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| Alphabetical [« »] being 81 belief 3 beliefs 1 belong 589 belong-either 1 belonged 14 belonging 31 | Frequency [« »] 727 in 658 but 599 all 589 belong 587 belongs 483 some 480 are | Aristotle Prior Analytics IntraText - Concordances belong |
Book, Paragraph
1 I, 1 | that it does or does not belong, without any mark to show 2 I, 1 | something does or does not belong to something else. Therefore 3 I, 3 | term necessarily does not belong to the other; in the latter 4 I, 4 | possible that the first should belong either to all or to none 5 I, 5 | relation is convertible, N will belong to no M: but M was assumed 6 I, 5 | M: but M was assumed to belong to all O: consequently N 7 I, 5 | all O: consequently N will belong to no O. This has already 8 I, 5 | but to no O, then N will belong to no O. For if M belongs 9 I, 5 | belongs to all N: O then will belong to no N: for the first figure 10 I, 5 | relation is convertible, N will belong to no O. Thus it will be 11 I, 5 | necessary that N does not belong to some O. For since the 12 I, 5 | statement is convertible, N will belong to no M: but M was admitted 13 I, 5 | M: but M was admitted to belong to some O: therefore N will 14 I, 5 | O: therefore N will not belong to some O: for the result 15 I, 5 | necessary that N does not belong to some O: for if N belongs 16 I, 5 | predicated also of all N, M must belong to all O: but we assumed 17 I, 5 | assumed that M does not belong to some O. And if M belongs 18 I, 5 | conclude that N does not belong to all O: the proof is the 19 I, 5 | be universal, e.g. let M belong to no N, and not to some 20 I, 5 | is possible then for N to belong either to all O or to no 21 I, 5 | to some O, and does not belong to some O. For if N belonged 22 I, 5 | M to no N, then M would belong to no O: but we assumed 23 I, 5 | is true that M does not belong to some O, even if it belongs 24 I, 5 | be universal, e.g. let M belong to all N and to some O. 25 I, 5 | is possible then for N to belong to all O or to no O. Terms 26 I, 5 | it is possible for N to belong either to all O or to no 27 I, 5 | the extremes, or does not belong to some of either, or belongs 28 I, 6 | of a third, or if both belong to all, or to none, of it, 29 I, 6 | universal, whenever both P and R belong to S, it follows that P 30 I, 6 | that P will necessarily belong to some R. For, since the 31 I, 6 | statement is convertible, S will belong to some R: consequently 32 I, 6 | and S to some R, P must belong to some R: for a syllogism 33 I, 6 | exposition. For if both P and R belong to all S, should one of 34 I, 6 | taken, both P and R will belong to this, and thus P will 35 I, 6 | to this, and thus P will belong to some R.~If R belongs 36 I, 6 | that P will necessarily not belong to some R. This may be demonstrated 37 I, 6 | the one extreme does not belong to some of the other: but 38 I, 6 | all S, P to some S, P must belong to some R. For since the 39 I, 6 | statement is convertible S will belong to some P: consequently 40 I, 6 | S to some P, R must also belong to some P: therefore P must 41 I, 6 | some P: therefore P must belong to some R.~Again if R belongs 42 I, 6 | and P to all S, P must belong to some R. This may be demonstrated 43 I, 6 | to all S, but P does not belong to some S, it is necessary 44 I, 6 | necessary that P does not belong to some R. For if P belongs 45 I, 6 | belongs to all S, then P will belong to all S: but we assumed 46 I, 6 | taken to which P does not belong.~But whenever the major 47 I, 6 | to all S and R does not belong to some S. Terms for the 48 I, 6 | to some S, and does not belong to some S. For if P belongs 49 I, 6 | R to some S, then P will belong to some R: but we assumed 50 I, 6 | expression "it does not belong to some" is indefinite, 51 I, 6 | belongs to some S, P will not belong to some R: for we shall 52 I, 6 | to some S, and does not belong to some S. For if P belongs 53 I, 6 | of the middle or does not belong, or one belongs and the 54 I, 7 | necessary that C does not belong to some A. Similarly also 55 I, 7 | last figure, if A and B belong to all C, it follows that 56 I, 7 | belongs to all C, A would belong to no C: but (as we stated) 57 I, 7 | belongs to all B, then B will belong to no C: this we know by 58 I, 7 | belongs to some C, A will not belong to some C: for if it belonged 59 I, 7 | belongs to no B, then B will belong to no C: and this (as we 60 I, 7 | something belongs or does not belong