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| Alphabetical [« »] avoid 1 awake 5 away 2 b 1000 b-so 1 ba 3 bad 4 | Frequency [« »] 1256 and 1148 that 1074 of 1000 b 963 it 869 if 854 not | Aristotle Prior Analytics IntraText - Concordances b |
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1 I, 2 | negative with the terms A and B. If no B is A, neither can 2 I, 2 | the terms A and B. If no B is A, neither can any A 3 I, 2 | A, neither can any A be B. For if some A (say C) were 4 I, 2 | For if some A (say C) were B, it would not be true that 5 I, 2 | would not be true that no B is A; for C is a B. But 6 I, 2 | that no B is A; for C is a B. But if every B is A then 7 I, 2 | for C is a B. But if every B is A then some A is B. For 8 I, 2 | every B is A then some A is B. For if no A were B, then 9 I, 2 | A is B. For if no A were B, then no B could be A. But 10 I, 2 | if no A were B, then no B could be A. But we assumed 11 I, 2 | But we assumed that every B is A. Similarly too, if 12 I, 2 | particular. For if some B is A, then some of the As 13 I, 2 | then some of the As must be B. For if none were, then 14 I, 2 | For if none were, then no B would be A. But if some 15 I, 2 | would be A. But if some B is not A, there is no necessity 16 I, 2 | of the As should not be B; e.g. let B stand for animal 17 I, 2 | should not be B; e.g. let B stand for animal and A for 18 I, 3 | it is necessary that no B is A, it is necessary also 19 I, 3 | necessary also that no A is B. For if it is possible that 20 I, 3 | possible that some A is B, it would be possible also 21 I, 3 | possible also that some B is A. If all or some B is 22 I, 3 | some B is A. If all or some B is A of necessity, it is 23 I, 3 | necessary also that some A is B: for if there were no necessity, 24 I, 3 | possible that all or some B is A, it will be possible 25 I, 3 | possible that some A is B. For if that were not possible, 26 I, 3 | were not possible, then no B could possibly be A. This 27 I, 3 | possible, either because B necessarily is A, or because 28 I, 3 | necessarily is A, or because B is not necessarily A, admits 29 I, 3 | that it is possible that no B is A or some B is not A 30 I, 3 | possible that no B is A or some B is not A is affirmative 31 I, 4 | If A is predicated of all B, and B of all C, A must 32 I, 4 | predicated of all B, and B of all C, A must be predicated 33 I, 4 | if A is predicated of no B, and B of all C, it is necessary 34 I, 4 | predicated of no B, and B of all C, it is necessary 35 I, 4 | under the middle. Let all B be A and some C be B. Then 36 I, 4 | all B be A and some C be B. Then if "predicated of 37 I, 4 | that some C is A. And if no B is A but some C is B, it 38 I, 4 | no B is A but some C is B, it is necessary that some 39 I, 4 | particular: e.g. if some B is or is not A, and all 40 I, 4 | or is not A, and all C is B. As an example of a positive 41 I, 4 | ignorance. Again if no C is B, but some B is or is not 42 I, 4 | Again if no C is B, but some B is or is not A or not every 43 I, 4 | or is not A or not every B is A, there cannot be a 44 I, 4 | particular: e.g. if all B is A and some C is not B, 45 I, 4 | B is A and some C is not B, or if not all C is B. For 46 I, 4 | not B, or if not all C is B. For the major term may 47 I, 4 | syllogism. Again let no B be A, but let some C not 48 I, 4 | A, but let some C not be B. Take the terms inanimate, 49 I, 4 | indefinite to say some C is not B, and it is true that some 50 I, 4 | true that some C is not B, whether no C is B, or not 51 I, 4 | is not B, whether no C is B, or not all C is B, and 52 I, 4 | C is B, or not all C is B, and since if terms are 53 I, 4 | assumed such that no C is B, no syllogism follows (this 54 I, 7 | A belongs to all or some B, and B belongs to no C: 55 I, 7 | belongs to all or some B, and B belongs to no C: for if 56 I, 7 | the last figure, if A and B belong to all C, it follows 57 I, 7 | follows that A belongs to some B: for if A belonged to no 58 I, 7 | for if A belonged to no B, and B belongs to all C, 59 I, 7 | A belonged to no B, and B belongs to all C, A would 60 I, 7 | e.g. if A belongs to all B, and B to some C, it follows 61 I, 7 | A belongs to all B, and B to some C, it follows that 62 I, 7 | no C, and belongs to all B, then B will belong to no 63 I, 7 | and belongs to all B, then B will belong to no C: this 64 I, 7 | For if A belongs to no B, and B belongs to some C, 65 I, 7 | if A belongs to no B, and B belongs to some C, A will 66 I, 7 | all C, and belongs to no B, then B will belong to no 67 I, 7 | and belongs to no B, then B will belong to no C: and 68 I, 9 | belonging or not belonging to B, but B is taken as simply 69 I, 9 | not belonging to B, but B is taken as simply belonging 70 I, 9 | does not belong, to every B, and since C is one of the 71 I, 9 | belongs necessarily to some B. But this is false; for 72 I, 9 | But this is false; for B may be such that it is possible 73 I, 9 | e.g. if A were movement, B animal, C man: man is an 74 I, 9 | and let A belong to all B necessarily, but let B simply 75 I, 9 | all B necessarily, but let B simply belong to some C: 76 I, 9 | necessarily: for C falls under B, and A was assumed to belong 77 I, 9 | belong necessarily to all B. Similarly also if the syllogism 78 I, 10| let A be possible of no B, and simply belong to C. 79 I, 10| statement is convertible, B is possible of no A. But 80 I, 10| belongs to all C; consequently B is possible of no C. For 81 I, 10| A: but A belongs to all B, consequently C is possible 82 I, 10| figure. Neither then is B possible of C: for conversion 83 I, 10| necessary. Let A belong to all B necessarily, but to no C 84 I, 10| belong to some A. For if B necessarily belongs to no 85 I, 10| necessarily belong to no B. But B at any rate must 86 I, 10| necessarily belong to no B. But B at any rate must belong 87 I, 10| necessarily belongs to all B. Consequently it is necessary 88 I, 10| example let A be animal, B man, C white, and let the 89 I, 10| let it be possible for no B that A should belong to 90 I, 10| be possible for no A that B should belong to it: but 91 I, 10| to some C; consequently B necessarily does not belong 92 I, 10| necessarily belongs to all B, but does not belong to 93 I, 10| some C, it is clear that B will not belong to some 94 I, 11| affirmative, and let A and B belong to all C, and let 95 I, 11| be necessary. Since then B belongs to all C, C also 96 I, 11| also will belong to some B, because the universal is 97 I, 11| C, and C belongs to some B, it is necessary that A 98 I, 11| A should belong to some B also. For B is under C. 99 I, 11| belong to some B also. For B is under C. The first figure 100 I, 11| some A: consequently if B belongs necessarily to all 101 I, 11| is convertible with some B, but A necessarily belongs 102 I, 11| necessarily not belong to some B either: for B is under C. 103 I, 11| belong to some B either: for B is under C. But if the affirmative 104 I, 11| also will belong to some B necessarily: consequently 105 I, 11| be "good", let that which B signifies be "animal", let 106 I, 11| then it is necessary that B should belong to all C, 107 I, 11| C, it is necessary that B should belong to some A. 108 I, 11| belong to some A. But if B must belong to some A, then 109 I, 11| then A must belong to some B: for conversion is possible. 110 I, 11| necessary and universal: for B falls under C. But if the 111 I, 11| terms. Let A be waking, B biped, and C animal. It 112 I, 11| animal. It is necessary that B should belong to some C, 113 I, 11| that A should belong to B is not necessary. For there 114 I, 11| should belong to any C, but B belongs to some C, it is 115 I, 11| should not belong to some B. But whenever the affirmative 116 I, 13| possible for A to belong to all B" into "it is possible for 117 I, 13| possible for A to belong to no B" or "not to all B", and " 118 I, 13| to no B" or "not to all B", and "it is possible for 119 I, 13| for A to belong to some B" into "it is possible for 120 I, 13| A not to belong to some B". And similarly the other 121 I, 13| that A should belong to B, it is possible also that 122 I, 13| it should not belong to B: and if it is possible that 123 I, 13| possible of the subject of B" means that it is possible 124 I, 13| either of that of which B is stated or of that of 125 I, 13| stated or of that of which B may possibly be stated. 