alone enters
from without ([Greek: thurathen]), and is alone divine ([Greek: theion],
not [Greek: theos]), because its activity communicates with no bodily
activity (_De Gen._ ii. 3, 736-737). A man then is a third kind of
substance, like a natural substance in bodily matter, like a
supernatural substance in divine reason or intellect. Such is
Aristotle's dual, or rather triple, realism, continued in his _De Anima_
and other biological writings, especially _De Generatione Animalium_,
ii.
There are three points about a man's life which both connect him with,
and distinguish him from, God. God's occupation is speculative; man's is
speculation, practice and production.
I. _Speculation_ ([Greek: theoria]).--Since things are individuals,
and there is nothing, and nothing universal, beyond them, there are
two kinds of knowledge ([Greek: gnosis]), sense ([Greek: aisthaesis])
of individuals, intellect ([Greek: nous]) of universals. Both powers
know by being passively receptive of essence propagated by an
efficient cause; but, while in sense the efficient cause is an
external object ([Greek: exothen]), in intelligence it is active
intellect ([Greek: nous to poiein]) propagating its essence in passive
intellect ([Greek: nous pathaetikos]). Nevertheless, without sense
there is no knowledge. Sense receives from the external world an
essence, e.g. of white, which is really universal as well as
individual, but apprehends it only as individual, e.g. this white
substance: intellect thereupon discovers the universal essence but
only in the individuals of sense. This intellectual discovery requires
sensation and retention of sensation; so that sense ([Greek:
aisthaesis]) receives impressions, imagination ([Greek: phantasia])
retains them as images, intellect ([Greek: nous]) generalizes the
universal, and, when it is intelligence of essence, is always true.
This is the origin of knowledge, psychologically regarded (in the _De
Anima_). Logically regarded, the origin of all teaching and learning
of an intellectual kind is a process of induction ([Greek: epagogae])
from particulars to universal, and of syllogism ([Greek: syllogismos])
from universal to further particulars; induction, whenever it starts
from sense, becomes the origin of scientific knowledge ([Greek:
epiostaemae]); while there is also a third process of example ([Greek:
paradeigma]) from particular to particular, which produces only
persuasion. In acquiring scientific knowledge, syllogism cannot start
from universals without induction, nor induction acquire universals
without sense. At the same time, there are three species of syllogism,
scientific, dialectical and eristical or sophistical; and in
consequence there are different ways of acquiring premisses. In order
to acquire the knowledge of the true and primary principles of
scientific knowledge, and especially the intelligence of the
universal essence of the subject, which is always true, the process of
knowledge consists of (1) sense ([Greek: aisthaesis]), which receives
the essence as individual, (2) memory ([Greek: mnaemae]), which is a
retention of sensible impression, (3) experience ([Greek: empeiria]),
which consists of a number of similar memories, (4) induction ([Greek:
epagogae]), which infers the universal as a fact ([Greek: to oti]),
(5) intellect ([Greek: nous]), which apprehends the principle ([Greek:
archae]); because it is a true apprehension that the universal induced
is the very essence and formal cause of the subject: thereupon,
scientific syllogism ([Greek: epistaemonikos syllogismos]), making the
definition ([Greek: horismos]) of this essence the middle term
([Greek: to meson]), becomes a demonstration ([Greek: apodeixis]) of
the consequences which follow from the essence in the conclusion. Such
then is science. In order to acquire the probabilities ([Greek: ta
endoxa]) of opinion ([Greek: doxa]), which are the premisses of
dialectical syllogism, the process is still induction, as in science,
but dialectical induction by interrogation from the opinions of the
answerers until the universal is conceded: thereupon the dialectical
syllogism ([Greek: dialektikos syllogismos]) deduces consequent
opinions in the conclusion. Nor does the process of acquiring the
premisses of eristical syllogism, which is fallacious either in its
premisses or in its process, differ, except that, when the premisses
are fallacious, the dialectical interrogations must be such as to
cause this fallacy. Hence, as science and dialectic are different, so
scientific induction and syllogism must be distinguished from
dialectical induction and syllogism. Dialectic is useful, for
exercise, for conversation and for philosophical sciences, where by
being critical it has a road to principles. But it is by a different
process of sense, memory, experience, induction, intelligence,
syllogism, that science becomes knowledge of real causes, of real
effects, and especially of real essences from which follow real
consequences, not beyond, but belonging to real substances. So can we
men, not, as Plato thought, by having in our souls universal
principles innate but forgotten, but by acquiring universal principles
from sense, which is the origin of knowledge, arrive at judgments
which are true, and true because they agree with the things which we
know by sense, by inference and by science. Such is Aristotle's
psychological and logical realism, contained in the _De Anima_ and
logical treatises.
