Book, Paragraph
1 I, 2 | i) a finite or (ii) an infinite plurality. If (i) finite (
2 I, 2 | some other number. If (ii) infinite, then either as Democritus
3 I, 2 | whether a finite or an infinite plurality. So they too are
4 I, 2 | Melissus says that Being is infinite. It is then a quantity.
5 I, 2 | then a quantity. For the infinite is in the category of quantity,
6 I, 2 | quality or affection cannot be infinite except through a concomitant
7 I, 2 | quantities. For to define the infinite you must use quantity in
8 I, 2 | only substance, it is not infinite and has no magnitude; for
9 I, 2 | and so the one will not be infinite, as Melissus says-nor, indeed,
10 I, 4 | substances and his contraries infinite in multitude, whereas Empedocles
11 I, 4 | that the principles are infinite in multitude was probably
12 I, 4 | contains the most.~Now (1) the infinite qua infinite is unknowable,
13 I, 4 | Now (1) the infinite qua infinite is unknowable, so that what
14 I, 4 | unknowable, so that what is infinite in multitude or size is
15 I, 4 | in quantity, and what is infinite in variety of kind is unknowable
16 I, 4 | principles in question are infinite both in multitude and in
17 I, 4 | possible, there will be an infinite multitude of finite equal
18 I, 4 | Lastly (4) in each of his infinite bodies there would be already
19 I, 4 | would be already present infinite flesh and blood and brain—
20 I, 4 | and no less real than the infinite bodies, and each infinite:
21 I, 4 | infinite bodies, and each infinite: which is contrary to reason.~
22 I, 6 | Empedocles, is better than an infinite multitude; for Empedocles
23 II, 6 | number of possible causes is infinite.~Spontaneity and chance
24 III, 1 | are continuous; and the infinite presents itself first in
25 III, 1 | how it comes about that "infinite" is often used in definitions
26 III, 4 | at least is necessarily infinite or finite, even if some
27 III, 4 | in physics to discuss the infinite and to inquire whether there
28 III, 4 | formulated views about the infinite, and indeed, to a man, make
29 III, 4 | Pythagoreans and Plato, make the infinite a principle in the sense
30 III, 4 | the Pythagoreans place the infinite among the objects of sense (
31 III, 4 | is outside the heaven is infinite. Plato, on the other hand,
32 III, 4 | are nowhere),yet that the infinite is present not only in the
33 III, 4 | Pythagoreans identify the infinite with the even. For this,
34 III, 4 | them, always regard the infinite as an attribute of a substance
35 III, 4 | in number never make them infinite in amount. But those who
36 III, 4 | those who make the elements infinite in number, as Anaxagoras
37 III, 4 | Democritus do, say that the infinite is continuous by contact-compounded
38 III, 4 | We cannot say that the infinite has no effect, and the only
39 III, 4 | cannot be a source of the infinite or limitless, for that would
40 III, 4 | recognize, alongside the infinite, other causes, such as Mind
41 III, 4 | in the existence of the infinite comes mainly from five considerations:~(
42 III, 4 | nature of time-for it is infinite.~(2) From the division of
43 III, 4 | also use the notion of the infinite.~(3) If coming to be and
44 III, 4 | which things come to be is infinite.~(4) Because the limited
45 III, 4 | heaven are supposed to be infinite because they never give
46 III, 4 | that what is outside is infinite) leads people to suppose
47 III, 4 | suppose that body also is infinite, and that there is an infinite
48 III, 4 | infinite, and that there is an infinite number of worlds. Why should
49 III, 4 | Also, if void and place are infinite, there must be infinite
50 III, 4 | infinite, there must be infinite body too, for in the case
51 III, 4 | But the problem of the infinite is difficult: many contradictions
52 III, 4 | there something which is infinite or some things which are
53 III, 4 | sensible magnitude which is infinite.~We must begin by distinguishing
54 III, 4 | senses in which the term "infinite" is used.~(1) What is incapable
55 III, 4 | Further, everything that is infinite may be so in respect of
56 III, 5 | it is impossible that the infinite should be a thing which