126 I, 13| possible of the subject of B, or all B admits of A. It 127 I, 13| the subject of B, or all B admits of A. It is clear 128 I, 13| may possibly belong to all B" might be used in two senses. 129 I, 13| syllogism which arises if B is possible of the subject 130 I, 13| possible of the subject of B. For thus both premisses 131 I, 13| possible of that of which B is true, one premiss is 132 I, 14| may possibly belong to all B, and B to all C, there will 133 I, 14| possibly belong to all B, and B to all C, there will be 134 I, 14| possible for A to belong no B, and for B to belong to 135 I, 14| to belong no B, and for B to belong to all C, then 136 I, 14| belong to that of which B may be true means (as we 137 I, 14| possibly fall under the term B is left out of account. 138 I, 14| whenever A may belong to all B, and B may belong to no 139 I, 14| may belong to all B, and B may belong to no C, then 140 I, 14| since it is possible that B should belong to no C, it 141 I, 14| stated above. Consequently if B is possible for all C, and 142 I, 14| and A is possible for all B, the same syllogism again 143 I, 14| belong to none of the Bs, and B to none of the Cs. No syllogism 144 I, 14| if A is possible for all B, and B for some C, then 145 I, 14| possible for all B, and B for some C, then A is possible 146 I, 14| Again if A may belong to no B, and B may belong to some 147 I, 14| may belong to no B, and B may belong to some of the 148 I, 14| e.g. A is possible for all B, B may possibly not belong 149 I, 14| A is possible for all B, B may possibly not belong 150 I, 14| and it is laid down that B possibly may belong to some 151 I, 14| possible. For nothing prevents B from reaching beyond A, 152 I, 14| Let C be that by which B extends beyond A. To C it 153 I, 14| convertible and it is possible for B to belong to more things 154 I, 15| Let A be possible for all B, and let B belong to all 155 I, 15| possible for all B, and let B belong to all C. Since C 156 I, 15| all C. Since C falls under B, and A is possible for all 157 I, 15| and A is possible for all B, clearly it is possible 158 I, 15| First we must state that if B’s being follows necessarily 159 I, 15| necessarily from A’s being, B’s possibility will follow 160 I, 15| that A is possible, and B is impossible. If then that 161 I, 15| same time A is possible and B impossible, it would be 162 I, 15| for A to happen without B, and if to happen, then 163 I, 15| understand the statement that B’s being depends on A’s being, 164 I, 15| some single thing A is, B will be: for nothing follows 165 I, 15| A, and the conclusion by B, it would not only result 166 I, 15| result that if A is necessary B is necessary, but also that 167 I, 15| also that if A is possible, B is possible.~Since this 168 I, 15| but not impossible, and if B is the consequence of A, 169 I, 15| is the consequence of A, B also will be false but not 170 I, 15| has been proved that if B’s being is the consequence 171 I, 15| consequence of A’s being, then B’s possibility will follow 172 I, 15| possible), consequently B will be possible: for if 173 I, 15| points, let A belong to all B, and B be possible for all 174 I, 15| let A belong to all B, and B be possible for all C: it 175 I, 15| possible, but assume that B belongs to all C: this is 176 I, 15| is not possible for C but B belongs to all C, then A 177 I, 15| is not possible for all B: for a syllogism is formed 178 I, 15| possible attribute for all B. It is necessary then that 179 I, 15| impossibility, by assuming that B belongs to C. For if B belongs 180 I, 15| that B belongs to C. For if B belongs to all C, and A 181 I, 15| and A is possible for all B, then A would be possible 182 I, 15| assume that A belongs to no B, but B possibly belongs 183 I, 15| that A belongs to no B, but B possibly belongs to all 184 I, 15| cannot belong, and that B belongs to C, as above. 