to something else are constituted, 61 I, 8 | necessarily belongs, or may belong to something else (for many 62 I, 8 | something else (for many things belong indeed, but not necessarily, 63 I, 8 | is possible for them to belong), it is clear that there 64 I, 8 | necessarily belongs (or does not belong) to something else, a syllogism 65 I, 8 | which the predicate does not belong, to make the syllogism in 66 I, 9 | way, A will necessarily belong or not belong to C. For 67 I, 9 | necessarily belong or not belong to C. For since necessarily 68 I, 9 | necessarily belongs, or does not belong, to every B, and since C 69 I, 9 | is possible that A should belong to none of it. Further, 70 I, 9 | be necessary, and let A belong to all B necessarily, but 71 I, 9 | necessarily, but let B simply belong to some C: it is necessary 72 I, 9 | B, and A was assumed to belong necessarily to all B. Similarly 73 I, 10| possible of no B, and simply belong to C. Since then the negative 74 I, 10| not be necessary. Let A belong to all B necessarily, but 75 I, 10| that C necessarily does not belong to some A. For if B necessarily 76 I, 10| no C, C will necessarily belong to no B. But B at any rate 77 I, 10| But B at any rate must belong to some A, if it is true ( 78 I, 10| necessary that C does not belong to some A. But nothing prevents 79 I, 10| it is possible for C to belong to all of it. Further one 80 I, 10| possible that animal should belong to nothing white. Man then 81 I, 10| white. Man then will not belong to anything white, but not 82 I, 10| possible for no B that A should belong to it, and let A simply 83 I, 10| to it, and let A simply belong to some C. Since the negative 84 I, 10| possible for no A that B should belong to it: but A belongs to 85 I, 10| consequently B necessarily does not belong to some of the Cs. Again 86 I, 10| belongs to all B, but does not belong to some C, it is clear that 87 I, 10| is clear that B will not belong to some C, but not necessarily. 88 I, 11| affirmative, and let A and B belong to all C, and let AC be 89 I, 11| belongs to all C, C also will belong to some B, because the universal 90 I, 11| necessary that A should belong to some B also. For B is 91 I, 11| necessarily to all C, it will belong necessarily also to some 92 I, 11| A will necessarily not belong to some B either: for B 93 I, 11| convertible, C also will belong to some B necessarily: consequently 94 I, 11| some of the Bs, A will not belong to some of the Bs-but not 95 I, 11| that the term good should belong to no horse, and it is necessary 96 I, 11| that the term animal should belong to every horse: but it is 97 I, 11| necessary that B should belong to all C, and A falls under 98 I, 11| necessary that B should belong to some A. But if B must 99 I, 11| to some A. But if B must belong to some A, then A must belong 100 I, 11| belong to some A, then A must belong to some B: for conversion 101 I, 11| and necessary, and let A belong to all C, not however necessarily. 102 I, 11| necessary that B should belong to some C, but it is possible 103 I, 11| it is possible for A to belong to C, and that A should 104 I, 11| to C, and that A should belong to B is not necessary. For 105 I, 11| not possible that A should belong to any C, but B belongs 106 I, 11| necessary that A should not belong to some B. But whenever 107 I, 11| necessary that animal should belong to some white thing, but 108 I, 11| possible that waking should belong to none, and it is not necessary 109 I, 11| necessary that waking should not belong to some animal. But when 110 I, 13| expressions "it is not possible to belong", "it is impossible to belong", 111 I, 13| belong", "it is impossible to belong", and "it is necessary not 112 I, 13| it is necessary not to belong" are either identical or 113 I, 13| also, "it is possible to belong", "it is not impossible 114 I, 13| it is not impossible to belong", and "it is not necessary 115 I, 13| is not necessary not to belong", will either be identical 116 I, 13| e.g. "it is possible to belong" may be converted into " 117 I, 13| into "it is possible not to belong", and "it is possible for 118 I, 13| it is possible for A to belong to all B" into "it is possible 119 I, 13| it is possible for A to belong to no B" or "not to all 120 I, 13| it is possible for A to belong to some B" into "it is possible 121 I, 13| is possible for A not to belong to some B". And similarly 122 I, 13| necessary may possibly not belong, it is clear that if it 123 I, 13| is