No More Learning

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. _ in the _Summa_ of St.
Thomas, to begin their consideration of a doctrine by a preliminary
rehearsal of all the arguments they could find or devise against the
conclusion they meant to adopt. Thus the first division of any article
in the _Summa Theologiae_ of Thomas is regularly constituted by arguments
based on the premisses of actual or possible antagonists, and is
strictly dialectical. (To be quite accurate Aristotle should, of
course, have observed that this dialectical method of defending a
principle becomes useless in the case of a logical axiom which is
presupposed by all deduction. For this reason Aristotle falls into
fallacy when he tries to defend the law of contradiction by dialectic.
It is true that if the law be denied, then any and every predicate may
be indifferently ascribed to any subject. But until the law of
contradiction has been admitted, you have no right to regard it as
absurd to ascribe all predicates indiscriminately to all subjects.
Thus, it is only assumed laws which are _not_ ultimate laws of logic
that admit of dialectical justification. If a truth is so ultimate that
it has either to be recognised by direct inspection or not at all, there
can be no arguing at all with one who cannot or will not see it. )




*CHAPTER III*

*FIRST PHILOSOPHY*


First Philosophy is defined by Aristotle as a "science which considers
What Is simply in its character of Being, and the properties which it
has as such. " That there is, or ought to be, such a science is urged on
the ground that every "special" science deals only with some restricted
department of what is, and thus considers its subject-matter not
universally in its character of being, or being real, but as determined
by some more special condition. Thus, First Philosophy, the science
which attempts to discover the most ultimate reasons of, or grounds for,
the character of things in general cannot be identified with any of the
"departmental" sciences. The same consideration explains why it is
"First Philosophy" which has to disentangle the "principles" of the
various sciences, and defend them by dialectic against those who impugn
them. It is no part of the duty of a geometer or a physicist to deal
with objections to such universal principles of reasoning as the law of
contradiction. They may safely assume such principles; if they are
attacked, it is not by specifically geometrical or physical
considerations that they can be defended. Even the "principles of the
special sciences" have not to be examined and defended by the special
sciences. They are the starting-points of the sciences which employ
them; these sciences are therefore justified in requiring that they
shall be admitted as a condition of geometrical, or physical, or
biological demonstrations. If they are called in question, the defence
of them is the business of logic.

First Philosophy, then, is the study of "What Is simply as such," the
universal principles of structure without which there could be no
ordered system of knowable objects. But the word "is" has more than one
sense. There are as many modes of being as there are types of
predication. "Substances," men, horses, and the like, have their own
specific mode of being--they are things; qualities, such as green or
sweet, have a different mode of being--they are not things, but
"affections" or "attributes" of things. Actions, again, such as
building, killing, are neither things nor yet "affections" of things;
their mode of being is that they are processes which produce or destroy
things. First Philosophy is concerned with the general character of all
these modes of being, but it is specially concerned with that mode of
being which belongs to _substances_. For this is the most primary of
all modes of being. We had to introduce a reference to it in our
attempt to say what the mode of being of qualities and actions is, and
it would have been the same had our illustrations been drawn from any
other "categories. " Hence the central and special problem of First
Philosophy is to analyse the notion of substance and to show the causes
of the existence of substances.

Next, we have to note that the word "substance" itself has two senses.
When we spoke of substance as one of the categories we were using it in
a secondary sense. We meant by substances "horse," "man," and the rest
of the "real kinds" which we find in Nature, and try to reproduce in a
scientific classification. In this sense of the word "substances" are a
special class of _predicates_, as when we affirm of Plato that he is a
man, or of Bucephalus that he is a horse. But in the primary sense a
substance means an absolutely individual thing, "_this_ man," or "_this_
horse. " We may therefore define primary substances from the logician's
point of view by saying that they can be only subjects of predication,
never predicates. Or again, it is peculiar to substances, that while
remaining numerically one a substance admits of incompatible
determinations, as Socrates, remaining one and the same Socrates, is
successively young and old. This is not true of "qualities," "actions,"
and the rest. The same colour cannot be first white and then black; the
same act cannot be first bad and then good. Thus we may say that
individual substances are the fixed and permanent factors in the world
of mutability, the invariants of existence. Processes go on in them,
they run the gamut of changes from birth to decay, processes take place
_among_ them, they act on and are acted on by one another, they
fluctuate in their qualities and their magnitude, but so long as a
substance exists it remains numerically one and the same throughout all
these changes. Their existence is the first and most fundamental
condition of the existence of the universe, since they are the bearers
of all qualities, the terms of all relations, and the agents and
patients in all interaction.

