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| Alphabetical [« »] belong-either 1 belonged 14 belonging 31 belongs 587 beloved 3 below 1 besides 4 | Frequency [« »] 658 but 599 all 589 belong 587 belongs 483 some 480 are 442 no | Aristotle Prior Analytics IntraText - Concordances belongs |
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1 I, 1 | the faculty to which it belongs: its subject is demonstration 2 I, 1 | statement that something belongs to all or none of something 3 I, 1 | else; by particular that it belongs to some or not to some or 4 I, 4 | A.~But if the first term belongs to all the middle, but the 5 I, 4 | when neither the first term belongs to any of the middle, nor 6 I, 5 | Whenever the same thing belongs to all of one subject, and 7 I, 5 | possible, whenever the middle belongs to all of one subject and 8 I, 5 | been proved. Again if M belongs to all N, but to no O, then 9 I, 5 | belong to no O. For if M belongs to no O, O belongs to no 10 I, 5 | if M belongs to no O, O belongs to no M: but M (as was said) 11 I, 5 | no M: but M (as was said) belongs to all N: O then will belong 12 I, 5 | particular is negative. For if M belongs to no N, but to some O, 13 I, 5 | first figure. Again if M belongs to all N, but not to some 14 I, 5 | belong to some O: for if N belongs to all O, and M is predicated 15 I, 5 | belong to some O. And if M belongs to all N but not to all 16 I, 5 | positively and universally, if M belongs to some O, and does not 17 I, 5 | but we assumed that it belongs to some O. In this way then 18 I, 5 | belong to some O, even if it belongs to no O, and since if it 19 I, 5 | to no O, and since if it belongs to no O a syllogism is ( 20 I, 5 | premiss is universal, and M belongs to no O, and not to some 21 I, 5 | possible if the middle term belongs to some of each of the extremes, 22 I, 5 | belong to some of either, or belongs to some of the one, not 23 I, 5 | to some of the other, or belongs to neither universally, 24 I, 6 | 6~But if one term belongs to all, and another to none, 25 I, 6 | R: consequently since P belongs to all S, and S to some 26 I, 6 | will belong to some R.~If R belongs to all S, and P to no S, 27 I, 6 | the former cases. But if R belongs to no S, P to all S, there 28 I, 6 | to prove that one extreme belongs to some of the other; but 29 I, 6 | premisses is universal. For if R belongs to all S, P to some S, P 30 I, 6 | P: consequently since R belongs to all S, and S to some 31 I, 6 | belong to some R.~Again if R belongs to some S, and P to all 32 I, 6 | is affirmative. For if R belongs to all S, but P does not 33 I, 6 | belong to some R. For if P belongs to all R, and R belongs 34 I, 6 | belongs to all R, and R belongs to all S, then P will belong 35 I, 6 | will be possible, e.g. if P belongs to all S and R does not 36 I, 6 | possible to get terms, if R belongs to some S, and does not 37 I, 6 | belong to some S. For if P belongs to all S, and R to some 38 I, 6 | but we assumed that it belongs to no R. We must put the 39 I, 6 | truly of that also which belongs to none. But if R belongs 40 I, 6 | belongs to none. But if R belongs to no S, no syllogism is 41 I, 6 | be a syllogism. For if P belongs to no S, and R belongs to 42 I, 6 | P belongs to no S, and R belongs to some S, P will not belong 43 I, 6 | terms cannot be found, if R belongs to some S, and does not 44 I, 6 | belong to some S. For if P belongs to all R, and R to some 45 I, 6 | and R to some S, then P belongs to some S: but we assumed 46 I, 6 | but we assumed that it belongs to no S. Our point, then, 47 I, 6 | if each of the extremes belongs to some of the middle or 48 I, 6 | does not belong, or one belongs and the other does not to 49 I, 6 | some of the middle, or one belongs to some of the middle, the 50 I, 7 | the major term, e.g. if A belongs to all or some B, and B 51 I, 7 | to all or some B, and B belongs to no C: for if the premisses 52 I, 7 | all C, it follows that A belongs to some B: for if A belonged 53 I, 7 | belonged to no B, and B belongs to all C, A would belong 54 I, 7 | C: but (as we stated) it belongs to all C. Similarly also 55 I, 7 | ad impossibile, e.g. if A belongs to all B, and B to some 56 I, 7 | some C, it follows that A belongs to some C. For if it belonged 57 I, 7 | it belonged to no C, and belongs to all B, then B will belong 58 I, 7 | of the negative. For if A belongs to no B, and B belongs to 59 I, 7 | A belongs to no B, and B belongs to some C, A will not belong 60 I, 7 | it belonged to all C, and belongs to no B, then B will belong 61 I, 