No More Learning

*Life of Aristotle. *--The main facts of Aristotle's life may be briefly
told. He was born in 385-4 B. C. at Stagirus, a little city of the
Chalcidic peninsula, still called, almost by its ancient name, Chalcis,
and died at the age of sixty-two at Chalcis in Euboea. Thus he is a
contemporary of Demosthenes, his manhood witnessed the struggle which
ended in the establishment of the Macedonian monarchy as the dominant
power in Hellas, and his later years the campaigns in which his pupil
Alexander the Great overthrew the Persian Empire and carried Greek
civilisation to the banks of the Jumna. In studying the constitutional
theories of Aristotle, it is necessary to bear these facts in mind.
They help to explain certain limitations of outlook which might
otherwise appear strange in so great a man. It throws a great deal of
light on the philosopher's intense conviction of the natural inferiority
of the "barbarian" intellect and character to remember that he grew up
in an outlying region where the "barbarian" was seen to disadvantage in
the ordinary course of life. Hence the distinction between Greek and
"barbarian" came to mean for him much what the "colour-line" does to an
American brought up in a Southern State. So, again, when we are struck
by his "provincialism," his apparent satisfaction with the ideal of a
small self-contained city-state with a decently oligarchical government,
a good system of public education, and no "social problems," but devoid
alike of great traditions and far-reaching ambitions, we must remember
that the philosopher himself belonged to just such a tiny community
without a past and without a future. The Chalcidic cities had been first
founded, as the name of the peninsula implies, as colonies from the town
of Chalcis in Euboea; Corinth had also been prominent in establishing
settlements in the same region. At the height of Athenian Imperial
prosperity in the age of Pericles the district had fallen politically
under Athenian control, but had been detached again from Athens, in the
last years of the Archidamian war, by the genius of the great Spartan
soldier and diplomat Brasidas. Early in the fourth century the Chalcidic
cities had attempted to form themselves into an independent federation,
but the movement had been put down by Sparta, and the cities had fallen
under the control of the rising Macedonian monarchy, when Aristotle was
a baby. A generation later, a double intrigue of the cities with Philip
of Macedon and Athens failed of its effect, and the peninsula was
finally incorporated with the Macedonian kingdom. It is also important
to note that the philosopher belonged by birth to a guild, the
Asclepiadae, in which the medical profession was hereditary. His father
Nicomachus was court physician to Amyntas II. , the king for whose
benefit the Spartans had put down the Chalcidic league. This early
connection with medicine and with the Macedonian court explains largely
both the predominantly biological cast of Aristotle's philosophical
thought and the intense dislike of "princes" and courts to which he more
than once gives expression. At the age of eighteen, in 367-6, Aristotle
was sent to Athens for "higher" education in philosophy and science, and
entered the famous Platonic Academy, where he remained as a member of
the scientific group gathered round the master for twenty years, until
Plato's death in 347-6. For the three years immediately following
Aristotle was in Asia Minor with his friend and fellow-student Hermeias,
who had become by force of sheer capacity monarch of the city of
Atarneus in the Troad, and was maintaining himself with much energy
against the Persian king. Pythias, the niece of Hermeias, became the
philosopher's wife, and it seems that the marriage was happy.
Examination of Aristotle's contributions to marine biology has shown
that his knowledge of the subject is specially good for the Aeolic coast
and the shores of the adjacent islands. This throws light on his
occupations during his residence with Hermeias, and suggests that Plato
had discerned the bent of his distinguished pupil's mind, and that his
special share in the researches of the Academy had, like that of
Speusippus, Plato's nephew and successor in the headship of the school,
been largely of a biological kind. We also know that, presumably
shortly after Plato's death, Aristotle had been one of the group of
disciples who edited their teacher's unpublished lectures. In 343
Hermeias was assassinated at the instigation of Persia; Aristotle
honoured his memory by a hymn setting forth the godlikeness of virtue as
illustrated by the life of his friend. Aristotle now removed to the
Macedonian court, where he received the position of tutor to the Crown
Prince, afterwards Alexander the Great, at this time (343 B. C. ) a boy of
thirteen. The association of the great philosopher and the great king as
tutor and pupil has naturally struck the imagination of later ages; even
in Plutarch's _Life of Alexander_ we meet already with the full-blown
legend of the influence of Aristotle's philosophical speculations on
Alexander. It is, however, improbable that Aristotle's influence
counted for much in forming the character of Alexander. Aristotle's
dislike of monarchies and their accessories is written large on many a
page of his _Ethics_ and _Politics_; the small self-contained city-state
with no political ambitions for which he reserves his admiration would
have seemed a mere relic of antiquity to Philip and Alexander. The only
piece of contemporary evidence as to the relations between the master
and the pupil is a sentence in a letter to the young Alexander from the
Athenian publicist Isocrates who maliciously congratulates the prince on
his preference for "rhetoric," the art of efficient public speech, and
his indifference to "logic-choppers. " How little sympathy Aristotle can
have had with his pupil's ambitions is shown by the fact that though his
political theories must have been worked out during the very years in
which Alexander was revolutionising Hellenism by the foundation of his
world-empire, they contain no allusion to so momentous a change in the
social order. For all that Aristotle tells us, Alexander might never
have existed, and the small city-state might have been the last word of
Hellenic political development. Hence it is probable that the selection
of Aristotle, who had not yet appeared before the world as an
independent thinker, to take part in the education of the Crown Prince
was due less to personal reputation than to the connection of his family
with the court, taken together with his own position as a pupil of
Plato, whose intervention in the public affairs of Sicily had caused the
Academy to be regarded as the special home of scientific interest in
politics and jurisprudence. It may be true that Alexander found time in
the midst of his conquests to supply his old tutor with zoological
specimens; it is as certain as such a thing can be that the ideals and
characters of the two men were too different to allow of any intimate
influence of either on the other.

When Alexander was suddenly called to the Macedonian throne by the
murder of his father in 336 B. C. , Aristotle's services were no longer
needed; he returned to Athens and gave himself to purely scientific
work. Just at this juncture the presidency of the Academy was vacant by
the death of Speusippus, Aristotle's old associate in biological
research. Possibly Aristotle thought himself injured when the school
passed him over and elected Xenocrates of Chalcedon as its new
president. At any rate, though he appears never to have wholly severed
his connection with the Academy, in 335 he opened a rival institution in
the Lyceum, or gymnasium attached to the temple of Apollo Lyceus, to
which he was followed by some of the most distinguished members of the
Academy. From the fact that his instruction was given in the
_peripatos_ or covered portico of the gymnasium the school has derived
its name of Peripatetic. For the next twelve years he was occupied in
the organisation of the school as an abode for the prosecution of
speculation and research in every department of inquiry, and in the
composition of numerous courses of lectures on scientific and
philosophical questions. The chief difference in general character
between the new school and the Academy is that while the scientific
interests of the Platonists centred in mathematics, the main
contributions of the Lyceum to science lay in the departments of biology
and history.