possible that A should belong to B, it is possible also 124 I, 13| also that it should not belong to B: and if it is possible 125 I, 13| possible that it should belong to all, it is also possible 126 I, 13| possible that it should not belong to all. The same holds good 127 I, 13| it does not necessarily belong (for in this sense it is 128 I, 13| is possible for this to belong to that" may be understood 129 I, 13| or that to which it may belong; for the expression "A is 130 I, 13| expression "A may possibly belong to all B" might be used 131 I, 14| Whenever A may possibly belong to all B, and B to all C, 132 I, 14| prove that A may possibly belong to all C. This is clear 133 I, 14| possible for one term to belong to all of another". Similarly 134 I, 14| it is possible for A to belong no B, and for B to belong 135 I, 14| belong no B, and for B to belong to all C, then it is possible 136 I, 14| it is possible for A to belong to no C. For the statement 137 I, 14| is possible for A not to belong to that of which B may be 138 I, 14| account. But whenever A may belong to all B, and B may belong 139 I, 14| belong to all B, and B may belong to no C, then indeed no 140 I, 14| is possible that B should belong to no C, it is possible 141 I, 14| possible also that it should belong to all C. This has been 142 I, 14| possible": e.g. if A may belong to none of the Bs, and B 143 I, 14| possible. Again if A may belong to no B, and B may belong 144 I, 14| belong to no B, and B may belong to some of the Cs, it is 145 I, 14| that A may possibly not belong to some of the Cs. The proof 146 I, 14| all B, B may possibly not belong to some C, then a clear 147 I, 14| down that B possibly may belong to some C, we shall have 148 I, 14| it is possible for B to belong to more things than A can. 149 I, 14| none of the minor and must belong to all of it. Take as terms 150 I, 14| possible that the major should belong to the minor. It is clear 151 I, 14| necessary that the major should belong to all the minor and not 152 I, 14| possible that it should belong to any. Consequently there 153 I, 15| major does not necessarily belong to any, or to all, of the 154 I, 15| possible that it should belong to none or not to all. Let 155 I, 15| possible for all B, and let B belong to all C. Since C falls 156 I, 15| defined these points, let A belong to all B, and B be possible 157 I, 15| Suppose that it cannot belong, and that B belongs to C, 158 I, 15| will be possible for A to belong to no C; for if at is supposed 159 I, 15| which does not necessarily belong to any part of the subject ( 160 I, 15| science", C "man". A then will belong to no B; but B is possible 161 I, 15| term does not necessarily belong to any instance of another 162 I, 15| possible, as before. Let A belong to all B, and let B possibly 163 I, 15| all B, and let B possibly belong to no C. If the terms are 164 I, 15| premiss states that A does not belong to B, and the minor premiss 165 I, 15| indicates that B may possibly belong to no C. Through the premisses 166 I, 15| no B, and B may possibly belong to no C. Through these comes 167 I, 15| assumed that B does not belong to any C, instead of possibly 168 I, 15| and B may possibly not belong to some C. For if the premiss 169 I, 16| for "not necessarily to belong" is different from "necessarily 170 I, 16| from "necessarily not to belong".~If the premisses are affirmative, 171 I, 16| syllogism to prove that A may belong to all C. That it is imperfect 172 I, 16| B, and let B necessarily belong to all C. We shall then 173 I, 16| syllogism to prove that A may belong to all C, not that A does 174 I, 16| to all C, not that A does belong to all C: and it is perfect, 175 I, 16| to no C. For suppose A to belong to all C or to some C. Now 176 I, 16| A. But A is supposed to belong to all C or to some C. Consequently 177 I, 16| and let A possibly not belong to any B, and let B necessarily 178 I, 16| B, and let B necessarily belong to all C. The syllogism 179 I, 16| that A possibly does not belong to any B, no impossible 180 I, 16| not possible that A should belong to any B, but B may belong 181 I, 16| belong to any B, but B may belong to some of the Cs, it is 182 I, 16| necessary that A should not belong to some of the Cs. For if 183 I, 16| belongs to all C, but cannot belong to any B, neither can B 184 I, 16| to any B, neither can B belong to any A. So if A belongs 185 I, 16| to none of the Cs can B belong. But it was laid down that 186 I, 16| was laid