diff --git a/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml b/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml
index 86d0187f7..a003a4e26 100644
--- a/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml
+++ b/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml
@@ -309,7 +309,7 @@
ed="P" unit="Loeb chap"/>Most of the earliest philosophers conceived only of material
principles as underlying all things. That of which all things consist, from which they
first come and into which on their destruction they are ultimately resolved, of which the
- essence persists although modified by its affections—this, they say, is an element
+ essence persists although modified by its affections—this, they say, is an element
and principle of existing things. Hence they believe that nothing is either generated or
destroyed, since this kind of primary entity always persists. Similarly we do not say that
Socrates comes into being absolutely when he becomes handsome or cultured,
@@ -337,7 +337,7 @@
gods, also held this same opinion about the primary entity. For theycf. Hom. Il. 14. 201,
Hom. Il. 14.246. represented Oceanus and
- Tethys to be the parents of creation, and the oath of the gods to be by water—
+ Tethys to be the parents of creation, and the oath of the gods to be by water—
Styx,Cf. Hom. Il.
2.755, Hom. Il. 14.271, Hom. Il.15.37. as they call it. Now what is most
@@ -362,13 +362,13 @@
anchored="yes">Fl. about 500 B.C. of Ephesus hold this of fire; and EmpedoclesOf Acragas; fl. 450
- B.C.—adding earth as a fourth to those already mentioned—takes all
+ B.C.—adding earth as a fourth to those already mentioned—takes all
four. These, he says, always persist, and are only generated in respect of multitude and
paucity, according as they are combined into unity or differentiated out of unity.Cf. Empedocles, Fr. 17 (Diels),
R.P. 166; Burnet, E.G.P. 108-109. Anaxagoras of Clazomenae—prior to
- Empedocles in point of age, but posterior in his activities—says that the first
+ />Anaxagoras of Clazomenae—prior to
+ Empedocles in point of age, but posterior in his activities—says that the first
principles are infinite in number. For he says that as a general rule all things which
are, like fire and water,This is Aristotle's
illustration; apparently Anaxagoras did not regard the "elements" as homoeomerous (i.e.
@@ -448,11 +448,11 @@
things than there are good and beautiful: in view of this another thinker introduced Love
and StrifeEmpedocles Fr. 17,
26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff. as the respective
- causes of these things— because if one
+ causes of these things— because if one
follows up and appreciates the statements of Empedocles with a view to his real meaning
and not to his obscure language, it will be found that Love is the cause of good, and
Strife of evil. Thus it would perhaps be correct to say that Empedocles in a sense spoke
- of evil and good as first principles, and was the first to do so—that is, if the
+ of evil and good as first principles, and was the first to do so—that is, if the
cause of all good things is absolute good. These thinkers then, as I say, down to the time of
Empedocles, seem to have grasped two of the causes which we have defined in the
@@ -478,9 +478,9 @@
his predecessors in that he first introduced the division of this cause, making the source
of motion not one but two contrary forces. Further, he was the first to maintain that the so-called material elements are
- four—not that he uses them as four, but as two only, treating fire on the one hand
- by itself, and the elements opposed to it—earth, air and water—on the other,
+ by itself, and the elements opposed to it—earth, air and water—on the other,
as a single nature.Cf. 3.14. This can be
seen from a study of his writings.e.g. Empedocles, Fr. 62 (Diels). however, and his disciple DemocritusOf Abdera;
fl. circa 420 B.C. E.G.P loc. cit. hold that the
- elements are the Full and the Void—calling the one "what is" and the other "what is
+ elements are the Full and the Void—calling the one "what is" and the other "what is
not." Of these they identify the full or solid with "what is," and the void or rare with
"what is not" (hence they hold that what is not is no less real than what is,For the probable connection between the Atomists and
@@ -524,13 +524,13 @@
principles, and they fancied that they could detect in numbers, to a greater extent than
in fire and earth and water, many analoguesCf.
Aristot. Met. 14.6ff.. of what is and
- comes into being—such and such a property of number being justice
+ comes into being—such and such a property of number being justice
,Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only
with properties of number but with numbers themselves. Thus justice
(properly=squareness)=4, the first square number; soul or mind=1, opportunity=7
(Alexander). and such and such soul or mind , another
- opportunity , and similarly, more or less, with all the rest—and
+ opportunity , and similarly, more or less, with all the rest—and
since they saw further that the properties and ratios of the musical scales are based on
numbers,Pythagoras himself is credited with
having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4
@@ -649,7 +649,7 @@
anchored="yes">The Pythagoreans; so called because Pythagoras founded his society at
Croton. philosophers the other
thinkers have expressed themselves vaguely on the subject, except that, as we have said,
- they actually employ two causes, and one of these—the source of motion —some
+ they actually employ two causes, and one of these—the source of motion —some
regard as one and others as two. The Pythagoreans, while they likewise spoke of two
principles, made this further addition, which is peculiar to them: they believed, not that
the Limited and the Unlimited are separate entities, like fire or water or some other such
@@ -659,10 +659,10 @@
nature of their pronouncements on this subject. They also began to discuss and define the
"what" of things; but their procedure was far too simple. They defined superficially, and
supposed that the essence of a thing is that to which the term under consideration first
- applies—e.g. as if it were to be thought that "double" and "2" are the same, because
+ applies—e.g. as if it were to be thought that "double" and "2" are the same, because
2 is the first number which is double another. But presumably "to be double a number" is not the same as "to be the number 2."
- Otherwise, one thing will be many—a consequence which actually followed in their
+ Otherwise, one thing will be many—a consequence which actually followed in their
system.i.e., the same number might be the first
to which each of several definitions applied; then that number would be each of the
concepts so defined. This much, then, can be learned from other and earlier
@@ -674,9 +674,9 @@
Italians. In his youth Plato first became
acquainted with CratylusCf. Aristot. Met. 4.5.18. and the Heraclitean
- doctrines—that the whole sensible world is always in a state of flux,Plat. Crat. 402a (fr.
- 41 Bywater). and that there is no scientific knowledge of it—and
+ 41 Bywater). and that there is no scientific knowledge of it—and
in after years he still held these opinions. And when Socrates, disregarding the physical
universe and confining his study to moral questions, sought in this sphere for the
@@ -697,7 +697,7 @@
things which bear the same name as the Forms exist by participation in them. (With regard
to the "participation," it was only the term that he changed; for whereas the Pythagoreans
say that things exist by imitation of numbers, Plato says that they exist by
- participation—merely a change of term. As
+ participation—merely a change of term. As
to what this "participation" or "imitation" may be, they left this an open
question.) Further, he states that besides sensible things
and the Forms there exists an intermediate class, the objects of
@@ -739,7 +739,7 @@
points out (note ad loc.), we may keep prw/twn in the
sense of "prime" if we suppose Aristotle to be referring either (a) to the numbers
within the decad (Aristot. Met. 13.8.17) and
- forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and
+ forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and
forgetting the entire class of compound odd numbers. Neither of these alternatives is
very satisfactory, but it seems better to keep the traditional text. can be
readily generated from it, as from a matrix.For a
@@ -767,7 +767,7 @@
the Forms are the cause of the essence in everything else, and the One is the cause of it
in the Forms. He also tells us what the
material substrate is of which the Forms are predicated in the case of sensible things,
- and the One in that of the Forms—that it is this the duality, the "Great and Small."
+ and the One in that of the Forms—that it is this the duality, the "Great and Small."
Further, he assigned to these two elements respectively the causation of goodCf. Plat. Phil.
25e-26b. and of evil; a problem which, as we have said,(for some have so described the primary element).
These, then, apprehended this cause only, but others apprehended the source of
- motion—e.g. all such as make Love and Strife, or Mind, or Desire a first
+ motion—e.g. all such as make Love and Strife, or Mind, or Desire a first
principle. As for the essence or
essential nature, nobody has definitely introduced it; but the inventors of the Forms
@@ -832,7 +832,7 @@
generation and destruction, and investigate the nature of everything; and at the same time
do away with the cause of motion. Then there is
their failure to regard the essence or formula as a cause of anything; and
- further their readiness to call any one of the simple bodies—except earth—a
+ further their readiness to call any one of the simple bodies—except earth—a
first principle, without inquiring how their reciprocal generation is effected. I refer to
fire, water, earth and air. Of these some are generated from each other by combination and
others by differentiation; and this difference
@@ -843,15 +843,15 @@
particles. Hence all who posit Fire as first
principle will be in the closest agreement with this theory. However, even among the other
thinkers everyone agrees that the primary corporeal element is of this kind. At any rate
- none of the Monists thought earth likely to be an element—obviously on account of
- the size of its particles— but each of
+ none of the Monists thought earth likely to be an element—obviously on account of
+ the size of its particles— but each of
the other three has had an advocate; for some name fire as the primary element, others
water, and others air.Cf. Aristot. Met. 3.5, 8. And yet why do they not
suggest earth too, as common opinion does? for people say "Everything is earth." And Hesiod too saysCf. Aristot. Met. 4.1. that
- earth was generated first of corporeal things—so ancient and popular is the
+ earth was generated first of corporeal things—so ancient and popular is the
conception found to be. Thus according to this theory anyone who suggests any of these
bodies other than fire, or who assumes something "denser than air but rarer than
water,"Cf. If one were to infer that
Anaxagoras recognized twoMind, and the "mixture" of
homoeomerous particles. elements, the inference would accord closely with a view
@@ -889,7 +889,7 @@
be separated). At the same time, if one were to follow his doctrine carefully and
interpret its meaning, perhaps it would be seen to be more up-to-date; because when nothing was yet differentiated, obviously nothing
- could be truly predicated of that substance—e.g. that it was white or black or buff
+ could be truly predicated of that substance—e.g. that it was white or black or buff
or any other color. It must necessarily have been colorless, since otherwise it would have
had one of these colors. Similarly by the same
argument it had no taste or any other such attribute; for it cannot have had any quality
@@ -920,7 +920,7 @@
and
observe what happens in respect of its parts and affections and activities, and they use
up their principles and causes in this connection, as though they agreed with the
- others—the physicists—that reality is just so much as is sensible and is
+ others—the physicists—that reality is just so much as is sensible and is
contained in the so-called "heavens." All the
same, as we have said,Aristot. Met. 1.8.17. the causes and principles
@@ -950,7 +950,7 @@
and a little above or below them Injustice and Separation or Mixture, and when they state
as proof of this that each of these abstractions is a number; and that also in this region
there is already a plurality of the magnitudes composed of number, inasmuch as these
- modifications of number correspond to these several regions,—is the number which we
+ modifications of number correspond to these several regions,—is the number which we
must understand each of these abstractions to be the same number which is present in the
sensible universe, or another kind of number?The
point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2,
@@ -971,7 +971,7 @@
n="Aristot. Met. 1.990a">Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5. in the first place in
their attempt to find the causes of things in our sensible world, they introduced an equal
- number of other entities—as though a man who wishes to count things should suppose
+ number of other entities—as though a man who wishes to count things should suppose
that it would be impossible when they are few, and should attempt to count them when he
has added to them. For the Forms are as many as, or not fewer than, the things in search
of whose causes these thinkers were led to the Forms; because corresponding to each thing
@@ -1139,7 +1139,7 @@
number <of units>, taken together, be one thing? And further, in addition to the
above objections, if the units are unlike, they should be treated as the thinkers who
assume two or four elements treat those elements; for not one of them applies the term
- "element" to the common substrate, e.g. body, but to fire and earth—whether there is
+ "element" to the common substrate, e.g. body, but to fire and earth—whether there is
a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that
there is not. As it is, the One is
@@ -1182,13 +1182,13 @@
n="Aristot. Met. 1.981a">Aristot. Met. 1.9. and in the belief that we
are accounting for their substance we assert the existence of other substances; but as to
how the latter are the substances of the former, our explanation is
- worthless—for "participation," as we have said before,Aristot. Met. 1.12. means
nothing. And as for that which we can see to
- be the cause in the sciences, and through which all mind and all nature works—this
+ be the cause in the sciences, and through which all mind and all nature works—this
causeThe final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one
- of the first principles—the Forms have not the slightest bearing upon it either.
+ of the first principles—the Forms have not the slightest bearing upon it either.
Philosophy has become mathematics for modern thinkers,e.g. Speusippus, for whom see Aristot.
Met. 7.2.4. although they profess it does not
follow, even if you grant them all their assumptions that everything is One, but only that
- there is an absolute One— and not even
+ there is an absolute One— and not even
this, unless you grant that the universal is a class; which is impossible in some
cases.Probably those of relative or negative
terms. Cf. Aristot. Met. 1.3. Nor is there
@@ -1237,7 +1237,7 @@
embraces everythinge.g. Plato's
Dialectic.(as some say), the student of it can have no previous
knowledge at all. But all learning proceeds, wholly or in part, from what is already
- known; whether it is through demonstration or through definition—since the parts of
+ known; whether it is through demonstration or through definition—since the parts of
the definition must be already known and familiar. The same is true of induction.
On the other hand, assuming that this knowledge should
@@ -1248,7 +1248,7 @@
how is one to know of what elements things consist? how is it to be
established? Even this presents a
difficulty, because the facts might be disputed, as happens in the case of certain
- syllables—for some say that ZA is composed of S, D and A, while others say that it
+ syllables—for some say that ZA is composed of S, D and A, while others say that it
is a distinct sound and not any one of those which are familiar to us.stoixei=on means both
"an element" and "a letter of the alphabet"; hence letters are often used as analogues
@@ -1277,8 +1277,8 @@
cause, but did not apply it generally. which is the definition or essence of a
thing. But by similar reasoning both flesh
and every other thing, or else nothing at all,
- must be ratio; for it must be because of this, and not because of their matter—which
- he calls fire, earth, water and air—that flesh and bone and every other thing
+ must be ratio; for it must be because of this, and not because of their matter—which
+ he calls fire, earth, water and air—that flesh and bone and every other thing
exists. If anyone else had stated this, he
would necessarily have agreed, but his own statement was not clear. These and similar points have been explained already. We will now return to
@@ -1307,7 +1307,7 @@
rather superficial opinions. They too have contributed something; by their preliminary
work they have formed our mental experience. If
there had been no Timotheus,Of Miletus, 446 (?)—357
+ key="perseus,Miletus">Miletus, 446 (?)—357
B.C. we should not possess much of our music; and if there had been no
Phrynis,Of Mytilene; he is referred to as still alive in Therefore in
every case the first principles of things must necessarily be true above everything
- else—since they are not merely sometimes true, nor is anything the
+ else—since they are not merely sometimes true, nor is anything the
cause of their existence, but they are the cause of the existence of other
- things,—and so as each thing is in respect of existence, so it is in respect of
+ things,—and so as each thing is in respect of existence, so it is in respect of
truth. Moreover,
it is obvious that there is some first principle, and that the causes of things are not
@@ -1339,7 +1339,7 @@
be moved by air, air by the sun, the sun by Strife,Aristotle is evidently thinking of Empedocles' system. with no limit to the
series). In the same way neither can the
- Final Cause recede to infinity—walking having health for its object, and health
+ Final Cause recede to infinity—walking having health for its object, and health
happiness, and happiness something else: one thing always being done for the sake of
another. And it is just the same with the
Formal Cause. For in the case of all intermediate terms of a series which are contained
@@ -1356,13 +1356,13 @@
downwards (where there is a beginning in the
upper direction) such that from fire comes water, and from water earth, and in this way
some other kind of thing is always being produced. There are two senses in which one thing
- "comes from" another—apart from that in which one thing is said to come
+ "comes from" another—apart from that in which one thing is said to come
after another, e.g. the Olympian "from"e)k means not only "from" but "after";
Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same
year as the Olympian festival; when this happened the former was held in the spring and
the latter in the summer. Cf. Aristot. Met.