7 | which prove that something belongs or does not belong to something 62 I, 8 | difference according as something belongs, necessarily belongs, or 63 I, 8 | something belongs, necessarily belongs, or may belong to something 64 I, 8 | then, whether something belongs or necessarily belongs ( 65 I, 8 | something belongs or necessarily belongs (or does not belong) to 66 I, 9 | C. For since necessarily belongs, or does not belong, to 67 I, 9 | through the third that A belongs necessarily to some B. But 68 I, 9 | is necessary then that A belongs to some C necessarily: for 69 I, 10| possible of no A. But A belongs to all C; consequently B 70 I, 10| possible of no A: but A belongs to all B, consequently C 71 I, 10| A. For if B necessarily belongs to no C, C will necessarily 72 I, 10| assumed) that A necessarily belongs to all B. Consequently it 73 I, 10| however so long as animal belongs to nothing white. Consequently 74 I, 10| should belong to it: but A belongs to some C; consequently 75 I, 10| affirmative. If then A necessarily belongs to all B, but does not belong 76 I, 11| necessary. Since then B belongs to all C, C also will belong 77 I, 11| particular: consequently if A belongs necessarily to all C, and 78 I, 11| necessarily to all C, and C belongs to some B, it is necessary 79 I, 11| some A: consequently if B belongs necessarily to all C, it 80 I, 11| some B, but A necessarily belongs to no C, A will necessarily 81 I, 11| necessarily: consequently if A belongs to none of the Cs, while 82 I, 11| none of the Cs, while C belongs to some of the Bs, A will 83 I, 11| should belong to any C, but B belongs to some C, it is necessary 84 I, 13| generally what naturally belongs to a thing (for this has 85 I, 13| either that to which "that" belongs or that to which it may 86 I, 14| man", where the major belongs necessarily to the minor; " 87 I, 14| syllogism proves that something belongs either simply or necessarily 88 I, 15| proving that A possibly belongs to no C.~It is clear that 89 I, 15| possible, but assume that B belongs to all C: this is false 90 I, 15| not possible for C but B belongs to all C, then A is not 91 I, 15| impossibility, by assuming that B belongs to C. For if B belongs to 92 I, 15| B belongs to C. For if B belongs to all C, and A is possible 93 I, 15| must understand "that which belongs to all" with no limitation 94 I, 15| negative, and assume that A belongs to no B, but B possibly 95 I, 15| to no B, but B possibly belongs to all C. These propositions 96 I, 15| necessary that A possibly belongs to no C. Suppose that it 97 I, 15| cannot belong, and that B belongs to C, as above. It is necessary 98 I, 15| is necessary then that A belongs to some B: for we have a 99 I, 15| supposed that A necessarily belongs to some C, but the syllogism 100 I, 15| intelligent", and C "man". A then belongs to no B: for no intelligent 101 I, 15| intelligent. But A necessarily belongs to no C: so the conclusion 102 I, 15| syllogism. Suppose that A belongs to no B, and B may possibly 103 I, 15| and problematic, e.g. if A belongs to all B or to no B, and 104 I, 16| necessary. Suppose A necessarily belongs to all B, and let B be possible 105 I, 16| is necessary then that A belongs to no C. For suppose A to 106 I, 16| it were supposed that A belongs to some C, and it is laid 107 I, 16| some of the Cs. For if A belongs to all C, but cannot belong 108 I, 16| belong to any A. So if A belongs to all C, to none of the 109 I, 17| true that B necessarily belongs to some of the As: consequently 110 I, 17| consequently A necessarily belongs to some of the Bs. But this 111 I, 17| say that what necessarily belongs to some A may possibly belong 112 I, 17| because in some cases it belongs necessarily, therefore we 113 I, 17| propositions "A necessarily belongs to some B" and "A necessarily 114 I, 17| opposed to the proposition "A belongs to all B". Similarly also 115 I, 17| not that A necessarily belongs to some B, but that A necessarily 116 I, 18| have a syllogism. Suppose A belongs to no B, but can belong 117 I, 19| Suppose that A necessarily belongs to no B, but may belong 118 I, 19| cannot belong to any B, and B belongs to some of the Cs, A cannot 119 I, 19| to no B, but necessarily belongs to all C. When the terms 120 I, 19| White then necessarily belongs to swan, but may belong 121 I, 19| man; and man necessarily belongs to no swan; Clearly then 122 I, 19| For motion necessarily belongs to what is awake, and is 123 I, 19| premisses are converted B belongs to no A, and A may possibly 124 I, 21| affirmative: suppose that A belongs to all C, and B may possibly 125 I, 21| impossibile. Suppose that B belongs to all C, and A may possibly 126 I, 21| B. For if A necessarily belongs to all B, and B (as has 127 I, 21| B (as has been assumed) belongs to all C, A will necessarily 128 I, 22| i.e. that A necessarily belongs to all C, and B may possibly 129 I, 22| no C, but B necessarily belongs to all C. We shall have 130 I, 22| A sometimes necessarily belongs to all B, and sometimes 131 I, 23| prove either that something belongs or that it does not, and 132 I, 23| premisses taken. Nor when C belongs to something else, and that 133 I, 26| for whether the predicate belongs to none or not to some, 134 I, 26| destroyed, whether the predicate belongs to all or to some: and this 135 I, 26| proving that the predicate belongs either to all or to none. 136 I, 28| must belong to all E: for F belongs to all E, and A to all C, 137 I, 28| to all C, consequently A belongs to all E. If C and G are 138 I, 28| to none of the Fs, but F belongs to all E. Again, if B and 139 I, 28| belong to all A since B belongs to A and E to B (for B was 140 I, 28| than to C alone. For if A belongs to KF, it belongs both to 141 I, 28| For if A belongs to KF, it belongs both to F and to E: but 142 I, 28| For it is proved that A belongs to all E, whenever an identical 143 I, 28| figure; the first, because A belongs to no F, since the negative 144 I, 28| statement is convertible, and F belongs to all E: the middle figure 145 I, 28| middle figure because D belongs to no A, and to all E. And 146 I, 28| be formed to prove that A belongs to none of the Es, not however 147 I, 29| ostensively, e.g. that A belongs to none of the Es. For suppose 148 I, 29| to some E: then since B belongs to all A and A to some of 149 I, 29| but it was assumed that it belongs to none. Again we may prove 150 I, 29| Again we may prove that A belongs to some E: for if A belonged 151 I, 29| to none of the Es, and E belongs to all G, A will belong 152 I, 29| it has been proved that A belongs to no E, because it turns 153 I, 29| turns out that otherwise B belongs to some of the Es and this 154 I, 29| now it is assumed that B belongs to no E and to all A, it 155 I, 29| ostensive syllogism that A belongs to no E, assume that A belongs 156 I, 29| belongs to no E, assume that A belongs to some E and it will be 157 I, 33| It is true then that A belongs to B. For Aristomenes as 158 I, 33| thought is eternal. But B also belongs to C: for Aristomenes is 159 I, 33| belong to that" or "This belongs to all of that".~ 160 I, 34| belong to any B (for health belongs to no disease) and again 161 I, 34| disease) and again that B belongs to every C (for every man 162 I, 35| isosceles triangle. A then belongs to C because of B: but A 163 I, 35| to C because of B: but A belongs to B without the mediation 164 I, 36| 36~That the first term belongs to the middle, and the middle 165 I, 36| contrary to one another. Then A belongs to B, not in the sense that 166 I, 36| right time: for opportunity belongs to God, but the right time 167 I, 37| 37~The expressions "this belongs to that" and "this holds 168 I, 41| fact or in speech, that A belongs to all of that to which 169 I, 41| to all of that to which B belongs, and that A belongs to all 170 I, 41| which B belongs, and that A belongs to all of that to all of 171 I, 41| of that to all of which B belongs: for nothing prevents B 172 I, 41| and C for white. If beauty belongs to something white, it is 173 I, 41| true to say that beauty belongs to that which is white; 174 I, 41| that is white. If then A belongs to B, but not to everything 175 I, 41| predicated, then whether B belongs to all C or merely belongs 176 I, 41| belongs to all C or merely belongs to C, it is not necessary 177 I, 41| even to C at all. But if A belongs to everything of which B 178 I, 45| clear in the sequel. If A belongs to no B, and B to all C, 179 I, 45| and B to all C, then A belongs to no C. Thus the first 180 I, 45| the middle figure. For B belongs to no A, and to all C. Similarly 181 I, 45| but particular, e.g. if A belongs to no B, and B to some C. 182 I, 45| be made first term. For C belongs to no A, and A to all B: 183 I, 45| A to all B: therefore C belongs to no B. B then belongs 184 I, 45| belongs to no B. B then belongs to no C: for the negative 185 I, 45| will be possible, e.g. if A belongs to no B and to some C: convert 186 I, 45| will be possible, e.g. if A belongs to all B, but not to all 187 I, 45| with either A or B: C then belongs to some B. Consequently 