down that B may belong to some C. But when the 187 I, 17| convertible, e.g. if A may belong to no B, it does not follow 188 I, 17| does not follow that B may belong to no A. For suppose it 189 I, 17| follow and assume that B may belong to no A. Since then problematic 190 I, 17| contradictories, and since B may belong to no A, it is clear that 191 I, 17| it is clear that B may belong to all A. But this is false: 192 I, 17| not incompatible, "A may belong to no B", "B necessarily 193 I, 17| B necessarily does not belong to some of the As"; e.g. 194 I, 17| since it is false that B may belong to no A, it is true that 195 I, 17| it is true that it cannot belong to no A, for the one statement 196 I, 17| which necessarily does not belong to some of the As may possibly 197 I, 17| the As may possibly not belong to any A, just as it is 198 I, 17| belongs to some A may possibly belong to all A. If any one then 199 I, 17| is not possible for C to belong to all D, it necessarily 200 I, 17| it necessarily does not belong to some D, he would make 201 I, 17| assumption: for it does belong to all D, but because in 202 I, 17| is not possible for it to belong to all. Hence both the propositions " 203 I, 17| A necessarily does not belong to some B" are opposed to 204 I, 17| to the proposition "A may belong to no B". It is clear then 205 I, 17| that A necessarily does not belong to some B. But if this is 206 I, 17| suppose it possible that A may belong to no B and to all C. By 207 I, 17| it is assumed that B can belong to all C, no false consequence 208 I, 17| consequence results: for A may belong both to all C and to no 209 I, 17| that the predicate cannot belong to the subject. Suppose 210 I, 17| is possible then for A to belong to all of the one and to 211 I, 17| is not possible for B to belong nor not to belong to C. 212 I, 17| for B to belong nor not to belong to C. That it is not possible 213 I, 17| is not possible for it to belong, is clear. For no horse 214 I, 17| it possible for it not to belong. For it is necessary that 215 I, 18| belongs to no B, but can belong to all C. If the negative 216 I, 18| proposition is converted, B will belong to no A. But ex hypothesi 217 I, 18| A. But ex hypothesi can belong to all C: so a syllogism 218 I, 18| first figure that B may belong to no C. Similarly also 219 I, 18| formed to prove that B may belong to no C, as before: for 220 I, 19| belongs to no B, but may belong to all C. If the negative 221 I, 19| premiss is converted B will belong to no A: but A ex hypothesi 222 I, 19| first figure that B may belong to no C. But at the same 223 I, 19| is clear that B will not belong to any C. For assume that 224 I, 19| it does: then if A cannot belong to any B, and B belongs 225 I, 19| some of the Cs, A cannot belong to some of the Cs: but ex 226 I, 19| but ex hypothesi it may belong to all. A similar proof 227 I, 19| i.e. suppose that A may belong to no B, but necessarily 228 I, 19| that B necessarily does not belong to C. Let A be white, B 229 I, 19| belongs to swan, but may belong to no man; and man necessarily 230 I, 19| arranged, that B should belong to C: for nothing prevents 231 I, 19| Suppose A necessarily does not belong to B, and possibly may not 232 I, 19| B, and possibly may not belong to C: if the premisses are 233 I, 19| no A, and A may possibly belong to all C: thus we have the 234 I, 19| which B necessarily will not belong to C; e.g. suppose that 235 I, 19| which B necessarily does not belong to C. A syllogism then is 236 I, 20| both A and B may possibly belong to every C. Since then the 237 I, 20| particular, and B may possibly belong to every C, it follows that 238 I, 20| follows that C may possibly belong to some B. So, if A is possible 239 I, 20| figure. And A if may possibly belong to no C, but B may possibly 240 I, 20| no C, but B may possibly belong to all C, it follows that 241 I, 20| that A may possibly not belong to some B: for we shall 242 I, 20| A and B may possibly not belong to C, if "may possibly belong" 243 I, 20| belong to C, if "may possibly belong" is substituted we shall 244 I, 20| Suppose that A may possibly belong to all C, and B to some 245 I, 20| can be formed: for A must belong sometimes to all B and sometimes 246 I, 21| all C, and B may possibly belong to all C. If the proposition 247 I, 21| conclusion that A may possibly belong to some of the Bs. For when 248 I, 21| and A may possibly not belong to some C: it follows that 249 I, 21| follows that may possibly not belong to some B. For if A necessarily 250 I, 21| all C, A will necessarily belong to all C: for this has been 251 I, 21| that A may possibly not belong to some C.