- 5.24.5. the Isthmian games—either as a man comes from a child as
+ 5.24.5. the Isthmian games—either as a man comes from a child as
it develops, or as air comes from water. Now we
say that a man "comes from" a child in the sense that that which has become
something comes from that which is becoming: i.e. the perfect from the
@@ -1477,7 +1477,7 @@
discussed Aristot. Met. 3.2.1-10, and answered
Aristot. Met. 4.1.(2.) Has that science
only to contemplate the first principles of substance, or is it also concerned with the
- principles which all use for demonstration—e.g. whether it is possible at the same
+ principles which all use for demonstration—e.g. whether it is possible at the same
time to assert and deny one and the same thing, and other similar principles?Discussed Aristot. Met.
3.2.10-15; answered Aristot. Met.
@@ -1510,7 +1510,7 @@
(vi.) whether the first principles and elements of things are the genera under which they
fall or the pre-existent parts into which each thing is divided; and if the genera,
whether they are those which are predicated ultimately of individuals, or the primary
- genera—e.g., whether "animal" or "man" is the first principle and the more
+ genera—e.g., whether "animal" or "man" is the first principle and the more
independent of the individual.DiscussedAristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13 Discussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.—both those in the
- definitions and those in the substrate—and (ix.) whether the principles of
+ n="Aristot. Met. 13.1086b">Aristot. Met. 13.10.—both those in the
+ definitions and those in the substrate—and (ix.) whether the principles of
perishable and of imperishable things are the same or different; and whether all are
imperishable, or those of perishable things are perishable.Discussed Aristot. Met. 3.4.11-23;
@@ -1658,7 +1658,7 @@
there is not one, with what sort of substance must we assume that this science is
concerned? On the other hand, it is not
probable that there is one science of all substances; for then there would be one
- demonstrative of all attributes—assuming that every demonstrative science proceeds from accepted beliefs and studies the essential
attributes concerned with some definite subject matter. Thus to study the essential attributes connected with the same genus
@@ -1853,7 +1853,7 @@
n="999b" unit="section"/>If nothing exists apart from individual things, nothing will be
intelligible; everything will be sensible, and there will be no knowledge of
- anything—unless it be maintained that sense-perception is knowledge. Nor again will
+ anything—unless it be maintained that sense-perception is knowledge. Nor again will
anything be eternal or immovable, since sensible things are all perishable and in
motion. Again, if nothing is eternal, even
generation is impossible; for there must be something which becomes something, i.e. out of
@@ -1889,7 +1889,7 @@
they are numerically one, and each of the principles is one, and not, as in the case of
sensible things, different in different instances (e.g. since a given syllable is always
the same in kind, its first principles are always the same in kind, but only in kind,
- since they are essentially different in number)—if the first principles are one, not
+ since they are essentially different in number)—if the first principles are one, not
in this sense, but numerically, there will be nothing else apart from the elements; for
"numerically one" and "individual" are identical in meaning. This is what we mean by
"individual": the numerically one; but by "universal" we mean what is predicable of
@@ -1897,7 +1897,7 @@
/>Hence just as, if the elements of
languageOr "letters of the alphabet." Cf. Aristot. Met. 1.9.36n. were limited in number,
- the whole of literature would be no more than those elements—that is, if there were
+ the whole of literature would be no more than those elements—that is, if there were
not two nor more than two of the same <so it would be in the case of existing things
and their principles>.For the answer to the
problem see Aristot. Met. 12.4-5, The school of Hesiod, and all the cosmologists, considered only what was convincing to
themselves, and gave no consideration to us. For they make the first principles Gods or
generated from Gods, and say that whatever did not taste of the nectar and ambrosia became
- mortal—clearly using these terms in a sense significant to themselves; but as regards the actual applications of these causes
their statements are beyond our comprehension. For if it is for pleasure that the Gods
partake of them, the nectar and ambrosia are in no sense causes of their existence; but if
@@ -1945,8 +1945,8 @@
earth perceive, by water water, By air bright air, by fire
consuming fire, Love too by love, and strife by grievous
strife.Empedocles, Fr.
- 109. But—and this is the point from
- which we started—thus much is clear: that it follows on his theory that Strife is no
+ 109. But—and this is the point from
+ which we started—thus much is clear: that it follows on his theory that Strife is no
more the cause of destruction than it is of Being. Nor, similarly, is Love the cause of
Being; for in combining things into one it destroys everything else.Cf. Aristot. Met.
@@ -1992,7 +1992,7 @@
Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this
is their nature, their essence being simply Being and Unity. But the physicists, e.g. Empedocles, explain what Unity is by reducing
- it to something, as it were, more intelligible—or it would seem that by Love
+ it to something, as it were, more intelligible—or it would seem that by Love
Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others
identify fire and others air with this Unity and Being of which things consist and from
which they have been generated. Those who
@@ -2034,7 +2034,7 @@
indivisible in such a way that it can be defended even against his argument (for such a
thinge.g., a point is indivisible and has no
magnitude, yet added to other points it increases their number. when added will
- increase a thing in number though not in size)—still how can a
+ increase a thing in number though not in size)—still how can a
magnitude be composed of one or more such indivisible things? It is like
saying that the line is composed of points. Moreover, even if one supposes the case to be As for those things
- which might be especially supposed to indicate substance—water, earth, fire and air,
- of which composite bodies are composed— their heat and cold and the like are
modifications, not substances; and it is only the body which undergoes these modifications
that persists as something real and a kind of substance. or sound,
- for the principles of these are determinate in number too— and similarly with the Intermediates, for in their case too there is
an infinity of objects similar in form), then if there is not another set of objects apart
from sensible and mathematical objects, such as the Forms are said to be, there will be no
@@ -2148,7 +2148,7 @@
term denotes an individual thing, but a type; and substance is an individual
thing. But if the common predicate be
hypostatized as an individual thing, Socrates will be several beings: himself, and Man,
- and Animal—that is, if each predicate denotes one particular thing. These then are the consequences if the principles are
universal. If on the other hand they are not universal but like particulars, they will not
be knowable; for the knowledge of everything is universal. Hence there will have to be
@@ -2177,8 +2177,8 @@
producing it or as indicating it or as receptive of it), and as "medical" relates to the art of medicine (either as possessing
- it or as naturally adapted for it or as being a function of medicine)—and we shall
- find other terms used similarly to these— so "being " is used in various senses, but always with reference to one principle. For
some things are said to "be" because they are substances; others because they are
modifications of substance; others because they are a process towards substance, or
@@ -2211,9 +2211,9 @@
these phrases has the same significance, and Unity is nothing distinct from
Being; and further if the substance of each
thing is one in no accidental sense, and similarly is of its very nature something which
- is—then there are just as many species of Being as of Unity. And to study the
+ is—then there are just as many species of Being as of Unity. And to study the
essence of these species (I mean, e.g., the study of Same and Other and all the other
- similar concepts— roughly speaking all
+ similar concepts— roughly speaking all
the "contraries" are reducible to this first principle; but we may consider that they
have been sufficiently studied in the "Selection of Contraries"For Being and Unity at once entail
genera, and so the sciences will correspond to these genera. The term "philosopher" is
- like the term "mathematician" in its uses; for mathematics too has divisions—there
+ like the term "mathematician" in its uses; for mathematics too has divisions—there
is a primary and a secondary science, and others successively, in the realm of
mathematics. Now since it is the province of one science to study opposites, and the opposite of
@@ -2233,10 +2233,10 @@
form that it is not present in a particular class; in the latter case Unity is modified by
the differentia, apart from the content of the negation (for the negation of Unity is its
absence); but in privation there is a substrate of which the privation is
- predicated.— The opposite of Unity,
- then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness,
+ predicated.— The opposite of Unity,
+ then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness,
Dissimilarity, Inequality and everything else which is derived from these or from
- Plurality or Unity— fall under the
+ Plurality or Unity— fall under the
cognizance of the aforesaid science. And one of them is Oppositeness; for this is a form
of Difference, and Difference is a form of Otherness. Hence since the term "one" is used in various senses, so too will
@@ -2288,7 +2288,7 @@
is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity
and Motion under Plurality. And nearly everyone agrees that substance and existing things
are composed of contraries; at any rate all speak of the first principles as
- contraries— some as Odd and Even,some as Odd and Even,The Pythagoreans. some as Hot and Cold,Perhaps Parmenides. some as Limit and
Unlimited,The Platonists. some as Love and
@@ -2302,7 +2302,7 @@
the contraries are Unity and Plurality. And these belong to one science, whether they have
reference to one common notion or not. Probably the truth is that they have not; but
nevertheless even if the term "one" is used in various senses, the others will be related
- to the primary sense (and similarly with the contraries)— even if Being or Unity is not a universal and the same in all cases,
or is not separable from particulars (as it presumably is not; the unity is in some cases
one of reference and in others one of succession). For this very reason it is not the
@@ -2318,15 +2318,15 @@
axioms in mathematics and substance, or to different sciences. It is obvious that the
investigation of these axioms too pertains to one science, namely the science of the
philosopher; for they apply to all existing things, and not to a particular class separate
- and distinct from the rest. Moreover all thinkers employ them—because they are
+ and distinct from the rest. Moreover all thinkers employ them—because they are
axioms of Being qua Being, and every genus possesses
- Being— but employ them only in so far
+ Being— but employ them only in so far
as their purposes require; i.e., so far as the genus extends about which they are carrying
out their proofs. Hence since these axioms apply to all things qua
Being (for this is what is common to them), it is the function of him who studies Being
qua Being to investigate them as well. For this reason no one who is pursuing a particular
- inquiry—neither a geometrician nor an arithmetician—attempts to state whether
+ inquiry—neither a geometrician nor an arithmetician—attempts to state whether
they are true or false; but some of the physicists did so, quite naturally; for they alone
professed to investigate nature as a whole, and Being. But inasmuch as there is a more ultimate type of thinker than the
@@ -2359,7 +2359,7 @@
anyone to suppose that the same thing is and is not, as some imagine that Heraclitus
saysFor examples of Heraclitus's paradoxes cf.
Heraclitus Fr. 36, 57, 59 (Bywater); and for their
- meaning see Burnet, E.G.P. 80.—for what a man says does not necessarily
+ meaning see Burnet, E.G.P. 80.—for what a man says does not necessarily
represent what he believes. And if it is
impossible for contrary attributes to belong at the same time to the same subject (the
usual qualifications must be added to this premiss also), and an opinion which contradicts
@@ -2481,8 +2481,8 @@
not even more than two accidents can be combined in predication. An accident cannot be an
accident of an accident unless both are accidents of the same thing. I mean, e.g., that "white" is "cultured" and "cultured" "white"
- merely because both are accidents of a man. But it is not in this sense—that both
- terms are accidents of something else—that Socrates is cultured. Therefore since
+ merely because both are accidents of a man. But it is not in this sense—that both
+ terms are accidents of something else—that Socrates is cultured. Therefore since
some accidents are predicated in the latter and some in the former sense, such as are
predicated in the way that "white" is of Socrates cannot be an infinite series in the
upper direction; e.g. there cannot be another accident of "white Socrates," for the sum of
@@ -2622,7 +2622,7 @@
(1.) The belief that contradictions and contraries can be true at the same time comes to
them from seeing the contraries generated from the same thing. Then if what is not cannot be generated, the thing must have existed
- before as both contraries equally—just as Anaxagoras saysCf. Aristot. Met. 4.4.28.
that everything is mixed in everything; and also Democritus, for he too saysCf. Aristot. Met.
@@ -2675,7 +2675,7 @@
he made Hector,The only passage in our text of
Homer to which this reference could apply isHom. Il.