57 III, 5 | a thing which is itself infinite, separable from sensible
58 III, 5 | sensible objects. If the infinite is neither a magnitude nor
59 III, 5 | if indivisible, then not infinite, except in the sense (1)
60 III, 5 | by those who say that the infinite exists, nor that in which
61 III, 5 | gone through". But if the infinite exists as an attribute,
62 III, 5 | attribute, it would not be, qua infinite an element in substances,
63 III, 5 | invisible.~Further, how can the infinite be itself any thing, unless
64 III, 5 | substances, a fortiori the infinite is not.~It is plain, too,
65 III, 5 | is plain, too, that the infinite cannot be an actual thing
66 III, 5 | it that is taken will be infinite, if it has parts: for "to
67 III, 5 | it has parts: for "to be infinite" and "the infinite" are
68 III, 5 | to be infinite" and "the infinite" are the same, if it is
69 III, 5 | is air, so a part of the infinite would be infinite, if it
70 III, 5 | of the infinite would be infinite, if it is supposed to be
71 III, 5 | principle.) Therefore the infinite must be without parts and
72 III, 5 | cannot be true of what is infinite in full completion: for
73 III, 5 | same breath they treat the infinite as substance, and divide
74 III, 5 | general question whether the infinite can be present in mathematical
75 III, 5 | among them a body which is infinite in the direction of increase.~
76 III, 5 | body there cannot be an infinite body either intelligible
77 III, 5 | taken in abstraction be infinite, for number or that which
78 III, 5 | possible to go through the infinite.~If, on the other hand,
79 III, 5 | to the same result.~The infinite body must be either (1)
80 III, 5 | possible.~(1) Compound the infinite body will not be, if the
81 III, 5 | and no one of them can be infinite. If one of the bodies falls
82 III, 5 | finite in amount while air is infinite and a given quantity of
83 III, 5 | numerically definite-the infinite body will obviously prevail
84 III, 5 | impossible that each should be infinite. "Body" is what has extension
85 III, 5 | in all directions and the infinite is what is boundlessly extended,
86 III, 5 | boundlessly extended, so that the infinite body would be extended in
87 III, 5 | infinitum.~Nor (2) can the infinite body be one and simple,
88 III, 5 | people who make this the infinite, and not air or water, in
89 III, 5 | by the element which is infinite. They have contrariety with
90 III, 5 | moist, fire hot; if one were infinite, the others by now would
91 III, 5 | As it is, they say, the infinite is different from them and
92 III, 5 | body; not because it is infinite on that point a general
93 III, 5 | other of the elements be infinite. For generally, and apart
94 III, 5 | how any of them could be infinite, the All, even if it were
95 III, 5 | that there should be an infinite sensible body. The following
96 III, 5 | spark.~Suppose (a) that the infinite sensible body is homogeneous.
97 III, 5 | of the body akin to it is infinite. Will it occupy the whole
98 III, 5 | will be either finite or infinite in variety of kind. (i)
99 III, 5 | for if the All is to be infinite, some of them would have
100 III, 5 | of them would have to be infinite, while the others were not,
101 III, 5 | e.g. fire or water will be infinite. But, as we have seen before,
102 III, 5 | made fire or earth the one infinite body, but either water or
103 III, 5 | But (ii) if the parts are infinite in number and simple, their
104 III, 5 | proper places too will be infinite in number, and the same
105 III, 5 | body would no longer be infinite), nor is the body larger
106 III, 5 | absurd account of why the infinite is at rest. He says that
107 III, 5 | at rest. He says that the infinite itself is the cause of its
108 III, 5 | carried along if it were infinite, provided it is held together
109 III, 5 | the earth, supposed to be infinite, it is at rest, not because
110 III, 5 | rest, not because it is infinite, but because it has weight
111 III, 5 | the centre, similarly the infinite also would rest in itself,
112 III, 5 | itself, not because it is infinite and fixes itself, but owing