185 I, 15| then that A belongs to some B: for we have a syllogism 186 I, 15| possibility. Let A be "raven", B "intelligent", and C "man". 187 I, 15| man". A then belongs to no B: for no intelligent thing 188 I, 15| intelligent thing is a raven. But B is possible for all C: for 189 I, 15| necessary. Let A be "moving", B "science", C "man". A then 190 I, 15| A then will belong to no B; but B is possible for all 191 I, 15| will belong to no B; but B is possible for all C. And 192 I, 15| before. Let A belong to all B, and let B possibly belong 193 I, 15| belong to all B, and let B possibly belong to no C. 194 I, 15| converted and it is assumed that B is possible for all C, a 195 I, 15| that A does not belong to B, and the minor premiss indicates 196 I, 15| minor premiss indicates that B may possibly belong to no 197 I, 15| Suppose that A belongs to no B, and B may possibly belong 198 I, 15| that A belongs to no B, and B may possibly belong to no 199 I, 15| nothing necessary. But if B is assumed to be possible 200 I, 15| But if it be assumed that B does not belong to any C, 201 I, 15| e.g. if A belongs to all B or to no B, and B may possibly 202 I, 15| belongs to all B or to no B, and B may possibly not 203 I, 15| to all B or to no B, and B may possibly not belong 204 I, 16| necessarily belongs to all B, and let B be possible for 205 I, 16| belongs to all B, and let B be possible for all C. We 206 I, 16| let A be possible for all B, and let B necessarily belong 207 I, 16| possible for all B, and let B necessarily belong to all 208 I, 16| not be possible for any B, but let B be possible for 209 I, 16| possible for any B, but let B be possible for all C. It 210 I, 16| is not possible for any B. Since then the negative 211 I, 16| proposition is convertible, B is not possible for any 212 I, 16| to some C. Consequently B will not be possible for 213 I, 16| originally laid down that B is possible for all C. And 214 I, 16| possibly not belong to any B, and let B necessarily belong 215 I, 16| belong to any B, and let B necessarily belong to all 216 I, 16| possibly does not belong to any B, no impossible relation 217 I, 16| impossible relation between B and C follows from these 218 I, 16| that A should belong to any B, but B may belong to some 219 I, 16| should belong to any B, but B may belong to some of the 220 I, 16| but cannot belong to any B, neither can B belong to 221 I, 16| belong to any B, neither can B belong to any A. So if A 222 I, 16| C, to none of the Cs can B belong. But it was laid 223 I, 16| But it was laid down that B may belong to some C. But 224 I, 17| e.g. if A may belong to no B, it does not follow that 225 I, 17| it does not follow that B may belong to no A. For 226 I, 17| to follow and assume that B may belong to no A. Since 227 I, 17| contradictories, and since B may belong to no A, it is 228 I, 17| to no A, it is clear that B may belong to all A. But 229 I, 17| incompatible, "A may belong to no B", "B necessarily does not 230 I, 17| A may belong to no B", "B necessarily does not belong 231 I, 17| since it is false that B may belong to no A, it is 232 I, 17| this is so, it is true that B necessarily belongs to some 233 I, 17| that some A is necessarily B, if it is not possible that 234 I, 17| possible that no A should be B. For the latter expression 235 I, 17| if A some is necessarily B, another if some A is necessarily 236 I, 17| some A is necessarily not B. For it is not true to say 237 I, 17| necessarily belongs to some B" and "A necessarily does 238 I, 17| does not belong to some B" are opposed to the proposition " 239 I, 17| proposition "A belongs to all B". Similarly also they are 240 I, 17| proposition "A may belong to no B". It is clear then that 241 I, 17| necessarily belongs to some B, but that A necessarily 242 I, 17| does not belong to some B. But if this is assumed, 243 I, 17| that A may belong to no B and to all C. By means of 244 I, 17| for if it is assumed that B can belong to all C, no 245 I, 17| necessary. Let A be white, B man, C horse. It is possible 246 I, 17| But it is not possible for B to belong nor not to belong 247 I, 18| Suppose A belongs to no B, but can belong to