23.698; but there the subject is Euryalus, not Hector. when he was
- stunned by the blow, lie with thoughts deranged—thus implying that even those who
+ stunned by the blow, lie with thoughts deranged—thus implying that even those who
are "out of their minds" still think, although not the same thoughts. Clearly then, if
both are kinds of thought, reality also will be "both so and not so." It is along this path that the consequences are most difficult;
@@ -2738,7 +2738,7 @@
the healthy or to the diseased; and whether heavy things are as they appear to the weak or
to the strong; and whether truth is as it appears to the waking or to the
sleeping. For clearly they do not really
- believe the latter alternative—at any rate no one, if in the night he thinks that he
+ believe the latter alternative—at any rate no one, if in the night he thinks that he
is at Athens whereas he is really in
Africa, starts off to the Odeum.A concert-hall (used also for other purposes) built by
@@ -2834,7 +2834,7 @@
since the contradiction of a statement cannot be true at the same time of the same thing,
it is obvious that contraries cannot apply at the same time to the same thing. For in each pair of contraries one is a privation no
- less than it is a contrary—a privation of substance. And privation is the negation
+ less than it is a contrary—a privation of substance. And privation is the negation
of a predicate to some defined genus. Therefore
if it is impossible at the same time to affirm and deny a thing truly, it is also
impossible for contraries to apply to a thing at the same time; either both must apply in
@@ -2898,7 +2898,7 @@
the mixture is neither good nor not-good; and so no statement is true. It is obvious from this
analysis that the one-sided and sweeping statements which some people make cannot be
- substantially true—some maintaining that nothing is true (for they say that there is
+ substantially true—some maintaining that nothing is true (for they say that there is
no reason why the same rule should not apply to everything as applies to the
commensurability of the diagonal of a squareA stock
example of impossibility and falsity; see Index.), and some that everything is
@@ -2974,14 +2974,14 @@
comes into being or becomes known; and some beginnings are originally inherent in things,
while others are not. Hence "nature" is a
beginning, and so is "element" and "understanding" and "choice" and "essence" and "final
- cause"—for in many cases the Good and the Beautiful are the beginning both of
+ cause"—for in many cases the Good and the Beautiful are the beginning both of
knowledge and of motion. "Cause" means: (a) in one sense, that as the result of whose presence
- something comes into being—e.g. the bronze of a statue and the silver of a cup, and
- the classessc. of material—metal, wood,
+ something comes into being—e.g. the bronze of a statue and the silver of a cup, and
+ the classessc. of material—metal, wood,
etc. which contain these; (b) in another sense, the form or pattern;
- that is, the essential formula and the classes which contain it—e.g. the ratio 2:1
- and number in general is the cause of the octave—and the parts of the
+ that is, the essential formula and the classes which contain it—e.g. the ratio 2:1
+ and number in general is the cause of the octave—and the parts of the
formula. (c) The source of the first
beginning of change or rest; e.g. the man who plans is a cause, and the father is the
cause of the child, and in general that which produces is the cause of that which is
@@ -3000,11 +3000,11 @@
different connections, but qua statue. However, they are not causes
in the same way, but the one as material and the other as the source of
motion. And things are causes of each other; as e.g. labor of vigor, and vigor of
- labor—but not in the same way; the one as an end , and the other as
+ labor—but not in the same way; the one as an end , and the other as
source of motion . And again the same thing is sometimes the cause of contrary results; because that which
by its presence is the cause of so-and-so we sometimes accuse of being, by its absence,
- the cause of the contrary—as, e.g., we say that the absence of the pilot is the
+ the cause of the contrary—as, e.g., we say that the absence of the pilot is the
cause of a capsize, whereas his presence was the cause of safety. And both, presence and privation, are moving
causes. Now there are four senses which are most obvious
@@ -3081,7 +3081,7 @@
metaphorically to any small unity which is useful for various purposes; and so that which
is small or simple or indivisible is called an "element." (e) Hence it comes that the most universal things are elements;
- because each of them, being a simple unity, is present in many things—either in all
+ because each of them, being a simple unity, is present in many things—either in all
or in as many as possible. Some too think that unity and the point are first
principles. (f) Therefore since what are
called generaThis must refer to the highest genera,
@@ -3094,9 +3094,9 @@
ed="P" unit="para"/>"Nature"On the meaning of fu/sis cf. Burnet, E.G.P. pp. 10-12, 363-364. means: (a) in one
- sense, the genesis of growing things—as would be suggested by pronouncing the
+ sense, the genesis of growing things—as would be suggested by pronouncing the
u of fu/sis
- long—and (b) in another, that immanent thingProbably the seed (Bonitz). from which a growing thing first begins to grow. (c)
The source from which the primary motion in every natural object is induced in that object
as such. All things are said to grow which gain
@@ -3127,7 +3127,7 @@
e.g. animals and their parts. And nature is both the primary matter (and this in two
senses: either primary in relation to the thing, or primary in general; e.g., in bronze
articles the primary matter in relation to those articles is bronze, but in general it is
- perhaps water—that is if all things which can be melted are water) and the form or
+ perhaps water—that is if all things which can be melted are water) and the form or
essence, i.e. the end of the process, of generation. Indeed from this sense of "nature,"
by an extension of meaning, every essence in general is called "nature," because the
nature of anything is a kind of essence. "Necessary" means: (a) That without which, as a concomitant condition,
life is impossible; e.g. respiration and food are necessary for an animal, because it
cannot exist without them. (b) The conditions without which good cannot be or come to be,
- or without which one cannot get rid or keep free of evil—e.g., drinking medicine is
+ or without which one cannot get rid or keep free of evil—e.g., drinking medicine is
necessary to escape from ill-health, and sailing to Aegina is necessary to recover one's money. (c) The compulsory and compulsion; i.e. that which hinders and
@@ -3230,7 +3230,7 @@
all animals); and that in a way very similar to that in which the matter is one. Sometimes these things are said to be "one" in this
sense, and sometimes their higher genus is said to be one and the same (if they are final
- species of their genus)—the genus, that is, which is above the genera of which their
+ species of their genus)—the genus, that is, which is above the genera of which their
proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same
figure (because they are both triangles), but not the same triangles. (d) Again, things are said to
@@ -3255,7 +3255,7 @@
unit="Loeb chap"/>Again, in one sense we call anything whatever "one" if it is
quantitative and continuous; and in another sense we say that it is not "one" unless it is
a whole of some kind, i.e. unless it is one in form (e.g., if we saw the
- parts of a shoe put together anyhow, we should not say that they were one — except
+ parts of a shoe put together anyhow, we should not say that they were one — except
in virtue of their continuity; but only if they were so put together as to be a shoe, and
to possess already some one form). Hence the
circumference of a circle is of all lines the most truly one, because it is whole and
@@ -3517,11 +3517,11 @@
happen, or because they might do so well . Even in inanimate things this kind
of potency is found; e.g. in instruments; for they say that one lyre "can" be played, and
another not at all, if it has not a good tone. "Impotence" is a privation of potency—a kind of
- abolition of the principle which has been described—either in general or in
+ n="12.8" ed="P" unit="Loeb chap"/>"Impotence" is a privation of potency—a kind of
+ abolition of the principle which has been described—either in general or in
something which would naturally possess that principle, or even at a time when it would
- naturally already possess it (for we should not use "impotence"—in respect of
- begetting—in the same sense of a boy, a man and a eunuch). Again, there is an "impotence" corresponding to each kind of
potency; both to the kinetic and to the successfully kinetic. Some things are said to be "impotent" in
@@ -3566,15 +3566,15 @@
of the former class some are quantitative in virtue of their substance, e.g. the fine
(because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this
- kind— e.g., "much" and "little," "long" and "short," "broad" and "narrow," "deep"
+ kind— e.g., "much" and "little," "long" and "short," "broad" and "narrow," "deep"
and "shallow," "heavy" and "light," etc. Moreover, "great" and "small," and "greater" and "smaller," whether used absolutely or
relatively to one another, are essential attributes of quantity; by an extension of
meaning, however, these terms are also applied to other things. Of things called quantitative in an accidental sense, one kind is so
called in the sense in which we said above that "cultured" or "white" is
- quantitative—because the subject to which they belong is quantitative; and others in
- the sense that motion and time are so called—for these too are said in a sense to be
+ quantitative—because the subject to which they belong is quantitative; and others in
+ the sense that motion and time are so called—for these too are said in a sense to be
quantitative and continuous, since the subjects of which they are attributes are
divisible. I mean, not the thing moved, but that through or along which the motion has
taken place; for it is because the latter is quantitative that the motion is quantitative,
@@ -3586,14 +3586,14 @@
/>which shows that the essential differentia
is quality. In this one sense, then, "quality"
means differentia of essence; but (b) in another it is used as of immovable and
- mathematical objects, in the sense that numbers are in a way qualitative—e.g. such
+ mathematical objects, in the sense that numbers are in a way qualitative—e.g. such
as are composite and are represented geometrically not by a line but by a plane or solid
- (these are products respectively of two and of three factors)—and in general means
+ (these are products respectively of two and of three factors)—and in general means
that which is present besides quantity in the essence. For the essence of each number is
that which goes into it once; e.g. that of 6 is not what goes twice or three times, but
what goes once; for 6 is once 6. (c) All
affections of substance in motion in respect of which bodies become different when they
- (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and
+ (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and
lightness, etc. (d) The term is used with reference to goodness and badness, and in
general to good and bad. Thus there are, roughly speaking, two meanings which the term
@@ -3660,9 +3660,9 @@
there is a thought which thinks it; but thought is not relative to that of which it is the
thought (for then the same thing would have been said twice). And similarly sight is the
sight of something; not of that of which it is the sight, although this is of course
- true—it is relative to some color or other similar thing. To describe it in the other way—"the sight of the object of
- sight"—would be to say the same thing twice. To describe it in the other way—"the sight of the object of
+ sight"—would be to say the same thing twice. Things, then, which are called relative of
their own nature are so called, some in these senses, and others because the classes which
contain them are of this kind. E.g., medicine is reckoned as relative because its genus,
@@ -3680,7 +3680,7 @@
are "perfect" when they have no deficiency in respect of the form of their peculiar
excellence. And thus by an extension of the
meaning we use the term in a bad connection, and speak of a "perfect" humbug and a
- "perfect" thief; since indeed we call them "good"— e.g. a "good" thief and a "good" humbug. (c) And goodness is a kind of perfection. For each thing, and every
substance, is perfect when, and only when, in respect of the form of its peculiar
@@ -3792,7 +3792,7 @@
so); and "invisible" either because it has no color at all or because it has only a faint
one; and "footless" either because it has no feet at all or because it has rudimentary
feet. Again, a negative affix may mean
- "having something in a small degree"—e.g. "stoneless"— that is, having it in some
rudimentary manner. Again, it may mean having it "not easily" or "not well"; e.g.,
"uncutable" means not only that which cannot be cut, but that which cannot be cut easily
@@ -3850,7 +3850,7 @@
in honor of Apollo and Artemis) at the end of May. "Part" means: (a) That into which a
quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we
+ rend="Italic">qua quantity is always called a part of that quantity—e.g., we
call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those
"parts" in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and
in another not. Again, (c) those divisions
@@ -3888,13 +3888,13 @@
singular qua one; all this number, all these units. We do not describe any
chance quantity as "mutilated"; it must have parts, and must be a whole. The number 2 is
- not mutilated if one of its 1's is taken away—because the part lost by mutilation is
- never equal to the remainder—nor in general is any number mutilated; because the
+ not mutilated if one of its 1's is taken away—because the part lost by mutilation is
+ never equal to the remainder—nor in general is any number mutilated; because the
essence must persist. If a cup is mutilated, it must still be a cup; but the number is no
longer the same. Moreover, not even all things
which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well
- as similar parts—e.g. 2, 3. But in general of things whose position makes no
- difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to
their essence. Further, they must be
continuous; for a musical scale is composed of dissimilar parts, and has position; but it
@@ -3923,7 +3923,7 @@
or a particular solid); i.e., that which underlies the differentiae. (d) In the sense that in formulae the first component, which is
stated as part of the essence, is the genus, and the qualities are said to be its
- differentiae. The term "genus," then, is used in all these senses—(a) in respect of
+ differentiae. The term "genus," then, is used in all these senses—(a) in respect of
continuous generation of the same type; (b) in respect of the first mover of the same type
as the things which it moves; (c) in the sense of material. For that to which the
differentia or quality belongs is the substrate, which we call material. Cf. Plat. Euthyd. 283e-284c, 286c, d. nearly so. But
it is possible to describe everything not only by its own definition but by that of
- something else; quite falsely, and yet also in a sense truly—e.g., 8 may be
+ something else; quite falsely, and yet also in a sense truly—e.g., 8 may be
described as "double" by the definition of 2. Such are the meanings of "false" in these cases. (3.)
A false man is one who readily and deliberately makes such statements, for the sake of
- doing so and for no other reason; and one who induces such statements in others—just
+ doing so and for no other reason; and one who induces such statements in others—just
as we call things false which induce a false impression. Hence the proof in the
HippiasPlat. Hipp. Min 365-375. that the same
@@ -3998,7 +3998,7 @@
his course by a storm, or captured by pirates. The accident has happened or exists, but in virtue not of itself but of something else;
for it was the storm which was the cause of his coming to a place for which he was not
- sailing—i.e. Aegina. Aegina. "Accident" has also another sense,i.e. "property." namely, whatever belongs to each thing in virtue
of itself, but is not in its essence; e.g. as having the sum of its angles equal to two
@@ -4030,7 +4030,7 @@
principle of motion and rest), obviously it is neither a practical nor a productive
science. For in the case of things produced
the principle of motion (either mind or art or some kind of potency) is in the producer;
- and in the case of things done the will is the agent—for the thing done and the
+ and in the case of things done the will is the agent—for the thing done and the
thing willed are the same. Thus if every intellectual activity is either practical or
productive or speculative, physics will be a speculative science; but speculative about
that kind of Being which can be moved, and about formulated substance for the most part
@@ -4042,9 +4042,9 @@
form with matter; because the "snub" is a concave nose , whereas concavity is
independent of sensible matter. Now if all physical
- terms are used in the same sense as "snub"—e.g. nose, eye, face, flesh, bone, and in
+ terms are used in the same sense as "snub"—e.g. nose, eye, face, flesh, bone, and in
general animal; leaf, root, bark, and in general vegetable (for not one of these has a
- definition without motion; the definition invariably includes matter)—it is clear
+ definition without motion; the definition invariably includes matter)—it is clear
how we should look for and define the essence in physical things, and why it is the
province of the physicist to study even some aspects of the soul, so far as it is not
independent of matter. Now all causes must
be eternal, but these especially; since they are the causes of what is visible of things
divine. Hence there will be three speculative philosophies: mathematics, physics, and
- theology— since it is obvious that if
+ theology— since it is obvious that if
the divine is present anywhere, it is present in this kind of entity; and also the most
honorable science must deal with the most honorable class of subject. The speculative sciences,
then, are to be preferred to the other sciences, and "theology" to the other speculative
sciences. One might indeed raise the question whether the primary philosophy is universal
or deals with some one genus or entity; because even the mathematical sciences differ in
- this respect—geometry and astronomy deal with a particular kind of entity, whereas
+ this respect—geometry and astronomy deal with a particular kind of entity, whereas
universal mathematics applies to all kinds alike. Then if there is not some other substance besides those which are
naturally composed, physics will be the primary science; but if there is a substance which
@@ -4099,7 +4099,7 @@
n="Plat. Soph. 254a">Plat. Soph. 254a. was not far wrong in making
sophistry deal with what is nonexistent; because the sophists discuss the accident more, perhaps, than any other
- people—whether "cultured" and "grammatical,"i.e. able to read and write. The sophistic argument is given by Alexander as follows: A
is grammatical; therefore grammatical A=A. A is cultured; therefore cultured A=A.
Therefore grammatical=cultured, and he who is grammatical must be cultured. But B,
@@ -4121,7 +4121,7 @@
considerations as the following: of things which are in other senses there is
generation and destruction, but of things which are accidentally there is
not.i.e., the process of becoming or change takes
- place in the subject—the man , who is accidentally cultured, becomes
+ place in the subject—the man , who is accidentally cultured, becomes
grammatical, and when the process is complete "the cultured" is
accidentally grammatical; but it does not become so. Nevertheless we
must state further, so far as it is possible, with regard to the accidental, what its
@@ -4163,11 +4163,11 @@
questions must be inquired into laterCf. Aristot. Met. 12.6-8.; but it is clear that there is no science of the
- accidental—because all scientific knowledge is of that which is always
+ accidental—because all scientific knowledge is of that which is always
or usually so. How else indeed can one learn it or teach it to another? For a
fact must be defined by being so always or usually; e.g., honey-water is usually
beneficial in case of fever. But science will
- not be able to state the exception to the rule: when it is not beneficial—e.g. at
+ not be able to state the exception to the rule: when it is not beneficial—e.g. at
the new moon; because that which happens at the new moon also happens either always or
usually; but the accidental is contrary to this. We have now explained the nature and
cause of the accidental, and that there is no science of it. Thus of necessity he will either die or
not die. And similarly if one jumps over to the past, the principle is the same; for
- this—I mean that which has just happened—is already present in something.
+ this—I mean that which has just happened—is already present in something.