Towards the end of Alexander's life his attention was unfavourably
directed on his old teacher. A relative of Aristotle named Callisthenes
had attended Alexander in his campaigns as historiographer, and had
provoked disfavour by his censure of the King's attempts to invest his
semi-constitutional position towards his Hellenic subjects with the pomp
of an Oriental despotism. The historian's independence proved fatal.
He was accused of instigating an assassination plot among Alexander's
pages, and hanged, or, as some said, thrown into a prison where he died
before trial. Alexander is reported to have held Aristotle responsible
for his relative's treason, and to have meditated revenge. If this is
so, he was fortunately diverted from the commission of a crime by
preoccupation with the invasion of India.

On the death of Alexander in 323 a brief but vigorous anti-Macedonian
agitation broke out at Athens. Aristotle, from his Macedonian
connections, naturally fell a victim, in spite of his want of sympathy
with the ideals of Philip and Alexander. Like Socrates, he was indicted
on the capital charge of "impiety," the pretext being that his poem on
the death of Hermeias, written twenty years before, was a virtual
deification of his friend. This was, however, only a pretext; the real
offence was political, and lay in his connection with the Macedonian
leader Antipater. As condemnation was certain, the philosopher
anticipated it by withdrawing with his disciples to Chalcis, the mother
city of his native Stagirus. Here he died in the following year, at the
age of sixty-two or sixty-three.

The features of Aristotle, familiar to us from busts and intaglios, are
handsome, but indicate refinement and acuteness rather than originality,
an impression in keeping with what we should expect from a study of his
writings. The anecdotes related of him reveal a kindly, affectionate
character, and show little trace of the self-importance which appears in
his work. His will, which has been preserved, exhibits the same traits
in its references to his happy family life and its solicitous care for
the future of his children and servants. He was twice married, first to
Pythias, and secondly to a certain Herpyllis, by whom he left a son
Nicomachus and a daughter. The "goodness" of Herpyllis to her husband
is specially mentioned in the clauses of the will which make provision
for her, while the warmth of the writer's feelings for Pythias is shown
by the direction that her remains are to be placed in the same tomb with
his own. The list of servants remembered and the bequests enumerated
show the philosopher to have been in easier circumstances than Plato.

*The Works of Aristotle*. --The so-called works of Aristotle present us
with a curious problem. When we turn from Plato to his pupil we seem to
have passed into a different atmosphere. The _Discourses of Socrates_
exhibit a prose style which is perhaps the most marvellous of all
literary achievements. Nowhere else do we meet with quite the same
combination of eloquence, imaginative splendour, incisive logic, and
irresistible wit and humour. The manner of Aristotle is dry and formal.
His language bristles with technicalities, makes little appeal to the
emotions, disdains graces of style, and frequently defies the simplest
rules of composition. Our surprise is all the greater that we find
later writers of antiquity, such as Cicero, commending Aristotle for his
copious and golden eloquence, a characteristic which is conspicuously
wanting in the Aristotelian writings we possess. The explanation of the
puzzle is, however, simple. Plato and Aristotle were at once what we
should call professors and men of letters; both wrote works for general
circulation, and both delivered courses of lectures to special students.
But while Plato's lectures have perished, his books have come down to
us. Aristotle's books have almost wholly been lost, but we possess many
of his lectures. The "works" of Aristotle praised by Cicero for their
eloquence were philosophical dialogues, and formed the model for
Cicero's own compositions in this kind. None of them have survived,
though some passages have been preserved in quotations by later writers.
That the "works" are actually the MSS. of a lecturer posthumously edited
by his pupils seems clear from external as well as from internal
evidence. In one instance we have the advantage of a double recension.
Aristotle's _Ethics_ or _Discourses on Conduct_ have come down to us in
two forms--the so-called _Nicomachean Ethics_, a redaction by the
philosopher's son, Nicomachus, preserving all the characteristics of an
oral course of lectures; and a freer and more readable recast by a
pupil, the mathematician Eudemus, known as the _Eudemian Ethics_. In
recent years we have also recovered from the sands of Egypt what appears
to be our one specimen of a "work" of Aristotle, intended to be read by
the public at large, the essay on the Constitution of Athens. The style
of this essay is easy, flowing, and popular, and shows that Aristotle
could write well and gracefully when he thought fit.




*CHAPTER II*

*THE CLASSIFICATION OF THE SCIENCES: SCIENTIFIC METHOD*


Philosophy, as understood by Aristotle, may be said to be the organised
whole of disinterested knowledge, that is, knowledge which we seek for
the satisfaction which it carries with itself, and not as a mere means
to utilitarian ends. The impulse which receives this satisfaction is
curiosity or wonder, which Aristotle regards as innate in man, though it
does not get full play until civilisation has advanced far enough to
make secure provision for the immediate material needs of life. Human
curiosity was naturally directed first to the outstanding "marvellous
works" of the physical world, the planets, the periodicity of their
movements, the return of the seasons, winds, thunder and lightning, and
the like. Hence the earliest Greek speculation was concerned with
problems of astronomy and meteorology. Then, as reflection developed,
men speculated about geometrical figure, and number, the possibility of
having assured knowledge at all, the character of the common principles
assumed in all branches of study or of the special principles assumed in
some one branch, and thus philosophy has finally become the
disinterested study of every department of Being or Reality. Since
Aristotle, like Hegel, thought that his own doctrine was, in essentials,
the last word of speculation, the complete expression of the principles
by which his predecessors had been unconsciously guided, he believes
himself in a position to make a final classification of the branches of
science, showing how they are related and how they are discriminated
from one another. This classification we have now to consider.