all C. 248 I, 18| proposition is converted, B will belong to no A. But 249 I, 18| of the first figure that B may belong to no C. Similarly 250 I, 18| is formed to prove that B may belong to no C, as before: 251 I, 19| necessarily belongs to no B, but may belong to all C. 252 I, 19| negative premiss is converted B will belong to no A: but 253 I, 19| by the first figure that B may belong to no C. But 254 I, 19| same time it is clear that B will not belong to any C. 255 I, 19| if A cannot belong to any B, and B belongs to some of 256 I, 19| cannot belong to any B, and B belongs to some of the Cs, 257 I, 19| that A may belong to no B, but necessarily belongs 258 I, 19| sometimes turns out that B necessarily does not belong 259 I, 19| belong to C. Let A be white, B man, C swan. White then 260 I, 19| terms are so arranged, that B should belong to C: for 261 I, 19| prevents C falling under B, A being possible for all 262 I, 19| A being possible for all B, and necessarily belonging 263 I, 19| if C stands for "awake", B for "animal", A for "motion". 264 I, 19| necessarily does not belong to B, and possibly may not belong 265 I, 19| premisses are converted B belongs to no A, and A may 266 I, 19| there are cases in which B necessarily will not belong 267 I, 19| suppose that A is white, B swan, C man. Nor can the 268 I, 19| have shown a case in which B necessarily does not belong 269 I, 20| suppose that both A and B may possibly belong to every 270 I, 20| convertible into a particular, and B may possibly belong to every 271 I, 20| possibly belong to some B. So, if A is possible for 272 I, 20| possibly belong to no C, but B may possibly belong to all 273 I, 20| possibly not belong to some B: for we shall have the first 274 I, 20| as before. For if A and B may possibly not belong 275 I, 20| possibly belong to all C, and B to some C. We shall have 276 I, 20| belong sometimes to all B and sometimes to no B. To 277 I, 20| all B and sometimes to no B. To illustrate the affirmative 278 I, 21| A belongs to all C, and B may possibly belong to all 279 I, 21| impossibile. Suppose that B belongs to all C, and A 280 I, 21| possibly not belong to some B. For if A necessarily belongs 281 I, 21| necessarily belongs to all B, and B (as has been assumed) 282 I, 21| necessarily belongs to all B, and B (as has been assumed) belongs 283 I, 22| necessarily belongs to all C, and B may possibly belong to all 284 I, 22| and C may belong to some B, it follows that A may ( 285 I, 22| not does) belong to some B: for so it resulted in the 286 I, 22| possibly belong to no C, but B necessarily belongs to all 287 I, 22| possibly not belong to some B but also that it does not 288 I, 22| does not belong to some B. For suppose that A necessarily 289 I, 22| does not belong to C, but B may belong to all C. If 290 I, 22| does not belong to some B. But when the minor premiss 291 I, 22| necessarily belongs to all B, and sometimes cannot possibly 292 I, 22| cannot possibly belong to any B. To illustrate the former 293 I, 23| prove syllogistically A of B, either as an attribute 294 I, 23| A should be asserted of B, the proposition originally 295 I, 23| will not be in relation to B through the premisses taken. 296 I, 23| however being made with B, will a syllogism be possible 297 I, 23| concerning A in its relation to B. For in general we stated 298 I, 23| premiss in reference to B, if we neither affirm nor 299 I, 23| a premiss relating A to B, if we take nothing common, 300 I, 23| predicating A of C, and C of B, or C of both, or both of 301 I, 23| establish the relation to B; for the figure will be 302 I, 24| Suppose the lines A and B have been drawn to the centre. 303 I, 25| through the propositions A and B, and through the propositions 304 I, 25| through the propositions A and B, or A and C, or B and C. 305 I, 25| A and B, or A and C, or B and C. For nothing prevents 306 I, 25| of the propositions A and B is obtained by syllogistic 307 I, 25| means of D and E, and again B by means of F and G. Or 308 I, 25| conclusions are many, e.g. A and B and C. But if this can be 309 I, 25| established by means of A and B. Suppose that the proposition 310 I, 25| inferred from the premisses A, B, C, and D. It is necessary 311 I, 25| stands in this relation to B. Some conclusion then follows 312 I, 25| syllogism will have A and B for its sole premisses. 