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| Alphabetical [« »] now 113 now-to 1 nowhere 1 number 325 number-and 1 number-only 1 number-the 1 | Frequency [« »] 352 e.g. 351 man 337 something 325 number 319 an 315 matter 305 sense | Aristotle Metaphysics IntraText - Concordances number |
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1 II, 2 | are infinite or finite in number.) But of series which are 2 II, 2 | it is impossible that the number of terms should be infinite. 3 II, 2 | causes had been infinite in number, then also knowledge would 4 III, 1 | whether it is one or more in number, and whether there is something 5 III, 1 | principles are limited in number or in kind, both those in 6 III, 3 | practically an infinite number of principles, especially 7 III, 3 | numbers, there will not be a Number apart from the kinds of 8 III, 4 | individuals are infinite in number, how then is it possible 9 III, 4 | articulate sound were limited in number; all the language in the 10 III, 4 | not a substance, evidently number also will not exist as an 11 III, 4 | the individual things; for number is units, and the unit is 12 III, 4 | will be more than one in number. For what is different from 13 III, 4 | there is a unity-itself, number cannot be a substance. We 14 III, 4 | when added will make the number, though not the size, greater),- 15 III, 4 | such that, as some say, number proceeds from unity-itself 16 III, 4 | product will be sometimes a number and sometimes a magnitude, 17 III, 4 | principle, or from some number and this principle.~ 18 III, 6 | principles cannot be limited in number (just as the elements of 19 III, 6 | world are not limited in number, but in kind, unless one 20 III, 6 | will be limited even in number; so is it also in the case 21 III, 6 | same kind are infinite in number), so that if there are not-besides 22 III, 6 | substance which is one in number, but only in kind, nor will 23 III, 6 | things be determinate in number, but only in kind:-if then 24 III, 6 | the principles are one in number, not in kind, we have mentioned 25 IV, 2 | these other things. For number qua number has peculiar 26 IV, 2 | other things. For number qua number has peculiar attributes, 27 IV, 4 | only they are limited in number; for to each definition 28 IV, 4 | only they were limited in number; for a peculiar name might 29 IV, 4 | the word has an infinite number of meanings, obviously reasoning 30 IV, 4 | attributes, which are infinite in number; let him, then, enumerate 31 IV, 5 | determined by the large or small number of those who hold a belief, 32 IV, 6 | one thing or to a definite number of things; and if the same 33 IV, 7 | of numbers there will be number which is neither odd nor 34 IV, 7 | on ad infinitum, and the number of realities will be not 35 IV, 8 | or falsity of an infinite number of statements; for that 36 V, 1 | are spoken of in an equal number of senses; for all causes 37 V, 2 | e.g. the ratio 2:1 and number in general are causes of 38 V, 2 | causes, and this is the number of their kinds, but the 39 V, 2 | varieties of causes are many in number, though when summarized 40 V, 2 | both "the ratio 2:1" and "number" are causes of the octave, 41 V, 2 | all these are but six in number, while each is spoken of 42 V, 6 | some kind of beginning of number; for the first measure is 43 V, 6 | some things are one in number, others in species, others 44 V, 6 | genus, others by analogy; in number those whose matter is one, 45 V, 6 | e.g. things that are one in number are also one in species, 46 V, 6 | species are not all one in number; but things that are one 47 V, 8 | the line; and in general number is thought by some to be 48 V, 9 | one either in kind or in number, and those whose essence 49 V, 9 | some respect, only not in number but either in species or 50 V, 9 | another thing the greater number or the more important of 51 V, 13 | these, limited plurality is number, limited length is a line, 52 V, 15 | numerical relation to a number; that which is n+I/n times 53 V, 15 | numerically quite indefinite; for number is always commensurate, 54 V, 15 | always commensurate, and "number" is not predicated of that 55 V, 15 | and are determinations of number, and so in another way are 56 V, 15 | beginning and measure of number, so that all these relations 57 V, 15 | all these relations imply number, though not in the same 58 V, 15 | Relative terms which imply number or potency, therefore, are 59 V, 18 | will found in the same number of senses as "cause"; for 60 V, 26 | Water and all liquids and number are called totals, but " 61 V, 26 | called totals, but "the whole number" or "the whole water" one 62 V, 26 | as separate; "this total number," "all these units."