Book
XI
1
That Wisdom is a
science of first principles is evident from the introductory chapters,
in which we have raised objections to the statements of others about the
first principles; but one might ask the question whether Wisdom is to be
conceived as one science or as several. If as one, it may be objected
that one science always deals with contraries, but the first principles
are not contrary. If it is not one, what sort of sciences are those with
which it is to be identified?
Further, is it the business of one science, or of
more than one, to examine the first principles of demonstration? If of
one, why of this rather than of any other? If of more, what sort of
sciences must these be said to be?
Further, does Wisdom investigate all substances or
not? If not all, it is hard to say which; but if, being one, it
investigates
them all, it is doubtful how the same science can embrace several
subject-matters.
Further, does it deal with substances only or also
with their attributes? If in the case of attributes demonstration is
possible, in that of substances it is not. But if the two sciences are
different, what is each of them and which is Wisdom? If we think of it
as demonstrative, the science of the attributes is Wisdom, but if as
dealing with what is primary, the science of substances claims the tide.
But again the science we are looking for must not be
supposed to deal with the causes which have been mentioned in the
Physics. For (A) it does not deal with the final cause (for that is the
nature of the good, and this is found in the field of action and
movement; and it is the first mover-for that is the nature of the
end-but in the case of things unmovable there is nothing that moved them
first), and (B) in general it is hard to say whether perchance the
science we are now looking for deals with perceptible substances or not
with them, but with certain others. If with others, it must deal either
with the Forms or with the objects of mathematics. Now (a) evidently the
Forms do not exist. (But it is hard to say, even if one suppose them to
exist, why in the world the same is not true of the other things of
which there are Forms, as of the objects of mathematics. I mean that
these thinkers place the objects of mathematics between the Forms and
perceptible things, as a kind of third set of things apart both from the
Forms and from the things in this world; but there is not a third man or
horse besides the ideal and the individuals. If on the other hand it is
not as they say, with what sort of things must the mathematician be
supposed to deal? Certainly not with the things in this world; for none
of these is the sort of thing which the mathematical sciences demand.)
Nor (b) does the science which we are now seeking treat of the objects
of mathematics; for none of them can exist separately. But again it does
not deal with perceptible substances; for they are perishable.
In general one might raise the question, to what kind
of science it belongs to discuss the difficulties about the matter of
the objects of mathematics. Neither to physics (because the whole
inquiry of the physicist is about the things that have in themselves a
principle of movement and rest), nor yet to the science which inquires
into demonstration and science; for this is just the subject which it
investigates. It remains then that it is the philosophy which we have
set before ourselves that treats of those subjects.
One might discuss the question whether the science we
are seeking should be said to deal with the principles which are by some
called elements; all men suppose these to be present in composite
things. But it might be thought that the science we seek should treat
rather of universals; for every definition and every science is of
universals and not of infimae species, so that as far as this goes it
would deal with the highest genera. These would turn out to be being and
unity; for these might most of all be supposed to contain all things
that are, and to be most like principles because they are by nature; for
if they perish all other things are destroyed with them; for everything
is and is one. But inasmuch as, if one is to suppose them to be genera,
they must be predicable of their differentiae, and no genus is
predicable of any of its differentiae, in this way it would seem that we
should not make them genera nor principles. Further, if the simpler is
more of a principle than the less simple, and the ultimate members of
the genus are simpler than the genera (for they are indivisible, but the
genera are divided into many and differing species), the species might
seem to be the principles, rather than the genera. But inasmuch as the
species are involved in the destruction of the genera, the genera are
more like principles; for that which involves another in its destruction
is a principle of it. These and others of the kind are the subjects that
involve difficulties.
2
Further, must we
suppose something apart from individual things, or is it these that the
science we are seeking treats of? But these are infinite in number. Yet
the things that are apart from the individuals are genera or species;
but the science we now seek treats of neither of these. The reason why
this is impossible has been stated. Indeed, it is in general hard to say
whether one must assume that there is a separable substance besides the
sensible substances (i.e. the substances in this world), or that these
are the real things and Wisdom is concerned with them. For we seem to
seek another kind of substance, and this is our problem, i.e. to see if
there is something which can exist apart by itself and belongs to no
sensible thing.-Further, if there is another substance apart from and
corresponding to sensible substances, which kinds of sensible substance
must be supposed to have this corresponding to them? Why should one
suppose men or horses to have it, more than either the other animals or
even all lifeless things? On the other hand to set up other and eternal
substances equal in number to the sensible and perishable substances
would seem to fall beyond the bounds of probability.
But if the principle we now seek is not separable from corporeal things,
what has a better claim to the name matter?
This, however, does not exist in actuality, but exists in potency. And
it would seem rather that the form or shape is a more important
principle than this; but the form is perishable, so that there is no
eternal substance at all which can exist apart and independent. But this
is paradoxical; for such a principle and substance seems to exist and is
sought by nearly all the most refined thinkers as something that exists;
for how is there to be order unless there is something eternal and
independent and permanent?