188 I, 45| get the first figure, if A belongs to all C, and C to some 189 I, 45| to some of the Bs. If A belongs to all C and B to some C, 190 I, 45| reference to C. But if B belongs to all C and A to some C, 191 I, 45| first term must be B: for B belongs to all C, and C to some 192 I, 45| C to some A, therefore B belongs to some A. But since the 193 I, 45| will be possible, e.g. if B belongs to all C, and A not belong 194 I, 45| resolution is possible. For if A belongs to no B and to some C, both 195 I, 45| relation to A, so that B belongs to no A and C to some A. 196 I, 45| middle term. But when A belongs to all B, and not to some 197 I, 45| is universal, e.g. if A belongs to no C, and B to some or 198 I, 46| to everything to which C belongs. For if it is true to say " 199 I, 46| either. On the other hand D belongs to everything to which A 200 I, 46| to everything to which A belongs. For either C or D belongs 201 I, 46| belongs. For either C or D belongs to everything to which A 202 I, 46| to everything to which A belongs. But since a thing cannot 203 I, 46| to everything to which A belongs. For of that which is white 204 I, 46| some of which something belongs which does not belong to 205 I, 46| one of the two necessarily belongs to everything, and again 206 I, 46| either C or D necessarily belongs to everything; and since 207 I, 46| belong to that to which B belongs, because it carries A along 208 I, 46| reciprocate with but A, but C or D belongs to everything, it is possible 209 I, 46| follows: it will result that B belongs necessarily to everything 210 I, 46| to everything to which D belongs": but this is false. "Assume 211 I, 46| denial. And ex hypothesi A belongs to everything ever thing 212 I, 46| everything ever thing to which C belongs. Therefore H belongs to 213 I, 46| which C belongs. Therefore H belongs to everything to which F 214 I, 46| to everything to which F belongs. Again since either F or 215 I, 46| Again since either F or B belongs to everything, and similarly 216 II, 1 | to belong to no B, then B belongs to no A. This is a different 217 II, 1 | the conclusion, e.g. if A belongs to no B and to all C; we 218 II, 1 | all C; we conclude that B belongs to no C. If then D is subordinate 219 II, 1 | through the syllogism that B belongs to no C, it has been assumed 220 II, 1 | the syllogism, e.g. if A belongs to all B and B to some C. 221 II, 2 | If then it is true that A belongs to all that to which B belongs, 222 II, 2 | belongs to all that to which B belongs, and that B belongs to all 223 II, 2 | which B belongs, and that B belongs to all that to which C belongs, 224 II, 2 | belongs to all that to which C belongs, it is necessary that A 225 II, 2 | belong to all that to which C belongs, and this cannot be false: 226 II, 2 | is possible, e.g. animal belongs to no stone, nor stone to 227 II, 2 | belong to any C, although A belongs to all B, e.g. if the same 228 II, 2 | for neither animal nor man belongs to any stone, but animal 229 II, 2 | to any stone, but animal belongs to every man. Consequently 230 II, 2 | the truth, e.g. if what belongs to none is assumed to belong 231 II, 2 | belong to all, or if what belongs to all is assumed to belong 232 II, 2 | wholly false, viz. that A belongs to all B, it is impossible 233 II, 2 | be a true conclusion if A belongs to all B, and B to all C, 234 II, 2 | also assumed, viz. that A belongs to nothing to which B belongs: 235 II, 2 | belongs to nothing to which B belongs: here the conclusion must 236 II, 2 | belong to all C, since A belongs to everything to which B 237 II, 2 | to everything to which B belongs, and B to all C. It is clear 238 II, 2 | conclusion is possible. For if A belongs to all C and to some B, 239 II, 2 | and to some B, and if B belongs to all C, e.g. animal to 240 II, 2 | take as premisses that A belongs to all B, and B to all C, 241 II, 2 | one should assume that A belongs to no B, and B to all C, 242 II, 2 | B and to all C, though B belongs to no C, e.g. these being 243 II, 2 | to the other: for animal belongs both to horse and to man, 244 II, 2 | then it is assumed that A belongs to all B and B to all C, 245 II, 2 | another genus: for animal belongs neither to music nor to 246 II, 2 | then it is assumed that A belongs to no B, and B to all C, 247 II, 2 | whole of B and of C, while B belongs to some C, e.g. a genus 248 II, 2 | and difference: for animal belongs to every man and to every 249 II, 2 | then it is assumed that A belongs to all B, and B to all C, 250 II, 2 | B nor to any C, though B belongs to some C, e.g. a genus 251 II, 2 | difference: for animal neither belongs to any wisdom nor to any 252 II, 2 | speculative", but wisdom belongs to some instance of "speculative". 