*Classification of the Sciences*. --To begin with, we have to
discriminate Philosophy from two rivals with which it might be
confounded on a superficial view, Dialectic and Sophistry. Dialectic is
the art of reasoning accurately from given premisses, true or false.
This art has its proper uses, and of one of these we shall have to
speak. But in itself it is indifferent to the truth of its premisses.
You may reason dialectically from premisses which you believe to be
false, for the express purpose of showing the absurd conclusions to
which they lead. Or you may reason from premisses which you assume
tentatively to see what conclusions you are committed to if you adopt
them. In either case your object is not directly to secure truth, but
only to secure consistency. Science or Philosophy aims directly at
_truth_, and hence requires to start with true and certain premisses.
Thus the distinction between Science and Dialectic is that Science
reasons from true premisses, Dialectic only from "probable" or
"plausible" premisses. Sophistry differs from Science in virtue of its
moral character. It is the profession of making a living by the abuse
of reasoning, the trick of employing logical skill for the apparent
demonstration of scientific or ethical falsehoods. "The sophist is one
who earns a living from an apparent but unreal wisdom. " (The emphasis
thus falls on the notion of making an "unreal wisdom" into a _trade_.
The sophist's real concern is to get his fee. ) Science or Philosophy is
thus the disinterested employment of the understanding in the discovery
of truth.

We may now distinguish the different branches of science as defined.
The first and most important division to be made is that between
Speculative or Theoretical Science and Practical Science. The broad
distinction is that which we should now draw between the Sciences and
the Arts (_i. e. _ the industrial and technical, not the "fine" arts).
Speculative or Theoretical Philosophy differs from Practical Philosophy
in its purpose, and, in consequence, in its subject-matter, and its
formal logical character. The purpose of the former is the
disinterested contemplation of truths which are what they are
independently of our own volition; its end is to _know_ and only to
_know_. The object of "practical" Science is to know, but not only to
know but also to turn our knowledge to account in devising ways of
successful interference with the course of events. (The real importance
of the distinction comes out in Aristotle's treatment of the problems of
moral and social science. Since we require knowledge of the moral and
social nature of men not merely to satisfy an intellectual interest, but
as a basis for a sound system of education and government, Politics, the
theory of government, and Ethics, the theory of goodness of conduct,
which for Aristotle is only a subordinate branch of Politics, belong to
Practical, not to Theoretical Philosophy, a view which is attended by
important consequences. )

It follows that there is a corresponding difference in the objects
investigated by the two branches of Philosophy. Speculative or
Theoretical Philosophy is concerned with "that which cannot possibly be
other than it is," truths and relations independent of human volition
for their subsistence, and calling simply for _recognition_ on our part.
Practical Philosophy has to do with relations which human volition can
modify, "things which may be other than they are," the contingent.
(Thus _e. g. _ not only politics, but medicine and economics will belong
to Practical Science. )

Hence again arises a logical difference between the conclusions of
Theoretical and those of Practical Philosophy. Those of the former are
universal truths deducible with logical necessity from self-evident[#]
principles. Those of the latter, because they relate to what "can be
otherwise," are never rigidly universal; they are _general_ rules which
hold good "in the majority of cases," but are liable to occasional
exceptions owing to the contingent character of the facts with which
they deal. It is a proof of a philosopher's lack of grounding in logic
that he looks to the results of a practical science (_e. g. _ to the
detailed precepts of medicine or ethics) for a higher degree of
certainty and validity than the nature of the subject-matter allows.
Thus for Aristotle the distinction between the necessary and the
contingent is real and not merely apparent, and "probability is the
guide" in studies which have to do with the direction of life.


[#] Self-evident, that is, in a purely logical sense. When you apprehend
the principles in question, you _see_ at once that they are true, and do
not require to have them _proved_. It is not meant that any and every
man _does_, in point of fact, always apprehend the principles, or that
they can be apprehended without preliminary mental discipline.


We proceed to the question how many subdivisions there are within
"theoretical" Philosophy itself. Plato had held that there are none.
All the sciences are deductions from a single set of ultimate principles
which it is the business of that supreme science to which Plato had
given the name of Dialectic to establish. This is not Aristotle's view.
According to him, "theoretical" Philosophy falls into a number of
distinct though not co-ordinate branches, each with its own special
subjects of investigation and its own special axiomatic principles. Of
these branches there are three, First Philosophy, Mathematics, and
Physics. First Philosophy--afterwards to be known to the Middle Ages as
Metaphysics[#]--treats, to use Aristotle's own expression, of "Being
_qua_ Being. " This means that it is concerned with the universal
characteristics which belong to the system of knowable reality as such,
and the principles of its organisation in their full universality. First
Philosophy alone investigates the character of those causative factors
in the system which are without body or shape and exempt from all
mutability. Since in Aristotle's system God is the supreme Cause of
this kind, First Philosophy culminates in the knowledge of God, and is
hence frequently called Theology. It thus includes an element which
would to-day be assigned to the theory of knowledge, as well as one
which we should ascribe to metaphysics, since it deals at once with the
ultimate postulates of knowledge and the ultimate causes of the order of
real existence.


[#] The origin of this name seems to be that Aristotle's lectures on
First Philosophy came to be studied as a continuation of his course on
Physics. Hence the lectures got the name _Metaphysica_ because they came
_after_ (_meta_) those on Physics. Finally the name was transferred (as
in the case of _Ethics_) from the lectures to the subject of which they
treat.


Mathematics is of narrower scope. What it studies is no longer "real
being as such," but only real being in so far as it exhibits number and
geometrical form. Since Aristotle holds the view that number and figure
only exist as determinations of objects given in perception (though by a
convenient fiction the mathematician treats of them in abstraction from
the perceived objects which they qualify), he marks the difference
between Mathematics and First Philosophy by saying that "whereas the
objects of First Philosophy are separate from matter and devoid of
motion, those of Mathematics, though incapable of motion, have no
separable existence but are inherent in matter. " Physics is concerned
with the study of objects which are both material and capable of motion.
Thus the principle of the distinction is the presence or absence of
initial restrictions of the range of the different branches of Science.
First Philosophy has the widest range, since its contemplation covers
the whole ground of the real and knowable; Physics the narrowest,
because it is confined to a "universe of discourse" restricted by the
double qualification that its members are all material and capable of
displacement. Mathematics holds an intermediate position, since in it,
one of these qualifications is removed, but the other still remains, for
the geometer's figures are boundaries and limits of sensible bodies, and
the arithmetician's numbers properties of collections of concrete
objects. It follows also that the initial axioms or postulates of
Mathematics form a less simple system than those of First Philosophy,
and those of Physics than those of Mathematics. Mathematics requires as
initial assumptions not only those which hold good for _all_ thought,
but certain other special axioms which are only valid and significant
for the realm of figure and number; Physics requires yet further axioms
which are only applicable to "what is in motion. " This is why, though
the three disciplines are treated as distinct, they are not strictly
co-ordinate, and "First Philosophy," though "first," is only _prima
inter pares_.