Further, if there is a substance or principle of such
a nature as that which we are now seeking, and if this is one for all
things, and the same for eternal and for perishable things, it is hard
to say why in the world, if there is the same principle, some of the
things that fall under the principle are eternal, and others are not
eternal; this is paradoxical.
But if there is one principle of perishable and another of eternal
things, we shall be in a like difficulty if the principle of perishable
things, as well as that of eternal, is eternal; for why, if the
principle is eternal, are not the things that fall under the principle
also eternal? But if it is perishable another principle is involved to
account for it, and another to account for that, and this will go on to
infinity.
If on the other hand we are to set up what are
thought to be the most unchangeable principles, being and unity,
firstly, if each of these does not indicate a 'this' or substance, how
will they be separable and independent? Yet we expect the eternal and
primary principles to be so. But if each of them does signify a 'this'
or substance, all things that are are substances; for being is
predicated of all things (and unity also of some); but that all things
that are are substance is false. Further, how can they be right who say
that the first principle is unity and this is substance, and generate
number as the first product from unity and from matter, assert that
number is substance? How are we to think of 'two', and each of the other
numbers composed of units, as one? On this point neither do they say
anything nor is it easy to say anything. But if we are to suppose lines
or what comes after these (I mean the primary surfaces) to be
principles, these at least are not separable
substances, but sections and divisions-the former of surfaces, the
latter of bodies (while points are sections and divisions of lines); and
further they are limits of these same things; and all these are in other
things and none is separable. Further, how are we to suppose that there
is a substance of unity and the point? Every substance comes into being
by a gradual process, but a point does not; for the point is a division.
A further difficulty is raised by the fact that all
knowledge is of universals and of the 'such', but substance is not a
universal, but is rather a 'this'-a separable thing, so that if there is
knowledge about the first principles, the question arises, how are we to
suppose the first principle to be substance?
Further, is there anything apart from the concrete
thing (by which I mean the matter and that which is joined with it), or
not? If not, we are met by the objection that all things that are in
matter are perishable. But if there is something, it must be the form or
shape. Now it is hard to determine in which cases this exists apart and
in which it does not; for in some cases the form is evidently not
separable, e.g. in the case of a house.
Further, are the principles the same in kind or in
number? If they are one in number, all things will be the same.
3
Since the science of
the philosopher treats of being qua being universally and not in respect
of a part of it, and 'being' has many senses and is not used in one only,
it follows that if the word is used equivocally and in virtue of nothing
common to its various uses, being does not fall under one science (for
the meanings of an equivocal term do not form one genus); but if the
word is used in virtue of something common, being will fall under one
science. The term seems to be used in the way we have mentioned, like
'medical' and 'healthy'. For each of these also we use in many senses.
Terms are used in this way by virtue of some kind of reference, in the
one case to medical science, in the other to health, in others to
something else, but in each case to one identical concept. For a
discussion and a knife are called medical because the former proceeds
from medical science, and the latter is useful to it. And a thing is
called healthy in a similar way; one thing because it is indicative of
health, another because it is productive of it. And the same is true in
the other cases.
Everything that is, then, is said to 'be' in this same way; each thing
that is is said to 'be' because it is a modification of being qua being
or a permanent or a transient state or a movement of it, or something
else of the sort.
And since everything that is may be referred to something single and
common, each of the contrarieties also may be referred to the first
differences and contrarieties of being, whether the first differences of
being are plurality and unity, or likeness and unlikeness, or some other
differences; let these be taken as already discussed. It makes no
difference whether that which is be referred to being or to unity. For
even if they are not the same but different, at least they are
convertible; for that which is one is also somehow being, and that which
is being is one.
But since every pair of contraries falls to be
examined by one and the same science, and in each pair one term is the
privative of the other though one might regarding some contraries raise
the question, how they can be privately related, viz. those which have
an intermediate, e.g. unjust and just-in all such cases one must
maintain that the privation is not of the whole definition, but of the
infima species. if the just man is 'by virtue of some permanent
disposition obedient to the laws', the unjust man will not in every case
have the whole definition denied of him, but may be merely 'in some
respect deficient in obedience to the laws', and in this respect the
privation will attach to him; and similarly in all other cases.
As the mathematician investigates abstractions (for
before beginning his investigation he strips off all the sensible
qualities, e.g. weight and lightness, hardness and its contrary, and
also heat and cold and the other sensible contrarieties, and leaves only
the quantitative and continuous, sometimes in one, sometimes in two,
sometimes in three dimensions, and the attributes of these quantitative
and continuous, and does not consider them in any other respect, and
examines the relative positions of some and the attributes of these, and
the commensurabilities and incommensurabilities of others, and the
ratios of others; but yet we posit one and the same science of all these
things--geometry) --the same is true with regard to being. For the
attributes of this in so far as it is being, and the contrarieties in it
qua being, it is the business of no other science than philosophy to
investigate; for to physics one would assign the study of things not qua
being, but rather qua sharing in movement; while dialectic and sophistic
deal with the attributes of things that are, but not of things qua
being, and not with being itself in so far as it is being; therefore it
remains that it is the philosopher who studies the things we have named,
in so far as they are being. Since all that is is to 'be' in virtue of
something single and common, though the term has many meanings, and
contraries are in the same case (for they are referred to the first
contrarieties and differences of being), and things of this sort can
fall under one science, the difficulty we stated at the beginning
appears to be solved,-I mean the question how there can be a single
science of things which are many and different in genus.