The point to note is that Aristotle begins his investigation into the
structure of What Is and the causes by which it is produced by starting
from the existence of individual things belonging to the physical order
and perceived by the senses. About any such thing we may ask two
questions, (1) into what constituent factors can it be logically
analysed? (2) and how has it come to exhibit the character which our
analysis shows it to have? The answer to these questions will appear
from a consideration of two standing antitheses which run through
Aristotle's philosophy, the contrast between Matter and Form, and that
between Potential and Actual, followed by a recapitulation of his
doctrine of the Four Causes, or four senses of the word Cause.

*Matter and Form*. --Consider any completely developed individual thing,
whether it is the product of human manufacture, as a copper bowl, or of
natural reproduction, as an oak-tree or a horse. We shall see at once
that the bowl is like other articles made of the same metal,
candlesticks, coal-vases, in being made of the same stuff, and unlike
them in having the special shape or structure which renders it fit for
being used as a bowl and not for holding a candle or containing coals.
So a botanist or a chemist will tell you that the constituent tissues of
an oak or horse, or the chemical elements out of which these tissues are
built up are of the same kind as those of an ash or an ox, but the oak
differs from the ash or the horse from the ox in characteristic
structure. We see thus that in any individual thing we can distinguish
two components, the stuff of which it consists--which may be identical
in kind with the stuff of which things of a very different kind
consist--and the structural law of formation or arrangement which is
peculiar to the "special" kind of thing under consideration. In the
actual individual thing these two are inseparably united; they do not
exist side by side, as chemists say the atoms of hydrogen and oxygen do
in a drop of water; the law of organisation or structure is manifested
in and through the copper, or the various tissues of the living body.
Aristotle expresses this by saying that you can distinguish two aspects
in an individual, its Matter, (_hyle, materia_) and its Form (_eidos,
forma_). The individual is the matter as organised in accord with a
determinate principle of structure, the form. Of these terms, the
former, _hyle_ (_materia_, matter) means literally timber, and more
specifically ship's timbers, and his selection of it to mean what is
most exactly rendered by our own word "stuff" may perhaps be due to a
reminiscence of an old Pythagorean fancy which looked on the universe as
a ship. The word for form is the same as Plato's, and its philosophical
uses are closely connected with its mathematical sense, "regular
figure," also a Pythagorean technicality which still survives in certain
stereotyped phrases in Euclid. Aristotle extends the analysis into
Matter and Form by analogy beyond the range of individual substances to
everything in which we can distinguish a relatively indeterminate
"somewhat" and a law or type of order and arrangement giving it
determination. Thus if you consider the relatively fixed or "formed"
character of a man in adult life, we may look upon this character as
produced out of the "raw material" of tendencies and dispositions, which
have received a specific development along definite lines, according to
the kind of training to which the mind has been subjected in the
"formative" period of its growth. We may therefore speak of native
disposition as the matter or stuff of which character is made, and the
practical problem of education is to devise a system of training which
shall impress on this matter precisely the form required if the grown
man is to be a good citizen of a good state. Since a man's character
itself is not a substance but a complex of habits or fixed ways of
reacting upon suggestions coming from the world around him, this is a
good instance of the extension of the antithesis of Matter and Form
beyond the category of substance. We see then that Matter in the
Aristotelian sense must not be confounded with body; the relatively
undetermined factor which receives completer determination by the
structural law or Form is Matter, whether it is corporeal or not. This
comes out with particular clearness in the metaphysical interpretation
put on the logical process of definition by genus and difference. When
I define any real kind by specifying a higher and wider class of which
it is a sub-kind, and adding the peculiar characteristics which
distinguish the sub-kind under consideration from the other sub-kinds of
the same genus, the genus may be said to stand to the "differences" as
Matter, the relatively indeterminate, to the Form which gives it its
structure.