We thus get the following diagrammatic scheme of the classification of
sciences:--

Science
|
+-----------+------------+
| |
Theoretical Practical
|
+---+---------+-----------+
| | |
First Philosophy Mathe- Physics
or matics
Theology


Practical Philosophy is not subjected by Aristotle to any similar
subdivision. Later students were accustomed to recognise a threefold
division into Ethics (the theory of individual conduct), Economics (the
theory of the management of the household), Politics (the theory of the
management of the State). Aristotle himself does not make these
distinctions. His general name for the theory of conduct is Politics,
the doctrine of individual conduct being for him inseparable from that
of the right ordering of society. Though he composed a separate course
of lectures on individual conduct (the _Ethics_), he takes care to open
the course by stating that the science of which it treats is Politics,
and offers an apology for dealing with the education of individual
character apart from the more general doctrine of the organisation of
society. No special recognition is given in Aristotle's own
classification to the Philosophy of Art. Modern students of Aristotle
have tried to fill in the omission by adding artistic creation to
contemplation and practice as a third fundamental form of mental
activity, and thus making a threefold division of Philosophy into
Theoretical, Practical, and Productive. The object of this is to find a
place in the classification for Aristotle's famous _Poetics_ and his
work on Rhetoric, the art of effective speech and writing. But the
admission of the third division of Science has no warrant in the text of
Aristotle, nor are the _Rhetoric_ and _Poetics_, properly speaking, a
contribution to Philosophy. They are intended as collections of
practical rules for the composition of a pamphlet or a tragedy, not as a
critical examination of the canons of literary taste. This was
correctly seen by the dramatic theorists of the seventeenth century.
They exaggerated the value of Aristotle's directions and entirely
misunderstood the meaning of some of them, but they were right in their
view that the _Poetics_ was meant to be a collection of rules by obeying
which the craftsman might make sure of turning out a successful play.
So far as Aristotle has a Philosophy of Fine Art at all, it forms part
of his more general theory of education and must be looked for in the
general discussion of the aims of education contained in his _Politics_.

*The Methods of Science*. --No place has been assigned in the scheme to
what we call logic and Aristotle called _Analytics_, the theory of
scientific method, or of proof and the estimation of evidence. The
reason is that since the fundamental character of proof is the same in
all science, Aristotle looks upon logic as a study of the methods common
to all science. At a later date it became a hotly debated question
whether logic should be regarded in this way as a study of the methods
instrumental to proof in all sciences, or as itself a special
constituent division of philosophy. The Aristotelian view was concisely
indicated by the name which became attached to the collection of
Aristotle's logical works. They were called the _Organon_, that is, the
"instrument," or the body of rules of method employed by Science. The
thought implied is thus that logic furnishes the _tools_ with which
every science has to work in establishing its results. Our space will
only permit of a brief statement as to the points in which the
Aristotelian formal logic appears to be really original, and the main
peculiarities of Aristotle's theory of knowledge.

(a) *Formal Logic*. --In compass the Aristotelian logic corresponds
roughly with the contents of modern elementary treatises on the same
subject, with the omission of the sections which deal with the so-called
Conditional Syllogism. The inclusion of arguments of this type in
mediaeval and modern expositions of formal logic is principally due to
the Stoics, who preferred to throw their reasoning into these forms and
subjected them to minute scrutiny. In his treatment of the doctrine of
Terms, Aristotle avoids the mistake of treating the isolated name as
though it had significance apart from the enunciations in which it
occurs. He is quite clear on the all-important point that the unit of
thought is the proposition in which something is affirmed or denied, the
one thought-form which can be properly called "true" or "false. " Such
an assertion he analyses into two factors, that about which something is
affirmed or denied (the Subject), and that which is affirmed or denied
of it (the Predicate). Consequently his doctrine of the classification
of Terms is based on a classification of Predicates, or of Propositions
according to the special kind of connection between the Subject and
Predicate which they affirm or deny. Two such classifications, which
cannot be made to fit into one another, meet us in Aristotle's logical
writings, the scheme of the ten "Categories," and that which was
afterwards known in the Middle Ages as the list of "Predicaments" or
"Heads of Predicates," or again as the "Five Words. " The list of
"Categories" reveals itself as an attempt to answer the question in how
many different senses the words "is a" or "are" are employed when we
assert that "_x_ is _y_" or "_x_ is a _y_" or "_x_s are _y_s. " Such a
statement may tell us (1) what _x_ is, as if I say "_x_ is a lion"; the
predicate is then said to fall under the category of Substance; (2) what
_x_ is like, as when I say "_x_ is white, or _x_ is wise,"--the category
of Quality; (3) how much or how many _x_ is, as when I say "_x_ is tall"
or "_x_ is five feet long,"--the category of Quantity; (4) how _x_ is
related to something else, as when I say "_x_ is to the right of _y_,"
"_x_ is the father of _y_,"--the category of Relation. These are the
four chief "categories" discussed by Aristotle. The remainder are (5)
Place, (6) Time, (7) and (8) Condition or State, as when I say "_x_ is
sitting down" or "_x_ has his armour on,"--(the only distinction between
the two cases seems to be that (7) denotes a more permanent state of _x_
than (8)); (9) Action or Activity, as when I say "_x_ is cutting," or
generally "_x_ is doing something to _y_"; (10) Passivity, as when I say
"_x_ is being cut," or more generally, "so-and-so is being done to _x_. "
No attempt is made to show that this list of "figures of predication" is
complete, or to point out any principle which has been followed in its
construction. It also happens that much the same enumeration is
incidentally made in one or two passages of Plato. Hence it is not
unlikely that the list was taken over by Aristotle as one which would be
familiar to pupils who had read their Plato, and therefore convenient
for practical purposes. The fivefold classification does depend on a
principle pointed out by Aristotle which guarantees its completeness,
and is therefore likely to have been thought out by him for himself, and
to be the genuine Aristotelian scheme. Consider an ordinary universal
affirmative proposition of the form "all _x_s are _y_s. " Now if this
statement is true it may also be true that "all _y_s are _x_s," or it
may not. On the first supposition we have two possible cases, (1) the
predicate may state precisely what the subject defined _is_; then _y_ is
the Definition of _x_, as when I say that "men are mortal animals,
capable of discourse. " Here it is also true to say that "mortal animals
capable of discourse are men," and Aristotle regards the predicate
"mortal animal capable of discourse" as expressing the inmost nature of
man. (2) The predicate may not express the inmost nature of the
subject, and yet may belong only to the class denoted by the subject and
to every member of that class. The predicate is then called a Proprium
or property, an exclusive attribute of the class in question.
Thus it
was held that "all men are capable of laughter" and "all beings capable
of laughter are men," but that the capacity for laughter is no part of
the inmost nature or "real essence" of humanity. It is therefore
reckoned as a Proprium.