Everything, then, which is to be, will be of necessity; e.g., he who is alive must
- die—for some stage of the process has been reached already; e.g., the contraries are
- present in the same body—but whether by disease or violence is not yet determined;
+ die—for some stage of the process has been reached already; e.g., the contraries are
+ present in the same body—but whether by disease or violence is not yet determined;
it depends upon whether so-and-so happens. Clearly, then, the series goes back to some starting-point, which does not go back to
something else. This, therefore, will be the starting-point of the fortuitous, and nothing
@@ -4207,10 +4207,10 @@
thought" I mean thinking them not as a succession but as a unitysc., "or not as a unity but as a succession" (this is
separating in thought).); for "falsity" and "truth" are not in
- things —the good, for example, being true, and the bad
- false—but in thought ; and with regard to simple concepts and essences
+ things —the good, for example, being true, and the bad
+ false—but in thought ; and with regard to simple concepts and essences
there is no truth or falsity even in thought; —what points we must study in connection with being and not-being in this sense,
+ />—what points we must study in connection with being and not-being in this sense,
we must consider later. But since the combination and separation exists in thought and not
in things, and this sense of "being" is different from the proper senses (since thought
attaches or detaches essence or quality or quantity or some other category), we may
@@ -4258,11 +4258,11 @@
alone; and it is primary also in definition,
because in the formula of each thing the formula of substance must be inherent; and we
assume that we know each particular thing most truly when we know what "man"
- or "fire" is— rather than its quality or quantity or position; because we know each of
these points too when we know what the quantity or quality is. Indeed, the question which was raised long ago, is
- still and always will be, and which always baffles us—"What is Being?"—is in
+ still and always will be, and which always baffles us—"What is Being?"—is in
other words "What is substance?" Some say that it is oneThe Milesians and Eleatics.; others, more than one; some,
finiteThe Pythagoreans and Empedocles.;
@@ -4277,8 +4277,8 @@
n="2.2" ed="P" unit="Loeb chap"/>We must consider whether (a) these are the only
substances, or (b) these and some others, or (c) some of these, or (d) some of these and
some others, or (e) none of these, but certain others. SomeThe Pythagoreans. hold that the bounds of body—i.e. the
- surface, line, point and unit—are substances, and in a truer sense than body or the
+ anchored="yes">The Pythagoreans. hold that the bounds of body—i.e. the
+ surface, line, point and unit—are substances, and in a truer sense than body or the
solid. Again, someThe pre-Socratics. believe that there is nothing of this kind
besides sensible things, while others believe in eternal entities more numerous and more
@@ -4291,7 +4291,7 @@
then another for the soul. In this way he multiplies the kinds of substance. SomeThe followers of Xenocrates, successor to
Speusippus. again hold that the Forms and numbers have the same nature, and that
- other things—lines and planes—are dependent upon them; and soon back to the
+ other things—lines and planes—are dependent upon them; and soon back to the
substance of the visible universe and sensible things. We must consider, then, with regard to these matters, which of the
views expressed is right and which wrong; and what things are substances; and whether
@@ -4312,7 +4312,7 @@
two, the concrete thing: the statue. Thus if the form is prior to the matter and more
truly existent, by the same argument it will also be prior to the combination. We have now stated in
- outline the nature of substance—that it is not that which is predicated of a
+ outline the nature of substance—that it is not that which is predicated of a
subject, but that of which the other things are predicated. But we must not merely define
it so, for it is not enough. Not only is the statement itself obscure, but also it makes
matter substance; for if matter is not substance, it is beyond our power to say what else
@@ -4335,8 +4335,8 @@
substance. But this is impossible; for it is accepted that separability and individuality
belong especially to substance. Hence it would seem that the form and the combination of
form and matter are more truly substance than matter is. The substance, then, which consists of both—I mean of matter and
- form—may be dismissed, since it is posterior and obvious. Matter too is in a sense
+ unit="Loeb chap"/>The substance, then, which consists of both—I mean of matter and
+ form—may be dismissed, since it is posterior and obvious. Matter too is in a sense
evident. We must consider the third type, for this is the most perplexing. Now it is agreed that some sensible things are substances, and so we
should begin our inquiry in connection with these. Hence essence will belong to nothing except species of
a genus, but to these only; for in these the predicate is not considered to be related to
the subject by participation or affection, nor as an accident. But of everything else as
- well, if it has a name, there will be a formula of what it means—that X
- belongs to Y; or instead of a simple formula one more exact—but no definition, nor
+ well, if it has a name, there will be a formula of what it means—that X
+ belongs to Y; or instead of a simple formula one more exact—but no definition, nor
essence. Or
perhaps "definition," like the "what," has more than one sense. For the "what" in one
sense means the substance and the individual, Now
although we must also consider how we should express ourselves in each particular case, it
is still more important to consider what the facts are. Hence now, since the language
@@ -4442,7 +4442,7 @@
they belong equally to other things too, but not primarily . For if we assume
this, it does not necessarily follow that there is a definition of anything which means
the same as any formula; it must mean the same as a particular kind of formula, i.e. the
- formula of one thing— one not by
+ formula of one thing— one not by
continuity like the Iliad, or things which are arbitrarily combined, but in
one of the proper senses of "one." And "one" has the same variety of senses as "being."
"Being" means sometimes the individual thing, sometimes the quantity, sometimes the
@@ -4619,7 +4619,7 @@
art of medicine or of building is the form of health or the house). By
substance without matter I mean the essence. In generations and motions part of the process is
- called cogitation, and part production—that which proceeds from the starting-point
+ called cogitation, and part production—that which proceeds from the starting-point
and the form is cogitation, and that which proceeds from the conclusion of the cogitation
is production. Each of the other intermediate measures is carried out in the same way. I
mean, e.g., that if A is to be healthy, his physical condition will have to be made
@@ -4633,7 +4633,7 @@
starting-point is, perhaps, the heating of the patient; and this the doctor produces by
friction. Heat in the body, then, is either a part of health, or is followed (directly or
through several intermediaries) by something similar which is a part of health. This is
- the ultimate thing, namely that produces, and in this sense is a part of, health—or
+ the ultimate thing, namely that produces, and in this sense is a part of, health—or
of the house (in the form of stones)There is no real analogy between the casual
relationship of heat to health and of stones to a house. The former is both material and
@@ -4654,9 +4654,9 @@
invalid" become healthy), but it is more
properly said to proceed from the privation; e.g., a man becomes healthy from being an
invalid rather than from being a man. Hence a healthy person is not called an invalid, but
- a man, and a healthy man. But where the privation is obscure and has no name—e.g. in
+ a man, and a healthy man. But where the privation is obscure and has no name—e.g. in
bronze the privation of any given shape, or in bricks and wood the privation of the shape
- of a house—the generation is considered to proceed from these materials, as in the
+ of a house—the generation is considered to proceed from these materials, as in the
former case from the invalid. Hence just as in
the former case the subject is not called that from which it is generated, so in this case
the statue is not called wood, but is called by a verbal change not wood, but wooden; not
@@ -4682,8 +4682,8 @@
unit="Loeb chap"/>If, then, we make the spherical form itself, clearly we shall have to
make it in the same way; and the processes of generation will continue to
infinity. It is therefore obvious that the form (or
- whatever we should call the shape in the sensible thing) is not generated—generation
- does not apply to it— nor is the essence generated; for this is that which is
+ whatever we should call the shape in the sensible thing) is not generated—generation
+ does not apply to it— nor is the essence generated; for this is that which is
induced in something else either by art or by nature or by potency. But we do cause a bronze sphere to be, for we produce it from
bronze and a sphere; we induce the form into this particular matter, and the result is a
@@ -4715,8 +4715,8 @@
generation and destruction, is useless; nor, for this reason at any rate, should they be
regarded as self-subsistent substances. Indeed
in some cases it is even obvious that that which generates is of the same kind as that
- which is generated—not however identical with it, nor numerically one with it, but
- formally one—e.g. in natural productions (for man begets man), unless something
+ which is generated—not however identical with it, nor numerically one with it, but
+ formally one—e.g. in natural productions (for man begets man), unless something
happens contrary to nature, as when a horse sires a mule. And even these cases are
similar; for that which would be common to both horse and ass, the genus immediately above
them, has no name; but it would probably be both, just as the mule is both.The question might be raised
- why some things are generated both artificially and spontaneously—e.g.
- health—and others not; e.g. a house. The reason is that in some cases the
- matter—which is the starting-point of the process in the production and generation
- of artificial things, and in which some part of the result is already existent—is
+ why some things are generated both artificially and spontaneously—e.g.
+ health—and others not; e.g. a house. The reason is that in some cases the
+ matter—which is the starting-point of the process in the production and generation
+ of artificial things, and in which some part of the result is already existent—is
such that it can initiate its own motion, and in other cases it is not; and of the former
kind some can initiate motion in a particular way, and some cannot. For many things can
move themselves, but not in a particular way, e.g. so as to dance. and that from which the seed comes has in
some sense the same name as the product (for we must not expect that all should have the
- same name in the sense that "man" is produced by "man"—since woman is also produced
+ same name in the sense that "man" is produced by "man"—since woman is also produced
by man); unless the product is a freak. This is why a mule is not produced by a
mule. Those
natural objects which are produced, like artificial objects, spontaneously, are those
@@ -4837,7 +4837,7 @@
ed="P" unit="Loeb chap"/>All things which are concrete combinations of form and matter
(e.g. "the snub" or the bronze circle) can be resolved into form and matter, and the
matter is a part of them; but such as are not concrete combinations with matter, but are
- without matter—whose formulae refer to the form only—cannot be resolved;
+ without matter—whose formulae refer to the form only—cannot be resolved;
either not at all, or at least not in this way. Thus these material components are principles and parts of the
concrete objects, but they are neither parts nor principles of the form. For this reason
@@ -4849,7 +4849,7 @@
unit="para"/>We have now stated the truth;
nevertheless let us recapitulate and state it more clearly. All constituents which are
parts of the formula, and into which the formula can be divided, are prior to their
- wholes—either all or some of them. But the formula of the right angle is not
+ wholes—either all or some of them. But the formula of the right angle is not
divisible into the formula of an acute angle, but vice versa; since in defining the acute
angle we use the right angle, because "the acute angle is less than a right
angle." It is the same with the circle and
@@ -4885,11 +4885,11 @@
formula refers to the universal; for "circle" is the same as "essence of circle," and "soul" the
same as "essence of soul." But when we come
- to the concrete thing, e.g. this circle—which is a particular individual, either
+ to the concrete thing, e.g. this circle—which is a particular individual, either
sensible or intelligible (by intelligible circles I mean those of mathematics,i.e., something very similar to the Platonic
"intermediates." Cf. Introduction. and by sensible those which are of bronze or
- wood)—of these individuals there is no definition; we apprehend them by intelligence or perception; and when they have
passed from the sphere of actuality it is uncertain whether they exist or not, but they
are always spoken of and apprehended by the universal formula. But the matter is in itself
@@ -4899,9 +4899,9 @@
resp="Tredennick" anchored="yes">See Aristot. Met.
13.2, 3. We have now discussed the case of the whole and part, and of prior and
- posterior. But we must answer the question, when we are asked which is prior—the
+ posterior. But we must answer the question, when we are asked which is prior—the
right angle and circle and animal, or that into which they are resolved and of which they
- are composed, i.e. their parts—by saying that neither is absolutely
+ are composed, i.e. their parts—by saying that neither is absolutely
prior. For if the soul also is
the animal or living thing, or the soul of the individual is the individual,
and "being a circle" is the circle, and "being a right angle" or the essence
@@ -4974,7 +4974,7 @@
which is not essence or form considered independently, but a particular thing. Thus the
semicircles will be parts not of the universal circle but of the particular circles, as we
said beforeAristot.
- Met. 7.10.17.—for some matter is sensible, and some
+ Met. 7.10.17.—for some matter is sensible, and some
intelligible. It is clear also that the
soul is the primary substance, and the body matter; and "man" or "animal" is the
combination of both taken universally. And " Socrates" or "Coriscus" has a double sense,
@@ -5006,7 +5006,7 @@
substance, e.g., in the case of a man, the formula of the soul; because the substance is
the indwelling form, of which and of the matter the so called concrete substance is
composed. E.g., concavity is such a form, since from this and "nose" is derived "snub
- nose" and "snubness"—for "nose" will be present twice over in these
+ nose" and "snubness"—for "nose" will be present twice over in these
expressions); but in the concrete
substance, e.g. snub nose or Callias, matter will be present too.Chapters. 10-11; and cf. Aristot. Met.
@@ -5076,7 +5076,7 @@
differentiae. If, then, we keep on taking a differentia of a differentia, one of them, the last, will
be the form and the substance. But if we proceed with reference to accidental
- qualities—e.g. if we divide "that which has feet" into white and black—there
+ qualities—e.g. if we divide "that which has feet" into white and black—there
will be as many differentiae as there are divisions. It is therefore obvious that the
definition is the formula derived from the differentiae, and strictly speaking from the
last of them. This will be clear if we change
@@ -5091,7 +5091,7 @@
of these are called substance, so too is the universal. With two of these we have already
dealt, i.e. with the essenceChs. 4-5.,10-12.
and the substrateCh. 3.; of the latter we
- have said that it underlies in two senses—either being an individual thing (as the
+ have said that it underlies in two senses—either being an individual thing (as the
animal underlies its attributes), or as matter underlies the actuality. The universal also is thought by someThe Platonists. to be in the truest sense a cause and a principle.
@@ -5136,7 +5136,7 @@
unit="Loeb chap"/>Again, it is clear in this way too. Substance can not consist of
substances actually present in it; for that which is actually two can never be actually
one, whereas if it is potentially two it can be one. E.g., the double consists of two
- halves—that is, potentially; for the actualization separates the halves. Thus if substance is one, it cannot consist of
substances present in it even in this sense, as Democritus rightly observes; he says that
it is impossible for two to come from one, or one from two, because he identifies
@@ -5211,7 +5211,7 @@
requires scientific knowledge, and if, just as knowledge cannot be sometimes knowledge and
sometimes ignorance (it is opinion that is of this nature), so too demonstration and
definition cannot vary (it is opinion that is concerned with that which can be otherwise
- than it is)— then clearly there can be neither definition nor demonstration of
individual sensible substances. For (a) things
which perish are obscure to those who have knowledge of them when they are removed from
@@ -5233,7 +5233,7 @@
to "two-footed" (and in the case of eternal elements this is even necessarily so; since
they are prior to the compound, and parts of it. Indeed they are also separable, if the term "man" is
- separable—for either neither can be separable, or both are so. If neither, the genus will not exist apart from the species, or
if it is so to exist, so will the differentia); (2.) that "animal" and "two-footed" are
prior in being to "two-footed animal," and that which is prior to something else is not
@@ -5249,10 +5249,10 @@
defining individuals is hard to realize when we are dealing with eternal entities,
especially in the case of such as are unique, e.g. the sun and moon. For people go wrong
not only by including in the definition attributes on whose removal it will still be
- sun—e.g., "that which goes round the earth," or "night-hidden " (for they suppose
+ sun—e.g., "that which goes round the earth," or "night-hidden " (for they suppose
that if it stops or becomes visiblesc. in the
night. it will no longer be sun; but it is absurd that this should be so, since
- "the sun "denotes a definite substance)—they also mention attributes which may apply
+ "the sun "denotes a definite substance)—they also mention attributes which may apply
to something else; e.g., if another thing with those attributes comes into being, clearly
it will be a sun. The formula, then, is general; but the sun was supposed to be an
@@ -5263,7 +5263,7 @@
which are thought to be substances the majority are potentialities; both the parts of
living things (for none of them has a separate substantial existence; and when they are
separated, although they still exist, they exist as matter), and earth, fire and air; for
- none of these is one thing —they are a mere aggregate before they are
+ none of these is one thing —they are a mere aggregate before they are
digested and some one thing is generated from them. It might be supposed very reasonably that the parts of living things
and the corresponding parts of their vital principle are both, i.e. exist both actually
@@ -5335,7 +5335,7 @@
predicated in this way of another. Or again,
"why are these things, e.g. bricks and stones, a house?" Clearly then we are inquiring for
the cause (i.e., to speak abstractly, the essence); which is in the case of some things,
- e.g. house or bed, the end , and in others the prime mover—for this
+ e.g. house or bed, the end , and in others the prime mover—for this
also is a cause. We look for the latter kind of cause in the case of generation and
destruction, but for the former also in the case of existence. What we are now looking for is
@@ -5358,7 +5358,7 @@
unit="Loeb chap"/>Now since that which is composed of something in such a way that the
whole is a unity; not as an aggregate is a unity, but as a syllable isThis sentence is not finished; the parenthesis which
- follows lasts until the end of the chapter.—the syllable is not the
+ follows lasts until the end of the chapter.—the syllable is not the
letters, nor is BA the same as B and A; nor is flesh fire and earth; because after
dissolution the compounds, e.g. flesh or the syllable, no longer exist; but the letters
exist, and so do fire and earth. Therefore the
@@ -5428,7 +5428,7 @@
separable); and thirdly there is the combination of the two, which alone admits of
generation and destruction,Cf. Aristot. Met. 7.8. and is separable in an
- unqualified sense—for of substances in the sense of formula some are separableIn point of fact the only form which is absolutely
separable is Mind or Reason. Cf. Aristot. Met.