2. _Practice_ ([Greek: praxis]).--In this natural world of real
substances, human good is not an imitation of a supernatural universal
form of the good, but is human happiness; and this good is the same
both of the individual as a part and of the state as a whole. Ethics
then is a kind of Politics. But in Ethics a man's individual good is
his own happiness; and his happiness is no mere state, but an activity
of soul according to virtue in a mature life, requiring as conditions
moderate bodily and external goods of fortune; his virtue is (1) moral
virtue, which is acquired by habituation, and is a purposive habit of
performing actions in the mean determined by right reason or prudence;
requiring him, not to exclude, but to moderate his desires; and (2)
intellectual virtue, which is either prudence of practical, or wisdom
of speculative intellect; and his happiness is a kind of ascending
scale of virtuous activities, in which moral virtue is limited by
prudence, and prudence by wisdom; so that the speculative life of
wisdom is the happiest and most divine, and the practical life of
prudence and moral virtue secondary and human. Good fortune in
moderation is also required as a condition of his happiness. Must we
then, on account of misfortunes, look with Solon at the end, and call
no man happy till he is dead? Or is this altogether absurd for us who
say that happiness is an activity? Virtuous activities determine
happiness, and a virtuous man is happy in this life, in spite of
misfortunes unless they be too great; while after death he will not
feel the misfortunes of the living so much as to change his happiness.
Still, for perfect happiness a man should prefer the speculative life
of divine intellect, and immortalize ([Greek: athanatizein]) as far as
possible. For intellect is what mainly makes a man what he is, and is
divine and immortal.
To turn from Ethics to Politics, the good of the individual on a small
scale becomes on a large scale the good of the citizen and the state,
whose end should be no far-off form of good, and no mere guarantee of
rights, but the happiness of virtuous action, the life according to
virtue, which is the general good of the citizen. Hence, the citizen
of the best state is he who has the power and the purpose to be
governed and govern for the sake of the life according to virtue.
A right government is one which aims at the general good, whereas any
government which aims at its own good is a deviation. Hence
governments are to be arranged from best to worst in the following
order:--
I. Right governments ([Greek: orthai politeiai]), aiming at the
general good:--
i. Monarchy, of one excelling in virtue:
ii. Aristocracy, of a class excelling in virtue:
iii. Commonwealth, of the majority excelling in virtue.
II. Deviations ([Greek: parekbaseis]), aiming at the good of the
government:--
i. Democracy, aiming at the good of the majority:
ii. Oligarchy, aiming at the good of the few:
iii. Tyranny, aiming at the good of one.
Such is Aristotle's practical philosophy, contained in his matured
_Nicomachean Ethics_, and his unfinished _Politics_.
3. _Production_ ([Greek: poiaesis]).--Production differs from practice
in being an activity ([Greek: enirgeia]; e.g. building) which is
always a means to a work ([Greek: ergon]; e.g. a house) beyond itself.
Productive science, or art, is an intellectual habit of true reasoning
from appropriate principles, acquired from experiences, and applied to
the production of the work which is the end of the art. All the arts
are therefore at once rational and productive. They are either for
necessity (e.g. medicine) or for occupation (e.g. poetry), the former
being inferior to the latter. Rhetoric is a faculty on any subject of
investigating what may be persuasive ([Greek: pithanon]), which is the
work of no other art; its means are artificial and inartificial
evidences ([Greek: pisteis]), and, among artificial evidences,
especially the logical arguments of example and enthymeme. Poetry is
the art of producing representations; (1) in words, rhythm and harmony
([Greek: harmonia], "harmony" in the original sense); (2) of men like
ourselves, or better as in tragedy, or worse as in comedy; (3) by
means of narrative as in epic, or by action as in the drama. The cause
of poetry is man's instinct of representation and his love of
representations caused by the pleasure of learning. Comedy is
representation of men inferior in being ludicrous: epic is like
tragedy a representation of superior men, but by means of narrative
and unlimited in time: tragedy is a representation of an action
superior and complete, in a day if possible, by means of action, and
accomplishing by pity and fear the purgation of such passions
(_Poetics_, 1449 b 24). Music is a part of moral education; and for
this end we should use the most moral harmonies. But music has also
other ends and uses, and on the whole four; namely amusement, virtue,
occupation and purgation of the affections; for some men are liable
more than others to pity and fear and enthusiasm, but from sacred
melodies we see them, when they have heard those which act
orgiastically on the soul, becoming settled by a kind of medicine and
purgation ([Greek: katharsis]), and being relieved with pleasure.