~Whenever both 252 I, 22| all C, and B may possibly belong to all C. Since then A must 253 I, 22| all C. Since then A must belong to all C, and C may belong 254 I, 22| belong to all C, and C may belong to some B, it follows that 255 I, 22| follows that A may (not does) belong to some B: for so it resulted 256 I, 22| i.e. suppose A may possibly belong to no C, but B necessarily 257 I, 22| that A may possibly not belong to some B but also that 258 I, 22| but also that it does not belong to some B. For suppose that 259 I, 22| that A necessarily does not belong to C, but B may belong to 260 I, 22| not belong to C, but B may belong to all C. If the affirmative 261 I, 22| that A might possibly not belong to some C, and that it did 262 I, 22| some C, and that it did not belong to some C; consequently 263 I, 22| follows that A does not belong to some B. But when the 264 I, 22| sometimes cannot possibly belong to any B. To illustrate 265 I, 27| and those which cannot belong to it. But those to which 266 I, 27| those to which it cannot belong need not be selected, because 267 I, 27| apparently and those which really belong. The larger the supply a 268 I, 27| follows man, and what does not belong to animal does not belong 269 I, 27| belong to animal does not belong to man); but we must choose 270 I, 27| all these also. But these belong more properly to the choice 271 I, 28| originally in question must belong to the subject originally 272 I, 28| attribute in question must belong to some of the subject in 273 I, 28| Whenever the one term has to belong to none of the other, one 274 I, 28| question cannot possibly belong to any of the other. For 275 I, 28| attributes which cannot possibly belong to the predicate in question. 276 I, 28| terms in question does not belong to some of the other. Perhaps 277 I, 28| attributes which cannot possibly belong to A by D. Suppose again 278 I, 28| attributes which cannot belong to E by H. If then one of 279 I, 28| with one of the Fs, A must belong to all E: for F belongs 280 I, 28| G are identical, A must belong to some of the Es: for A 281 I, 28| D are identical, A will belong to none of the Es by a prosyllogism: 282 I, 28| identical with D, A will belong to none of the Fs, but F 283 I, 28| H are identical, A will belong to none of the Es: for B 284 I, 28| none of the Es: for B will belong to all A, but to no E: for 285 I, 28| are identical, A will not belong to some of the Es: for it 286 I, 28| the Es: for it will not belong to G, because it does not 287 I, 28| to G, because it does not belong to D: but G falls under 288 I, 28| consequently A will not belong to some of the Es. If B 289 I, 28| converted syllogism: for E will belong to all A since B belongs 290 I, 28| with G): but that A should belong to all E is not necessary, 291 I, 28| not necessary, but it must belong to some E because it is 292 I, 28| figure is formed. And A will belong to some E, whenever C and 293 I, 28| middle term. And A will belong to no E, when D and F are 294 I, 28| to all E. And A will not belong to some E, whenever D and 295 I, 28| last figure: for A will belong to no G, and E will belong 296 I, 28| belong to no G, and E will belong to all G. Clearly then all 297 I, 28| for the middle term must belong to the one, and not belong 298 I, 28| belong to the one, and not belong to the other.~It is clear 299 I, 28| attributes which cannot possibly belong to E, or if those attributes 300 I, 28| are identical which cannot belong to either term: for no syllogism 301 I, 28| attributes which cannot belong to E, e.g. C with H, we 302 I, 28| attributes which cannot belong to either term are identical, 303 I, 28| contraries or terms which cannot belong to the same thing, all arguments 304 I, 28| are contraries or cannot belong to the same thing. For if 305 I, 28| aforesaid mood. For B will belong to all A and to no E. Consequently 306 I, 28| Again, if B and G cannot belong to the same thing, it follows 307 I, 28| follows that A will not belong to some of the Es: for then 308 I, 28| middle figure: for B will belong to all A and to no G. Consequently 309 I, 28| fact that B and G cannot belong to the same thing differs 310 I, 28| everything which cannot belong to E.