313 I, 25| of the propositions A and B, or something other than 314 I, 25| it is (i) E, or (ii) A or B, either (i) the syllogisms 315 I, 25| is other than E or A or B, the syllogisms will be 316 I, 25| from the propositions A and B there follows not E but 317 I, 25| from C and D either A or B follows or something else, 318 I, 25| the other in relation to B. Similarly with any further 319 I, 28| consequents of A are designated by B, the antecedents of A by 320 I, 28| belongs to all E. Again, if B and H are identical, A will 321 I, 28| belong to none of the Es: for B will belong to all A, but 322 I, 28| belong to some of the Es. If B is identical with G, there 323 I, 28| will belong to all A since B belongs to A and E to B ( 324 I, 28| B belongs to A and E to B (for B was found to be identical 325 I, 28| belongs to A and E to B (for B was found to be identical 326 I, 28| consequents are identical, e.g. B and F, we have the middle 327 I, 28| aforesaid moods, e.g. if B and F are contraries or 328 I, 28| the aforesaid mood. For B will belong to all A and 329 I, 28| and to no E. Consequently B must be identical with one 330 I, 28| one of the Hs. Again, if B and G cannot belong to the 331 I, 28| have the middle figure: for B will belong to all A and 332 I, 28| and to no G. Consequently B must be identical with some 333 I, 28| the Hs. For the fact that B and G cannot belong to the 334 I, 28| no way from the fact that B is identical with some of 335 I, 28| syllogism results; but if B and F are contraries B must 336 I, 28| if B and F are contraries B must be identical with one 337 I, 29| belong to some E: then since B belongs to all A and A to 338 I, 29| and A to some of the Es, B will belong to some of the 339 I, 29| turns out that otherwise B belongs to some of the Es 340 I, 29| impossible-if now it is assumed that B belongs to no E and to all 341 I, 31| signified by A, mortal by B, and immortal by C, and 342 I, 31| whatever is A is all either B or C. Again, always dividing, 343 I, 31| is that every D is either B or C, consequently man must 344 I, 31| taking A as mortal animal, B as footed, C as footless, 345 I, 31| that A inheres either in B or in C (for every mortal 346 I, 31| incommensurate or commensurate", B for "length", C for "diagonal". 347 I, 33| E.g. if A is stated of B, and B of C: it would seem 348 I, 33| if A is stated of B, and B of C: it would seem that 349 I, 33| the term "being eternal", B "Aristomenes as an object 350 I, 33| true then that A belongs to B. For Aristomenes as an object 351 I, 33| thought is eternal. But B also belongs to C: for Aristomenes 352 I, 33| C stand for "Miccalus", B for "musical Miccalus", 353 I, 33| It is true to predicate B of C: for Miccalus is musical 354 I, 33| Also A can be predicated of B: for musical Miccalus might 355 I, 34| suppose A to be health, B disease, C man. It is true 356 I, 34| that A cannot belong to any B (for health belongs to no 357 I, 34| disease) and again that B belongs to every C (for 358 I, 35| stand for two right angles, B for triangle, C for isosceles 359 I, 35| belongs to C because of B: but A belongs to B without 360 I, 35| because of B: but A belongs to B without the mediation of 361 I, 36| being a single science", and B for things which are contrary 362 I, 36| another. Then A belongs to B, not in the sense that contraries 363 I, 38| knowledge that it is good", B for good, C for justice. 