12.7, 9. and some are not. We must therefore comprehend
- the various kinds of differences—for these will be principles of being—i.e.
+ the various kinds of differences—for these will be principles of being—i.e.
the differences in degree, or in density and rarity, and in other such modifications, for
they are all instances of excess and defect. And if anything differs in shape or in smoothness or roughness, all these are
@@ -5520,7 +5520,7 @@
substance is, and in what sense it exists; either as matter, or as form and actuality, or
thirdly as the combination of the two. We must not fail to realize that sometimes it is doubtful
- whether a name denotes the composite substance or the actuality and the form—e.g.
+ whether a name denotes the composite substance or the actuality and the form—e.g.
whether "house" denotes the composite thing, "a covering made of bricks and stones
arranged in such-and-such a way," or the actuality and form, "a covering"; and whether
"line" means "duality in length" or "duality"Cf.
@@ -5607,7 +5607,7 @@
matter or the four elements.; i.e. even if all things that are generated have the
same matter for their first principle, nevertheless each thing has some matter peculiar to
it; e.g., "the sweet" or "the viscous" is the proximate matter of mucus, and "the bitter"
- or some such thing is that of bile— although probably mucus and bile are derived from the same ultimate matter. The result is that there is more than one matter of the
same thing, when one thing is the matter of the other; e.g., mucus is derived from "the
@@ -5652,11 +5652,11 @@
/>Since some things both are and are not,
without being liable to generation and destructionCf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.—e.g. points,Aristot. Met. 7.8.3.—e.g. points,Cf. Aristot. Met.
3.5.8, 9. if they exist at all; and in general the forms and shapes of
things (because white does not come to be, but the wood becomes white, since everything
- which comes into being comes from something and becomes something)—not all the
+ which comes into being comes from something and becomes something)—not all the
contrariesi.e., we must distinguish "contraries"
in the sense of "contrary qualities" from "contraries" in the sense of "things
characterized by contrary qualities." can be generated from each other. White is
@@ -5696,11 +5696,11 @@
"two-footed"? Why are not these Ideas "man,"
and why should not man exist by participation, not in any "man," but in two Ideas, those
of "animal" and "two-footed"? And in general
- "man" will be not one, but two things—"animal" and "two-footed." Evidently if we
+ "man" will be not one, but two things—"animal" and "two-footed." Evidently if we
proceed in this way, as it is usual to define and explain, it will be impossible to answer
and solve the difficulty. But if, as we
- maintain, man is part matter and part form—the matter being potentially, and the
- form actually man—, the point which we are investigating will no longer seem to be a
+ maintain, man is part matter and part form—the matter being potentially, and the
+ form actually man—, the point which we are investigating will no longer seem to be a
difficulty. For this difficulty is just the same as we should have if the definition of
XLiterally "cloak"; cf. Aristot. Met. 7.4.7 n. were "round bronze";
@@ -5762,7 +5762,7 @@
or quality or quantity, but also in accordance with potentiality and actuality and
function, let us also gain a clear understanding about potentiality and actuality; and
first about potentiality in the sense which is most proper to the word, but not most
- useful for our present purpose— for potentiality and actuality extend beyond the sphere
of terms which only refer to motion. When we
have discussed this sense of potentiality we will, in the course of our definitions of
@@ -5782,7 +5782,7 @@
by the action of some other thing, or of itself qua other. Another
is a positive state of impassivity in respect of deterioration or destruction by something
else or by itself qua something else; i.e. by a transformatory
- principle—for all these definitions contain the formula of the primary sense of
+ principle—for all these definitions contain the formula of the primary sense of
potentiality. Again, all these potentialities
are so called either because they merely act or are acted upon in a particular way, or
because they do so well . Hence in their formulae also the formulae of
@@ -5795,7 +5795,7 @@
a certain principle, and because even the matter is a kind of principle, that the patient
is acted upon; i.e., one thing is acted upon by another: oily stuff is inflammable, and
stuff which yields in a certain way is breakable, and similarly in other
- cases)— and partly in the agent; e.g.
+ cases)— and partly in the agent; e.g.
heat and the art of building: the former in that which produces heat, and the latter in
that which builds. Hence in so far as it is a natural unity, nothing is acted upon by
itself; because it is one, and not a separate thing. Privation has several sensesCf.
- Aristot. Met. 5.22.—it is applied
+ Aristot. Met. 5.22.—it is applied
(1.) to anything which does not possess a certain attribute; (2.) to that which would
naturally possess it, but does not; either (a) in general, or (b) when it would naturally
possess it; and either (1) in a particular way, e.g. entirely, or (2) in any way at all.
@@ -5822,7 +5822,7 @@
rational account, and the same account explains both the thing and its privation, though
not in the same way; and in one sense it applies to both, and in another sense rather to
the actual fact. Therefore such sciences must
- treat of contraries—essentially of the one, and non-essentially of the other; for
+ treat of contraries—essentially of the one, and non-essentially of the other; for
the rational account also applies essentially to the one, but to the other in a kind of
accidental way, since it is by negation and removal that it throws light on the contrary.
For the contrary is the primary privation,Cf. is or will
be, will be in error, for this is what "incapable" meant.i.e., we have just said that that which is incapable is deprived of its
- potency—in this case, of its potency for happening. Thus these theories do away with both motion and generation;
for that which is standing will always stand, and that which is sitting will always sit;
because if it is sitting it will not get up, since it is impossible that anything which is
@@ -5908,8 +5908,8 @@
it cannot be true to say that so-and-so is possible, but will not be, this view entirely
loses sight of the instances of impossibility.If it
is true to say that a thing which is possible will not be, anything may be possible, and
- nothing impossible. I mean, suppose that someone—i.e. the sort of man who
- does not take the impossible into account—were to say that it is possible to measure
+ nothing impossible. I mean, suppose that someone—i.e. the sort of man who
+ does not take the impossible into account—were to say that it is possible to measure
the diagonal of a square, but that it will not be measured, because there is nothing to
prevent a thing which is capable of being or coming to be from neither being nor being
likely ever to be. But from our premisses this
@@ -5935,7 +5935,7 @@
real, then B must be real at that time and in that way. Since all potencies are either innate,
like the senses, or acquired by practice, like flute-playing, or by study, as in the arts,
- some—such as are acquired by practice or a rational formula—we can only
+ some—such as are acquired by practice or a rational formula—we can only
possess when we have first exercised themCf. Aristot. Met. 9.8.6, 7.; in the case of others
which are not of this kind and which imply passivity, this is not necessary. Let actuality be defined by one
member of this antithesis, and the potential by the other. But things are not all said to exist actually in the same sense, but only by
- analogy—as A is in B or to B, so is C in or to D; for the relation is either that of
+ analogy—as A is in B or to B, so is C in or to D; for the relation is either that of
motion to potentiality, or that of substance to some particular matter. Infinity and void and other
concepts of this kind are said to "be" potentially or actually in a different sense from
@@ -6020,8 +6020,8 @@
time, like the thinning-process; but it has not ceased at the present moment; we both are
living and have lived. Now of these processes we should call
the one type motions, and the other actualizations. Every motion is incomplete—the processes of thinning, learning,
- walking, building—these are motions, and incomplete at that. For it is not the same
+ unit="Loeb chap"/>Every motion is incomplete—the processes of thinning, learning,
+ walking, building—these are motions, and incomplete at that. For it is not the same
thing which at the same time is walking and has walked, or is building and has built, or
is becoming and has become, or is being moved and has been moved, but two different
things; and that which is causing motion is different from that which has caused
@@ -6064,10 +6064,10 @@
n="Aristot. Met. 7.1033a">Aristot. Met. 7.7.10-12. and wood is not earth, but earthen material; and earth also is
an illustration of our point if it is similarly not some other thing, but a definite
- material—it is always the latter term in this series which is, in the fullest sense,
+ material—it is always the latter term in this series which is, in the fullest sense,
potentially something else. E.g., a box is not
earth, nor earthen, but wooden; for it is this that is potentially a box, and this is the
- matter of the box—that is, wooden material in general is the matter of "box" in
+ matter of the box—that is, wooden material in general is the matter of "box" in
general, whereas the matter of a particular box is a particular piece of wood. If there is some primary stuff, which is not further called the
material of some other thing, this is primary matter. E.g., if earth is "made of air," and
@@ -6112,7 +6112,7 @@
already exist in actuality. But prior in time
to these potential entities are other actual entities from which the former are generated;
for the actually existent is always generated from the potentially existent by something
- which is actually existent—e.g., man by man, cultured by cultured—there is
+ which is actually existent—e.g., man by man, cultured by cultured—there is
always some prime mover; and that which initiates motion exists already in
actuality. We have saidAristot. Met. 7.7, 8. in
@@ -6142,7 +6142,7 @@
they may see. Similarly men possess the art of
building in order that they may build, and the power of speculation that they may
speculate; they do not speculate in order that they may have the power of
- speculation—except those who are learning by practice; and they do not really
+ speculation—except those who are learning by practice; and they do not really
speculate, but only in a limited sense, or about a subject about which they have no desire
to speculate. Further, matter exists potentially, because it
may attain to the form; but when it exists actually, it is then in the form.
@@ -6199,7 +6199,7 @@
is it potentially in motion (except in respect of some starting-point or destination), and
there is no reason why the matter of such a thing should not exist. Hence the sun and stars and the whole visible heaven are always
- active, and there is no fear that they will ever stop—a fear which the writerse.g. Empedocles; cf. Aristot. Met. 5.23.3 n. on physics entertain. Nor do the heavenly
bodies tire in their activity; for motion does not imply for them, as it does for
@@ -6256,7 +6256,7 @@
n="Plat. Laws 896e">Plat. Laws 896e, Plat. Laws
898c). Nor is there in things
which are original and eternal any evil or error, or anything which has been
- destroyed—for destruction is an evil. Geometrical constructions, too, are discovered by an
actualization, because it is by dividing that we discover them. If the division were
already done, they would be obvious; but as it is the division is only there potentially.
@@ -6327,7 +6327,7 @@
does not exist in that way, it does not exist at all. Truth means to think these objects, and there is no falsity or deception, but only
- ignorance—not, however, ignorance such as blindness is; for blindness is like a
+ ignorance—not, however, ignorance such as blindness is; for blindness is like a
total absence of the power of thinking. And it is obvious that with regard to immovable
things also, if one assumes that there are immovable things, there is no deception in
respect of time. E.g., if we suppose that the
@@ -6395,7 +6395,7 @@
is known by unity, and that by which quantities are primarily known is absolute
unity. Thus unity is the starting point of
number qua number. Hence in other cases too "measure" means that by
- which each thing is primarily known, and the measure of each thing is a unit—in
+ which each thing is primarily known, and the measure of each thing is a unit—in
length, breadth, depth, weight and speed. (The
terms "weight" and "speed" are common to both contraries, for each of them has a double
meaning; e.g., "weight" applies to that which has the least amount of gravity and also to
@@ -6419,7 +6419,7 @@
kind is the starting point and measure; for they assume that the motion of the heavens is
uniform and the most rapid, and by it they judge the others. In music the measure is the
quarter tone, because it is the smallest interval; and in language the letter. All these
- are examples of units in this sense—not in the sense that unity is something common
+ are examples of units in this sense—not in the sense that unity is something common
to them all, but in the sense which we have described. The measure is not always numerically one, but sometimes more than
one; e.g., there are two quarter tones, distinguished not by our hearing but by their
@@ -6437,14 +6437,14 @@
n="20" ed="Bekker" unit="line"/>in respect of either quantity or form. Hence unity is indivisible, because that which is
primary in each class of things is indivisible. But not every unit is indivisible in the
- same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely
+ same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely
indivisible, and the former must be classed as indivisible with respect to our power of
perception, as we have already stated; since presumably everything which is continuous is
divisible. The measure is always akin to the thing measured. The measure of magnitude is magnitude,
and in particular the measure of length is a length; of breadth, a breadth; of sounds, a
sound; of weight, a weight; of units, a unit; for this is the view that we must take, and
not that the measure of numbers is a number. The latter, indeed, would necessarily be
- true, if the analogy held good; but the supposition is not analogous—it is as though
+ true, if the analogy held good; but the supposition is not analogous—it is as though
one were to suppose that the measure of units is units, and not a unit; for number is a
plurality of units. We also speak of knowledge or sense perception as a measure of things
@@ -6470,8 +6470,8 @@
which we approached in our discussion of difficultiesAristot. Met. 3.4.24-27.:
what unity is, and what view we are to take of it; whether that unity
- itself is a kind of substance—as first the Pythagoreans, and later Plato, both
- maintain—or whether rather some nature underlies it, and we should give a more
+ itself is a kind of substance—as first the Pythagoreans, and later Plato, both
+ maintain—or whether rather some nature underlies it, and we should give a more
intelligible account of it, and more after the manner of the physicists; for of them
oneEmpedocles. holds that the One is Love,
anotherAnaximenes. Air, and anotherClearly of colors. And unity would be some one color, e.g. white.