~It is clear then that 311 I, 29| the Es. For suppose A to belong to some E: then since B 312 I, 29| to some of the Es, B will belong to some of the Es: but it 313 I, 29| belongs to all G, A will belong to none of the Gs: but it 314 I, 29| Gs: but it was assumed to belong to all. Similarly with the 315 I, 29| it is clear that A will belong to no E. Again if it has 316 I, 29| proved per impossibile to belong to no E. Similarly with 317 I, 29| but E should be assumed to belong to the Gs only, then A would 318 I, 29| the Gs only, then A would belong to every E: and again if 319 I, 29| it follows that A will belong to none of the Es. Clearly 320 I, 29| relations, as well as terms that belong, terms which can belong 321 I, 29| belong, terms which can belong though they actually do 322 I, 30| give the principles which belong to each subject. I mean 323 I, 33| thought. But A does not belong to C: for Aristomenes is 324 I, 33| difference whether we said "This belong to that" or "This belongs 325 I, 34| true to say that A cannot belong to any B (for health belongs 326 I, 34| follow that health cannot belong to any man. The reason for 327 I, 34| that being healthy cannot belong to one who is diseased. 328 I, 34| possible that health should belong to no man. Again the fallacy 329 I, 34| possible that health should belong to any disease, but it is 330 I, 34| possible that health should belong to every man, consequently 331 I, 34| possible that disease should belong to any man". In the third 332 I, 34| contraries, may possibly belong to the same thing, but cannot 333 I, 34| the same thing, but cannot belong to one another. This is 334 I, 34| when several things could belong to the same thing, they 335 I, 34| the same thing, they could belong to one another.~It is evident 336 I, 36| must suppose the verb "to belong" to have as many meanings 337 I, 36| negative. For "that does not belong to this" does not always 338 I, 41| necessary that A should belong, I do not say to all C, 339 I, 45| particular syllogisms. Let A belong to no B and to all C. Convert 340 I, 45| first figure. For B will belong to no A and A to all C. 341 I, 45| first figure. For B will belong to no A and A to some C. 342 I, 45| resolved into the third. Let A belong to all B and B to some C. 343 I, 45| affirmative is convertible, C will belong to some B: but A belonged 344 I, 45| convertible: therefore A will belong to no B, and to some C.~ 345 I, 45| statement is convertible, A will belong to some B. If the syllogism 346 I, 45| in a similar way. Let B belong to all C, and A to no C: 347 I, 45| and A to no C: then C will belong to some B, and A to no C; 348 I, 45| affirmative particular: for A will belong to no C, and C to some of 349 I, 45| belongs to all C, and A not belong to some C: convert the statement 350 I, 45| or all C. For C then will belong to no A and to some B. But 351 I, 46| incapacity to walk will belong at the same time to the 352 I, 46| opposed to one another do not belong at the same time to the 353 I, 46| Then either A or B will belong to everything, but they 354 I, 46| everything, but they will never belong to the same thing; and either 355 I, 46| and either C or D will belong to everything, but they 356 I, 46| everything, but they will never belong to the same thing. And B 357 I, 46| the same thing. And B must belong to everything to which C 358 I, 46| the affirmation does not belong, the denial must belong. 359 I, 46| belong, the denial must belong. But C does not always belong 360 I, 46| belong. But C does not always belong to B: for what is not a 361 I, 46| not-white and white, D must belong to everything to which A 362 I, 46| A and C cannot together belong to the same thing, and that 363 I, 46| that B and D may possibly belong to the same thing.~Privative 364 I, 46| something belongs which does not belong to others, the negation 365 I, 46| are such that they cannot belong at the same time to the 366 I, 46| reversed. And A and D may belong to the same thing, but B 367 I, 46| everything; and since C cannot belong to that to which B belongs, 368 I, 46| with it and A and B cannot belong to the same thing; it is 369 I, 46| possible that A and D should belong to the same thing. But B 370 I, 46| thing. But B and C cannot belong to the same thing, because 371 I, 46| possible that D and A should belong at the same time to the 372 I, 46| rightly, one of which must belong to everything, e.g. we may 373 I, 46| that "if A and B cannot belong at the same time to the 374 I, 46| that one of them should belong to whatever the other does 375 I, 