~ 63 V, 27 | remainder), but in general no number is thus mutilated; for it 64 V, 27 | still be a cup; but the number is no longer the same. Further, 65 V, 27 | mutilated, for in a sense a number has unlike parts (e.g. two 66 V, 29 | be described as a double number by the use of the definition 67 VII, 1 | assert to be limited in number, others unlimited. And so 68 VII, 2 | substances which are more in number and more real; e.g. Plato 69 VII, 5 | cannot be defined apart from number; nor can female be defined 70 VII, 5 | coupled terms also, like "odd number", will not be definable ( 71 VII, 8 | however, the same nor one in number, but in form), i.e. in the 72 VII, 12 | with feet will be equal in number to the differentiae. If 73 VII, 13 | the same will hold good of number, if number is a synthesis 74 VII, 13 | hold good of number, if number is a synthesis of units, 75 VII, 14 | either one and the same in number, or different. (In formula 76 VII, 14 | practically an infinite number of things whose substance 77 VIII, 3 | definition is a sort of number; for (1) it is divisible, 78 VIII, 3 | formulae are not infinite), and number also is of this nature. 79 VIII, 3 | of the parts of which a number consists has been taken 80 VIII, 3 | taken from or added to the number, it is no longer the same 81 VIII, 3 | it is no longer the same number, but a different one, even 82 VIII, 3 | away or added. And (3) the number must be something in virtue 83 VIII, 3 | definite nature. And (4) as number does not admit of the more 84 VIII, 3 | the reduction of things to number.~ 85 VIII, 4 | really these and of this number and we have to learn the 86 IX, 8 | in species though not in number with a potentially existing 87 IX, 10 | may suppose that no even number is prime, we may suppose 88 IX, 10 | regarding a numerically single number not even this form of error 89 X, 1 | indivisible in kind or in number. (3) In number, then, the 90 X, 1 | kind or in number. (3) In number, then, the individual is 91 X, 1 | either by a "one" or by a number, and all number is known 92 X, 1 | or by a number, and all number is known by a "one". Therefore 93 X, 1 | is the starting-point of number qua number. And hence in 94 X, 1 | starting-point of number qua number. And hence in the other 95 X, 1 | is exact (hence that of number is most exact; for we posit 96 X, 1 | measure is not always one in number—sometimes there are several; 97 X, 1 | measure of numbers is a number; we ought indeed to say 98 X, 1 | is units and not a unit; number is a plurality of units.)~ 99 X, 2 | things would have been a number, indeed, but of what? Clearly 100 X, 2 | they would have been a number, but a number of quarter-tones, 101 X, 2 | have been a number, but a number of quarter-tones, and their 102 X, 2 | essence would not have been number; and the one would have 103 X, 2 | they would have been a number of letters, and the one 104 X, 2 | they would have been a number of figures, and the one 105 X, 2 | movement, in all cases the number is a number of particular 106 X, 2 | all cases the number is a number of particular things and 107 X, 3 | both in definition and in number, e.g. you are one with yourself 108 X, 4 | in others there is not (a number must be either odd or even). 109 X, 6 | in another sense it means number, in which sense alone it 110 X, 6 | are so called. For each number is said to be many because 111 X, 6 | of ones and because each number is measurable by one; and 112 X, 6 | were the class to which number belongs; for number is plurality 113 X, 6 | which number belongs; for number is plurality measurable 114 X, 6 | measurable by one, and one and number are in a sense opposed, 115 X, 6 | everything that is one is a number; i.e. if the thing is indivisible 116 X, 6 | indivisible it is not a number. But though knowledge is 117 X, 6 | knowable, if plurality is number and the one is a measure.~ 118 XI, 2 | But these are infinite in number. Yet the things that are 119 XI, 2 | eternal substances equal in number to the sensible and perishable 120 XI, 2 | substance, and generate number as the first product from 121 XI, 2 | from matter, assert that number is substance? How are we 122 XI, 2 | principles the same in kind or in number? If they are one in number, 123 XI, 2 | number? If they are one in number, all things will be the 124 XI, 6 | they appear to be of that number) and again one (for to those 125 XI, 10 | exist by itself, unless number and magnitude also exist 126 XI, 10 | accident-the air or the even number.