- Similarly if all existing things were tunes, there would be a number—of
+ Similarly if all existing things were tunes, there would be a number—of
quarter-tones; but their substance would not be a number; and unity would be something
whose substance is not unity but a quarter-tone. Similarly in the case of sounds, existing
@@ -6514,7 +6514,7 @@
so too in the sphere of substance the One-itself is one substance. And that in a sense unity means the same as being is clear (a)
from the fact that it has a meaning corresponding to each of the categories, and is
- contained in none of them—e.g., it is contained neither in substance nor in quality,
+ contained in none of them—e.g., it is contained neither in substance nor in quality,
but is related to them exactly as being is; (b) from the fact that in "one man" nothing
more is predicated than in "man"Cf. Aristot. Met. 4.2.6-8.(just as Being too does
@@ -6526,8 +6526,8 @@
undivided is called one. Then since opposition is of four kinds, and one of the present
pairs of opposites is used in a privative sense, they must be contraries, and neither
contradictories nor relative terms. Unity is
- described and explained by its contrary—the indivisible by the
- divisible—because plurality, i.e. the divisible, is more easily perceptible than the
+ described and explained by its contrary—the indivisible by the
+ divisible—because plurality, i.e. the divisible, is more easily perceptible than the
indivisible; and so in formula plurality is prior to the indivisible, on account of our
powers of perception. To Unity belong (as we showed by
tabulation in our distinction of the contrariesCf.
@@ -6548,7 +6548,7 @@
straight lines are similar. These are similar, but not absolutely the same. (b) If, having
the same form, and being capable of difference in degree, they have no difference of
degree. (c) If things have an attribute which
- is the same and one in form—e.g. white—in different degrees, we say that they
+ is the same and one in form—e.g. white—in different degrees, we say that they
are similar because their form is one. (d) If the respects in which they are the same are
more than those in which they differ, either in general or as regards their more prominent
qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being
@@ -6574,7 +6574,7 @@
either "other" or "the same." But that which is different from something is different in
some particular respect, so that that in which they differ must be the same sort of thing;
i.e. the same genus or species. For everything
- which is different differs either in genus or in species—in genus, such things as
+ which is different differs either in genus or in species—in genus, such things as
have not common matter and cannot be generated into or out of each other, e.g. things
which belong to different categories; and in species, such things as are of the same genus
(genus meaning that which is predicated of both the different things alike in respect of
@@ -6621,7 +6621,7 @@
most different things which come under the same faculty are contraries; for one science
treats of one class of things, in which complete difference is the greatest. "Positive state" and
- "Privation" constitute primary contrariety—not every form of privation (for it has
+ "Privation" constitute primary contrariety—not every form of privation (for it has
several senses), but any form which is complete. All other contraries must be so called
with respect to these; some because they possess these, others because they produce them
or are productive of them, and others because they are acquisitions or losses of these or
@@ -6634,7 +6634,7 @@
which is totally incapable of possessing some attribute,This is not a proper example of privation. Cf. Aristot. Met. 5.22. or that which would
- naturally possess some attribute but does not, that suffers privation—either
+ naturally possess some attribute but does not, that suffers privation—either
absolutely or in some specified way. Here we already have several meanings, which we have
distinguished elsewhere. Thus privation is a kind of contradiction or incapacity which is
determinate or associated with the receptive material. And the differences are as we have stated: one case is, if a
thing is merely deprived; another, if it is deprived at a certain time or in a certain
- part—e.g. at a certain age or in the important part—or entirely. Hence in some
+ part—e.g. at a certain age or in the important part—or entirely. Hence in some
cases there is an intermediate (there are men who are neither good nor bad), and in others
- there is not—a thing must be either odd or even. Again, some have a determinate subject, and others have not. Thus it
is evident that one of a pair of contraries always has a privative sense; but it is enough
if this is true of the primary or generic contraries, e.g. unity and plurality; for the
others can be reduced to them. Since one thing has one contrary, it might be asked in what sense
unity is opposed to plurality, and the equal to the great and to the small. For if we
- always use the word "whether" in an antithesis—e.g., "whether it is white or black,"
+ always use the word "whether" in an antithesis—e.g., "whether it is white or black,"
or "whether it is white or not" (but we do not ask "whether it is a man or white," unless
we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who
came or Socrates. This is not a necessary
disjunction in any class of things, but is derived from the use in the case of
- opposites—for it is only opposites that cannot be true at the same time—and we
+ opposites—for it is only opposites that cannot be true at the same time—and we
have this same use here in the question "which of the two came?" for if both alternatives were
possible, the question would be absurd; but even so the question falls into an antithesis:
- that of "one" or "many"—i.e., "whether both came, or one")— if, then, the question "whether" is always concerned with
opposites, and we can ask "whether it is greater or smaller, or equal," what is the nature
of the antithesis between "equal" and "greater or smaller"? It is contrary neither to one
@@ -6691,7 +6691,7 @@
negation or as privation. Now it cannot be so opposed to one of the two, for it is no more
opposed to the great than to the small. Therefore it is a privative negation of both. For this reason we say "whether" with
- reference to both, and not to one of the two—e.g., "whether it is greater or equal,"
+ reference to both, and not to one of the two—e.g., "whether it is greater or equal,"
or "whether it is equal or smaller"; there are
always three alternatives. But it is not a necessary privation; for not everything is
equal which is not greater or smaller, but only things which would naturally have these
@@ -6706,7 +6706,7 @@
unit="para"/>Therefore those persons are
wrong in their criticism who imagine that all terms are used analogously, so that that
which is neither a shoe nor a hand will be intermediate between "shoe" and "hand," because
- that which is neither good nor bad is intermediate between good and bad—as though
+ that which is neither good nor bad is intermediate between good and bad—as though
there must be an intermediate in all cases; but this does not necessarily
follow. For the one is a joint negation of
opposites where there is an intermediate and a natural interval; sc. "and then the absurdity of his view would have been
apparent, for," etc. Aristotle assumes the Anaxagoras meant "smallness" (MIKRO/THS) to be the opposite of "multitude" (PLH=QOS); but he meant just what he said—that the
+ lang="greek">PLH=QOS); but he meant just what he said—that the
particles of which things consist are infinitely many and infinitely small. See Bowman
in Classical Review 30, 42-44. for things cannot be infinite in fewness), since
fewness is constituted not by one, as some hold, but by two. Aristot. Met. 5.15.8, 9.
- that things are called relative in two senses—either as being contraries, or as
+ that things are called relative in two senses—either as being contraries, or as
knowledge is related to the knowable, A being related to B because B is described in
relation to A. There is no reason why one should not be fewer than something, e.g. two; for if it is
@@ -6763,7 +6763,7 @@
is a plurality measurable by one. And in a sense one and number are opposed; not, however,
as being contrary, but as we have said some relative terms to be; for it is qua measure and measurable that they are opposed. (Hence not everything which is one is a number—e.g., a
+ ed="P" unit="Loeb chap"/>(Hence not everything which is one is a number—e.g., a
thing which is indivisible.) But although the relation between knowledge and the knowable
is said to be similar to this, it turns out not to be similar. For it would seem that
knowledge is a measure, and the knowable that which is measurable by it; but it happens
@@ -6796,9 +6796,9 @@
intermediate term); of the remaining types of opposites some are relative, others
privative, and others contrary. Those relative
opposites which are not contrary have no intermediate. The reason for this is that they
- are not in the same genus— for what is intermediate between knowledge and the
- knowable?—but between great and small there is an intermediate. Now since
+ knowable?—but between great and small there is an intermediate. Now since
intermediates are in the same genus, as has been shown, and are between contraries, they
must be composed of those contraries. For the contraries must either belong to a genus or
not. And if there is a genus in such a way that
@@ -7157,7 +7157,7 @@
permanent or temporary state or motion or some other such affection of Being qua Being. And since
everything that is can be referred to some one common concept, each of the contrarieties
- too can be referred to the primary differentiae and contrarieties of Being—whether
+ too can be referred to the primary differentiae and contrarieties of Being—whether
the primary differentiae of Being are plurality and unity, or similarity and
dissimilarity, or something else; for we may take them as already discussed.Cf. Aristot. Met. 4.2.9
@@ -7169,7 +7169,7 @@
contraries pertains to one and the same science, and each contrary is so called in virtue of privation (although indeed one might wonder
in what sense they can be called contraries in virtue of privation when they admit of a
- middle term—e.g. "unjust" and "just"), in all such cases we must regard the
+ middle term—e.g. "unjust" and "just"), in all such cases we must regard the
privation as being not of the whole definition but of the ultimate species. E.g., if the
just man is "one who is obedient to the laws in virtue of some volitional state," the
unjust man will not be entirely deprived of the whole definition, but will be "one who is
@@ -7178,8 +7178,8 @@
cases). And just as the mathematician makes a
study of abstractions (for in his investigations he first abstracts everything that is
sensible, such as weight and lightness, hardness and its contrary, and also heat and cold
- and all other sensible contrarieties, leaving only quantity and continuity—sometimes
- in one, sometimes in two and sometimes in three dimensions—and their affections qua quantitative and continuous, and does not study them with respect
to any other thing; and in some cases investigates the relative positions of things and
the properties of these, Aristot. Met.
11.1.1. may be regarded as solvedAlso the problem stated in ch. i. 3.—I mean the problem as to how there
+ >Also the problem stated in ch. i. 3.—I mean the problem as to how there
can be one science of several things which are different in genus. Since even the mathematician
uses the common axioms only in a particular application, it will be the province of
@@ -7227,7 +7227,7 @@
is a principle in existing things about which we cannot make a mistakeThis chapter corresponds to Aristot. Met. 4.3.7-4.31.; of which, on the
- contrary, we must always realize the truth—viz. that the same thing cannot at one
+ contrary, we must always realize the truth—viz. that the same thing cannot at one
and the same time be and not be, nor admit of any other similar pair of opposites. Of such
axioms although there is a proof ad hominem, there is no absolute proof; And
- further, if nothing can be truly affirmed, then this very statement—that there is no
- such thing as a true affirmation—will be false. But if there is such a thing, the
+ further, if nothing can be truly affirmed, then this very statement—that there is no
+ such thing as a true affirmation—will be false. But if there is such a thing, the
contentions of those who raise objections of this kind and utterly destroy rational
discourse may be considered to be refuted.Cf. Aristot. Met. 4.8.4, 5. And since every
science must have some knowledge of the essence and must use it as a starting-point, we must be careful to observe how the natural
- philosopher should define, and how he should regard the formula of essence—whether
+ philosopher should define, and how he should regard the formula of essence—whether
in the same way as the term "snub," or rather as the term "concave." For of these the formula of "snub" is stated in conjunction
with the matter of the object, whereas that of "concave" is stated apart from the matter;
@@ -7446,7 +7446,7 @@
permanent things, but not with things which can exist separately. Hence there is a science distinct from both of these, which deals with
that which exists separately and is immovable; that is, if there really is a substance of
- this kind—I mean separately existent and immovable—as we shall endeavor to
+ this kind—I mean separately existent and immovable—as we shall endeavor to
prove.Aristot.
Met. 12.6, 7. And if there is an entity of this kind in the world of
reality, here surely must be the Divine, and this must be the first and most fundamental
@@ -7481,7 +7481,7 @@
cultured, when he has become lettered, will be both at once although he was not before;
but that which is but was not always so must have come to be; therefore he must have
become at the same time cultured and lettered" —none of the recognized sciences considers this, except sophistry. This is the
+ />—none of the recognized sciences considers this, except sophistry. This is the
only science which concerns itself with the accidental, and hence Plato was not far wrong
in sayingPlat. Sop.
254a. that the sophist spends his time in the study of unreality. But
@@ -7551,11 +7551,11 @@
(generation and destruction); quantitative (increase and decrease); qualitative
(alteration); spatial (locomotion). Cf. Aristot. Met.
11.12.1, 2.; and there is nothing which is common to these and in no one
- category. Each category belongs to all its members in two ways—e.g. substance, for
+ category. Each category belongs to all its members in two ways—e.g. substance, for
this is sometimes the form of the thing and sometimes its privation; and as regards quality there is white and black; and as regards
quantity, complete and incomplete; and as regards spatial motion there is up and down or
- light and heavy—so that there are as many forms of motion and change as there are of
+ light and heavy—so that there are as many forms of motion and change as there are of
Being.This is inaccurate; see previous
note. Now since every kind of thing is divided into
the potential and the real, I call the actualization of the potential as such,(This is obvious in the case of
contraries; for the potentiality for health and the potentiality for illness are not the
- same—for if they were, health and illness would be the same too—but the
+ same—for if they were, health and illness would be the same too—but the
substrate which becomes healthy or ill, whether it is moisture or blood, is one and the
same.) And since it is not the same, just as "color" and "visible" are not the same, it is
the complete reality of the potential qua potential that is
@@ -7593,8 +7593,8 @@
everything may sometimes be actual, and sometimes not; e.g. the "buildable" qua "buildable"; and the actualization of the "buildable" qua "buildable" is the act of building. For the actualization is either this—the act of
- building—or a house. But when the house exists, it will no longer be buildable; the
+ unit="Loeb chap"/>For the actualization is either this—the act of
+ building—or a house. But when the house exists, it will no longer be buildable; the
buildable is that which is being built. Hence the actualization must be the
act of building, and the act of building is a kind of motion. The same argument applies to
the other kinds of motion. The region proper to the body which
is homogeneous with the clod is infinite. Then will the clod occupy the whole of that
region? How can it? Then what of its rest or motion? It will either rest
- everywhere—in which case it cannot move—or move everywhere; in which case it
+ everywhere—in which case it cannot move—or move everywhere; in which case it
cannot rest.If earth is an infinite body, its
region must be infinite. But the infinite has no center (cf. sect. 13). Therefore a
clod, which cannot occupy the whole region proper to earth, will have no region proper
@@ -7746,8 +7746,8 @@
whole must be finite. In general, there cannot be an infinite body and a place
for bodies if every body which is sensible has either weight or lightness; for it will
- have to move either towards the center or upwards, and the infinite—either the whole
- or the half—cannot do either; for how can you divide it? How can the infinite be
+ have to move either towards the center or upwards, and the infinite—either the whole
+ or the half—cannot do either; for how can you divide it? How can the infinite be
part up and part down, or part extreme and part center? Further, every sensible body is in some place, and of place there are
six kinds,i.e., above and below, before and behind,
@@ -7780,9 +7780,9 @@
affirmation. Thus there must be three forms of change; for that which is from negative into negative is not change, because they
are neither contraries nor contradictories, since they entail no opposition. The change
- from the negative into its contradictory positive is generation—absolute change
+ from the negative into its contradictory positive is generation—absolute change
absolute generation, and qualified change qualified generation; and the change from the
- positive to the negative is destruction—absolute change absolute destruction, and
+ positive to the negative is destruction—absolute change absolute destruction, and
qualified change qualified destruction.The change
from positive to positive is omitted here (but cf. sect. 7). Aristotle no doubt intended
to use it as an example of non-substantial change, e.g. from "poor man" to "rich man";
@@ -7809,7 +7809,7 @@
3. and of these those which relate to generation and destruction are not motions,
and these are the changes between contradictories, the change from positive to positive
must alone be motion. The subjects are either contraries or intermediates (for privative
- terms may also be regarded as contraries) and are denoted by a positive term—e.g.
+ terms may also be regarded as contraries) and are denoted by a positive term—e.g.