Finally, art is not morality, because its end is always a work of art,
not virtuous action: on the other hand, art is subordinate to
morality, because all the ends of art are but means to the end of
life, and therefore a work of art which offends against morality is
opposed to the happiness and the good of man. Such is Aristotle's
productive science or art, contained in his _Rhetoric_ and _Poetics_,
compared with his _Ethics_ and _Politics_.
Aristotle, even in this sketch of his system, shows himself to be the
philosopher of facts, who can best of all men bear criticism; and indeed
it must be confessed that he retained many errors of Platonism and laid
himself open to the following objections. Two substances, being
individuals, e.g. Socrates and Callias, are in no way the same, but only
similar, even in essence, e.g. Socrates is one rational animal, Callias
another. A universal, e.g. the species man, is not predicate of many
individuals ([Greek: en kata pollon], _Post. An._ i. II), but a whole
number of similar individuals, e.g. all men; and not a whole species,
but only an individual, is a predicate of such individual, e.g. Socrates
is a man, not all men, and one white thing, not all white things.
Consequently, a species or genus is not a substance, as Aristotle says
it is in the _Categories_ (inconsistently with his own doctrine of
substances), but a whole number of substances, e.g. all men, all
animals. Similarly, the universal essence of a species is not one and
the same as each individual essence, but is the whole number of similar
individual essences of the similar individuals of the species, e.g. all
rational animals. Consequently, the universal essence of a species of
substances is not one and the same eternal essence in all the
individuals of a species but only similar, and is not substance as
Aristotle calls it in the _Metaphysics_, inconsistently with his own
doctrine of substance, but is a whole number of similar substances, e.g.
all rational animals which are what all men are. Hence again, the
natural world of species and essences is not eternal, but only endures
as long as there are individual substances. Hence, moreover, a natural
substance or body as an efficient cause or force causes an effect on
another, not by propagating one eternal essence of a species into the
matter of the other, but so far as we really understand force, by their
reciprocally preventing one another from occupying the same place at the
same moment on account of the mutual resistance of any two bodies. The
essence of a natural substance, e.g. wood, is not immateriate, but is
the whole body as what it is. The matter of a natural substance is not a
primary matter which is one indeterminate substratum of all natural
substances, but is only one body as able to be changed by a force which
is another substance able to change it, e.g. a seed becoming wood, wood
becoming coal, &c. A natural substance or body, therefore, is not a
heterogeneous compound of essence and matter, but is essence as what it
is, matter as able passively to be changed, force as able actively to
change. The simple bodies which are the matter of the rest are not
terrestrial earth, water, air, fire, and a different celestial aether,
but whatever elementary bodies natural science, starting anew from
mechanics and chemistry, may determine to be the matter of all other
bodies whatever. Nature does not aim at God as end, but God, thinking
and willing ends, produces and acts on nature. Soul is not an
immateriate essence of an organic body capable, but an immateriate
conscious substance within an organic body. Sensation is not the
reception of the selfsame essence of an external body, but one's
perception of one's sentient organism as affected, and especially of its
organs resisting one another, e.g. one's lips, hands, &c., preventing
one another from occupying the same place at the same moment within
one's organism. Intelligence does not differ from sense by having no
bodily organ, but the nervous system is the bodily organ of both.
Intelligence is not active intellect propagating universal essence in
passive intellect, but only logical inference starting from sense, and
both requiring nervous body and conscious soul. It is not always a true
apprehension of essence, but often, especially in physical matter, such
as sound or heat or light, takes superficial effects to be the essence
of the thing. Aristotle did not altogether solve the question, What is,
and scarcely solved at all the question, How do we know the external
world?