We further observe that Matter and Form are strictly correlative. The
matter is called so relatively to the form which gives it further
determination. When the words are used in their strictest sense, with
reference to an individual thing, the Form is taken to mean the _last_
determination by which the thing acquires its complete character, and
the Matter is that which has yet to receive this last determination.
Thus in the case of a copper globe, the spherical figure is said to be
its Form, the copper its material. In the case of the human body, the
Matter is the various tissues, muscles, bones, skin, &c. But each of
these things which are counted as belonging to the Matter of the globe
or the human body has, according to Aristotle, a development behind it.
Copper is not an "element" but a specific combination of "elements," and
the same thing is even more true of the highly elaborate tissues of the
living body. Thus what is Matter relatively to the globe or living body
is Matter already determined by Form if we consider it relatively to its
own constituents. The so-called "elements" of Empedocles, earth, water,
air, fire, are the matter of all chemical compounds, the Form of each
compound being its specific law of composition; the immediate or
"proximate" Matter of the tissues of the animal body is, according to
Aristotle's biology, the "superfluous" blood of the female parent, out
of which the various tissues in the offspring are developed, and the
Matter of this blood is in turn the various substances which are taken
into the body of the parent as food and converted by assimilation into
blood. Their Matter, once more, is the earth, air, fire, and water of
which they are composed. Thus at every stage of a process of manufacture
or growth a fresh Form is superinduced on, or developed within, a Matter
which is already itself a combination of Matter and Form relatively to
the process by which it has itself been originated. Fully thought out,
such a view would lead to the conclusion that in the end the simple
ultimate matter of all individual things is one and the same throughout
the universe, and has absolutely no definite structure at all. The
introduction of Form or determinate structure of any kind would then
have to be thought of as coming from an outside source, since
structureless Matter cannot be supposed to give itself all sorts of
specific determinations, as has been demonstrated in our own times by
the collapse of the "Synthetic Philosophy. " Aristotle avoids the
difficulty by holding that "pure Matter" is a creation of our thought.
In actual fact the crudest form in which matter is found is that of the
"elements. " Since the transmutability of the "elements" is an
indispensable tenet in Aristotle's Physics, we cannot avoid regarding
earth, water, fire air as themselves determinations by specific Form of
a still simpler Matter, though this "prime Matter" "all alone, before a
rag of Form is on," is never to be found existing in its simplicity. [#]


[#] _Hudibras_, Pt. 1, Canto 1, 560.

"He had First Matter seen undressed;
He took her naked all alone,
Before one rag of Form was on. "


*The Potential and the Actual*. --So far we have been looking at the
analysis of the individual thing, as the current jargon puts it,
statically; we have arrived at the antithesis of Matter and Form by
contrasting an unfinished condition of anything with its finished
condition. But we may study the same contrast dynamically, with special
reference to the process of making or growth by which the relatively
undetermined or unfinished becomes determined or finished. The contrast
of Matter with Form then passes into the contrast between Potentiality
and Actuality. What this antithesis means we can best see from the case
of the growth of a living organism. Consider the embryos of two animals,
or the seeds of two plants. Even a botanist or a physiologist may be
unable to pronounce with certainty on the species to which the germ
submitted to him belongs, and chemical analysis may be equally at a
loss. Even at a later stage of development, the embryo of one
vertebrate animal may be indistinguishable from that of another. Yet it
is certain that one of two originally indistinguishable germs will grow
into an oak and the other into an elm, or one into a chimpanzee and the
other into a man. However indistinguishable, they therefore may be said
to have different latent tendencies or possibilities of development
within them. Hence we may say of a given germ, "though this is not yet
actually an oak, it is potentially an oak," meaning not merely that, if
uninterfered with, it will in time be an oak, but also that by no
interference can it be made to grow into an elm or a beech.
So we may
look upon all processes of production or development as processes by
which what at first possessed only the tendency to grow along certain
lines or to be worked up into a certain form, has become actually
endowed with the character to which it possessed the tendency. The
acorn becomes in process of time an actual oak, the baby an actual man,
the copper is made into an actual vase, right education brings out into
active exercise the special capacities of the learner. Hence the
distinction between Matter and Form may also be expressed by saying that
the Matter is the persistent underlying _substratum_ in which the
development of the Form takes place, or that the individual when finally
determined by the Form is the Actuality of which the undeveloped Matter
was the Potentiality. The process of conception, birth, and growth to
maturity in Nature, or of the production of a finished article by the
"arts" whose business it is to "imitate" Nature, may be said to be one
of continuous advance towards the actual embodiment of a Form, or law of
organisation, in a Matter having the latent potentiality of developing
along those special lines. When Aristotle is speaking most strictly he
distinguishes the process by which a Form is realised, which he calls
Energeia, from the manifestation of the realised Form, calling the
latter Entelechy (literally "finished" or "completed" condition).
Often, however, he uses the word Energeia more loosely for the actual
manifestation of the Form itself, and in this he is followed by the
scholastic writers, who render Energeia by _actus_ or _actus purus_.