253 II, 2 | should be assumed that A belongs to no B, and B to all C, 254 II, 2 | B to some C, e.g. animal belongs to no snow, but to some 255 II, 2 | and it is assumed that A belongs to the whole of B, and B 256 II, 2 | not to some C, although B belongs to some C, e.g. animal belongs 257 II, 2 | belongs to some C, e.g. animal belongs to every man, but does not 258 II, 2 | follow some white, but man belongs to some white; consequently 259 II, 2 | and it is assumed that A belongs to no B but B belongs to 260 II, 2 | A belongs to no B but B belongs to some C, the conclusion 261 II, 2 | B and to some C, while B belongs to no C, e.g. animal to 262 II, 2 | black things, though swan belongs to no black thing. Consequently 263 II, 2 | should be assumed that A belongs to all B, and B to some 264 II, 2 | and not to some C, while B belongs to no C, e.g. a genus to 265 II, 2 | own species: for animal belongs to no number and not to 266 II, 2 | white things, and number belongs to nothing white. If then 267 II, 2 | and it is assumed that A belongs to no B, and B to some C, 268 II, 2 | and to some C, though B belongs to no C, e.g. if B is the 269 II, 2 | the same genus: for animal belongs to some white things and 270 II, 2 | black things, but white belongs to no black thing. If then 271 II, 2 | then it is assumed that A belongs to all B, and B to some 272 II, 2 | B and to some C, while B belongs to no C, e.g. a genus in 273 II, 2 | own species: for animal belongs to no number, but to some 274 II, 2 | then it is assumed that A belongs to all B and B to some C, 275 II, 2 | and not to some C, while B belongs to no C, e.g. animal belongs 276 II, 2 | belongs to no C, e.g. animal belongs to every swan, and not to 277 II, 2 | some black things, and swan belongs to nothing black. Consequently 278 II, 2 | if it is assumed that A belongs to no B, and B to some C, 279 II, 3 | partially true. For (1) if A belongs to no B and to all C, e.g. 280 II, 3 | and it is assumed that A belongs to all B and to no C, though 281 II, 3 | conclusion. Similarly if A belongs to all B and to no C: for 282 II, 3 | B and to all C, though B belongs to no C, e.g. a genus to 283 II, 3 | co-ordinate species. For animal belongs to every horse and man, 284 II, 3 | it is assumed that animal belongs to all of the one, and none 285 II, 3 | B and to all C, though B belongs to no C, e.g. animal to 286 II, 3 | every raven, though white belongs to no raven. If then it 287 II, 3 | then it is assumed that A belongs to no B, but to the whole 288 II, 3 | to C as a whole, while B belongs to no C, e.g. animal belongs 289 II, 3 | belongs to no C, e.g. animal belongs to some white things, but 290 II, 3 | but to no pitch, and white belongs to no pitch. Consequently 291 II, 3 | if it is assumed that A belongs to the whole of B, but to 292 II, 3 | black things, though white belongs to nothing black. If then 293 II, 3 | then it is assumed that A belongs to all B and to no C, both 294 II, 3 | then it is stated that A belongs to no B and to some C, the 295 II, 3 | belong to some C, e.g. animal belongs to nothing lifeless, and 296 II, 3 | then it is stated that A belongs to all B and not to some 297 II, 3 | belong to some C, e.g. animal belongs to no number nor to anything 298 II, 3 | then it is stated that A belongs to no B and to some C, the 299 II, 3 | if it is assumed that A belongs to the whole of B, but does 300 II, 3 | if it is assumed that A belongs to no B and to some C, the 301 II, 4 | belonging to any C, while A belongs to some B, e.g. neither 302 II, 4 | anything lifeless, though man belongs to some footed things. If 303 II, 4 | belong to some B, e.g. black belongs to no swan, animal to every 304 II, 4 | if it is assumed that B belongs to all C, and A to no C, 305 II, 4 | belonging to some C while A belongs to some B, e.g. white and 306 II, 4 | some animals, beautiful belongs to some animals, and white 307 II, 4 | if it is assumed that A belongs to no C, and B to all C, 308 II, 4 | terms, if one assumes that B belongs to the whole of C, but A 309 II, 4 | belonging to C at all, though A belongs to some B, e.g. animal belongs 310 II, 4 | belongs to some B, e.g. animal belongs to every swan, black to 311 II, 4 | and A to some C, while A belongs to some B, e.g. biped belongs 312 II, 4 | belongs to some B, e.g. biped belongs to every man, beautiful 313 II, 4 | therefore it is