4
Since even the
mathematician uses the common axioms only in a special application, it
must be the business of first philosophy to examine the principles of
mathematics also. That when equals are taken from equals the remainders
are equal, is common to all quantities, but mathematics studies a part
of its proper matter which it has detached, e.g. lines or angles or
numbers or some other kind of quantity-not, however, qua being but in so
far as each of them is continuous in
one or two or three dimensions; but philosophy does not inquire about
particular subjects in so far as each of them has some attribute or
other, but speculates about being, in so far as each particular thing
is.-Physics is in the same position as mathematics; for physics studies
the attributes and the principles of the things that are, qua moving and
not qua being (whereas the primary science, we have said, deals with
these, only in so far as the underlying subjects are existent, and not
in virtue of any other character); and so both physics and mathematics
must be classed as parts of Wisdom.
5
There is a principle
in things, about which we cannot be deceived, but must always, on the
contrary recognize the truth,-viz. that the same thing cannot at one and
the same time be and not be, or admit any other similar pair of
opposites. About such matters there is no proof in the full sense,
though there is proof ad hominem. For it is not possible to infer this
truth itself from a more certain principle, yet this is necessary if
there is to be completed proof of it in the full sense. But he who wants
to prove to the asserter of opposites that he is wrong must get from him
an admission which shall be identical with the principle that the same
thing cannot be and not be at one and the same time, but shall not seem
to be identical; for
thus alone can his thesis be demonstrated to the man who asserts that
opposite statements can be truly made about the same subject. Those,
then, who are to join in argument with one another must to some extent
understand one another; for if this does not happen how are they to join
in argument with one another? Therefore every word must be
intelligible and indicate something, and not many things but only one;
and if it signifies more than one thing, it must be made plain to which
of these the word is being applied. He, then, who says 'this is and is
not' denies what he affirms, so that what the word signifies, he says it
does not signify; and this is impossible.
Therefore if 'this is' signifies something, one cannot truly assert its
contradictory.
Further, if the word signifies something and this is
asserted truly, this connexion must be necessary; and it is not possible
that that which necessarily is should ever not be; it is not possible
therefore to make the opposed affirmations and negations truly of the
same subject. Further, if the affirmation is no more true than the
negation, he who says 'man' will be no more right than he who says
'not-man'. It would seem also that in saying the man is not a horse one
would be either more or not less right than in saying he is not a man,
so that one will also be right in saying that the same person is a
horse; for it was assumed to be possible to make opposite statements
equally truly. It follows then that the same person is a man and a
horse, or any other animal.
While, then, there is no proof of these things in the
full sense, there is a proof which may suffice against one who will make
these suppositions. And perhaps if one had questioned Heraclitus himself
in this way one might have forced him to confess that opposite
statements can never be true of the same subjects. But, as it is, he
adopted this opinion without understanding what his statement involves.
But in any case if what is said by him is true, not even this itself
will be true-viz. that the same thing can at one and the same time both
be and not be. For as, when the statements are separated, the
affirmation is no more true than the negation, in the same way-the
combined and complex statement being like a single
affirmation-the whole taken as an affirmation will be no more true than
the negation. Further, if it is not possible to affirm anything truly,
this itself will be false-the assertion that there is no true
affirmation. But if a true affirmation exists, this appears to refute
what is said by those who raise such objections and utterly destroy
rational discourse.
6
The saying of
Protagoras is like the views we have mentioned; he said that man is the
measure of all things, meaning simply that that which seems to each man
also assuredly is. If this is so, it follows that the same thing both is
and is not, and is bad and good, and that the contents of all other
opposite statements are true, because often a particular thing appears
beautiful to some and the contrary of beautiful to others, and that
which appears to each man is the measure.
This difficulty may be solved by considering the source of this opinion.
It seems to have arisen in some cases from the doctrine of the natural
philosophers, and in others from the fact that all men have not the same
views about the same things, but a particular thing appears pleasant to
some and the contrary of pleasant to others.
That nothing comes to be out of that which is not,
but everything out of that which is, is a dogma common to nearly all the
natural philosophers. Since, then, white cannot come to be if the
perfectly white and in no respect not-white existed before, that which
becomes white must come from that which is not white; so that it must
come to be out of that which is not (so they argue), unless the same
thing was at the beginning white and not-white.
But it is not hard to solve this difficulty; for we have said in our
works on physics in what sense things that come to be come to be from
that which is not, and in what sense from that which is.
But to attend equally to the opinions and the fancies
of disputing parties is childish; for clearly one of them must be
mistaken. And this is evident from what happens in respect of sensation;
for the same thing never appears sweet to some and the contrary of sweet
to others, unless in the one case the sense-organ which discriminates
the aforesaid flavours has been perverted and injured. And if this is so
the one party must be taken to be the measure, and the other must not.