One presupposition of this process must be specially noted. It is not an
unending process of development of unrealised capacities, but always has
an End in the perfectly simple sense of a last stage. We see this best
in the case of growth. The acorn grows into the sapling and the sapling
into the oak, but there is nothing related to the oak as the oak is to
the sapling. The oak does not grow into something else. The process of
development from potential to actual in this special case comes to an
end with the emergence of the mature oak. In the organic world the end
or last state is recognised by the fact that the organism can now
exercise the power of reproducing its like. This tendency of organic
process to culminate in a last stage of complete maturity is the key to
the treatment of the problem of the "true end" of life in Aristotle's
_Ethics_.

*The Four Causes*. --The conception of the world involved in these
antitheses of Form and Matter, Potential and Actual, finds its fullest
expression in Aristotle's doctrine of the Four Causes or conditions of
the production of things. This doctrine is looked on by Aristotle as
the final solution of the problem which had always been the central one
for Greek philosophy, What are the causes of the world-order? All the
previous philosophies he regards as inadequate attempts to formulate the
answer to this question which is only given completely by his own
system. Hence the doctrine requires to be stated with some fullness.
We may best approach it by starting from the literal meaning of the
Greek terms _aitia_, _aition_, which Aristotle uses to convey the notion
of cause. _Aition_ is properly an adjective used substantially, and
means "that on which the legal responsibility for a given state of
affairs can be laid. " Similarly _aitia_, the substantive, means the
"credit" for good or bad, the legal "responsibility," for an act. Now
when we ask, "what is responsible for the fact that such and such a
state of things now exists? " there are four partial answers which may be
given, and each of these corresponds to one of the "causes. " A complete
answer requires the enumeration of them all. We may mention (1) the
_matter_ or _material_ cause of the thing, (2) the law according to
which it has grown or developed, the _form_ or _formal_ cause, (3) the
agent with whose initial impulse the development began--the
"starting-point of the process," or, as the later Aristotelians call it,
the _efficient_ cause, (4) the completed result of the whole process,
which is present in the case of human manufacture as a preconceived idea
determining the maker's whole method of handling his material, and in
organic development in Nature as implied in and determining the
successive stages of growth--the _end_ or _final_ cause. If any one of
these had been different, the resultant state of things would also have
been different. Hence all four must be specified in completely
accounting for it. Obvious illustrations can be given from artificial
products of human skill, but it seems clear that it was rather
reflection on the biological process of reproduction and growth which
originally suggested the analysis. Suppose we ask what was requisite in
order that there should be now an oak on a given spot. There must have
been (1) a germ from which the oak has grown, and this germ must have
had the latent tendencies towards development which are characteristic
of oaks. This is the material cause of the oak. (2) This germ must
have followed a definite law of growth; it must have had a tendency to
grow in the way characteristic of oaks and to develop the structure of
an oak, not that of a plane or an ash. This is form or formal cause.
(3) Also the germ of the oak did not come from nowhere; it grew on a
parent oak. The parent oak and its acorn-bearing activity thus
constitute the _efficient_ cause of the present oak. (4) And there must
be a final stage to which the whole process of growth is relative, in
which the germ or sapling is no longer becoming but is an adult oak
bearing fresh acorns. This is the _end_ of the process. One would not
be going far wrong in saying that Aristotle's biological cast of thought
leads him to conceive of this "end" in the case of reproduction as a
sub-conscious purpose, just as the workman's thought of the result to be
attained by his action forms a conscious directing purpose in the case
of manufacture. Both in Nature and in "art" the "form," the "efficient
cause," and the "end" tend to coalesce. Thus in Nature "a man begets a
man," organic beings give birth to other organic beings of the same
kind, or, in the technical language of the Aristotelian theory of
Causation, the efficient cause produces, as the "end" of its action, a
second being having the same "form" as itself, though realised in
different "matter," and numerically distinct from itself. Thus the
efficient cause (_i. e. _ the parent) is a "form" realised in matter, and
the "end" is the same "form" realised in other matter. So in "products
of art" the true "source of the process" is the "form" the realisation
of which is the "end" or final cause, only with this difference, that as
efficient cause the "form" exists not in the material but by way of
"idea" or "representation" in the mind of the craftsman. A house does
not produce another house, but the house as existing in "idea" in the
builder's mind sets him at work building, and so produces a
corresponding house in brick or stone. Thus the ultimate opposition is
between the "cause as matter," a passive and inert substratum of change
and development and the "formal" cause which, in the sense just
explained, is one with both the "efficient" or starting-point, and the
"end" or goal of development. It will, of course, be seen that
individual bearers of "forms" are indispensable in the theory; hence the
notion of _activity_ is essential to the causal relation. It is a
relation between things, not between events. Aristotle has no sense of
the word cause corresponding to Mill's conception of a cause as an event
which is the uniform precursor of another event.