Again in the case where it is true that "all _x_s are _y_s," but not
true that all "_y_s are _x_s," _y_ may be part of the definition of _x_
or it may not. If it is part of the definition of _x_ it will be either
(3) a genus or wider class of which _x_ forms a subdivision, as when I
say, "All men are animals," or (4) a difference, that is, one of the
distinctive marks by which the _x_s are distinguished from other
sub-classes or species of the same genus, as when I say, "All men are
capable of discourse. " Or finally (5) _y_ may be no part of the
definition of _x_, but a characteristic which belongs both to the _x_s
and some things other than _x_s. The predicate is then called an
Accident. We have now exhausted all the possible cases, and may say
that the predicate of a universal affirmative proposition is always
either a definition, a proprium, a genus, a difference, or an accident.
This classification reached the Middle Ages not in the precise form in
which it is given by Aristotle, but with modifications mainly due to the
Neo-Platonic philosopher Porphyry. In its modified form it is regarded
as a classification of terms generally. Definition disappears from the
list, as the definition is regarded as a complex made up of the genus,
or next highest class to which the class to be defined belongs, and the
differences which mark off this particular species or sub-class. The
species itself which figures as the subject-term in a definition is
added, and thus the "Five Words" of mediaeval logic are enumerated as
genus, species, difference, proprium, accident.

The one point of philosophical interest about this doctrine appears
alike in the scheme of the "Categories" in the presence of a category of
"substance," and in the list of "Predicaments" in the sharp distinction
drawn between "definition" and "proprium. " From a logical point of view
it does not appear why _any_ proprium, _any_ character belonging to all
the members of a class and to them alone, should not be taken as
defining the class. Why should it be assumed that there is only _one_
predicate, viz. _man_, which precisely answers the question, "What is
Socrates? " Why should it not be equally correct to answer, "a Greek,"
or "a philosopher"? The explanation is that Aristotle takes it for
granted that not all the distinctions we can make between "kinds" of
things are arbitrary and subjective. Nature herself has made certain
hard and fast divisions between kinds which it is the business of our
thought to recognise and follow. Thus according to Aristotle there is a
real gulf, a genuine difference in kind, between the horse and the ass,
and this is illustrated by the fact that the mule, the offspring of a
horse and an ass, is not capable of reproduction. It is thus a sort of
imperfect being, a kind of "monster" existing _contra naturam_. Such
differences as we find when we compare _e. g. _ Egyptians with Greeks do
not amount to a difference in "kind. " To say that Socrates is a man
tells me what Socrates is, because the statement places Socrates in the
real kind to which he actually belongs; to say that he is wise, or old,
or a philosopher merely tells me some of his attributes. It follows from
this belief in "real" or "natural" kinds that the problem of definition
acquires an enormous importance for science. We, who are accustomed to
regard the whole business of classification as a matter of making a
grouping of our materials such as is most pertinent to the special
question we have in hand, tend to look upon any predicate which belongs
universally and exclusively to the members of a group, as a sufficient
basis for a possible definition of the group. Hence we are prone to
take the "nominalist" view of definition, _i. e. _ to look upon a
definition as no more than a declaration of the sense which we intend
henceforward to put on a word or other symbol. And consequently we
readily admit that there may be as many definitions of a class as it has
different propria. But in a philosophy like that of Aristotle, in which
it is held that a true classification must not only be formally
satisfactory, but must also conform to the actual lines of cleavage
which Nature has established between kind and kind, the task of
classificatory science becomes much more difficult. Science is called
on to supply not merely a definition but _the_ definition of the classes
it considers, _the_ definition which faithfully reflects the "lines of
cleavage" in Nature. This is why the Aristotelian view is that a true
definition should always be _per genus et differentias_. It should
"place" a given class by mentioning the wider class next above it in the
objective hierarchy, and then enumerating the most deep-seated
distinctions by which Nature herself marks off this class from others
belonging to the same wider class. Modern evolutionary thought may
possibly bring us back to this Aristotelian standpoint. Modern
evolutionary science differs from Aristotelianism on one point of the
first importance. It regards the difference between kinds, not as a
primary fact of Nature, but as produced by a long process of
accumulation of slight differences. But a world in which the process
has progressed far enough will exhibit much the same character as the
Nature of Aristotle. As the intermediate links between "species" drop
out because they are less thoroughly adapted to maintain themselves than
the extremes between which they form links, the world produced
approximates more and more to a system of species between which there
are unbridgeable chasms; evolution tends more and more to the final
establishment of "real kinds," marked by the fact that there is no
permanent possibility of cross-breeding between them. This makes it
once more possible to distinguish between a "nominal" definition and a
"real" definition. From an evolutionary point of view, a "real"
definition would be one which specifies not merely enough characters to
mark off the group defined from others, but selects also for the purpose
those characters which indicate the line of historical development by
which the group has successively separated itself from other groups
descended from the same ancestors. We shall learn yet more of the
significance of this conception of a "real kind" as we go on to make
acquaintance with the outlines of First Philosophy. Over the rest of
the formal logic of Aristotle we must be content to pass more rapidly.
In connection with the doctrine of Propositions, Aristotle lays down the
familiar distinction between the four types of proposition according to
their quantity (as universal or particular) and quality (as affirmative
or negative), and treats of their contrary and contradictory opposition
in a way which still forms the basis of the handling of the subject in
elementary works on formal logic. He also considers at great length a
subject nowadays commonly excluded from the elementary books, the modal
distinction between the Problematic proposition (_x_ may be _y_), the
Assertory (_x_ is _y_), and the Necessary (_x_ must be _y_), and the way
in which all these forms may be contradicted. For him, modality is a
formal distinction like quantity or quality, because he believes that
contingency and necessity are not merely relative to the state of our
knowledge, but represent real and objective features of the order of
Nature.