And say the same of good and bad, and beautiful and ugly, and all other
such qualities. For to maintain the view we are opposing is just like
maintaining that the things that appear to people who put their finger
under their eye and make the object appear two instead of one must be
two (because they appear to be of that number) and again one (for to
those who do not interfere with their eye the one object appears one).
In general, it is absurd to make the fact that the
things of this earth are observed to change and never to remain in the
same state, the basis of our judgement about the truth. For in pursuing
the truth one must start from the things that are always in the same
state and suffer no change. Such are the heavenly bodies; for these do
not appear to be now of one nature and again of another, but are
manifestly always the same and share in no change.
Further, if there is movement, there is also
something moved, and everything is moved out of something and into
something; it follows that that that which is moved must first be in
that out of which it is to be moved, and then not be in it, and move
into the other and come to be in it, and that the contradictory
statements are not true at the same time, as these thinkers assert they
are.
And if the things of this earth continuously flow and
move in respect of quantity-if one were to suppose this, although it is
not true-why should they not endure in respect of quality? For the
assertion of contradictory statements about the same thing seems to have
arisen largely from the belief that the quantity of bodies does not
endure, which, our opponents hold, justifies them in saying that the
same thing both is and is not four cubits long. But essence depends on
quality, and this is of determinate nature, though quantity is of
indeterminate.
Further, when the doctor orders people to take some
particular food, why do they take it? In what respect is 'this is bread'
truer than 'this is not bread'? And so it would make no difference
whether one ate or not. But as a matter of fact they take the food which
is ordered, assuming that they know the truth about it and that it is
bread. Yet they should not, if there were no fixed constant nature in
sensible things, but all natures moved and flowed for ever.
Again, if we are always changing and never remain the
same, what wonder is it if to us, as to the sick, things never appear
the same? (For to them also, because they are not in the same condition
as when they were well, sensible qualities do not appear alike; yet, for
all that, the sensible things themselves need not share in any change,
though they produce different, and not identical, sensations in the
sick. And the same must surely happen to the healthy if the afore-said
change takes place.) But if we do not change but remain the same, there
will be something that endures.
As for those to whom the difficulties mentioned are
suggested by reasoning, it is not easy to solve the difficulties to
their
satisfaction, unless they will posit something and no longer demand a
reason for it; for it is only thus that all reasoning and all proof is
accomplished; if they posit nothing, they destroy discussion and all
reasoning. Therefore with such men there is no reasoning. But as for
those who are perplexed by the traditional difficulties, it is easy to
meet them and to dissipate the causes of their perplexity. This is
evident from what has been said.
It is manifest, therefore, from these arguments that
contradictory statements cannot be truly made about the same subject at
one time, nor can contrary statements, because every contrariety depends
on privation. This is evident if we reduce the definitions of contraries
to their principle.
Similarly, no intermediate between contraries can be
predicated of one and the same subject, of which one of the contraries
is predicated. If the subject is white we shall be wrong in saying it is
neither black nor white, for then it follows that it is and is not
white; for the second of the two terms we have put together is true of
it, and this is the contradictory of white.
We could not be right, then, in accepting the views
either of Heraclitus or of Anaxagoras. If we were, it would follow that
contraries would be predicated of the same subject; for when Anaxagoras
says that in everything there is a part of everything, he says nothing
is sweet any more than it is bitter, and so with any other pair of
contraries, since in everything everything is present not potentially
only, but actually and separately. And similarly all statements cannot
be false nor all true, both because of many other difficulties which
might be adduced as arising from this position, and because if all are
false it will not be true to say even this, and if all are true it will
not be false to say all are false.
7
Every science seeks
certain principles and causes for each of its objects-e.g. medicine and
gymnastics and each of the other sciences, whether productive or
mathematical. For each of these marks off a certain class of things for
itself and busies itself about this as about something existing and
real,-not however qua real; the science that does this is another
distinct from these. Of the sciences mentioned each gets somehow the
'what' in some class of things and tries to prove the other truths, with
more or less precision. Some get the 'what' through perception, others
by hypothesis; so that it is clear from an induction of this sort that
there is no demonstration of the substance or 'what'.
There is a science of nature, and evidently it must
be different both from practical and from productive science. For in the
case of productive science the principle of movement is in the producer
and not in the product, and is either an art or some other faculty. And
similarly in practical science the movement is not in the thing done,
but rather in the doers. But the science of the natural philosopher
deals with the things that have in themselves a principle of movement.
It is clear from these facts, then, that natural science must be neither
practical nor productive, but theoretical (for it must fall into some
one of these classes). And since each of the sciences must somehow know
the 'what' and use this as a principle, we must not fall to observe how
the natural philosopher should define things and how he should state the
definition of the essence-whether as akin to 'snub' or rather to
'concave'. For of these the definition of 'snub' includes the matter of
the thing, but that of 'concave' is independent of the matter; for
snubness is found in a nose, so that we look for its definition without
eliminating the nose, for what is snub is a concave nose. Evidently then
the definition of flesh also and of the eye and of the other parts must
always be stated without eliminating the matter.