~This inquiry is universal; 127 XI, 10 | a separate and infinite number, for number or that which 128 XI, 10 | and infinite number, for number or that which has a number 129 XI, 10 | number or that which has a number is numerable. Concretely, 130 XI, 10 | there will be an infinite number of elements; and if this 131 XI, 12 | Now since of an infinite number of terms there is not a 132 XII, 8 | have said nothing about the number of the substances that can 133 XII, 8 | unlimited, now as limited by the number 10; but as for the reason 134 XII, 8 | substances which are of the same number as the movements of the 135 XII, 8 | is evident. But in the number of the movements we reach 136 XII, 8 | movement. But as to the actual number of these movements, we now-to 137 XII, 8 | thought may have some definite number to grasp; but, for the rest, 138 XII, 8 | while he assigned the same number as Eudoxus did to Jupiter 139 XII, 8 | two planets will be six in number, and the spheres which counteract 140 XII, 8 | be sixteen; therefore the number of all the spheres—both 141 XII, 8 | spheres will be forty-seven in number.~Let this, then, be taken 142 XII, 8 | this, then, be taken as the number of the spheres, so that 143 XII, 8 | named, but this must be the number of the substances. For if 144 XII, 8 | will be one in form but in number many. But all things that 145 XII, 8 | things that are many in number have matter; for one and 146 XII, 8 | both in definition and in number; so too, therefore, is that 147 XII, 10 | of unextended parts? For number will not, either as mover 148 XII, 10 | those who say mathematical number is first and go on to generate 149 XIII, 2 | substance which is neither number nor points nor spatial magnitude 150 XIII, 4 | follows that not the dyad but number is first, and that prior 151 XIII, 4 | first, and that prior to number is the relative, and that 152 XIII, 6 | first causes of things. If number is an entity and its substance 153 XIII, 6 | nothing other than just number, as some say, it follows 154 XIII, 6 | the case with mathematical number; for in mathematical number 155 XIII, 6 | number; for in mathematical number no one unit is in any way 156 XIII, 6 | and then the rest of the number series, and the units in 157 XIII, 6 | series, and the units in each number are associable, e.g. those 158 XIII, 6 | And so while mathematical number is counted thus-after 1, 159 XIII, 6 | numbers similarly, ideal number is counted thus-after 1, 160 XIII, 6 | the 2 and the rest of the number series similarly. Or (2) 161 XIII, 6 | similarly. Or (2) one kind of number must be like the first that 162 XIII, 6 | of all things, and that number is formed from the 1 and 163 XIII, 6 | every one has described number in one of these ways; only 164 XIII, 6 | Some say both kinds of number exist, that which has a 165 XIII, 6 | Ideas, and mathematical number being different from the 166 XIII, 6 | others say mathematical number alone exists, as the first 167 XIII, 6 | thinker says the first kind of number, that of the Forms, alone 168 XIII, 6 | and some say mathematical number is identical with this.~ 169 XIII, 7 | that those in each ideal number are inassociable with those 170 XIII, 7 | number-only one kind of number, and the Ideas cannot be 171 XIII, 7 | numbers. For what sort of number will man-himself or animal-itself 172 XIII, 7 | will the Ideas come? It is number that comes from the 1 and 173 XIII, 7 | principles and elements of number, and the Ideas cannot be 174 XIII, 7 | inassociable with any other, number of this sort cannot be mathematical 175 XIII, 7 | sort cannot be mathematical number; for mathematical number 176 XIII, 7 | number; for mathematical number consists of undifferentiated 177 XIII, 7 | character. Nor can it be ideal number. For 2 will not proceed 178 XIII, 7 | different each from each, number must be counted by addition, 179 XIII, 7 | differentiated, but those in the same number are alone undifferentiated 180 XIII, 7 | itself is not any chance number nor composed of any chance 181 XIII, 7 | differing from unit, and number must be either equal or 182 XIII, 7 | either equal or unequal-all number but especially that which 183 XIII, 7 | abstract units-so that if one number is neither greater nor less 184 XIII, 7 | two units are 2.~If the number of the 3-itself is not greater 185 XIII, 7 | clearly there is also a number in it equal to the 2, so 186 XIII, 7 | is a first and a second number.~Nor will the Ideas be numbers. 187 XIII, 7 | proceed by adding to the given number; for if we do, neither will 188 XIII, 7 | indefinite dyad, nor can a number be an Idea; for then one 189 XIII, 8 | seems to be possible. But number qua number differs in quantity. 190 XIII, 8 | possible. But number qua number differs in quantity. And 191 XIII, 8 | did differ in quantity, number would differ from number, 192 XIII, 8 | number would differ from number, though equal in number 193 XIII, 8 | number, though equal in number of units. Again, are the 194 XIII, 8 | the facts with regard to number are so, and one supposes 195 XIII, 8 | one supposes mathematical number alone to exist, the 1 is 196 XIII, 8 | so that if neither is, number cannot exist separately.