assumed that B belongs to the whole of C, and A 314 II, 4 | has been proved that if A belongs to no C and B to some C, 315 II, 4 | if it is assumed that A belongs to no C, and B to all C, 316 II, 4 | whether one assumes that what belongs to none belongs to all or 317 II, 4 | that what belongs to none belongs to all or that what belongs 318 II, 4 | belongs to all or that what belongs to some belongs to all. 319 II, 4 | that what belongs to some belongs to all. The same applies 320 II, 5 | necessary to prove that A belongs to all C, and it has been 321 II, 5 | to B by assuming that A belongs to C, and C to B-so A belongs 322 II, 5 | belongs to C, and C to B-so A belongs to B: but in the first syllogism 323 II, 5 | was assumed, viz. that B belongs to C. Or suppose it is necessary 324 II, 5 | necessary to prove that B belongs to C, and A is assumed to 325 II, 5 | earlier syllogism, viz. that A belongs to B. In no other way is 326 II, 5 | these terms that the third belongs to the middle or the middle 327 II, 5 | then it is assumed that B belongs to all C, and C to all A, 328 II, 5 | if it is assumed that C belongs to all A, and A to all B, 329 II, 5 | then it is assumed that C belongs to all B, and B to all A, 330 II, 5 | the Bs: we conclude that A belongs to none of the Cs. If again 331 II, 5 | necessary to prove that A belongs to none of the Bs (which 332 II, 5 | necessary to prove that B belongs to C, the proposition AB 333 II, 5 | before: for the premiss "B belongs to no A" is identical with 334 II, 5 | identical with the premiss "A belongs to no B". But we must assume 335 II, 5 | But we must assume that B belongs to all of that to none of 336 II, 5 | conclusion) and assume that B belongs to all of that to none of 337 II, 5 | that to none of which A belongs. It is necessary then that 338 II, 5 | then it is assumed that B belongs to all A and the conclusion 339 II, 5 | universal syllogism, i.e "B belongs to some of that to some 340 II, 6 | no C: we conclude that B belongs to no C. If then it is assumed 341 II, 6 | then it is assumed that B belongs to all A, it is necessary 342 II, 6 | the first figure. For C belongs to all A and B to no C, 343 II, 6 | to no C, consequently B belongs to no A: neither then does 344 II, 6 | then it is assumed that B belongs to all A, but not to all 345 II, 6 | if it is assumed that A belongs to some of that to some 346 II, 7 | then it is assumed that C belongs to all A, it has been proved 347 II, 7 | it has been proved that C belongs to some B, but that B belongs 348 II, 7 | belongs to some B, but that B belongs to some C has not been proved. 349 II, 7 | yet it is necessary, if C belongs to some B, that B should 350 II, 7 | assume besides that if this belongs to some of that, that belongs 351 II, 7 | belongs to some of that, that belongs to some of this. But if 352 II, 7 | other premiss. But if B belongs to all C, and A to some 353 II, 7 | when it is assumed that C belongs to all B, and A to some 354 II, 7 | and A to some B. For if C belongs to all B and A to some B, 355 II, 7 | is assumed further that C belongs to all B, it is necessary 356 II, 7 | it is assumed that that belongs to some of that, to some 357 II, 7 | does not belong, e.g. if A belongs to no C, and B to some C: 358 II, 7 | then it is assumed that C belongs to some of that to some 359 II, 7 | it is assumed that that belongs to all of that to none of 360 II, 7 | that to none of which this belongs. In the middle figure, when 361 II, 8 | should be assumed that A belongs to no C, but to all B, B 362 II, 8 | belong to no C. And if A belongs to no C, and B to all C, 363 II, 8 | it has been proved that A belongs to no C through B. Then 364 II, 8 | if it is assumed that A belongs to all C, and to no B, B 365 II, 8 | converted as stated. Then if A belongs not to all C, but to all 366 II, 8 | belong not to all C. And if A belongs not to all C, but B belongs 367 II, 8 | belongs not to all C, but B belongs to all C, A will belong 368 II, 8 | syllogism is negative. For if A belongs to some C, and to no B, 369 II, 8 | but-not to some C. And if A belongs to some C, and B to all 370 II, 8 | then it is assumed that A belongs to no C, and B to some C, 371 II, 8 | belong to some B: and if A belongs to no C, but to all B, B 372 II, 8 | to some of the Cs, but B belongs to some of the Cs, neither 373 II, 8 | should be assumed that A belongs to all C, both premisses 374 II, 8 | the assumption is that A belongs to some C, neither premiss 375 II, 9 | then it is assumed that B belongs to all C, and the proposition 