In connection with the doctrine of Inference, it is worth while to give
his definition of Syllogism or Inference (literally "computation") in
his own words. "Syllogism is a discourse wherein certain things (viz.
the premisses) being admitted, something else, different from what has
been admitted, follows of necessity because the admissions are what they
are. " The last clause shows that Aristotle is aware that the
all-important thing in an inference is not that the conclusion should be
novel but that it should be proved. We may have known the conclusion as
a fact before; what the inference does for us is to connect it with the
rest of our knowledge, and thus to show _why_ it is true. He also
formulates the axiom upon which syllogistic inference rests, that "if A
is predicated universally of B and B of C, A is necessarily predicated
universally of C. " Stated in the language of class-inclusion, and
adapted to include the case where B is denied of C this becomes the
formula, "whatever is asserted universally, whether positively or
negatively, of a class B is asserted in like manner of any class C which
is wholly contained in B," the axiom _de omni et nullo_ of mediaeval
logic. The syllogism of the "first figure," to which this principle
immediately applies, is accordingly regarded by Aristotle as the natural
and perfect form of inference. Syllogisms of the second and third
figures can only be shown to fall under the dictum by a process of
"reduction" or transformation into corresponding arguments in the first
"figure," and are therefore called "imperfect" or "incomplete," because
they do not exhibit the conclusive force of the reasoning with equal
clearness, and also because no universal affirmative conclusion can be
proved in them, and the aim of science is always to establish such
affirmatives. The list of "moods" of the three figures, and the
doctrine of the methods by which each mood of the imperfect figures can
be replaced by an equivalent mood of the first is worked out
substantially as in our current text-books. The so-called "fourth"
figure is not recognised, its moods being regarded merely as unnatural
and distorted statements of those of the first figure.

*Induction*. --Of the use of "induction" in Aristotle's philosophy we
shall speak under the head of "Theory of Knowledge. " Formally it is
called "the way of proceeding from particular facts to universals," and
Aristotle insists that the conclusion is only proved if _all_ the
particulars have been examined. Thus he gives as an example the
following argument, "_x_, _y_, _z_ are long-lived species of animals;
_x_, _y_, _z_ are the only species which have no gall; _ergo_ all
animals which have no gall are long-lived. " This is the "induction by
simple enumeration" denounced by Francis Bacon on the ground that it may
always be discredited by the production of a single "contrary instance,"
_e. g. _ a single instance of an animal which has no gall and yet is not
long-lived. Aristotle is quite aware that his "induction" does not
establish its conclusion unless all the cases have been included in the
examination. In fact, as his own example shows, an induction which
gives certainty does not start with "particular facts" at all. It is a
method of arguing that what has been proved true of each sub-class of a
wider class will be true of the wider class as a whole. The premisses
are strictly universal throughout. In general, Aristotle does not
regard "induction" as _proof_ at all. Historically "induction" is held
by Aristotle to have been first made prominent in philosophy by
Socrates, who constantly employed the method in his attempts to
establish universal results in moral science. Thus he gives, as a
characteristic argument for the famous Socratic doctrine that knowledge
is the one thing needful, the "induction," "he who understands the
theory of navigation is the best navigator, he who understands the
theory of chariot-driving the best driver; from these examples we see
that universally he who understands the theory of a thing is the best
practitioner," where it is evident that _all_ the relevant cases have
_not_ been examined, and consequently that the reasoning does not amount
to proof. Mill's so-called reasoning from particulars to particulars
finds a place in Aristotle's theory under the name of "arguing from an
example. " He gives as an illustration, "A war between Athens and Thebes
will be a bad thing, for we see that the war between Thebes and Phocis
was so. " He is careful to point out that the whole force of the
argument depends on the _implied_ assumption of a universal proposition
which covers both cases, such as "wars between _neighbours_ are bad
things. " Hence he calls such appeals to example "rhetorical" reasoning,
because the politician is accustomed to leave his hearers to supply the
relevant universal consideration for themselves.

*Theory of Knowledge*. --Here, as everywhere in Aristotle's philosophy,
we are confronted by an initial and insuperable difficulty. Aristotle
is always anxious to insist on the difference between his own doctrines
and those of Plato, and his bias in this direction regularly leads him
to speak as though he held a thorough-going naturalistic and empirical
theory with no "transcendental moonshine" about it. Yet his final
conclusions on all points of importance are hardly distinguishable from
those of Plato except by the fact that, as they are so much at variance
with the naturalistic side of his philosophy, they have the appearance
of being sudden lapses into an alogical mysticism. We shall find the
presence of this "fault" more pronouncedly in his metaphysics,
psychology, and ethics than in his theory of knowledge, but it is not
absent from any part of his philosophy. He is everywhere a Platonist
_malgre lui_, and it is just the Platonic element in his thought to
which it owes its hold over men's minds.

Plato's doctrine on the subject may be stated with enough accuracy for
our purpose as follows. There is a radical distinction between
sense-perception and scientific knowledge. A scientific truth is exact
and definite, it is also true once and for all, and never becomes truer
or falser with the lapse of time. This is the character of the
propositions of the science which Plato regarded as the type of what
true science ought to be, pure mathematics. It is very different with
the judgments which we try to base on our sense-perceptions of the
visible and tangible world. The colours, tastes, shapes of sensible
things seem different to different percipients, and moreover they are
constantly changing in incalculable ways. We can never be certain that
two lines which seem to our senses to be equal are really so; it may be
that the inequality is merely too slight to be perceptible to our
senses. No figure which we can draw and see actually has the exact
properties ascribed by the mathematician to a circle or a square. Hence
Plato concludes that if the word science be taken in its fullest sense,
there can be no science about the world which our senses reveal. We can
have only an approximate knowledge, a knowledge which is after all, at
best, probable opinion. The objects of which the mathematician has
certain, exact, and final knowledge cannot be anything which the senses
reveal. They are objects of _thought_, and the function of visible
models and diagrams in mathematics is not to present _examples_ of them
to us, but only to show us imperfect _approximations_ to them and so to
"remind" the soul of objects and relations between them which she has
never cognised with the bodily senses. Thus mathematical straightness
is never actually beheld, but when we see lines of less and more
approximate straightness we are "put in mind" of that absolute
straightness to which sense-perception only approximates. So in the
moral sciences, the various "virtues" are not presented in their
perfection by the course of daily life. We do not meet with men who are
perfectly brave or just, but the experience that one man is braver or
juster than another "calls into our mind" the thought of the absolute
standard of courage or justice implied in the conviction that one man
comes nearer to it than another, and it is these absolute standards
which are the real objects of our attention when we try to define the
terms by which we describe the moral life. This is the
"epistemological" side of the famous doctrine of the "Ideas. " The main
points are two, (1) that strict science deals throughout with objects
and relations between objects which are of a purely intellectual or
conceptual order, no sense-data entering into their constitution; (2)
since the objects of science are of this character, it follows that the
"Idea" or "concept" or "universal" is not arrived at by any process of
"abstracting" from our experience of sensible things the features common
to them all. As the particular fact never actually exhibits the
"universal" except approximately, the "universal" cannot be simply
disentangled from particulars by abstraction. As Plato puts it, it is
"apart from" particulars, or, as we might reword his thought, the pure
concepts of science represent "upper limits" to which the comparative
series which we can form out of sensible data continually approximate
but do not reach them.