~ 197 XIII, 8 | view ideal and mathematical number is the same. For two mistakes 198 XIII, 8 | opinion. (1) Mathematical number cannot be of this sort, 199 XIII, 8 | confront those who speak of number in the sense of "Forms".~ 200 XIII, 8 | itself. For not thinking of number as capable of existing separately 201 XIII, 8 | this should be mathematical number, is impossible. For it is 202 XIII, 8 | indivisibles? But arithmetical number, at least, consists of units, 203 XIII, 8 | these thinkers identify number with real things; at any 204 XIII, 8 | then, it is necessary, if number is a self-subsistent real 205 XIII, 8 | any of these, evidently number has no such nature as those 206 XIII, 8 | function was to double.~Again, number must be either infinite 207 XIII, 8 | these thinkers think of number as capable of existing separately, 208 XIII, 8 | be infinite; for infinite number is neither odd nor even, 209 XIII, 8 | of an odd or of an even number; in one way, when 1 operates 210 XIII, 8 | when 1 operates on an even number, an odd number is produced; 211 XIII, 8 | on an even number, an odd number is produced; in another 212 XIII, 8 | numbers are Ideas, infinite number itself will be an Idea of 213 XIII, 8 | Ideas as they do.~But if number is finite, how far does 214 XIII, 8 | should be stated. But if number goes only up to 10 as some 215 XIII, 8 | if 3 is man-himself, what number will be the horse-itself? 216 XIII, 8 | there will be an infinite number of men; if each 3 is an 217 XIII, 8 | men. And if the smaller number is part of the greater ( 218 XIII, 8 | part of the greater (being number of such a sort that the 219 XIII, 8 | that the units in the same number are associable), then if 220 XIII, 8 | it is paradoxical-if the number series up to 10 is more 221 XIII, 8 | going beyond a definite number; e.g. the first, the indivisible, 222 XIII, 8 | only up to 10.~Again, if number can exist separately, one 223 XIII, 8 | 3 or 2? Inasmuch as the number is composite, 1 is prior, 224 XIII, 8 | and the form is prior, the number is prior; for each of the 225 XIII, 8 | the units is part of the number as its matter, and the number 226 XIII, 8 | number as its matter, and the number acts as form. And in a sense 227 XIII, 8 | potentially (at least if the number is a unity and not like 228 XIII, 8 | which can be predicated of a number, as in this sense also a 229 XIII, 8 | sense also a part of the number. But these characteristics 230 XIII, 9 | classes of things posterior to number,-the line, the plane, and 231 XIII, 9 | happens as in regard to number; for "long and short", & 232 XIII, 9 | in 2, or in general in a number, do we apprehend a thing-itself 233 XIII, 9 | will he a line.~Again, how number can consist of the one and 234 XIII, 9 | confront those who construct number out of the one and the indefinite 235 XIII, 9 | For the one view generates number from the universally predicated 236 XIII, 9 | nothing but presuppose another number; for his plurality of indivisibles 237 XIII, 9 | plurality of indivisibles is a number. Again, we must inquire, 238 XIII, 9 | theory also, whether the number is infinite or finite. For 239 XIII, 9 | the one comes the finite number of units. And there is another 240 XIII, 9 | parts of plurality; for number consists of indivisibles, 241 XIII, 9 | sort make it evident that number and spatial magnitudes cannot 242 XIII, 9 | fictitiousness, abandoned ideal number and posited mathematical. 243 XIII, 9 | principles, how mathematical number was to exist apart from 244 XIII, 9 | made ideal and mathematical number the same-in words, since 245 XIII, 9 | since in fact mathematical number has been destroyed; for 246 XIII, 10| will be just of the same number as the elements, and (b) 247 XIII, 10| form but each is one in number and a "this" and not a kind 248 XIII, 10| cannot exist in the plural number. But if this is so, there 249 XIII, 10| as this goes, an infinite number of similar syllables. The 250 XIV, 1 | in definition, but not in number. But they do not describe 251 XIV, 1 | nature to magnitude than to number; and others name rather 252 XIV, 1 | consistency requires that number should come from the elements 253 XIV, 1 | elements before does; for number is more universal than as 254 XIV, 1 | of some plurality, and "number" means a measured plurality 255 XIV, 1 | natural that one is not a number; for the measure is not 256 XIV, 1 | living being", and the number of them will be a number 257 XIV, 1 | number of them will be a number of living beings. If the 258 XIV, 1 | these will scarcely have a number, because all belong to a 259 XIV, 1 | which is one and the same in number, yet the