Since there is a science of being qua being and
capable of existing apart, we must consider whether this is to be
regarded as the same as physics or rather as different. Physics deals
with the things that have a principle of movement in themselves;
mathematics is theoretical, and is a science that deals with things that
are at rest, but its subjects cannot exist apart. Therefore about that
which can exist apart and is unmovable there is a science different from
both of these, if there is a substance of this nature (I mean separable
and unmovable), as we shall try to prove there is. And if there is such
a kind of thing in the world, here must surely be the divine, and this
must be the first and most dominant principle. Evidently, then, there
are three kinds of theoretical sciences-physics, mathematics, theology.
The class of theoretical sciences is the best, and of these themselves
the last named is best; for it deals with the highest of existing
things, and each science is called better or worse in virtue of its
proper object.
One might raise the question whether the science of
being qua being is to be regarded as universal or not. Each of the
mathematical sciences deals with some one determinate class of things,
but universal mathematics applies alike to all.
Now if natural substances are the first of existing things, physics must
be the first of sciences; but if there is another entity and substance,
separable and unmovable, the knowledge of it must be different and prior
to physics and universal because it is prior.
8
Since 'being' in
general has several senses, of which one is 'being by accident', we must
consider first that which 'is' in this sense. Evidently none of the
traditional sciences busies itself about the accidental. For neither
does architecture consider what will happen to those who are to use the
house (e.g. whether they have a painful life in it or not), nor does
weaving, or shoemaking, or the confectioner's art, do the like; but each
of these sciences considers only what is peculiar to it, i.e. its proper
end. And as for the argument that 'when he who is musical becomes
lettered he'll be both at once, not having been both before; and that
which is, not always having been, must have come to be; therefore he
must have at once become musical and lettered',-this none of the
recognized sciences considers, but only sophistic; for this alone busies
itself
about the accidental, so that Plato is not far wrong when he says that
the sophist spends his time on non-being.
That a science of the accidental is not even possible
will be evident if we try to see what the accidental really is. We say
that everything either is always and of necessity (necessity not in the
sense of violence, but that which we appeal to in demonstrations), or is
for the most part, or is neither for the most part, nor always and of
necessity, but merely as it chances; e.g. there might be cold in the dog days, but this occurs neither always and of necessity, nor for the
most part, though it might happen sometimes. The accidental, then, is
what occurs, but not always nor of necessity, nor for the most part. Now
we have said what the accidental is, and it is obvious why there is no
science of such a thing; for all science is of
that which is always or for the most part, but the accidental is in
neither of these classes.
Evidently there are not causes and principles of the
accidental, of the same kind as there are of the essential; for if there
were, everything would be of necessity. If A is when B is, and B is when
C is, and if C exists not by chance but of necessity, that also of which
C was cause will exist of necessity, down to the last causatum as it is
called (but this was supposed to be accidental). Therefore all things
will be of necessity, and chance and the possibility of a thing's either
occurring or not occurring are removed entirely from the range of
events. And if the cause be supposed not to exist but to be coming to
be, the same results will follow; everything will occur of necessity.
For to-morrow's eclipse will occur if A occurs, and A if B occurs, and B
if C occurs; and in this way if we subtract time from the limited time
between now and to-morrow we shall come sometime to the already existing
condition. Therefore since this exists, everything after this will occur
of necessity, so that all things occur of necessity.
As to that which 'is' in the sense of being true or
of being by accident, the former depends on a combination in thought and
is an affection of thought (which is the reason why it is the
principles, not of that which 'is' in this sense, but of that which is
outside and can exist apart, that are sought); and the latter is not
necessary but indeterminate (I mean the accidental); and of such a thing
the causes are unordered and indefinite.
Adaptation to an end is found in events that happen
by nature or as the result of thought. It is 'luck' when one of these
events happens by accident. For as a thing may exist, so it may be a
cause, either by its own nature or by accident. Luck is an accidental
cause at work in such events adapted to an end as are usually effected
in accordance with purpose. And so luck and thought are concerned with
the same sphere; for purpose cannot exist without thought. The causes
from which lucky results might happen are indeterminate; and so luck is
obscure to human calculation and is a cause by accident, but
in the unqualified sense a cause of nothing. It is good or bad luck when
the result is good or evil; and prosperity or misfortune when the scale
of the results is large.
Since nothing accidental is prior to the essential,
neither are accidental causes prior. If, then, luck or spontaneity is a
cause of the material universe, reason and nature are causes before it.
9
Some things are only
actually, some potentially, some potentially and actually, what they
are, viz. in one case a particular reality, in another, characterized by
a particular quantity, or the like. There is no movement apart from
things; for change is always according to the categories of being, and
there is nothing common to these and in no one category. But each of the
categories belongs to all its subjects in either of two ways (e.g.
'this-ness'-for one kind of it is 'positive form', and the other is
'privation'; and as regards quality one kind is 'white' and the other
'black', and as regards quantity one kind is 'complete' and the other
'incomplete', and as regards spatial movement one is 'upwards' and the
other 'downwards', or one thing is 'light' and another 'heavy'); so that
there are as many kinds of movement and change as of being. There being
a distinction in each class of things between the potential and the
completely real, I call the actuality of the potential as such,
movement. That what we say is true, is plain from the following facts.