376 II, 9 | figure is produced. If B belongs to all C, and A to no C, 377 II, 9 | C, and A to no C, then A belongs not to all B: the figure 378 II, 9 | contradictory. For if B belongs to some C, and A to no C, 379 II, 9 | belong to some B. Again if B belongs to some C, and A to all 380 II, 9 | refuted. Suppose that A belongs to no B, and to some C: 381 II, 9 | then it is assumed that B belongs to some C, and the statement 382 II, 9 | not to some C. Again if B belongs to some C and A to some 383 II, 9 | can be refuted. For if B belongs to all C, and A to no B, 384 II, 9 | belong to some C. Again if B belongs to all C and A to some C, 385 II, 10| it has been proved that A belongs to some B, C being taken 386 II, 10| belong to some B, but B belongs to all C, no syllogism is 387 II, 10| not belong to some B, but belongs to all C, will a syllogism 388 II, 10| can be refuted. For if A belongs to no B, and B to all C, 389 II, 10| and B to all C, then A belongs to no C: again if A belongs 390 II, 10| belongs to no C: again if A belongs to no B, and to all C, B 391 II, 10| to no B, and to all C, B belongs to no C. And similarly if 392 II, 10| not universal. For if A belongs to no B, and B to some C, 393 II, 10| not belong to some C: if A belongs to no B, and to C, B will 394 II, 10| not be possible. For if A belongs to some B, and B to all 395 II, 10| about A and C. Nor, if A belongs to some B, and to no C, 396 II, 10| they are refuted. For if A belongs to all B, and B to C, A 397 II, 10| to all B, and B to C, A belongs to all C: but A was supposed 398 II, 10| belong to no C. Again if A belongs to all B, and to no C, then 399 II, 10| all B, and to no C, then B belongs to no C: but it was supposed 400 II, 10| and affirmative. If then A belongs to all B, and B to some 401 II, 10| some C, it results that A belongs to some C: but it was supposed 402 II, 10| belong to no C. Again if A belongs to all B, and to no C, then 403 II, 10| all B, and to no C, then B belongs to no C: but it was assumed 404 II, 10| to belong to some C. If A belongs to some B and B to some 405 II, 10| syllogism results: nor yet if A belongs to some B, and to no C. 406 II, 11| same way. For example if A belongs to all B, C being middle, 407 II, 11| does not belong to all B or belongs to no B, but to all C (which 408 II, 11| true), it follows that C belongs to no B or not to all B. 409 II, 11| the first. Suppose that A belongs not to all B, or to no B, 410 II, 11| of the terms, viz. that C belongs to all A, or that B belongs 411 II, 11| belongs to all A, or that B belongs to all D; thus we get the 412 II, 11| if it is supposed that A belongs to no B, when the premiss 413 II, 11| problem proposed. For if A belongs to no B, and B belongs to 414 II, 11| A belongs to no B, and B belongs to all D, A belongs to no 415 II, 11| and B belongs to all D, A belongs to no D. Let this be impossible: 416 II, 11| impossible: it is false then A belongs to no B. But the universal 417 II, 11| be proved. Suppose that A belongs to no B, and let it have 418 II, 11| have been assumed that B belongs to all or to some C. Then 419 II, 11| be true and clear that A belongs to all C): consequently 420 II, 11| contradictory.~Again suppose that A belongs to some B, and let it have 421 II, 11| have been assumed that C belongs to all A. It is necessary 422 II, 11| that case it is true that A belongs to no B. We may proceed 423 II, 11| not proved. Suppose that A belongs to all B, and let it have 424 II, 11| have been assumed that C belongs to all A. It is necessary 425 II, 11| that it is false that A belongs to all B. But we have not 426 II, 11| it to be necessary that A belongs to no B, if it does not 427 II, 11| we must suppose that it belongs to all B: for if A belongs 428 II, 11| belongs to all B: for if A belongs to all B, and C to all A, 429 II, 11| and C to all A, then C belongs to all B; so that if this 430 II, 11| the hypothesis is that A belongs not to all but to some B, 431 II, 11| it is not proved that A belongs not to all B, but that it 432 II, 11| not to all B, but that it belongs to no B. For if A belongs 433 II, 11| belongs to no B. For if A belongs to some B, and C to all 434 II, 11| impossible, it is false that A belongs to some B; consequently 435 II, 11| consequently it is true that A belongs to no B. But if this is 436 II, 11| original conclusion was that A belongs to some B, and does not 437 II, 11| in fact it is true: for A belongs to some B. Consequently 438 II, 11| must not suppose that A belongs to some B, but that it belongs 439 II, 11| belongs to some B, but that it belongs to all B. Similarly if we 440 II, 12| have been assumed that A belongs to all C. If then A belongs 441 II, 12| belongs to all C. If then A belongs not to all B, but to all 442 II, 12| suppose it to be clear that C belongs to all B): consequently 443 II, 12| It is true then that A belongs to all B. But if the contrary 444 II, 12| is not proved. For if A belongs to no B, and to all C, C 445 II, 12| that it is false that A belongs to no B. But though this 446 II, 12| follow that it is true that A belongs to all B.