number of these 260 XIV, 1 | same in number, yet the number of these will be a number 261 XIV, 1 | number of these will be a number of "kinds" or of some such 262 XIV, 1 | magnitudes-the many and few of number, and the great and small 263 XIV, 1 | both apart and together of number, and long and short of the 264 XIV, 1 | is many (if there is no number which is greater than 10), 265 XIV, 1 | then, in view of this, can number consist of few and many? 266 XIV, 2 | so, however everlasting number or anything else that has 267 XIV, 2 | just as that which is any number of years old is as capable 268 XIV, 2 | thinkers, whether it is ideal number, or mathematical, that they 269 XIV, 2 | quantities are many. For all "number" means a quantity, and so 270 XIV, 2 | existing things, since each number is an Idea, and the Idea 271 XIV, 2 | who posits mathematical number, why must we believe his 272 XIV, 2 | his statement that such number exists, and of what use 273 XIV, 2 | and of what use is such number to other things? Neither 274 XIV, 3 | least to explain somehow why number must exist. Since their 275 XIV, 3 | assert the existence of number. Again, the Pythagoreans, 276 XIV, 3 | who say that mathematical number alone exists cannot according 277 XIV, 3 | sensible. But those who make number separable assume that it 278 XIV, 3 | satisfied, we may, regarding all number and the objects of mathematics, 279 XIV, 3 | to the posterior; for if number did not exist, none the 280 XIV, 3 | magnitudes out of matter and number, lines out of the number 281 XIV, 3 | number, lines out of the number planes doubtless out of 282 XIV, 3 | first posited two kinds of number, that of the Forms and that 283 XIV, 3 | can say how mathematical number is to exist and of what 284 XIV, 3 | between ideal and sensible number. If (i) it consists of the 285 XIV, 3 | each of the two kinds of number is a 1, unity will be something 286 XIV, 3 | while at the same time number, according to him, cannot 287 XIV, 4 | no generation of the odd number, which evidently implies 288 XIV, 4 | an element-and generating number from the one.) The old poets 289 XIV, 4 | but only of mathematical number). For on this view all the 290 XIV, 5 | then said in which sense number comes from its first principles.~ 291 XIV, 5 | and (2) he who thinks of number will be able to think of 292 XIV, 5 | and the plurality apart; number then will be this-a unit 293 XIV, 5 | are not; which sense does number come from these elements? 294 XIV, 5 | are present in them. Does number come, then, from its elements 295 XIV, 5 | treating the 1 as equal, number must be being treated as 296 XIV, 5 | to produce them), while number does not? Nothing is said 297 XIV, 5 | Eurytus decided what was the number of what (e.g. one of man 298 XIV, 5 | is the essence, while the number the causes of the form; 299 XIV, 5 | is the essence, while the number is the matter. E.g. the 300 XIV, 5 | essence of flesh or bone is number only in this way, "three 301 XIV, 5 | and two of earth". And a number, whatever number it is, 302 XIV, 5 | And a number, whatever number it is, is always a number 303 XIV, 5 | number it is, is always a number of certain things, either 304 XIV, 5 | and this is no longer a number but a ratio of mixture of 305 XIV, 5 | corporeal or of any other kind.~Number, then, whether it be number 306 XIV, 5 | Number, then, whether it be number in general or the number 307 XIV, 5 | number in general or the number which consists of abstract 308 XIV, 6 | composition is expressible by a number, either by one which is 309 XIV, 6 | calculable or by an odd number. For in fact honey-water 310 XIV, 6 | measurable by that factor. The number of fire, then, cannot be 311 XIV, 6 | all things must share in number, it must follow that many 312 XIV, 6 | are the same, and the same number must belong to one thing 313 XIV, 6 | thing and to another. Is number the cause, then, and does 314 XIV, 6 | thing exist because of its number, or is this not certain? 315 XIV, 6 | motions of the sun have a number, and again those of the 316 XIV, 6 | were assumed to share in number. And it was assumed that 317 XIV, 6 | might fall under the same number. Therefore if the same number 318 XIV, 6 | number. Therefore if the same number had belonged to certain 319 XIV, 6 | have had the same form of number; e.g. sun and moon would 320 XIV, 6 | Is it then because the number is the kind of number it 321 XIV, 6 | the number is the kind of number it is, that the champions 322 XIV, 6 | syllables, which is equal in number to the two strings, and 323 XIV, 6 | the highest, and that the number of this note is equal to 324 XIV, 6 | and a particular kind of number go together; and the other 325 XIV, 6 | surface, perhaps the odd in number, and the white in colour.~