Two more remarks may be made in this connection. (1) The prominence of
the notion of "end" gives Aristotle's philosophy a thorough-going
"ideological" character. God and Nature, he tells us, do nothing
aimlessly. We should probably be mistaken if we took this to mean that
"God and Nature" act everywhere with conscious design. The meaning is
rather that every natural process has a last stage in which the "form"
which was to begin with present in the agent or "source of change" is
fully realised in the matter in which the agent has set up the process
of change. The normal thing is _e. g. _ for animals to reproduce "their
kind"; if the reproduction is imperfect or distorted, as in monstrous
births, this is an exception due to the occasional presence in "matter"
of imperfections which hinder the course of development, and must be
regarded as "contrary to the normal course of Nature. " So hybrid
reproduction is exceptional and "against Nature," and this is shown by
the sterility of hybrids, a sort of lesser monstrosity. Even females,
being "arrested developments," are a sort of still minor deviation from
principle. (2) It may just be mentioned that Aristotle has a
classification of efficient causes under the three heads of Nature,
Intelligence (or Man), and Chance. The difference between Nature and
Man or Intelligence as efficient causes has already been illustrated.
It is that in causation by Nature, such as sexual reproduction, or the
assimilation of nutriment, or the conversion of one element into another
in which Aristotle believed, the form which is superinduced on the
matter by the agent already exists in the agent itself as _its_ form.
The oak springs from a parent oak, the conversion of nutriment into
organic tissue is due to the agency of already existing organic tissue.
In the case of human intelligence or art, the "form" to be superinduced
exists in the agent not as _his_ characteristic form, but by way of
representation, as a contemplated design. The man who builds a house is
not himself a house; the form characteristic of a house is very
different from that characteristic of a man, but it is present in
contemplation to the builder before it is embodied in the actual house.
A word may be added about the third sort of efficient causality,
causation by chance. This is confined to cases which are exceptions
from the general course of Nature, remarkable coincidences. It is what
we may call "simulated purposiveness. " When something in human affairs
happens in a way which subserves the achievement of a result but was not
really brought about by any intention to secure the result, we speak of
it as a remarkable coincidence. Thus it would be a coincidence if a man
should be held to ransom by brigands and his best friend should, without
knowing anything of the matter, turn up on the spot with the means of
ransoming him. The events could not have happened more opportunely if
they had been planned, and yet they were not planned but merely fell out
so: and since such a combination of circumstances simulating design is
unusual, it is not proper to say that the events happened "in the course
of Nature. " We therefore say it happened by chance. This doctrine of
chance has its significance for mediaeval Ethics. In an age when the
Protestant superstition that worldly success is proof of nearness to God
had not yet been invented, the want of correspondence between men's
"deserts" and their prosperity was accounted for by the view that the
distribution of worldly goods is, as a rule, the work of Fortune or
Chance in the Aristotelian sense; that is, it is due to special
coincidences which may look like deliberate design but are not really
so. (See the elaborate exposition of this in Dante, _Inferno_, vii.
67-97. )

*Motion*. --We have seen that causation, natural or artificial, requires
the production in a certain "matter" of a certain "form" under the
influence of a certain "agent. " What is the character of the process
set up by the agent in the matter and culminating in the appearance of
the form? Aristotle answers that it is Motion (_kinesis_). The effect
of the agent on the matter is to set up in it a motion which ends in its
assuming a definite form. The important point to be noted here is that
Aristotle regards this motion as falling wholly within the matter which
is to assume the form. It is not necessary that the agent should itself
be in motion, but only that it should induce motion in something else.
Thus in all cases of intentional action the ultimate efficient cause is
the "idea of the result to be attained," but this idea does not move
about. By its presence to the mind it sets something else (the members
of the body) moving. This conception of an efficient cause which, not
moving itself, by its mere presence induces movement in that to which it
is present, is of the highest importance in Aristotle's theology. Of
course it follows that since the motion by which the transition from
potentiality to actuality is achieved falls wholly within the matter
acted upon, Aristotle is not troubled with any of the questions as to
the way in which motion can be transferred from one body to another
which were so much agitated in the early days of the modern mechanical
interpretation of natural processes. Aristotle's way of conceiving
Nature is thoroughly non-mechanical, and approximates to what would now
be called the ascription of vital or quasi-vital characteristics to the
inorganic. As, in the causality of "art" the mere presence of the
"form" to be embodied in a given material to the mind of the craftsman
brings about and directs the process of manufacture, so in some
analogous fashion the presence of an efficient cause in Nature to that
on which it works is thought of as itself constituting the "efficiency"
of the cause. As Lotze phrases it, things "take note of" one another's
compresence in the universe, or we might say the efficient cause and
that on which it exercises its efficiency are _en rapport_. "Matter" is
sensitive to the presence of the "efficient cause," and in response to
this sensitivity, puts forth successive determinations, expands its
latent tendencies on definite lines.