In his theory of knowledge Aristotle begins by brushing aside the
Platonic view. Science requires no such "Ideas," transcending
sense-experience, as Plato had spoken of; they are, in fact, no more
than "poetic metaphors. " What is required for science is not that there
should be a "one over and above the many" (that is, such pure concepts,
unrealised in the world of actual perception, as Plato had spoken of),
but only that it should be possible to predicate one term universally of
many others. This, by itself, means that the "universal" is looked on
as a mere residue of the characteristics found in each member of a
group, got by abstraction, _i. e. _ by leaving out of view the
characteristics which are peculiar to some of the group and retaining
only those which are common to all. If Aristotle had held consistently
to this point of view, his theory of knowledge would have been a purely
empirical one. He would have had to say that, since all the objects of
knowledge are particular facts given in sense-perception, the universal
laws of science are a mere convenient way of describing the observed
uniformities in the behaviour of sensible things. But, since it is
obvious that in pure mathematics we are not concerned with the actual
relations between sensible data or the actual ways in which they behave,
but with so-called "pure cases" or ideals to which the perceived world
only approximately conforms, he would also have had to say that the
propositions of mathematics are not strictly true. In modern times
consistent empiricists have said this, but it is not a position possible
to one who had passed twenty years in association with the
mathematicians of the Academy, and Aristotle's theory only begins in
naturalism to end in Platonism. We may condense its most striking
positions into the following statement. By science we mean _proved_
knowledge. And proved knowledge is always "mediated"; it is the
knowledge of _conclusions_ from premisses. A truth that is
scientifically known does not stand alone. The "proof" is simply the
pointing out of the connection between the truth we call the conclusion,
and other truths which we call the premisses of our demonstration.
Science points out the _reason why_ of things, and this is what is meant
by the Aristotelian principle that to have science is to know things
through their _causes_ or _reasons why_. In an ordered digest of
scientific truths, the proper arrangement is to begin with the simplest
and most widely extended principles and to reason down, through
successive inferences, to the most complex propositions, the _reason
why_ of which can only be exhibited by long chains of deductions. This
is the order of logical dependence, and is described by Aristotle as
reasoning _from_ what is "more knowable in its own nature,"[#] the
simple, to what is usually "more familiar to _us_," because less removed
from the infinite wealth of sense-perception, the complex. In
_discovery_ we have usually to reverse the process and argue from "the
familiar to us," highly complex facts, to "the more knowable in its own
nature," the simpler principles implied in the facts.


[#] This simple expression acquires a mysterious appearance in mediaeval
philosophy from the standing mistranslation _notiora naturae_, "better
known to nature. "


It follows that Aristotle, after all, admits the disparateness of
sense-perception and scientific knowledge. Sense-perception of itself
never gives us scientific truth, because it can only assure us that a
fact is so; it cannot _explain_ the fact by showing its connection with
the rest of the system of facts, "it does not give the _reason_ for the
fact. " Knowledge of perception is always "immediate," and for that very
reason is never scientific. If we stood on the moon and saw the earth,
interposing between us and the sun, we should still not have scientific
knowledge about the eclipse, because "we should still have to ask for
the _reason why_. " (In fact, we should not know the reason _why_
without a theory of light including the proposition that light-waves are
propagated in straight lines and several others. ) Similarly Aristotle
insists that Induction does not yield scientific truth. "He who makes
an induction points out something, but does not demonstrate anything. "

For instance, if we know that _each_ species of animal which is without
a gall is long-lived, we may make the induction that _all_ animals
without a gall are long-lived, but in doing so we have got no nearer to
seeing _why_ or _how_ the absence of a gall makes for longevity. The
question which we may raise in science may all be reduced to four heads,
(1) Does this thing exist? (2) Does this event occur? (3) If the thing
exists, precisely what is it? and (4) If the event occurs, _why_ does it
occur? and science has not completed its task unless it can advance from
the solution of the first two questions to that of the latter two.
Science is no mere catalogue of things and events, it consists of
inquiries into the "real essences" and characteristics of things and the
laws of connection between events.

Looking at scientific reasoning, then, from the point of view of its
formal character, we may say that all science consists in the search for
"middle terms" of syllogisms, by which to connect the truth which
appears as a conclusion with the less complex truths which appear as the
premisses from which it is drawn. When we ask, "does such a thing
exist? " or "does such an event happen? " we are asking, "is there a
middle term which can connect the thing or event in question with the
rest of known reality? " Since it is a rule of the syllogism that the
middle term must be taken universally, at least once in the premisses,
the search for middle terms may also be described as the search for
universals, and we may speak of science as knowledge of the universal
interconnections between facts and events.

A science, then, may be analysed into three constituents. These are: (1)
a determinate class of objects which form the subject-matter of its
inquiries. In an orderly exhibition of the contents of the science,
these appear, as in Euclid, as the initial data about which the science
reasons; (2) a number of principles, postulates, and axioms, from which
our demonstrations must start. Some of these will be principles
employed in all scientific reasoning. Others will be specific to the
subject-matter with which a particular science is concerned; (3) certain
characteristics of the objects under study which can be shown by means
of our axioms and postulates to follow from our initial definitions, the
_accidentia per se_ of the objects defined. It is these last which are
expressed by the conclusions of scientific demonstration. We are said
to know scientifically that B is true of A when we show that this
follows, in virtue of the principles of some science, from the initial
definition of A. Thus if we convinced ourselves that the sum of the
angles of a plane triangle is equal to two right angles by measurement,
we could not be said to have scientific knowledge of the proposition.
But if we show that the same proposition follows from the definition of
a plane triangle by repeated applications of admitted axioms or
postulates of geometry, our knowledge is genuinely scientific. We now
know that it is so, and we see _why_ it is so; we see the connection of
this truth with the simple initial truths of geometry.