We might continue to object. But at bottom there remains the fundamental
position of Aristotelianism, that all things are substances, individuals
separate though related; that some things are attributes, real only as
being some individual substance somehow affected, or, as we should say,
modified or determined; and that without individual substances there is
nothing, and nothing universal apart from individuals. There remains too
the consequence that there are different substances, separate from but
related to one another; and these substances of three irreducible kinds,
natural, supernatural, human. Aristotelianism has to be considered
against the philosophy which preceded it and against the philosophy
which has since followed it. Platonism preceded it, and was the
metaphysical doctrine that all things are supernatural--forms, gods,
souls. Idealism has since followed it, and is the metaphysical doctrine
that all things are mind and states of mind. Aristotelianism intervenes
between ancient Platonism and modern Idealism, and is the metaphysical
doctrine that all things are substances, natural and supernatural and
human. It is a philosophy of substantial things, standing as a _via
media_ between a philosophy of the supernatural and a philosophy of
mind. There are three alternatives, which may be put as questions which
every thinker must ask himself. Are the things which surround me in what
I call the environment,--the men, the animals, the plants, the ground,
the stones, the water, the air, the moon, the sun, the stars and
God--are they shadows, unsubstantial things, as formerly Platonism made
all things to be except the supernatural world of forms, gods and souls?
Or are they, as modern Idealism says, mind and states of mind? Or are
they really substances separate from, though related to, myself, who am
also a substance? The Aristotelian answer is--"Yes, all things are
substances, but not all supernatural, nor all mental; for some are
natural substances, or bodies"; and by that answer Aristotelianism
stands or falls.
LITERATURE.--The Aristotelian philosophy is to be studied first in
Aristotle's works, which are the best commentaries on one another; the
best complete edition is the Berlin edition (1831-1870), by Bekker and
Brandis, in which also are the fragments collected by V. Rose, the
scholia collected by Brandis, and the index compiled by Bonitz. After
reading the remains of the Peripatetic school, the Greek commentators
should be further studied in this edition. The Latin commentators, the
Arabians and the schoolmen show how Aristotle has been the chief
author of modern culture; while the vindication of modern independence
comes out in his critics, the greatest of whom were Roger and Francis
Bacon. Since the modern discovery of the science of motion by Galileo
which changed natural science, and the modern revolution of philosophy
by Descartes which changed metaphysics, the study of Aristotle has
become less universal; but it did not die out, and received a fresh
stimulus especially from Julius Pacius, who going back through G.
Zabarella to the Arabians, and himself gifted with great logical
powers, always deserves study in his editions of the _Organon_ and the
_Physics_ and in his _Doctrinae Peripateticae_. In more recent times,
as part of the growing conviction of the essentiality of everything
Greek, Aristotle has received marked attention. In France there are
the works of Cousin (1835), Felix Ravaisson, who wrote on the
_Metaphysics_ (1837-1846), and Barthelemy St Hilaire, who translated
the _Organon_ and other works (1844 seq.). In Germany there has been a
host of commentaries, among which we may mention the _Organon_ edited
(1844-1846) by F. Th. Waitz (not so well as by Pacius), the _De Anima_
edited (1833) by F.A. Trendelenburg and later by A. Torstrik, the
_Historia Animalium_ by H. Aubert and F. Wimmer (1868), the _Ethics_
by K.L. Michelet (1827), the _Metaphysics_ by A. Schwegler (1847) and
(best of all) by H. Bonitz (1848), who is the most faithful of all
commentators, because to great industry and acumen he adds the rare
gift of confessing when he does not understand, and when he does not
know what Aristotle might have thought. With Aristotle's works before
one, with the _Index Aristotelicus_, and the edition and translation
of the _Metaphysics_ by Bonitz on one side, and Zeller's _Die
Philosophie der Griechen_, ii. 2, "Aristoteles" (trans. by Costelloe
and Muirhead), on the other side, one can go a considerable way
towards understanding the foundations of Aristotelianism.
In England scholars tend to take up certain parts of Aristotle's
philosophy. Grote indeed intended to write a general account of
Aristotle like that of Plato; but his _Aristotle_ went little further
than the logical writings. From Cambridge we have J.W. Blakesley's
_Life of Aristotle_, E.M. Cope's _Rhetoric_, Dr Henry Jackson's
_Nicomachean Ethics_, v., S.H. Butcher's _Poetics_, Hicks's _De
Anima_, J.E. Sandys's _Athenian Constitution_, Jebb's _Rhetoric_ (ed.