The name "motion" has a wider sense for Aristotle than it has for
ourselves. He includes under the one common name all the processes by
which things come to be what they are or cease to be what they have
been. Thus he distinguishes the following varieties of "motion":
_generation_ (the coming of an individual thing into being), with its
opposite _decay_ or _corruption_ (the passing of a thing out of being),
_alteration_ (change of _quality_ in a thing), _augmentation_ and
_diminution_ (change in the _magnitude_ of a thing), _motion through
space_ (of which latter he recognises two sub-species, rectilinear
_transference_ and _rotation_ in a circular orbit about an axis). It is
this last variety, motion through space, which is the most fundamental
of all, since its occurrence is involved in that of any of the other
types of process mentioned, though Aristotle does not hold the
thorough-going mechanical view that the other processes are only
apparent, and that, as we should put it, qualitative change is a mere
disguise which mechanical motion wears for our senses.

*The Eternity of Motion*. --Certain very important consequences follow
from the conception of efficient causation which we have been
describing. Aristotle has no sympathy with the "evolutionist" views
which had been favoured by some of his predecessors. According to his
theory of organic generation, "it takes a man to beget a man "; where
there is a baby, there must have been a father. Biological kinds
representing real clefts in Nature, the process of the production of a
young generation by an already adult generation must be thought of as
without beginning and without end. There can be no natural "evolution"
of animals of one species from individuals of a different kind. Nor
does it occur to Aristotle to take into account the possibility of
"Creationism," the sudden coming into being of a fully fledged first
generation at a stroke. This possibility is excluded by the doctrine
that the "matter" of a thing must exist beforehand as an indispensable
condition of the production of that thing. Every baby, as we said, must
have had a father, but that father must also have been a baby before he
was a full-grown man. Hence the perpetuation of unchanging species must
be without beginning and without end. And it is implied that all the
various processes, within and without the organism, apart from which its
life could not be kept up, must be equally without beginning and without
end. The "cosmos," or orderly world of natural processes, is strictly
"eternal"; "motion" is everlasting and continuous, or unbroken. Even
the great Christian theologians who built upon Aristotle could not
absolutely break with him on this point. St. Thomas, though obliged to
admit that the world was actually created a few thousand years before
his own time, maintains that this can only be known to be true from
revelation, philosophically it is equably tenable that the world should
have been "created from all eternity. " And it is the general doctrine
of scholasticism that the expression "creation" only denotes the
absolute dependence of the world on God for its being. When we say "God
created the world out of nothing," we mean that He did not make it out
of pre-existing matter, that it depends for its being on Him only; the
expression is purely negative in its import.

*God*. --With the doctrine of the eternity of the world and the processes
which make up its life we come close to the culminating theory of
Aristotelian First Philosophy, its doctrine of God, as the eternal,
unchanging source of all change, movement, and process. All motion is a
process within matter by which the forms latent in it are brought into
actual manifestation. And the process only takes place in the presence
of an adequate efficient cause or source of motion. Hence the eternity
of natural processes involves the existence of one or more eternal
sources of motion. For, if we do not admit the existence of an
unoriginated and ever-present source or sources of motion, our only
alternative is to hold that the world-process is due to a series of
sources of motion existing successively. But such a view would leave the
unity and unbroken continuity of the world-process unaccounted for. It
would give us a succession of processes, temporally contiguous, not one
unbroken process. Hence we argue from the continuity of motion to its
dependence on a source or sources which are permanent and present
throughout the whole everlasting world-process. And when we come to the
question whether there is only one such ultimate source of movement for
the whole universe, or several, Aristotle's answer is that the supreme
"Unmoved Mover" is one. One is enough for the purpose, and the law of
parcimony forbids us to assume the superfluous. This then is the
Aristotelian conception of God and God's relation to the world. God is
the one supreme unchanging being to whose presence the world responds
with the whole process of cosmic development, the ultimate educer of the
series of "forms" latent in the "matter" of the world into actual
manifestation. Standing, as He does, outside the whole process which by
His mere presence He initiates in Nature, He is not himself a composite
of "form" and "matter," as the products of development are. He is a pure
individual "form" or "actuality," with no history of gradual development
behind it. Thus He is a purely immaterial being, indispensable to the
world's existence but transcending it and standing outside it. _How_
His presence inspires the world to move Aristotle tries to explain by
the metaphor of appetition. Just as the good I desire and conceive,
without itself "moving" "moves" my appetition, so God moves the universe
by being its good. This directly brings about a uniform unbroken
rotation of the whole universe round its axis (in fact, the alternation
of day and night). And since this rotation is communicated from the
outermost "sphere" of heaven to all the lesser "spheres" between it and
the immovable centre, the effects of God's presence are felt
universally. At the same time, we must note that though God is the
supreme Mover of the Universe, He is not regarded by Aristotle as its
Creator, even in the sense in which creation can be reconciled with the
eternity of the world. For the effect of God's presence is simply to
lead to the development of "form" in an already existing "matter. "
Without God there could be no "form" or order in things, not even as
much as is implied in the differentiation of matter into the four
"elements," yet "primary matter" is no less than God a precondition of
all that happens.