113 III, 5 | same time. Any part of the infinite body ought to remain at
114 III, 5 | remain at rest. Just as the infinite remains at rest in itself
115 III, 5 | itself is the place of the infinite, that also will be appropriate
116 III, 5 | the view that there is an infinite body is plainly incompatible
117 III, 5 | would need to be true of the infinite also. But neither character
118 III, 5 | divide it? or how can the infinite have the one part up and
119 III, 5 | whole itself. But in the infinite body they cannot exist.
120 III, 5 | that there should be an infinite place, and if every body
121 III, 5 | place, there cannot be an infinite body.~Surely what is in
122 III, 5 | place. Just, then, as the infinite cannot be quantity-that
123 III, 5 | no body which is actually infinite.~
124 III, 6 | hand to suppose that the infinite does not exist in any way
125 III, 6 | magnitudes, number will not be infinite. If, then, in view of the
126 III, 6 | is a sense in which the infinite exists and another in which
127 III, 6 | is. Further, a thing is infinite either by addition or by
128 III, 6 | magnitude is not actually infinite. But by division it is infinite. (
129 III, 6 | infinite. But by division it is infinite. (There is no difficulty
130 III, 6 | alternative then remains that the infinite has a potential existence.~
131 III, 6 | statue. It is not so with the infinite. There will not be an actual
132 III, 6 | There will not be an actual infinite. The word "is" has many
133 III, 6 | senses, and we say that the infinite "is" in the sense in which
134 III, 6 | actually occurring.~The infinite exhibits itself in different
135 III, 6 | magnitudes. For generally the infinite has this mode of existence:
136 III, 6 | that we must not regard the infinite as a "this", such as a man
137 III, 6 | gives out.~In a way the infinite by addition is the same
138 III, 6 | is the same thing as the infinite by division. In a finite
139 III, 6 | a finite magnitude, the infinite by addition comes about
140 III, 6 | quantity however small.~The infinite, then, exists in no other
141 III, 6 | there is potentially an infinite, namely, what we have described
142 III, 6 | a sense the same as the infinite in respect of division.
143 III, 6 | addition there cannot be an infinite which even potentially exceeds
144 III, 6 | attribute of being actually infinite, as the physicists hold
145 III, 6 | a sensible body which is infinite in the full sense, evidently
146 III, 6 | body which is potentially infinite in respect of addition,
147 III, 6 | except as the inverse of the infinite by division, as we have
148 III, 6 | For in the numbers the infinite in the direction of reduction
149 III, 6 | the smallest; nor is the infinite in the direction of increase,
150 III, 6 | only up to the decad.~The infinite turns out to be the contrary
151 III, 6 | nothing outside it that is infinite, but what always has something
152 III, 6 | as follows:~A quantity is infinite if it is such that we can
153 III, 6 | latter says that the whole is infinite, but the former describes
154 III, 6 | middle". For to connect the infinite with the all and the whole
155 III, 6 | but, in so far as it is infinite, is contained. Consequently,
156 III, 6 | also, it is unknowable, qua infinite; for the matter has no form. (
157 III, 6 | Hence it is plain that the infinite stands in the relation of
158 III, 7 | should not be held to be an infinite in respect of addition such
159 III, 7 | be thought to be such an infinite in the direction of division.
160 III, 7 | For the matter and the infinite are contained inside what
161 III, 7 | other direction there is no infinite magnitude. The reason is
162 III, 7 | magnitude can be bisected is infinite. Hence this infinite is
163 III, 7 | is infinite. Hence this infinite is potential, never actual:
164 III, 7 | infinitum, but there is no infinite in the direction of increase.
165 III, 7 | no sensible magnitude is infinite, it is impossible to exceed
166 III, 7 | bigger than the heavens.~The infinite is not the same in magnitude
167 III, 7 | i.e. movement is called infinite in virtue of the magnitude
168 III, 7 | actual existence of the infinite in the direction of increase,