"naked" or "toothless" or "black." Now since the categories are distinguished as substance,
quality, place, activity or passivity, relation and quantity,the last belongs to some other science, if there is no
principle common to all three. Sensible substance is liable to change. Now if change proceeds from
- opposites or intermediates—not however from all opposites (for speech is not white),
+ opposites or intermediates—not however from all opposites (for speech is not white),
but only from the contraryCf. Aristot. Met. 10.7.—then there must be
+ n="Aristot. Met. 10.1057a">Aristot. Met. 10.7.—then there must be
something underlying which changes into the opposite contrary; for the contrariesi.e., contrary qualities. Cf. Aristot. Met. 8.5.1. do not change. these are all matter, and the last is the matter of a substance in the
strictest sense); (2.) the "nature"i.e.,
- form.(existing individually)—i.e. a kind of positive state which is the
+ form.(existing individually)—i.e. a kind of positive state which is the
terminus of motion; and (3.) the particular combination of these, e.g. Socrates or
Callias. In some cases the individuality does not exist apart from the composite substance
(e.g., the form of a house does not exist separately, except as the art of
@@ -8229,8 +8229,8 @@
or the doctrine of the physicists that "all things were together,"Cf. Aristot. Met. 12.2.3.
we have the same impossibility; for how can there be motion if there is no actual cause?
- Wood will not move itself—carpentry must act upon it; nor will the menses or the
- earth move themselves—the seeds must act upon the earth, and the semen on the
+ Wood will not move itself—carpentry must act upon it; nor will the menses or the
+ earth move themselves—the seeds must act upon the earth, and the semen on the
menses. Hence some, e.g. LeucippusCf. Aristot. Met.
1.4.12, Aristot. De Caelo 300b 8, and
@@ -8255,7 +8255,7 @@
Empedocles with his theory of Love and Strife, and by those who hold that motion is
eternal, e.g. Leucippus. Therefore Chaos or Night did not
endure for an unlimited time, but the same things have always existed, either passing
- through a cycle or in accordance with some other principle—that is, if actuality is
+ through a cycle or in accordance with some other principle—that is, if actuality is
prior to potentiality. Now if there is a
regular cycle, there must be somethingThe sphere of
the fixed stars, Aristot. Met. 12.8.9; cf. For the primary kind of change is locomotion,Proved in Aristot. Physics 8.7.
@@ -8345,7 +8345,7 @@
concerned with that which is in itself best, and thinking in the highest sense with that
which is in the highest sense best.Since the prime
mover is pure actuality, and has or rather is the highest form of life, Aristotle
- identifies it with the highest activity—pure thinking. And thought thinks
itself through participation in the object of thought; for it becomes an object of thought
by the act of apprehension and thinking, so that thought and the object of thought are the
@@ -8373,7 +8373,7 @@
n="7.11" ed="P" unit="Loeb chap"/>For seed comes from prior creatures which are perfect,
and that which is first is not the seed but the perfect creature. E.g., one might say that prior
- to the seed is the man—not he who is produced from the seed, but another man from
+ to the seed is the man—not he who is produced from the seed, but another man from
whom the seed comes.Cf. Aristot. Met. 9.8.4, 5. Thus it is evident from the
@@ -8408,8 +8408,8 @@
and since we can see that besides the simple spatial motion of the universei.e., the (apparent) diurnal revolution of the
heavens.(which we hold to be excited by the primary immovable substance) there
- are other spatial motions—those of the planets—which are eternal (because a
- body which moves in a circle is eternal and is never at rest—this has been proved in
+ are other spatial motions—those of the planets—which are eternal (because a
+ body which moves in a circle is eternal and is never at rest—this has been proved in
our physical treatisesAristot. Physics 8.8, 9, Aristot. De Caelo 1.2,
2.3-8.); then each of these spatial motions must also be excited by a
@@ -8495,7 +8495,7 @@
in calculation see Ross ad loc. spheres in all. This, then, may be taken to be the number of the spheres; and thus it is reasonable to
suppose that there are as many immovable substances and principles,i.e., the movers of the spheres.—the statement of logical
+ anchored="yes">i.e., the movers of the spheres.—the statement of logical
necessity may be left to more competent thinkers. If there can be no spatial motion which is not
conducive to the motion of a star, and if
@@ -8645,7 +8645,7 @@
resp="Tredennick" anchored="yes">See Aristot. Met.
12.7.10 does not even regard the Good and the Bad as principles; yet the
Good is in the truest sense a principle in all things. The former school is right in
- holding that the Good is a principle, but they do not explain how it is a principle—
+ holding that the Good is a principle, but they do not explain how it is a principle—
whether
as an end or as a moving cause or as form. Empedocles theory is also absurd, for he identifies
@@ -8663,7 +8663,7 @@
moves things, but moves them for some end, and therefore there must be some other
GoodMotion presupposes a final cause, which was
not what Anaxagoras meant by "Mind." Cf. Aristot. Met.
- 1.7.5.—unless it is as we say; for on our view the art of medicine
+ 1.7.5.—unless it is as we say; for on our view the art of medicine
is in a sense health.Aristotle identifies the
efficient cause, in a sense, with the final cause. Cf. Aristot. Met. 7.9.3. It is absurd also not to provide a contrary for
@@ -8745,19 +8745,19 @@
Ideas are substances. Now since someThis was the orthodox Platonist view; cf. Aristot. Met. 1.6.4. recognize these as two
- classes— the Ideas and the mathematical
- numbers—and othersXenocrates and his
+ classes— the Ideas and the mathematical
+ numbers—and othersXenocrates and his
followers. regard both as having one nature, and yet othersThe Pythagoreans and Speusippus. hold that only
the mathematical substances are substances, we must first consider the mathematical
- objects, without imputing to them any other characteristic—e.g. by asking whether
+ objects, without imputing to them any other characteristic—e.g. by asking whether
they are really Ideas or not, or whether they are principles and substances of existing
- things or not—and merely inquire whether as mathematical objects they exist or not,
+ things or not—and merely inquire whether as mathematical objects they exist or not,
and if they do, in what sense; then after this we must separately consider the Ideas
themselves, simply and in so far as the accepted procedure requires; for most of the
arguments have been made familiar already by the criticisms of other thinkers. And further, the greater part of our discussion must
- bear directly upon this second question—viz. when we are considering whether the
+ bear directly upon this second question—viz. when we are considering whether the
substances and first principles of existing things are numbers and Ideas; for after we
have dealt with the Ideas there remains this third question. Now if the objects of mathematics exist,
@@ -8769,7 +8769,7 @@
that they are is a fabrication, has been observed already in our discussion of
difficultiesCf. Aristot. Met. 3.2.23-30.
- —the
+ —the
reasons being (a) that two solids cannot occupy the same space, and (b) that on this same
theory all other potentialities and characteristics would exist in sensible things, and
none of them would exist separately. This, then, has been already stated; Now the accumulation becomes absurd; because whereas we get
only one class of solids besides sensible solids, we get three classes of planes besides
- sensible planes—those which exist separately from sensible planes, those which exist
+ sensible planes—those which exist separately from sensible planes, those which exist
in the mathematical solids, and those which exist separately from those in the
- mathematical solids—four classes of lines, and five of points; with which of these, then, will the mathematical sciences deal?
Not, surely, with the planes, lines and points in the immovable solid; for knowledge is
always concerned with that which is prior. And the same argument applies to numbers; for
@@ -8860,9 +8860,9 @@
indissociable. For if attributes, such as
"moving" or "white," do not exist apart from their substances, "white" will be prior in
formula to "white man," but not in substantiality; for it cannot exist in separation, but
- always exists conjointly with the concrete whole—by which I mean "white
+ always exists conjointly with the concrete whole—by which I mean "white
man." Thus it is obvious that neither is the
- result of abstraction prior, nor the result of adding a determinant posterior—for
+ result of abstraction prior, nor the result of adding a determinant posterior—for
the expression "white man" is the result of adding a determinant to "white." Thus we have sufficiently shown (a) that the objects of mathematics
are not more substantial than corporeal objects; (b) that they are not prior in point of
@@ -8893,14 +8893,14 @@
say in a general sense that mathematical objects exist, and in such a form as
mathematicians describe them. And just as it is
true to say generally of the other sciences that they deal with a particular
- subject—not with that which is accidental to it (e.g. not with "white" if "the
+ subject—not with that which is accidental to it (e.g. not with "white" if "the
healthy" is white, and the subject of the science is "the healthy"), but with that which
is the subject of the particular science; with the healthy if it treats of things qua healthy, and with man if qua man—so this is also
+ >qua healthy, and with man if qua man—so this is also
true of geometry. If the things of which it treats are accidentally sensible although it
does not treat of them qua sensible, it does not follow that the
- mathematical sciences treat of sensible things—nor, on the other hand, that they
+ mathematical sciences treat of sensible things—nor, on the other hand, that they
treat of other things which exist independently apart from these. Many attributes are essential
properties of things as possessing a particular characteristic; e.g., there are attributes
@@ -8979,8 +8979,8 @@
>Aristot. De Part. Anim. 642a 24. and defined, after a fashion, "the
hot" and "the cold"; while the PythagoreansCf.
Aristot. Met. 1.5.2, 16. at an earlier
- date had arrived at definitions of some few things—whose formulae they connected
- with numbers—e.g., what "opportunity" is, or "justice" or "marriage"); and he
+ date had arrived at definitions of some few things—whose formulae they connected
+ with numbers—e.g., what "opportunity" is, or "justice" or "marriage"); and he
naturally inquired into the essence of things; for he was trying to reason logically, and the starting-point of all logical reasoning
is the essence. At that time there was as yet no such proficiency in Dialectic that men
@@ -9114,7 +9114,7 @@
Confusion (or textual inaccuracy) is further suggested by the fact that Aristotle offers
no alternative statement of the nature of number in general, such as we should expect
from his language. In any case the classification is arbitrary and
- incomplete.— and this applies
+ incomplete.— and this applies
directly to units, and any given unit is inaddible to any other given unit; or (b) theyThe
units. are all directly successive, and any units can be added to any other
@@ -9139,7 +9139,7 @@
resp="Tredennick" anchored="yes">In Aristot. Met.
13.2.1-3. but in the sense that sensible things are composed of numbers
which are present in themThe Pythagorean
- number-atomist view; See Introduction.)—either some of them and not others,
+ number-atomist view; See Introduction.)—either some of them and not others,
or all of them.i.e., either all numbers are
material elements of things, or some are and others are not. These are of necessity the only ways in which the numbers can
@@ -9157,10 +9157,10 @@
n="Aristot. Met. 12.1075b">Aristot. Met. 12.10.14. being the primary
reality and separate from sensible things. The Pythagoreans also believe in one kind of
- number—the mathematical; only they maintain that it is not separate, but that
+ number—the mathematical; only they maintain that it is not separate, but that
sensible substances are composed of it. For they construct the whole universe of numbers,
but not of numbers consisting of abstract units; they suppose the units to be extended—but as for how the first extended unit was
+ />they suppose the units to be extended—but as for how the first extended unit was
formed they appear to be at a loss.Cf. Aristot. Met. 13.8.9, 10, Aristot. Met. 14.3.15, Aristot. Met. 1.9.30.; and of those who
treat the subject in a different manner someSpeusippus; cf. sect. 7 above. speak of the mathematical objects and in a
- mathematical way—viz. those who do not regard the Ideas as numbers, nor indeed hold
- that the Ideas exist—and othersXenocrates.
+ mathematical way—viz. those who do not regard the Ideas as numbers, nor indeed hold
+ that the Ideas exist—and othersXenocrates.
For his belief in indivisible lines see Ritter and Preller 362. Aristotle ascribes the
doctrine to Plato in Aristot. Met.
1.9.25. speak of the mathematical objects, but not in a mathematical way;
@@ -9236,7 +9236,7 @@
>i.e., the Great-and-Small, which Aristotle wrongly understands as two unequal things.
It is practically certain that Plato used the term (as he did that of "Indeterminate
Dyad") to describe indeterminate quantity. See Introduction.(coming into being
- when these were equalized), or otherwise— since if we regard the one unit as prior to the other,This is a necessary implication of the theory of inaddible units (cf.
Aristot. Met. 13.6.1, 2). it will be
@@ -9301,7 +9301,7 @@
10 is not a chance number,I think Ross's
interpretation of this passage must be right. The Ideal 10 is a unique number, and the
numbers contained in it must be ideal and unique; therefore the two 5's must be
- specifically different, and so must their units—which contradicts the view under
+ specifically different, and so must their units—which contradicts the view under
discussion. and is not composed of chance 5's, any more than of chance units, the
units in this number 10 must be different; for
if they are not different, the 5's of which the 10 is composed will not be different; but
@@ -9343,7 +9343,7 @@
unit="Loeb chap"/>In general, to regard units as different in any way whatsoever is
absurd and fictitious (by "fictitious" I mean "dragged in to support a hypothesis"). For
we can see that one unit differs from another neither in quantity nor in quality; and a
- number must be either equal or unequal—this applies to all numbers, but especially
+ number must be either equal or unequal—this applies to all numbers, but especially
to numbers consisting of abstract units. Thus
if a number is neither more nor less, it is equal; and things which are equal and entirely
without difference we assume, in the sphere of number, to be identical. Otherwise even the
@@ -9351,7 +9351,7 @@
that they are not different, what reason will he be able to allege? Again, if every unit plus
another unit makes 2, a unit from the Ideal 2 plus one from the Ideal 3 will make
- 2—a 2 composed of different unitsWhich
+ 2—a 2 composed of different unitsWhich
conflicts with the view under discussion.; will this be prior or posterior to 3?
It rather seems that it must be prior, because one of the units is contemporaneous with 3,
and the other with 2.The implication seems to be,
@@ -9430,8 +9430,8 @@
abstract existence. From these considerations it is also clear that the third
alternativeCf. Aristot. Met. 13.6.7.—that Ideal number and mathematical number
- are the same—is the worst; for two errors have to be combined to make one theory.
+ >Aristot. Met. 13.6.7.—that Ideal number and mathematical number
+ are the same—is the worst; for two errors have to be combined to make one theory.
(1.) Mathematical number cannot be of this nature, but the propounder of this view has to
spin it out by making peculiar assumptions; (2.) his theory must admit all the
difficulties which confront those who speak of Ideal number. Aristot. Met.
1.6.10. Proportion alone of the "derivatives" here mentioned appears to be
derived from number. As Syrianus says, the three types of proportion can be illustrated
- by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4,
+ by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4,
harmonic 2. 3. 6. Hence they
identify the odd with Unity; because if oddness depended on 3, how could 5 be odd?sc. because (on their theory) 3 is not contained in 5.