It is characteristic of Aristotle that his God is as far from
discharging the functions of a Providence as He is from being a Creator.
His "activity" is not, as Plato had made it, that of the great "Shepherd
of the sheep. " As far as the world is concerned, God's only function is
to be there to move its appetition. For the rest, the unbroken activity
of this life is directed wholly inward. Aristotle expressly calls it an
"activity of immobility. " More precisely, he tells us, it is activity
of thought, exercised unbrokenly and everlastingly upon the only object
adequate to exercise God's contemplation, Himself. His life is one of
everlasting _self_-contemplation or "thinking of thought itself. " Like
all unimpeded exercise of activity, it is attended by pleasure, and as
the activity is continuous, so the pleasure of it is continuous too. At
our best, when we give ourselves up to the pure contemplative activity
of scientific thought or aesthetic appreciation, we enter for a while
into this divine life and share the happiness of God. But that is a
theme for our chapter on the _Ethics_.

It is a far cry from this conception of a God untroubled by care for a
world to which He is only related as the object of its aspiration to the
God who cares even for the fall of the sparrow and of whom it is
written, _Sic Deus dilexit mundum_, but it was the standing task of the
philosophical theologians of the Middle Ages to fuse the two
conceptions. Plato's God, who, if not quite the Creator, is the "Father
and Fashioner" of us all, and keeps providential watch over the world He
has fashioned, would have lent Himself better to their purposes, but
Plato was held by the mediaeval church to have denied the resurrection of
the body. The combination of Aristotle's Theism with the Theism of
early Christianity was effected by exquisitely subtle logical devices,
but even in St. Thomas one cannot help seeing the seams.

Nor can one help seeing in Aristotle's own doctrine the usual want of
coherence between an initial anti-Platonic bias and a final reversion to
the very Platonic positions Aristotle is fond of impugning. We are told
at the outset that the Platonic "separate forms" are empty names, and
that the real individual thing is always a composite of matter and a
form which only exists "in matter. " We find in the end that the source
of the whole process by which "matter" becomes imbued with "form" is a
being which is "pure" form and stands outside the whole development
which its presence sets up. And the issue of Aristotle's warning against
"poetic metaphors" is the doctrine that God moves the world by being
"the object of the world's desire. "