46| whatever the other does not belong to: and again C and D are 376 I, 46| that either A or F should belong to everything: for either 377 I, 46| affirmation or the denial must belong. And again either C or H 378 I, 46| again either C or H must belong to everything: for they 379 I, 46| necessary that A or F should belong to everything, or that F 380 I, 46| everything, or that F or B should belong to everything: for F is 381 II, 1 | or to some B, then B must belong to some A: and if A has 382 II, 1 | if A has been proved to belong to no B, then B belongs 383 II, 1 | former. But if A does not belong to some B, it is not necessary 384 II, 1 | necessary that B should not belong to some A: for it may possibly 385 II, 1 | some A: for it may possibly belong to all A.~This then is the 386 II, 1 | to C, clearly B does not belong to it. But that B does not 387 II, 1 | it. But that B does not belong to what is subordinate to 388 II, 1 | syllogism. And yet B does not belong to E, if E is subordinate 389 II, 1 | without proof that B does not belong to A, consequently it does 390 II, 1 | syllogism that B does not belong to E.~But in particular 391 II, 2 | necessary that A should belong to all that to which C belongs, 392 II, 2 | then the same thing will belong and not belong at the same 393 II, 2 | thing will belong and not belong at the same time. So A is 394 II, 2 | two is false. (1) Let A belong to the whole of C, but to 395 II, 2 | of the Bs, neither let B belong to C. This is possible, 396 II, 2 | man. If then A is taken to belong to all B and B to all C, 397 II, 2 | B and B to all C, A will belong to all C; consequently though 398 II, 2 | that neither A nor B should belong to any C, although A belongs 399 II, 2 | if one term is taken to belong to none of that to which 400 II, 2 | of that to which it does belong, and the other term is taken 401 II, 2 | the other term is taken to belong to all of that to which 402 II, 2 | that to which it does not belong, though both the premisses 403 II, 2 | belongs to none is assumed to belong to all, or if what belongs 404 II, 2 | belongs to all is assumed to belong to none. Let A belong to 405 II, 2 | to belong to none. Let A belong to no B, and B to all C. 406 II, 2 | must be false. For A will belong to all C, since A belongs 407 II, 2 | and B to all C, A will belong to all C truly: for every 408 II, 2 | is possible that A should belong to some B and to no C, and 409 II, 2 | no C, and that B should belong to all C, e.g. animal to 410 II, 2 | and B to all C, then will belong to no C.~(5) But if the 411 II, 2 | is possible that A should belong neither to any B nor to 412 II, 2 | C, and that B should not belong to any C, e.g. a genus to 413 II, 2 | healing, nor does music belong to the art of healing. If 414 II, 2 | and B to all C, A will belong to all C: and this ex hypothesi 415 II, 2 | possible that A should neither belong to any B nor to any C, though 416 II, 2 | B, and B to all C, will belong to no C: and this ex hypothesi 417 II, 2 | is possible that A should belong to the whole of B, but not 418 II, 2 | If then A is assumed to belong to all B, and B to some 419 II, 2 | is possible that A should belong to no B, and not to some 420 II, 2 | some C, then A will not belong to some C, which ex hypothesi 421 II, 2 | it is possible that A may belong to no B and to some C, while 422 II, 2 | some C, then A does not belong to some C. The conclusion 423 II, 3 | is possible that A should belong to some B and to all C, 424 II, 3 | is possible that A should belong to some B and to some C, 425 II, 3 | some C, though B does not belong to some C, e.g. animal to 426 II, 3 | things, though man will not belong to some white things. If 427 II, 3 | is possible that A should belong to no B, and not to some 428 II, 3 | some C, though B does not belong to some C, e.g. animal belongs 429 II, 3 | nothing lifeless, and does not belong to some white things, and 430 II, 3 | things, and lifeless will not belong to some white things. If 431 II, 3 | at all, while B does not belong to some C, e.g. animal belongs 432 II, 3 | is possible that should A belong both to B and to C as wholes, 433 II, 3 | whole of B, but does not belong to some C, the universal 434 II, 3 | is possible that A should belong both to B and to C as wholes, 435 II, 3 | all C, though B does not belong to some C, e.g. animal follows 436 II, 3 | If then A is assumed to belong to the whole of B, and not 437 II, 4 | is assumed that A and B belong to all C, the premisses 438 II, 4 | is possible that B should belong to no C, but A to all C, 439 II, 4 | all C, and that should not belong to some B, e.g. black belongs 440 II, 4 | and A to no C, A will not belong to some B: and the conclusion 441 II, 4 | e.g. white and beautiful belong to some animals, and white 442 II, 4 | it is stated that A and B belong to all C, the premisses 443 II, 4 | some C, while A does not belong to all B, e.g. white does 444 II, 4 | all B, e.g. white does not belong to some animals, beautiful 445 II, 4 | animals, and white does not belong to everything beautiful. 