When the 'buildable', in so far as it is what we mean by 'buildable',
exists actually, it is being built, and this is the process of building.
Similarly with learning, healing, walking, leaping, ageing, ripening.
Movement takes when the complete reality itself exists, and neither
earlier nor later.
The complete reality, then, of that which exists potentially, when it is
completely real and actual, not qua itself, but qua movable, is
movement. By qua I mean this: bronze is potentially a statue; but yet it
is not the complete reality of bronze qua bronze that is movement. For
it is not the same thing to be bronze and to be a certain potency. If it
were absolutely the same in its definition, the complete reality of
bronze would have been a movement. But it is not the same. (This is
evident in the case of contraries; for to be capable of being well and
to be capable of being ill are not the same-for if they were, being well
and being ill would have been the same-it is that which underlies and is
healthy or diseased, whether it is moisture or blood, that is one and
the same.) And since it is not. the same, as colour and the visible are
not the same, it is the complete reality of the potential, and as
potential, that is movement. That it is this, and that movement takes
place when the complete reality itself exists, and neither earlier nor
later, is evident. For each thing is capable of being sometimes actual,
sometimes not, e.g. the buildable qua buildable; and the actuality of
the buildable qua buildable is building.
For the actuality is either this-the act of building-or the house. But
when the house exists, it is no longer buildable; the buildable is what
is being built. The actuality, then, must be the act of building, and
this is a movement. And the same account applies to all other movements.
That what we have said is right is evident from what
all others say about movement, and from the fact that it is not easy to
define it otherwise. For firstly one cannot put it in any class. This is
evident from what people say. Some call it otherness and inequality and
the unreal; none of these, however, is necessarily moved, and further,
change is not either to these or from these any more than from their
opposites. The reason why people put movement in these classes is that
it is thought to be something indefinite, and the principles in one of
the two 'columns of contraries' are indefinite because they are
privative, for none of them is either a 'this' or a 'such' or in any of
the other categories. And the reason why movement is thought to be
indefinite is that it cannot be classed either with the potency of
things or with their actuality; for neither that which is capable
of being of a certain quantity, nor that which is actually of a certain
quantity, is of necessity moved, and movement is thought to be an
actuality, but incomplete; the reason is that the potential, whose
actuality it is, is incomplete. And therefore it is hard to grasp what
movement is; for it must be classed either under privation or under
potency or under absolute actuality, but evidently none of these is
possible. Therefore what remains is that it must be what we said-both
actuality and the actuality we have described-which is hard to detect
but capable of existing.
And evidently movement is in the movable; for it is
the complete realization of this by that which is capable of causing
movement. And the actuality of that which is capable of causing movement
is no other than that of the movable. For it must be the complete
reality of both. For while a thing is capable of causing movement
because it can do this, it is a mover because it is active; but it is on
the movable that it is capable of acting, so that the actuality of both
is one, just as there is the same interval from one to two as from two
to one, and as the steep ascent and the steep descent are one, but the
being of them is not one; the case of the mover and the moved is
similar.
10
The infinite is either
that which is incapable of being traversed because it is not its nature
to be traversed (this
corresponds to the sense in which the voice is 'invisible'), or that
which admits only of incomplete traverse or scarcely admits of traverse,
or that which, though it naturally admits of traverse, is not traversed
or limited; further, a thing may be infinite in
respect of addition or of subtraction, or both. The infinite cannot be a
separate, independent thing. For if it is neither a spatial
magnitude nor a plurality, but infinity itself is its substance and not
an accident of it, it will be indivisible; for the divisible is
either magnitude or plurality. But if indivisible, it is not infinite,
except as the voice is invisible; but people do not mean this, nor are
we examining this sort of infinite, but the infinite as untraversable.
Further, how can an infinite exist by itself, unless number and
magnitude also exist by themselvess-since infinity is an attribute of
these? Further, if the infinite is an accident of something else, it
cannot be qua infinite an element in things, as the invisible is not an
element in speech, though the voice is invisible. And evidently the
infinite cannot exist actually. For then any part of it that might be
taken would be infinite (for 'to be infinite' and 'the infinite' are the
same, if the infinite is substance and not predicated of a subject).
Therefore it is either indivisible, or if it is partible, it is
divisible into infinites; but the same thing cannot be many infinites
(as a part of air is air, so a part of the infinite would be infinite,
if the infinite is substance and a principle). Therefore it must be
impartible and indivisible. But the actually infinite cannot be
indivisible; for it must be of a certain quantity. Therefore infinity
belongs to its subject incidentally. But if so, then (as we have said)
it cannot be it that is a principle, but that of which it is an
accident-the air or the even number.
This inquiry is universal; but that the infinite is
not among sensible things, is evident from the following argument. If
the
definition of a body is 'that which is bounded by planes', there cannot
be an infinite body either sensible or intelligible; nor a
separate and infinite number, for number or that which has a number is
numerable. Concretely, the truth is evident from the following argument.