~When A belongs 447 II, 12| belongs to all B.~When A belongs to some B, suppose that 448 II, 12| to some B, suppose that A belongs to no B, and let A belong 449 II, 12| figure.~Again suppose that A belongs to some B, and let A belong 450 II, 13| belong to some B, but C belongs to all B: then A does not 451 II, 13| so that it is true that A belongs to all B. But if it is supposed 452 II, 13| if it is supposed that A belongs to no B, we shall have a 453 II, 13| before.~But to prove that A belongs to some B, this hypothesis 454 II, 13| hypothesis must be made. If A belongs to no B, and C to some B, 455 II, 13| false, it is true that A belongs to some B.~When A belongs 456 II, 13| belongs to some B.~When A belongs to no B, suppose A belongs 457 II, 13| belongs to no B, suppose A belongs to some B, and let it have 458 II, 13| have been assumed that C belongs to all B. Then it is necessary 459 II, 13| some C. But ex hypothesi it belongs to no C, so that it is false 460 II, 13| that it is false that A belongs to some B. But if it is 461 II, 13| if it is supposed that A belongs to all B, the problem is 462 II, 13| made if we are prove that A belongs not to all B. For if A belongs 463 II, 13| belongs not to all B. For if A belongs to all B and C to some B, 464 II, 13| and C to some B, then A belongs to some C. But this we assumed 465 II, 13| so, so it is false that A belongs to all B. But in that case 466 II, 13| that case it is true that A belongs not to all B. If however 467 II, 13| however it is assumed that A belongs to some B, we shall have 468 II, 14| hypothesis must have been that A belongs to some B, and the original 469 II, 14| original premisses that C belongs to all A and to no B. For 470 II, 14| the middle figure, if C belongs to all A and to no B. And 471 II, 14| from these premisses that A belongs to no B. Similarly if has 472 II, 14| the hypothesis is that A belongs to all B; and the original 473 II, 14| original premisses are that C belongs to all A but not to all 474 II, 14| it has been proved that A belongs to some B. The hypothesis 475 II, 14| hypothesis here is that is that A belongs to no B; and the original 476 II, 14| original premisses that B belongs to all C, and A either to 477 II, 14| the middle figure that A belongs to all B. Then the hypothesis 478 II, 14| hypothesis must have been that A belongs not to all B, and the original 479 II, 14| original premisses that A belongs to all C, and C to all B: 480 II, 14| is impossible. But if A belongs to all C, and C to all B, 481 II, 14| it has been proved that A belongs to some B: for the hypothesis 482 II, 14| then must have been that A belongs to no B, and the original 483 II, 14| original premisses that A belongs to all C, and C to some 484 II, 14| hypothesis must have been that A belongs to some B, and the original 485 II, 14| original premisses that A belongs to no C, and C to all B, 486 II, 14| The hypothesis is that A belongs to all B, the original premisses 487 II, 14| original premisses that A belongs to no C, and C belongs to 488 II, 14| A belongs to no C, and C belongs to some B: for thus we get 489 II, 14| the third figure that A belongs to all B. Then the hypothesis 490 II, 14| hypothesis must have been that A belongs not to all B, and the original 491 II, 14| original premisses that C belongs to all B, and A belongs 492 II, 14| belongs to all B, and A belongs to all C; for thus we shall 493 II, 14| then must have been that A belongs to no B, and the original 494 II, 14| original premisses that C belongs to some B, and A to all 495 II, 14| hypothesis must have been that A belongs to some B, and the original 496 II, 14| original premisses that C belongs to no A and to all B, and 497 II, 14| hypothesis will then be that A belongs to all B, the premisses 498 II, 14| B, the premisses that C belongs to no A and to some B: and 499 II, 15| and no science is good, A belongs to all B and to no C, so 500 II, 15| B and to no C, so that B belongs to no C: no science then