Sandys). Oxford in particular, since the beginning of the 19th
century, has kept alive the study of Aristotle. E. Cardwell in his
edition of the _Nicomachean Ethics_ (1828) had the wisdom to found his
text on the Laurentian Manuscript (Kb); E. Poste wrote translations of
the _Posterior Analytics_ and _Sophistici Elenchi_; R. Congreve edited
the _Politics_; A. Grant edited the _Nicomachean Ethics_; E. Wallace
translated and annotated the _De Anima_; B. Jowett translated the
_Politics_; W.L. Newman has edited the _Politics_ in four volumes; Dr
Ogle has translated the _De Partibus Animalium_, with notes; R. Shute
wrote a _History of the Aristotelian Writings_; Professor J.A.
Stewart has written _Notes on the Nicomachean Ethics_; Professor J.
Burnet has issued an annotated edition of the _Nicomachean Ethics_,
and W.D. Ross has translated the _Metaphysics_. All these are, or
were, Oxford men; and it remains to mention two others: I. Bywater,
who as an Aristotelian scholar has done much for the improvement of
Bekker's text, especially of the _Nicomachean Ethics_ and the
_Poetics_; and F.G. Kenyon, who has the proud distinction of having
been the first modern editor of the [Greek: Athaenaion politeia].
(T. Ca.)
ARISTOXENUS, of Tarentum (4th century B.C.), a Greek peripatetic
philosopher, and writer on music and rhythm. He was taught first by his
father Spintharus, a pupil of Socrates, and later by the Pythagoreans,
Lamprus of Erythrae and Xenophilus, from whom he learned the theory of
music. Finally he studied under Aristotle at Athens, and was deeply
annoyed, it is said, when Theophrastus was appointed head of the school
on Aristotle's death. His writings, said to have numbered four hundred
and fifty-three, were in the style of Aristotle, and dealt with
philosophy, ethics and music. The empirical tendency of his thought is
shown in his theory that the soul is related to the body as harmony to
the parts of a musical instrument. We have no evidence as to the method
by which he deduced this theory (cf. T. Gomperz, _Greek Thinkers_, Eng.
trans. 1905, vol. iii. p. 43). In music he held that the notes of the
scale are to be judged, not as the Pythagoreans held, by mathematical
ratio, but by the ear. The only work of his that has come down to us is
the three books of the _Elements of Harmony_ ([Greek: rythmika
stoicheia]), an incomplete musical treatise. Grenfell and Hunt's
_Oxyrhynchus Papyri_ (vol. i., 1898) contains a five-column fragment of
a treatise on metre, probably this treatise of Aristoxenus.
The best edition is by Paul Marquard, with German translation and full
commentary, _Die harmonischen Fragmente des Aristoxenus_ (Berlin,
1868). The fragments are also given in C.W. Muller, _Frag. Hist.
Graec._, ii. 269 sqq.; and R. Westphal, _Melik und Rhythmik d. klass.
Hellenenthums_ (2nd vol. edited by F. Saran, Leipzig, 1893). Eng.
trans. by H.S. Macran (Oxford, 1902). See also W.L. Mahne, _Diatribe
de Aristoxeno_ (Amsterdam, 1793); B. Brill, _Aristoxenus' rhythmische
und metrische Messungen_ (1871); R. Westphal, _Griechische Rhythmik
und Harmonik_ (Leipzig, 1867); L. Laloy, _Aristoxene de Tarente et la
musique de l'antiquite_ (Paris, 1904); See PERIPATETICS, PYTHAGORAS
(_Music_) and art. "Greek Music" in Grove's _Dict. of Music_ (1904).
For the Oxyrhynchus fragment see _Classical Review_ (January 1898),
and C. van Jan in Bursian's _Jahresbericht_, civ. (1901).
ARISUGAWA, the name of one of the royal families of Japan, going back to
the seventh son of the mikado Go-Yozei (d. 1638). After the revolution
of 1868, when the mikado Mutsu-hito was restored, his uncle, Prince
Taruhito Arisugawa (1835-1895), became commander-in-chief, and in 1875
president of the senate. After his suppression of the Satsuma rebellion
he was made a field-marshal, and he was chief of the staff in the war
with China (1894-95). His younger brother, Prince Takehito Arisugawa (b.