The infinite can neither be composite nor simple. For (a) it cannot be a
composite body, since the elements are limited in multitude. For the
contraries must be equal and no one of them must be infinite; for if one
of the two bodies falls at all short of the other in potency, the finite
will be destroyed by the infinite. And that each should be infinite is
impossible. For body is that which has extension in all directions, and
the infinite is the boundlessly extended, so that if the infinite is a
body it will be infinite in every direction. Nor (b) can the infinite
body be one and simple-neither, as some say, something apart from the
elements, from which they generate these (for there is no such body
apart from the elements; for everything can be resolved into that of
which it consists, but no such product of analysis is observed except
the simple bodies), nor fire nor any other of the elements. For apart
from the question how any of them could be infinite, the All, even if it
is finite, cannot either be or become any one of them, as Heraclitus
says all things sometime become fire. The same argument applies to this
as to the One which the natural philosophers posit besides the elements.
For everything changes from contrary to contrary, e.g. from hot to cold.
Further, a sensible body is somewhere, and whole and
part have the same proper place, e.g. the whole earth and part of the
earth. Therefore if (a) the infinite body is homogeneous, it will be
unmovable or it will be always moving. But this is impossible; for why
should it rather rest, or move, down, up, or anywhere, rather than
anywhere else? E.g. if there were a clod which were part of an infinite
body, where will this move or rest? The proper place of the body which
is homogeneous with it is infinite. Will the clod occupy the whole
place, then? And how? (This is impossible.) What then is its rest or its
movement? It will either rest everywhere, and then it cannot move; or it
will move everywhere, and then it cannot be still.
But (b) if the All has unlike parts, the proper places of the parts are
unlike also, and, firstly, the body of the All is not one
except by contact, and, secondly, the parts will be either finite or
infinite in variety of kind. Finite they cannot be; for then those of
one kind will be infinite in quantity and those of another will not (if
the All is infinite), e.g. fire or water would be infinite, but such an
infinite element would be destruction to the contrary elements. But if
the parts are infinite and simple, their places also are infinite and
there will be an infinite number of elements; and if this is impossible,
and the places are finite, the All also must be limited.
In general, there cannot be an infinite body and also
a proper place for bodies, if every sensible body has either weight or
lightness. For it must move either towards the middle or upwards, and
the infinite either the whole or the half of it-cannot do
either; for how will you divide it? Or how will part of the infinite be
down and part up, or part extreme and part middle?
Further, every sensible body is in a place, and there are six kinds of
place, but these cannot exist in an infinite body.
In general, if there cannot be an infinite place, there cannot be an
infinite body; (and there cannot be an infinite place,) for that which
is in a place is somewhere, and this means either up or down or in one
of the other directions, and each of these is a limit.
The infinite is not the same in the sense that it is
a single thing whether exhibited in distance or in movement or in time,
but the posterior among these is called infinite in virtue of its
relation to the prior; i.e. a movement is called infinite in virtue of
the distance covered by the spatial movement or alteration or growth,
and a time is called infinite because of the movement which occupies it.
11
Of things which
change, some change in an accidental sense, like that in which 'the
musical' may be said to walk, and others are said, without
qualification, to change, because something in them changes, i.e. the
things that change in parts; the body becomes healthy, because the eye
does. But there is something which is by its own nature moved directly,
and this is the essentially movable. The same distinction is found in
the case of the mover; for it causes movement either in an accidental
sense or in respect of a part of itself or essentially. There is
something that directly causes movement; and there is something that is
moved, also the time in which it is moved, and that from which and that
into which it is moved.
But the forms and the affections and the place, which are the terminals
of the movement of moving things, are unmovable, e.g. knowledge or heat;
it is not heat that is a movement, but heating. Change which is not
accidental is found not in all things, but between contraries, and their
intermediates, and between contradictories.
We may convince ourselves of this by induction.
That which changes changes either from positive into
positive, or from negative into negative, or from positive into
negative, or from negative into positive. (By positive I mean that which
is expressed by an affirmative term.) Therefore there must be
three changes; that from negative into negative is not change,
because (since the terms are neither contraries nor contradictories)
there is no opposition. The change from the negative into the positive
which is its contradictory is generation-absolute change absolute
generation, and partial change partial generation; and the change from
positive to negative is destruction-absolute change absolute
destruction, and partial change partial destruction. If, then, 'that
which is not' has several senses, and movement can attach neither to
that which implies putting together or separating, nor to that which
implies potency and is opposed to that which is in the full sense (true,
the not-white or not-good can be moved incidentally, for the not-white
might be a man; but that which is not a particular thing at all can in
no wise be moved), that which is not cannot be moved (and if this is so,
generation cannot be movement; for that which is not is generated; for
even if we admit to the full that its generation is accidental, yet it
is true to say that 'not-being' is predicable of that which is generated
absolutely). Similarly rest cannot be longto that which is not. These
consequences, then, turn out to be awkward, and also this, that
everything that is moved is in a place, but that which is not is not in
a place; for then it would be somewhere. Nor is destruction movement;
for the contrary of movement is rest, but the contrary of destruction is
generation. Since every movement is a change, and the kinds of change
are the three named above, and of these those in the way of generation
and destruction are not movements, and these are the changes from a
thing to its contradictory, it follows that only the change from
positive into positive is movement. And the positives are either
contrary or intermediate (for even privation must be regarded as
contrary), and are expressed by an affirmative term, e.g. 'naked' or
'toothless' or 'black'.