446 II, 4 | all C, though A does not belong to some B, e.g. animal and 447 II, 4 | though animal does not belong to everything white. Taking 448 II, 4 | whole of C, but A does not belong to C at all, the premiss 449 II, 4 | is assumed that A and B belong to every C, the premiss 450 II, 4 | is possible that B should belong to all C, and A to some 451 II, 4 | assumed that both A and B belong to the whole of C, the premiss 452 II, 4 | is possible that B should belong to the whole of C, and A 453 II, 4 | are so, that A should not belong to all B, therefore it is 454 II, 4 | possible that A should not belong to some C, it is clear that 455 II, 5 | should now be proved to belong to B by assuming that A 456 II, 5 | to C, and A is assumed to belong to C, which was the conclusion 457 II, 5 | first syllogism, and B to belong to A but the converse was 458 II, 5 | and A to all B, C must belong to all B. In both these 459 II, 5 | been proved, and C must belong to A. It is clear then that 460 II, 5 | proof is as follows. Let B belong to all C, and A to none 461 II, 5 | previously assumed) A must belong to no C, and C to all B: 462 II, 5 | none of which longs. Let A belong to none of the Cs (which 463 II, 5 | necessary then that B should belong to all C. Consequently each 464 II, 5 | conclusion is retained, B will belong to some C: for we obtain 465 II, 5 | some of which A does not belong": otherwise no syllogism 466 II, 6 | proved as follows. Let A belong to all B, and to no C: we 467 II, 6 | necessary that A should belong to no C: for we get the 468 II, 6 | no A: neither then does A belong to B. Through the conclusion, 469 II, 6 | statement is affirmative. Let A belong to all B, and not to all 470 II, 6 | not to all C, A will not belong to some C, B being middle. 471 II, 6 | some of which B does not belong.~ 472 II, 7 | extreme, impossible. Let A belong to all C and B to some C: 473 II, 7 | to some B, that B should belong to some C. But it is not 474 II, 7 | the same that this should belong to that, and that to this: 475 II, 7 | necessary that A should belong to some C, B being middle. 476 II, 7 | premiss can be proved. Let B belong to all C, and A not to some 477 II, 7 | conclusion is that A does not belong to some B. If then it is 478 II, 7 | necessary that A should not belong to some C, B being middle. 479 II, 7 | some of which this does not belong, e.g. if A belongs to no 480 II, 7 | conclusion is that A does not belong to some B. If then it is 481 II, 7 | to some of which does not belong, it is necessary that C 482 II, 7 | necessary that C should belong to some of the Bs. In no 483 II, 8 | either the extreme cannot belong to the middle or the middle 484 II, 8 | C, but to all B, B will belong to no C. And if A belongs 485 II, 8 | and B to all C, A will belong, not to no B at all, but 486 II, 8 | all C, and to no B, B will belong to none of the Cs. And if 487 II, 8 | of the Cs. And if A and B belong to all C, A will belong 488 II, 8 | belong to all C, A will belong to some B: but in the original 489 II, 8 | C, but to all B, B will belong not to all C. And if A belongs 490 II, 8 | belongs to all C, A will belong not to all B. Similarly 491 II, 8 | some C, and to no B, B will belong, not to no C at all, but-not 492 II, 8 | originally assumed, A will belong to some B.~In particular 493 II, 8 | B to some C, A will not belong to some B: and if A belongs 494 II, 8 | C, but to all B, B will belong to no C. Thus both premisses 495 II, 8 | contrary. For if A does not belong to some C, but to all B, 496 II, 8 | to all B, then B will not belong to some C. But the original 497 II, 8 | is possible that B should belong to some C, and should not 498 II, 8 | to some C, and should not belong to some C. The universal 499 II, 8 | at all: for if A does not belong to some of the Cs, but B 500 II, 9 | the contradictory. Let A belong to all B and to no C: conclusion