1862), was from 1879 to 1882 in the British navy, serving in the Channel
Squadron, and studied at the Naval College, Greenwich. In the
Chino-Japanese War of 1894-95 he was in command of a cruiser, and
subsequently became admiral-superintendent at Yokosuka. Prince Arisugawa
represented Japan in England together with Marquis Ito at the Diamond
Jubilee (1897), and in 1905 was again received there as the king's
guest.
ARITHMETIC (Gr. [Greek: arithmaetikae], sc. [Greek: technae], the art of
counting, from [Greek: arithmos], number), the art of dealing with
numerical quantities in their numerical relations.
1. Arithmetic is usually divided into _Abstract Arithmetic_ and
_Concrete Arithmetic_, the former dealing with numbers and the latter
with concrete objects. This distinction, however, might be misleading.
In stating that the sum of 11d. and 9d. is 1s. 8d. we do not mean that
nine pennies when added to eleven pennies produce a shilling and eight
pennies. The sum of money corresponding to 11d. may in fact be made up
of coins in several different ways, so that the symbol "11d." cannot be
taken as denoting any definite concrete objects. The arithmetical fact
is that 11 and 9 may be regrouped as 12 and 8, and the statement "11d. +
9d. = 1s. 8d." is only an arithmetical statement in so far as each of
the three expressions denotes a numerical quantity (S 11).
2. The various stages in the study of arithmetic may be arranged in
different ways, and the arrangement adopted must be influenced by the
purpose in view. There are three main purposes, the practical, the
educational, and the scientific; i.e. the subject may be studied with a
view to technical skill in dealing with the arithmetical problems that
arise in actual life, or for the sake of its general influence on mental
development, or as an elementary stage in mathematical study.
3. The practical aspect is an important one. The daily activities of the
great mass of the adult population, in countries where commodities are
sold at definite prices for definite quantities, include calculations
which have often to be performed rapidly, on data orally given, and
leading in general to results which can only be approximate; and almost
every branch of manufacture or commerce has its own range of
applications of arithmetic. Arithmetic as a school subject has been
largely regarded from this point of view.
4. From the educational point of view, the value of arithmetic has
usually been regarded as consisting in the stress it lays on accuracy.
This aspect of the matter, however, belongs mainly to the period when
arithmetic was studied almost entirely for commercial purposes; and even
then accuracy was not found always to harmonize with actuality. The
development of physical science has tended to emphasize an exactly
opposite aspect, viz. the impossibility, outside a certain limited range
of subjects, of ever obtaining absolute accuracy, and the consequent
importance of not wasting time in attempting to obtain results beyond a
certain degree of approximation.
5. As a branch of mathematics, arithmetic may be treated logically,
psychologically, or historically. All these aspects are of importance to
the teacher: the logical, in order that he may know the end which he
seeks to attain; the psychological, that he may know how best to attain
this end; and the historical, for the light that history throws on
psychology,
The logical arrangement of the subject is not the best for elementary
study. The division into abstract and concrete, for instance, is
logical, if the former is taken as relating to number and the latter to
numerical quantity (S 11). But the result of a rigid application of this
principle would be that the calculation of the cost of 3 lb. of tea at
2s. a lb. would be deferred until after the study of logarithms. The
psychological treatment recognizes the fact that the concrete precedes
the abstract and that the abstract is based on the concrete; and it also
recognizes the futility of attempting a strictly continuous development
of the subject.
On the other hand, logical analysis is necessary if the subject is to be
understood. As an illustration, we may take the elementary processes of
addition, subtraction, multiplication and division. These are still
called in text-books the "four simple rules"; but this name ignores
certain essential differences. (i) If we consider that we are dealing
with numerical quantities, we must recognize the fact that, while
addition and subtraction might in the first instance be limited to such
quantities, multiplication and division necessarily introduce the idea
of pure number. (ii) If on the other hand we regard ourselves as dealing
with pure number throughout, then, as multiplication is continued
addition, we ought to include in our classification involution as
continued multiplication. Or we might say that, since multiplication is
a form of addition, and division a form of subtraction, there are really
only two fundamental processes, viz. addition and subtraction. (iii) The
inclusion of the four processes under one general head fails to indicate
the essential difference between addition and multiplication, as direct
processes, on the one hand, and subtraction and division, as inverse
processes, on the other (S 59).
6. The present article deals mainly with the principles of the subject,
for which a logical arrangement is on the whole the more convenient. It
is not suggested that this is the proper order to be adopted by the
teacher.