12
If the categories are
classified as substance, quality, place, acting or being acted on,
relation, quantity, there must be three kinds of movement-of quality, of
quantity, of place. There is no movement in respect of substance
(because there is nothing contrary to substance), nor of relation (for
it is possible that if one of two things in relation changes, the
relative term which was true of the other thing ceases to be true,
though this other does not change at all,-so that their movement is
accidental), nor of agent and patient, or mover and moved, because there
is no movement of movement nor generation of generation, nor, in
general, change of change. For there might be movement of movement in
two senses; (1) movement might be the subject moved, as a man is moved
because he changes from pale to dark,-so that on this showing movement,
too, may be either heated or cooled or change its place or increase. But
this is impossible; for change is not a subject. Or (2) some other
subject might change from change into some other form of existence (e.g.
a man from disease into health). But this also is not possible except
incidentally. For every movement is change from something into
something.
(And so are generation and destruction; only, these are changes into
things opposed in certain ways while the other, movement, is into things
opposed in another way.) A thing changes, then, at the same time from
health into illness, and from this change itself into another. Clearly,
then, if it has become ill, it will have changed into whatever may be
the other change concerned (though it may be at rest), and, further,
into a determinate change each time; and that new change will be from
something definite into some other definite thing; therefore it will be
the opposite change, that of growing well. We answer that this happens
only incidentally; e.g. there is a change from the process of
recollection to that of forgetting, only because that to which the
process attaches is changing, now into a state of knowledge, now into
one of ignorance.
Further, the process will go on to infinity, if there
is to be change of change and coming to be of coming to be. What is true
of the later, then, must be true of the earlier; e.g. if the simple
coming to be was once coming to be, that which comes to be something was
also once coming to be; therefore that which simply comes to be
something was not yet in existence, but something which was coming to be
coming to be something was already in existence.
And this was once coming to be, so that at that time it was not yet
coming to be something else. Now since of an infinite number of terms
there is not a first, the first in this series will not exist, and
therefore no following term exist. Nothing, then, can either come term
wi to be or move or change. Further, that which is capable of a movement
is also capable of the contrary movement and rest, and that which comes
to be also ceases to be. Therefore that which is coming to be is ceasing
to be when it has come to be coming to be; for it cannot cease to be as
soon as it is coming to be coming to be, nor after it has come to be;
for that which is ceasing to be must be. Further, there must be a matter
underlying that which comes to be and changes. What will this be,
then,-what is it that becomes movement or becoming, as body or soul is
that which suffers alteration? And; again, what is it that they move
into? For it must be the movement or becoming of something from
something into something. How, then, can this condition be fulfilled?
There can be no learning of learning, and therefore no becoming of
becoming. Since there is not movement either of substance or of relation
or of activity and passivity, it remains that movement is in respect of
quality and quantity and place; for each of these admits of contrariety.
By quality I mean not that which is in the substance (for even the
differentia is a quality), but the passive quality, in virtue of which a
thing is said to be acted on or to be incapable of being acted on. The
immobile is either that which is wholly incapable of being moved, or
that which is moved with difficulty in a long time or begins slowly, or
that which is of a nature to be moved and can be moved but is not moved
when and where and as it would naturally be moved.
This alone among immobiles I describe as being at rest; for rest is
contrary to movement, so that it must be a privation in that which is
receptive of movement.
Things which are in one proximate place are together
in place, and things which are in different places are apart: things
whose extremes are together touch: that at which a changing thing, if it
changes continuously according to its nature, naturally arrives before
it arrives at the extreme into which it is changing, is between.
That which is most distant in a straight line is contrary in place. That
is successive which is after the beginning (the order being determined
by position or form or in some other way) and has nothing of the same
class between it and that which it succeeds, e.g. lines in the case of a
line, units in that of a unit, or a house in that of a house. (There is
nothing to prevent a thing of some other class from being between.) For
the successive succeeds something and is something later; 'one' does not
succeed 'two', nor the first day of the month the second. That which,
being successive, touches, is contiguous. (Since all change is between
opposites, and these are either contraries or contradictories, and there
is no middle term for contradictories, clearly that which is between is
between contraries.)
The continuous is a species of the contiguous. I call two things
continuous when the limits of each, with which they touch and by which
they are kept together, become one and the same, so that plainly the
continuous is found in the things out of which a unity naturally arises
in virtue of their contact. And plainly the successive is the first of
these concepts (for the successive does not necessarily touch, but that
which touches is successive; and if a thing is continuous, it touches,
but if it touches, it is not necessarily continuous; and in things in
which there is no touching, there is no organic unity); therefore a
point is not the same as a unit; for contact belongs to points, but not
to units, which have only succession; and there is something between two
of the former, but not between two of the latter.
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