*CHAPTER IV*

*PHYSICS*


There is no part of Aristotle's system which has been more carefully
thought out than his Physics; at the same time it is almost wholly on
account of his physical doctrines that his long ascendancy over thought
is so much to be regretted. Aristotle's qualifications as a man of
science have been much overrated. In one department, that of descriptive
natural history, he shows himself a master of minute and careful
observation who could obtain unqualified praise from so great a
naturalist as Darwin. But in Astronomy and Physics proper his
inferiority in mathematical thinking and his dislike for mechanical ways
of explaining facts put him at a great disadvantage, as compared with
Plato and Plato's Pythagorean friends. Thus his authority was for
centuries one of the chief influences which prevented the development of
Astronomy on right lines. Plato had himself both taught the mobility of
the earth and denied correctly that the earth is at the centre of the
universe, and the "Copernican" hypothesis in Astronomy probably
originated in the Academy. Aristotle, however, insists on the central
position of the earth, and violently attacks Plato for believing in its
motion. It is equally serious that he insists on treating the so-called
"four elements" as ultimately unanalysable forms of matter, though Plato
had not only observed that so far from being the ABC (_stoicheia_ or
_elementa_, literally, letters of the alphabet) of Nature they do not
deserve to be called even "syllables," but had also definitely put
forward the view that it is the geometrical structure of the
"corpuscles" of body upon which sensible qualities depend. It is on
this doctrine, of course, that all mathematical physics rests.
Aristotle reverts to the older theory that the differences between one
"element" and another are qualitative differences of a sensible kind.
Even in the biological sciences Aristotle shows an unfortunate proneness
to disregard established fact when it conflicts with the theories for
which he has a personal liking. Thus, though the importance of the
brain as the central organ of the sensori-motor system had been
discovered in the late sixth or early fifth century by the physician
Alemacon of Crotona, and taught by the great Hippocrates in the fifth
and by Plato in the fourth century, Aristotle's prejudices in favour of
the doctrines of a different school of biologists led him to revert to
the view that it is the heart which is the centre of what we now call
the "nervous system. " It is mainly on account of these reactionary
scientific views that he was attacked in the early seventeenth century
by writers like our own Francis Bacon, who found in veneration for
Aristotle one of the chief hindrances to the free development of natural
science. The same complaints had been made long before by critics
belonging to the Platonic Academy. It is a Platonist of the time of
Marcus Aurelius who sums up a vigorous attack on the Aristotelian
astronomy by the remark that Aristotle never understood that the true
task of the physicist is not to prescribe laws to Nature, but to learn
from observation of the facts what the laws followed by Nature are.

In determining the scope of Physics, we have to begin by considering
what is the special characteristic of things produced by Nature as
contrasted with those produced by "art. " The obvious distinction,
intimated by the very etymology of the word "Nature" (_physis_,
connected with _phyesthai_, to grow, to be born, as _natura_ is with
_nasci_), is that "what is by Nature" is born and grows, whereas what is
as a result of artifice is _made_. The "natural" may thus be said to
consist of living bodies and of their constituent parts. Hence
inorganic matter also is included in "Nature," on the ground that living
tissue can be analysed back into compounds of the "elements. " Now
things which are alive and grow are distinguished from things which are
made by "a source of motion and quiescence within themselves"; all of
them exhibit motions, changes of quality, processes of growth and
decline which are initiated from within. Hence Nature may be defined as
the totality of things which have a source of motion internal to
themselves and of the constituent parts of such things. Nature then
comprises all beings capable of spontaneous change. Whatever either does
not change at all, or only changes in consequence of external
influences, is excluded from Nature.

Thus the fundamental fact everywhere present in Nature is "change,"
"process," "motion. " Since motion in the literal sense of change of
position is involved as a condition of every such process, and such
motion requires space through which to move and time to move in, the
doctrine of space and time will also form part of Physics. Hence a
great part of Aristotle's special lectures on Physics is occupied with
discussion of the nature of space and time, and of the continuity which
we must ascribe to them if the "continuous motion" on which the unbroken
life of the universe depends is to be real Aristotle knows nothing of
the modern questions whether space and time are "real" or only
"phenomenal," whether they are "objective" or "subjective. " Just as he
simply assumes that bodies are things that really exist, whether we
happen to perceive them or not, so he assumes that the space and time in
which they move are real features of a world that does not depend for
its existence on our perceiving it.

His treatment of space is singularly _naif_. He conceives it as a sort
of vessel, into which you can pour different liquids. Just as the same
pot may hold first wine and then water, so, if you can say, "there was
water here, but now there is air here," this implies the existence of a
receptacle which once held the water, but now holds the air. Hence a
jug or pot may be called a "place that can be carried about," and space
or place may be called "an immovable vessel. " Hence the "place" of a
thing may be defined as the boundary, or inner surface, of the body
which immediately surrounds the thing. It follows from this that there
can be no empty space. In the last resort, "absolute space" is the
actual surface of the outermost "heaven" which contains everything else
in itself but is not contained in any remoter body. Thus all things
whatever are "in" this "heaven. " But it is not itself "in" anything
else. In accord with the standing Greek identification of determinate
character with limitation, Aristotle holds that this outermost heaven
must be at a limited distance from us. Actual space is thus finite in
the sense that the volume of the universe could be expressed as a finite
number of cubic miles or yards, though, since it must be "continuous,"
it is infinitely divisible. However often you subdivide a length, an
area, or a volume, you will always be dividing it into lesser lengths,
&c. , which can once more be divided. You will never by division come to
"points," _i. e. _ mere positions without magnitude of divisibility.

The treatment of time is more thoughtful. Time is inseparably connected
with movement or change. We only perceive that time has elapsed when we
perceive that change has occurred. But time is not the same as change.