169 III, 7 | fact they do not need the infinite and do not use it. They
170 III, 7 | to them to have such an infinite instead, while its existence
171 III, 7 | causes, it is plain that the infinite is a cause in the sense
172 III, 7 | too, evidently treat the infinite as matter-that is why it
173 III, 8 | support the view that the infinite exists not only potentially
174 III, 8 | sensible body which is actually infinite. The passing away of one
175 III, 8 | indeed and movement are infinite, and also thinking, in the
176 III, 8 | existence.~(b) Magnitude is not infinite either in the way of reduction
177 III, 8 | of the way in which the infinite exists, and of the way in
178 IV, 3 | affection. So we escape the infinite regress.~Another thing is
179 IV, 6 | were inhales it, from the infinite air. Further it is the void
180 IV, 8 | throughout the void or the infinite? For in so far as it is
181 IV, 8 | For in so far as it is infinite, there will be no up or
182 IV, 10 | is not yet. Yet time-both infinite time and any time you like
183 V, 2 | becoming, we shall have an infinite regress. Thus if one of
184 V, 2 | becoming. And since in an infinite series there is no first
185 VI, 2 | the same. And if either is infinite, so is the other, and the
186 VI, 2 | the other; i.e. if time is infinite in respect of its extremities,
187 VI, 2 | extremities, length is also infinite in respect of its extremities:
188 VI, 2 | extremities: if time is infinite in respect of divisibility,
189 VI, 2 | divisibility, length is also infinite in respect of divisibility:
190 VI, 2 | divisibility: and if time is infinite in both respects, magnitude
191 VI, 2 | respects, magnitude is also infinite in both respects.~Hence
192 VI, 2 | to come in contact with infinite things in a finite time.
193 VI, 2 | anything continuous are called "infinite": they are called so either
194 VI, 2 | with things quantitatively infinite, it can come in contact
195 VI, 2 | come in contact with things infinite in respect of divisibility:
196 VI, 2 | the time itself is also infinite: and so we find that the
197 VI, 2 | by the passage over the infinite is not a finite but an infinite
198 VI, 2 | infinite is not a finite but an infinite time, and the contact with
199 VI, 2 | of moments not finite but infinite in number.~The passage over
200 VI, 2 | number.~The passage over the infinite, then, cannot occupy a finite
201 VI, 2 | finite cannot occupy an infinite time: if the time is infinite
202 VI, 2 | infinite time: if the time is infinite the magnitude must be infinite
203 VI, 2 | infinite the magnitude must be infinite also, and if the magnitude
204 VI, 2 | and if the magnitude is infinite, so also is the time. This
205 VI, 2 | that it is traversed in infinite time G, and let a finite
206 VI, 2 | if it is the case that infinite time is not occupied in
207 VI, 2 | magnitude is finite. That infinite time will not be occupied
208 VI, 2 | falsity of the assumption that infinite length can be traversed
209 VI, 4 | of their being finite or infinite, they will all alike be
210 VI, 4 | the terms are divisible or infinite is a direct consequence
211 VI, 4 | changes is divisible or infinite: for the attributes "divisible"
212 VI, 4 | attributes "divisible" and "infinite" belong in the first instance
213 VI, 5 | effected: for the divisions are infinite.~So, too, of that which
214 VI, 6 | changing must have completed an infinite number of changes.~Again,
215 VI, 6 | consequently, since the moments are infinite in number, everything that
216 VI, 6 | changing must have completed an infinite number of changes.~And not
217 VI, 6 | magnitude and divisible into an infinite number of segments: consequently,
218 VI, 6 | the process of division is infinite, just as lines may be infinitely
219 VI, 7 | undergo a finite motion in an infinite time, if this is understood
220 VI, 7 | repeated, but that the whole infinite time is occupied by the
221 VI, 7 | time, and let GD be the infinite time. Now if one part of
222 VI, 7 | a certain period of the infinite time: it cannot itself occupy
223 VI, 7 | cannot itself occupy an infinite time, for we are assuming