This leads us to the consideration of the most characteristic point of
Aristotle's whole theory. Science is demonstrated knowledge, that is,
it is the knowledge that certain truths follow from still simpler
truths. Hence the simplest of all the truths of any science cannot
themselves be capable of being known by inference. You cannot infer
that the axioms of geometry are true because its conclusions are true,
since the truth of the conclusions is itself a consequence of the truth
of the axioms. Nor yet must you ask for demonstration of the axioms as
consequences of still simpler premisses, because if all truths can be
proved, they ought to be proved, and you would therefore require an
infinity of successive demonstrations to prove anything whatever. But
under such conditions all knowledge of demonstrated truth would be
impossible. The first principles of any science must therefore be
indemonstrable. They must be known, as facts of sense-perception are
known, immediately and not mediately. How then do we come by our
knowledge of them? Aristotle's answer to this question appears at first
sight curiously contradictory. He seems to say that these simplest
truths are apprehended intuitively, or on inspection, as self-evident by
Intelligence or Mind. On the other hand, he also says that they are
known _to us_ as a result of induction from sense-experience. Thus he
_seems_ to be either a Platonist or an empiricist, according as you
choose to remember one set of his utterances or another, and this
apparent inconsistency has led to his authority being claimed in their
favour by thinkers of the most widely different types. But more careful
study will show that the seeming confusion is due to the fact that he
tries to combine in one statement his answers to two quite different
questions, (1) how we come to reflect on the axioms, (2) what evidence
there is for their truth. To the first question he replies, "by
induction from experience," and so far he might seem to be a precursor
of John Stuart Mill. Successive repetitions of the same
sense-perceptions give rise to a single experience, and it is by
reflection on experience that we become aware of the most ultimate
simple and universal principles. We might illustrate his point by
considering how the thought that two and two are four may be brought
before a child's mind. We might first take two apples, and two other
apples and set the child to count them. By repeating the process with
different apples we may teach the child to dissociate the result of the
counting from the particular apples employed, and to advance to the
thought, "any two apples and any two other apples make four apples. "
Then we might substitute pears or cherries for the apples, so as to
suggest the thought, "two fruits and two fruits make four fruits. " And
by similar methods we should in the end evoke the thought, "any two
objects whatever and any other two objects whatever make four objects. "
This exactly illustrates Aristotle's conception of the function of
induction, or comparison of instances, in fixing attention on a
universal principle of which one had not been conscious before the
comparison was made.

Now comes in the point where Aristotle differs wholly from all
empiricists, later and earlier. Mill regards the instances produced in
the induction as having a double function; they not merely fix the
attention on the principle, they also are the evidence of its truth.
This gives rise to the greatest difficulty in his whole logical theory.
Induction by imperfect enumeration is pronounced to be (as it clearly
is) fallacious, yet the principle of the uniformity of Nature which Mill
regards as the ultimate premiss of all science, is itself supposed to be
proved by this radically fallacious method. Aristotle avoids a similar
inconsistency by holding that the sole function of the induction is to
fix our attention on a principle which it does not prove. He holds that
ultimate principles neither permit of nor require proof. When the
induction has done its work in calling attention to the principle, you
have to see for yourself that the principle is true. You see that it is
true by immediate inspection just as in sense-perception you have to see
that the colour before your eyes is red or blue. This is why Aristotle
holds that the knowledge of the principles of science is not itself
science (demonstrated knowledge), but what he calls intelligence, and we
may call intellectual intuition. Thus his doctrine is sharply
distinguished not only from empiricism (the doctrine that universal
principles are proved by particular facts), but also from all theories
of the Hegelian type which regard the principles and the facts as
somehow reciprocally proving each other, and from the doctrine of some
eminent modern logicians who hold that "self-evidence" is not required
in the ultimate principles of science, as we are only concerned in logic
with the question what consequences follow from our initial assumptions,
and not with the truth or falsehood of the assumptions themselves.

The result is that Aristotle does little more than repeat the Platonic
view of the nature of science. Science consists of deductions from
universal principles which sensible experience "suggests," but into
which, as they are apprehended by a purely intellectual inspection, no
sense-data enter as constituents. The apparent rejection of
"transcendental moonshine" has, after all, led to nothing. The only
difference between Plato and his scholar lies in the clearness of
intellectual vision which Plato shows when he expressly maintains in
plain words that the universals of exact science are not "in" our
sense-perceptions and therefore to be extracted from them by a process
of abstraction, but are "apart from" or "over" them, and form an ideal
system of interconnected concepts which the experiences of sense merely
"imitate" or make approximation to.

One more point remains to be considered to complete our outline of the
Aristotelian theory of knowledge. The sciences have "principles" which
are discerned to be true by immediate inspection. But what if one man
professes to see the self-evident truth of such an alleged principle,
while another is doubtful of its truth, or even denies it? There can be
no question of silencing the objector by a demonstration, since no
genuine simple principle admits of demonstration. All that can be done,
_e. g. _ if a man doubts whether things equal to the same thing are equal
to one another, or whether the law of contradiction is true, is to
examine the consequences of a denial of the axiom and to show that they
include some which are false, or which your antagonist at least
considers false. In this way, by showing the falsity of consequences
which follow from the denial of a given "principle," you indirectly
establish its truth. Now reasoning of this kind differs from "science"
precisely in the point that you take as your major premiss, not what you
regard as true, but the opposite thesis of your antagonist, which you
regard as false. Your object is not to prove a true conclusion but to
show your opponent that _his_ premisses lead to false conclusions. This
is "dialectical" reasoning in Aristotle's sense of the word, _i. e. _
reasoning not from your own but from some one else's premisses. Hence
the chief philosophical importance which Aristotle ascribes to
"dialectic" is that it provides a method of defending the undemonstrable
axioms against objections. Dialectic of this kind became highly
important in the mediaeval Aristotelianism of the schoolmen, with whom it
became a regular method, as may be seen _e. g.