Thus oddness had to be referred to not a number but a
- principle—unity. Again, they hold that
+ principle—unity. Again, they hold that
spatial magnitudes and the like have a certain limit; e.g. the first or indivisible line, then the
2, and so on; these too extending up to 10.The
@@ -9544,8 +9544,8 @@
unit="Loeb chap"/>Now if we regard number as composite, Unity is prior; but if we regard
the universal or form as prior, number is prior, because each unit is a material part of
number, while number is the form of the units. And there is a sense in which the right
- angle is prior to the acute angle—since it is definite and is involved in the
- definition of the acute angle—and another sense in which the acute angle is prior,
+ angle is prior to the acute angle—since it is definite and is involved in the
+ definition of the acute angle—and another sense in which the acute angle is prior,
because it is a part of the other, i.e., the right angle is divided into acute
angles. Thus regarded as matter the acute
angle and element and unit are prior; but with respect to form and substance in the sense
@@ -9563,15 +9563,15 @@
impossible; for in one sense it is the One qua form or
essence, and in the other the One qua part or matter, that is primary. There is a sense in which both
- number and unit are one; they are so in truth potentially—that is, if a number is
+ number and unit are one; they are so in truth potentially—that is, if a number is
not an aggregate but a unity consisting of units distinct from those of other numbers, as
- the Platonists hold— but each of the
+ the Platonists hold— but each of the
twoAristotle takes the number two as an example,
but the principle is of course universal. In a sense both number and unit are one; but
if the number exists as an actual unity, the unit can only exist potentially.
units is not one in complete reality. The cause of the error which befell the Platonists
- was that they were pursuing their inquiry from two points of view—that of
- mathematics and that of general definition—at the same time. Hence as a result of
+ was that they were pursuing their inquiry from two points of view—that of
+ mathematics and that of general definition—at the same time. Hence as a result of
the former they conceived of the One or first principle as a point, for the unit is a
point without position. (Thus they too, just like certain others, represented existing things as composed of that which is
@@ -9596,13 +9596,13 @@
Further, if
2 itself and 3 itself are each one thing, both together make 2. From what, then, does this
2 come? Since
- there is no contact in numbers, but units which have nothing between them—e.g. those
- in 2 or 3—are successive, the question might be raised whether or not they are
+ there is no contact in numbers, but units which have nothing between them—e.g. those
+ in 2 or 3—are successive, the question might be raised whether or not they are
successive to Unity itself, and whether of the numbers which succeed it 2 or one of the
units in 2 is prior. We find similar difficulties in the case of the genera posterior to
numberCf. Aristot. Met. 13.6.10.—the line, plane and solid. Some derive
+ >Aristot. Met. 13.6.10.—the line, plane and solid. Some derive
these from the species of the Great and Small; viz. lines from the Long and Short, planes
from the Broad and Narrow, and solids from the Deep and Shallow. These are species of the
Great and Small. As for the geometrical first
@@ -9620,7 +9620,7 @@
from the Straight and Crooked, or solids from the Smooth and Rough. Common to all these Platonic
theories is the same problem which presents itself in the case of species of a genus when
- we posit universals—viz. whether it is the Ideal animal that is present in the
+ we posit universals—viz. whether it is the Ideal animal that is present in the
particular animal, or some other "animal" distinct from the Ideal animal. This question
will cause no difficulty if the universal is not separable; but if, as the Platonists say,
Unity and the numbers exist separately, then it is not easy to solve (if we should apply
@@ -9637,7 +9637,7 @@
if the matter is one, line, plane and solid will be the same; because the product of the
same elements must be one and the same. If on the other hand there is more than one kind of
- matter—one of the line, another of the plane, and another of the solid—either
+ matter—one of the line, another of the plane, and another of the solid—either
the kinds are associated with each other, or they are not. Thus the same result will
follow in this case also; for either the plane will not contain a line, or it will be a
line. Further, no attempt is made to explain how number can be generated from unity and
@@ -9658,12 +9658,12 @@
indivisible; otherwise it will be a plurality and the unit will be divisible, and unity and plurality will not be its elements,
because each unit will not be generated from pluralitysc. but from an indivisible part of plurality—which is not a
+ anchored="yes">sc. but from an indivisible part of plurality—which is not a
plurality but a unity. and unity. (b)
The exponent of this theory merely introduces another number; because plurality is a
number of indivisible parts.i.e., to say that
number is derived from plurality is to say that number is derived from
- number—which explains nothing. Again, we must
+ number—which explains nothing. Again, we must
inquire from the exponent of this theory whether the numbersc. which plurality has been shown to be. is infinite or
finite. There was, it appears, a finite
@@ -9696,7 +9696,7 @@
posits theseUnity and the indeterminate dyad; for
the difficulty see Aristot. Met. 13.7.3,
4. as first principles, mathematical number can exist besides Ideal
- number, identified Ideal with mathematical number,—but only in theory, since
+ number, identified Ideal with mathematical number,—but only in theory, since
actually mathematical number is done away with, because the hypotheses which they state
are peculiar to them and not mathematical.Cf. Aristot. Met. 13.6.10. Cf. previous note. in all), are the elements of
numbers; the two former as matter, and Unity as form. Others speak of the Many and Few,
because the Great and the Small are in their nature more suited to be the principles of
- magnitude; and others use the more general term which covers these—"the exceeding"
+ magnitude; and others use the more general term which covers these—"the exceeding"
and "the exceeded." But none of these
variations makes any appreciable difference with respect to some of the consequences of
the theory; they only affect the abstract
@@ -9872,7 +9872,7 @@
and if there is either no contrary to unity, or if there is to be any contrary it is
plurality; and if the unequal is contrary to the equal, and the different to the same, and
the other to the thing itself then those who oppose unity to plurality have the best claim
- to credibility—but even their theory is inadequate, because then unity will be few.
+ to credibility—but even their theory is inadequate, because then unity will be few.
For plurality is opposed to paucity, and many to few. That "unity" denotes a measureCf. Aristot. Met.
@@ -9900,8 +9900,8 @@
regard the unequal as a unity, and the dyad as an indeterminate compound of great and
small, hold theories which are very far from being probable or possible. For these terms
represent affections and attributes, rather than substrates, of numbers and
- magnitudes—"many" and "few" applying to number, and "great" and "small" to
- magnitude— just as odd and even, smooth
+ magnitudes—"many" and "few" applying to number, and "great" and "small" to
+ magnitude— just as odd and even, smooth
and rough, straight and crooked, are attributes. Further, in addition to this error, "great" and "small" and all other
such terms must be relative. And the relative is of all the categories in the least degree
@@ -9955,7 +9955,7 @@
have had occasion to say elsewhere.Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just
- been saying—that no substance is eternal unless it is actuality—is true
+ been saying—that no substance is eternal unless it is actuality—is true
universally, and the elements are the matter of substance, an eternal substance can have
no elements of which, as inherent in it, it consists. There are some who, while making the
@@ -9973,8 +9973,8 @@
they encountered and refuted Parmenides' dictum: It will
ne'er be proved that things which are not, are,Parmenides Fr. 7 (Diels). i.e., that they must show that that which is not, is; for only so—of
- that which is, and of something else—could existing things be composed, if they are
+ unit="para"/>i.e., that they must show that that which is not, is; for only so—of
+ that which is, and of something else—could existing things be composed, if they are
more than one.Cf. Plat.
Soph. 237a, 241d, 256e. However, (i) in the first place, if "being" has several
@@ -10006,7 +10006,7 @@
generated from or resolved into not-being in this sense. But not only has "not-being" in
its various cases as many meanings as there are categories, but moreover the false and the
potential are called "not-being"; and it is from the latter that generation takes
- place—man comes to be from that which is not man but is potentially man, and white
+ place—man comes to be from that which is not man but is potentially man, and white
from that which is not white but is potentially white; no matter whether one thing is
generated or many. Clearly the point at issue is how "being" in the sense of the
@@ -10038,7 +10038,7 @@
ed="P" unit="Loeb chap"/>We must, then, as I say, presuppose in the case of each thing
that which is it potentially. The authorPlato. of this theory further explained what it is that is potentially a
- particular thing or substance, but is not per se existent—that it is the relative
+ particular thing or substance, but is not per se existent—that it is the relative
(he might as well have said "quality"); which is neither potentially unity or Being, nor a
negation of unity or Being, but just a
particular kind of Being. And it was still
@@ -10123,7 +10123,7 @@
has to face the question why sensible things exhibit numerical attributes. can
make out a case for the contrary view, and that those who hold this theory must find a
solution for the difficulty which was recently raisedsect. 3.—why it is that while numbers are in no way present
+ anchored="yes">sect. 3.—why it is that while numbers are in no way present
in sensible things, their attributes are present in sensible things. There are someProbably Pythagoreans.
Cf. Aristot. Met. 7.2.2, like a poorly constructed drama. ThoseXenocrates
(that the reference is not to Plato is clear from sect. 11). who posit the Ideas
escape this difficulty, because they construct spatial magnitudes out of matter and a
- number—2 in the case of lines, and 3, presumably, in that of planes, and 4 in that
+ number—2 in the case of lines, and 3, presumably, in that of planes, and 4 in that
of solids; or out of other numbers, for it makes no difference. But are we to regard these magnitudes as Ideas, or what is their mode
of existence? and what contribution do they make to reality? They contribute nothing; just
@@ -10197,8 +10197,8 @@
this theory, to introduce generation of things which are eternal. There is no reason to doubt whether the Pythagoreans do or do
not introduce it; for they clearly state that when the One had been
- constituted—whether out of planes or superficies or seed or out of something that
- they cannot explain—immediately the nearest part of the Infinite began to be drawn
+ constituted—whether out of planes or superficies or seed or out of something that
+ they cannot explain—immediately the nearest part of the Infinite began to be drawn
in and limited by the Limit.Cf. Aristot. Physics 3.4, Aristot. Physics 4.6, and Burnet, E.G.P. sect. 53. which clearly
implies that there is generation of even ones; and some hold that the even is constructed
- first out of unequals—the Great and Small—when they are equalized.Cf. Aristot. Met.
13.7.5. Therefore the inequality must apply to them before they are
equalized. If they had always been equalized they would not have been unequal before; for
@@ -10237,14 +10237,14 @@
goodness to the first principle as an attribute, but from treating unity as a principle,
and a principle in the sense of an element, and then deriving number from unity. The early
poets agree with this view in so far as they assert that it was not the original
- forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and
+ forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and
ruler. It was, however, on the ground of the
changing of the rulers of the world that the poets were led to state these theories;
because those of them who compromise by not describing everything in mythological
- language—e.g. PherecydesOf Of Syros (circa 600-525 B.C.). He made Zeus one of the three primary beings
- (Diels,Vorsokratiker201, 202). and certain others—make the
+ (Diels,Vorsokratiker201, 202). and certain others—make the
primary generator the Supreme Good; and so do the Magi,The Zoroastrian priestly caste. and some of the later philosophers
such as Empedocles and Anaxagoras: the one making Love an element,mathematical number). For on this view all units become identical with
some good, and we get a great abundance of goods.If
unity is goodness, and every unit is a kind of unity, every unit must be a kind of
- goodness—which is absurd. Further, if the Forms are numbers, all Forms become identical with some good. Again, let
+ goodness—which is absurd. Further, if the Forms are numbers, all Forms become identical with some good. Again, let
us assume that there are Ideas of anything that we choose. If there are Ideas only of
goods, the Ideas will not be substancesBecause they
are Ideas not of substances but of qualities.; and if there are Ideas of
@@ -10283,7 +10283,7 @@
contraries, the nature of plurality would then necessarily be bad. OthersPlato and
Xenocrates. hold that inequality is the nature of the bad. It follows, then, that
- all things partake of the Bad except one—absolute unity; and that numbers partake of
+ all things partake of the Bad except one—absolute unity; and that numbers partake of
it in a more unmitigated form than do spatial magnitudesAs being more directly derived from the first principles. Cf. Aristot. Met. 1.9.23 n.; And if, as we said,Aristot. Met. 14.1.17. the matter of each
- thing is that which is it potentially—e.g., the matter of actual fire is that which
- is potentially fire—then the Bad will be simply the potentially Good. Thus all these objections follow because (1.) they make every
principle an element; (2.) they make contraries principles; (3.) they make unity a
principle; and (4.) they make numbers the primary substances, and separable, and
@@ -10312,7 +10312,7 @@
objects that the imperfect does not really exist, and so Speusippus deprives his first
principle of reality. He is wrong;
for even in the natural world the principles from which these things are derived are
- perfect and complete—for it is man that begets man; the seed does not come
+ perfect and complete—for it is man that begets man; the seed does not come
first.Cf. Aristot. Met. 9.8.5. It is absurd also to generate space simultaneously
with the mathematical solids (for space is peculiar to particular things, which is why
@@ -10333,7 +10333,7 @@
as they intend it to be. Is it by composition,
as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of
unity and plurality we shall think of them separately. This, then, is what number will
- be—a unit plus plurality, or unity plus the
+ be—a unit plus plurality, or unity plus the
Unequal. And since a thing is derived from elements either
as inherent or as not inherent in it, in which way is number so derived? Derivation from
inherent elements is only possible for things which admit of generation. and as EurytusDisciple of Philolaus;
he "flourished" in the early fourth century B.C. determined which number belongs
- to which thing—e.g. this number to man, and this to horse—by using pebbles to
+ to which thing—e.g. this number to man, and this to horse—by using pebbles to
copy the shape of natural objects, like those who arrange numbers in the form of
geometrical figures, the triangle and the square.cf. Burnet, E.G.P. sect. 47. Or is
it because harmony is a ratio of numbers, and so too is man and everything else? But in
- what sense are attributes—white, and sweet, and hot—numbers?This is an objection to the view that numbers are
causes as bounds. And clearly numbers are not the essence of things, nor are they
causes of the form; for the ratioOr
@@ -10391,7 +10391,7 @@
particles of fire or earth, or of units. But the essence is the proportion of one quantity
to another in the mixture; i.e. no longer a number, but a ratio of the mixture of numbers,
either of corporeal particles or of any other kind. Thus number is not an efficient
- cause—neither number in general, nor that which consists of abstract units—nor
+ cause—neither number in general, nor that which consists of abstract units—nor
is it the matter, nor the formula or form of things. Nor again is it a final
cause. The
question might also be raised as to what the good is which things derive from numbers
@@ -10448,7 +10448,7 @@
C with the fifth, and Y with the octave. and that because there are three concords, there
are three double consonants. They ignore the fact that there might be thousands of double
- consonants—because there might be one symbol for *G*R. But if they say that each of these letters is double any of the others,
whereas no other is,Q,
F, and X are aspirated, not double,
@@ -10456,7 +10456,7 @@
resp="Tredennick" anchored="yes">Palate, lips, and teeth. of the mouth, and that
one consonant is combined with S in each region, it is for
this reason that there are only three double consonants, and not because there are three
- concords—because there are really more than three; but there cannot be more than
+ concords—because there are really more than three; but there cannot be more than
three double consonants. Thus these thinkers are like the ancient Homeric scholars, who see
minor similarities but overlook important ones. Some say
@@ -10500,7 +10500,7 @@
the same force. Hence they would seem to be
mere coincidences, for they are accidental; but all the examples are appropriate to each
other, and they are one by analogy. For there is analogy between all the categories of
- Being—as "straight" is in length, so is
+ Being—as "straight" is in length, so is
"level" in breadth, perhaps "odd" in number, and "white" in color. Again, it is not the Ideal
numbers that are the causes of harmonic relations, etc. (for Ideal numbers, even when they