224 VI, 7 | will be a measure of the infinite time (for the infinite cannot
225 VI, 7 | the infinite time (for the infinite cannot be composed of finite
226 VI, 7 | time there cannot be an infinite extent of motion or of coming
227 VI, 7 | subtraction of its parts, the infinite magnitude will not be thus
228 VI, 7 | is made. Consequently the infinite magnitude will not be traversed
229 VI, 7 | whether the magnitude is infinite in only one direction or
230 VI, 7 | finite magnitude traverse an infinite magnitude in a finite time,
231 VI, 7 | magnitude will not traverse an infinite in a finite time, it is
232 VI, 7 | clear that neither will an infinite traverse a finite in a finite
233 VI, 7 | finite time. For if the infinite could traverse the finite,
234 VI, 7 | finite could traverse the infinite; for it makes no difference
235 VI, 7 | involves the traversing of the infinite by the finite. For when
236 VI, 7 | the finite. For when the infinite magnitude A is in motion
237 VI, 7 | results will coincide: the infinite will have completed a motion
238 VI, 7 | will have traversed the infinite: for it would seem to be
239 VI, 7 | impossible for the motion of the infinite over the finite to occur
240 VI, 7 | the finite traversing the infinite either by locomotion over
241 VI, 7 | this is impossible, the infinite cannot traverse the finite.~
242 VI, 7 | finite.~Nor again will the infinite traverse the infinite in
243 VI, 7 | the infinite traverse the infinite in a finite time. Otherwise
244 VI, 7 | traverse the finite, for the infinite includes the finite. We
245 VI, 7 | the finite traverse the infinite, nor the infinite the finite,
246 VI, 7 | traverse the infinite, nor the infinite the finite, nor the infinite
247 VI, 7 | infinite the finite, nor the infinite the infinite, it is evident
248 VI, 7 | finite, nor the infinite the infinite, it is evident also that
249 VI, 7 | finite time there cannot be infinite motion: for what difference
250 VI, 7 | motion or the magnitude to be infinite? If either of the two is
251 VI, 7 | If either of the two is infinite, the other must be so likewise:
252 VI, 8 | continuous is divisible into an infinite number of parts.~And since
253 VI, 10 | no process of change is infinite: for every change, whether
254 VI, 10 | Consequently its motion is not infinite, and it will not be in locomotion
255 VI, 10 | be in locomotion over an infinite distance, for it cannot
256 VI, 10 | process of change cannot be infinite in the sense that it is
257 VI, 10 | process of change may be infinite in respect of the time which
258 VI, 10 | nothing to prevent its being infinite in this sense; e.g. if a
259 VI, 10 | process, no motion can be infinite in respect of the time that
260 VII, 1 | and take the series to be infinite. Let A then be moved by
261 VII, 1 | to something and is not infinite in respect of its extreme
262 VII, 1 | and the things moved are infinite, the motion EZHO, i.e. the
263 VII, 1 | individual motions, must be infinite. For the motions of A, B,
264 VII, 1 | cases the whole motion is infinite. And since the motion of
265 VII, 1 | consequently the motion will be infinite in a finite time, which
266 VII, 1 | finite time there may be an infinite motion, though not of one
267 VII, 1 | this unity is finite or infinite makes no difference to our
268 VII, 1 | the things in motion are infinite in number the whole motion
269 VII, 1 | the whole motion will be infinite, if, as is theoretically
270 VII, 1 | then, A, B, G, D form an infinite magnitude that passes through
271 VII, 1 | involves the conclusion that an infinite motion is passed through
272 VII, 1 | in question is finite or infinite this is in either case impossible.
273 VIII, 1 | who say that there is an infinite number of worlds, some of
274 VIII, 1 | together and at rest for an infinite period of time, and that
275 VIII, 1 | ratio in the relation of the infinite to the infinite, whereas
276 VIII, 1 | relation of the infinite to the infinite, whereas order always means
277 VIII, 1 | first a state of rest for an infinite time, and then motion is
278 VIII, 2 | could also occur in the infinite; that is, if the infinite
279 VIII, 2 | infinite; that is, if the infinite could as a whole possibly
280 VIII, 3 | decrease is divisible into an infinite number of parts it does
281 VIII, 3 | assert, that the existent is infinite and motionless, it certainly
282 VIII, 5 | that there should be an infinite series of movents, each
283 VIII, 5 | something else, since in an infinite series there is no first
284 VIII, 5 | or else there will be an infinite series. If, then, anything
285 VIII, 5 | stop somewhere and not be infinite. Thus, if the stick moves
286 VIII, 6 | sum of these movents is infinite and they do not all exist
287 VIII, 6 | a finite rather than an infinite number. When the consequences
288 VIII, 6 | things are finite rather than infinite in number, since in things
289 VIII, 8 | that there should be an infinite motion that is single and
290 VIII, 8 | these half-distances are infinite in number, and that it is
291 VIII, 8 | impossible to traverse distances infinite in number-or some on the
292 VIII, 8 | traversed we have reckoned an infinite number, which is admittedly
293 VIII, 8 | contains within itself an infinite number of units: there is
294 VIII, 8 | supposing the traversing of infinite distances in infinite time,
295 VIII, 8 | of infinite distances in infinite time, and the element of
296 VIII, 8 | to traverse or reckon an infinite number of units), nevertheless
297 VIII, 8 | finite time to traverse an infinite number of distances, and
298 VIII, 8 | for the time contains an infinite number of divisions): then
299 VIII, 8 | is continuous contains an infinite number of halves, they are
300 VIII, 8 | possible to pass through an infinite number of units either of
301 VIII, 8 | traveller has traversed an infinite number of units in an accidental
302 VIII, 8 | of the distance to be an infinite number of half-distances,
303 VIII, 9 | rectilinear motion cannot be infinite: for there is no such thing
304 VIII, 9 | there is no such thing as an infinite straight line; and even
305 VIII, 9 | impossible to traverse an infinite distance. On the other hand
306 VIII, 10| can cause motion during an infinite time. We have three things,
307 VIII, 10| and these are either all infinite or all finite or partly-that
308 VIII, 10| of them-finite and partly infinite. Let A be the movement,
309 VIII, 10| B the moved, and G the infinite time. Now let us suppose
310 VIII, 10| follows that the time Z is not infinite. Now we see that by continuing
311 VIII, 10| amount from it, because it is infinite. Consequently the duration
312 VIII, 10| cannot impart to anything an infinite motion. It is clear, then,
313 VIII, 10| to cause motion during an infinite time.~It has now to be shown
314 VIII, 10| case is it possible for an infinite force to reside in a finite
315 VIII, 10| magnitude possessing an infinite force as well as by anything
316 VIII, 10| anything else, since the infinite force is greater than any
317 VIII, 10| the time occupied by the infinite power in the performance
318 VIII, 10| performing the motive act as the infinite force. But this is impossible.
319 VIII, 10| nothing finite can possess an infinite force. So it is also impossible
320 VIII, 10| finite force to reside in an infinite magnitude. It is true that
321 VIII, 10| greater. Now let AB be an infinite magnitude. Then BG possesses
322 VIII, 10| Therefore the force must be infinite, since it exceeds any finite
323 VIII, 10| that which resides in the infinite magnitude, so that this
324 VIII, 10| finite force residing in the infinite magnitude.~It is plain,
325 VIII, 10| it is impossible for an infinite force to reside in a finite
326 VIII, 10| finite force to reside in an infinite magnitude. But before proceeding
327 VIII, 10| be either a finite or an infinite magnitude. Now we have already’
328 VIII, 10| that there cannot be an infinite magnitude: and we have now
329 VIII, 10| finite magnitude to have an infinite force, and also that it
330 VIII, 10| finite magnitude during an infinite time. But the first movent
331 VIII, 10| does cause it during an infinite time. It is clear, therefore,
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