364 I, 38| is true to predicate A of B. For of the good there is 365 I, 38| it is true to predicate B of C. For justice is identical 366 I, 38| it is good" were added to B, the conclusion will not 367 I, 38| follow: for A will be true of B, but B will not be true 368 I, 38| A will be true of B, but B will not be true of C. For 369 I, 38| knowledge that it is something", B stand for "something", and 370 I, 38| is true to predicate A of B: for ex hypothesi there 371 I, 38| something, that it is something. B too is true of C: for that 372 I, 38| for knowledge that it is, B for being, C for good. Clearly 373 I, 41| to all of that to which B belongs, and that A belongs 374 I, 41| of that to all of which B belongs: for nothing prevents 375 I, 41| belongs: for nothing prevents B from belonging to C, though 376 I, 41| though not to all C: e.g. let B stand for beautiful, and 377 I, 41| white. If then A belongs to B, but not to everything of 378 I, 41| not to everything of which B is predicated, then whether 379 I, 41| predicated, then whether B belongs to all C or merely 380 I, 41| belongs to everything of which B is truly stated, it will 381 I, 41| of that of all of which B is said. If however A is 382 I, 41| of that of all of which B may be said, nothing prevents 383 I, 41| be said, nothing prevents B belonging to C, and yet 384 I, 41| is said of all of which B is said" means this, "A 385 I, 41| all the things of which B is said". And if B is said 386 I, 41| which B is said". And if B is said of all of a third 387 I, 41| term, so also is A: but if B is not said of all of the 388 I, 45| sequel. If A belongs to no B, and B to all C, then A 389 I, 45| If A belongs to no B, and B to all C, then A belongs 390 I, 45| have the middle figure. For B belongs to no A, and to 391 I, 45| e.g. if A belongs to no B, and B to some C. Convert 392 I, 45| if A belongs to no B, and B to some C. Convert the negative 393 I, 45| syllogisms. Let A belong to no B and to all C. Convert the 394 I, 45| have the first figure. For B will belong to no A and 395 I, 45| affirmative statement concerns B, and the negative C, C must 396 I, 45| belongs to no A, and A to all B: therefore C belongs to 397 I, 45| therefore C belongs to no B. B then belongs to no C: 398 I, 45| therefore C belongs to no B. B then belongs to no C: for 399 I, 45| e.g. if A belongs to no B and to some C: convert the 400 I, 45| have the first figure. For B will belong to no A and 401 I, 45| e.g. if A belongs to all B, but not to all C: for the 402 I, 45| third. Let A belong to all B and B to some C. Since the 403 I, 45| Let A belong to all B and B to some C. Since the particular 404 I, 45| convertible, C will belong to some B: but A belonged to all B: 405 I, 45| B: but A belonged to all B: so that the third figure 406 I, 45| therefore A will belong to no B, and to some C.~Of the syllogisms 407 I, 45| can be resolved. Let A and B be affirmed of all C: then 408 I, 45| partially with either A or B: C then belongs to some 409 I, 45| C then belongs to some B. Consequently we shall get 410 I, 45| If A belongs to all C and B to some C, the argument 411 I, 45| argument is the same: for B is convertible in reference 412 I, 45| in reference to C. But if B belongs to all C and A to 413 I, 45| the first term must be B: for B belongs to all C, 414 I, 45| first term must be B: for B belongs to all C, and C 415 I, 45| and C to some A, therefore B belongs to some A. But since 416 I, 45| convertible, A will belong to some B. If the syllogism is negative, 417 I, 45| them in a similar way. Let B belong to all C, and A to 418 I, 45| then C will belong to some B, and A to no C; and so C 419 I, 45| will be possible, e.g. if B belongs to all C, and A 420 I, 45| For if A belongs to no B and to some C, both B and 421 I, 45| no B and to some C, both B and C alike are convertible 422 I, 45| in relation to A, so that B belongs to no A and C to 423 I, 45| But when A belongs to all B, and not to some C, resolution 424 I, 45| if A belongs to no C, and B to some or all C. For C 425 I, 45| belong to no A and to some B. But if the negative statement 426 I, 46| stand for "to be good", B for "not to be good", let 427 I, 46| not-good" and be placed under B, and let D stand for not 428 I, 46| under A. Then either A or B will belong to everything, 429 I, 46| belong to the same thing. And B must belong to everything 430 I, 46| does not always belong to B: for what is not a log at 431 I, 46| the same thing, and that B and D may possibly belong 432 I, 46| Let A stand for "equal", B for "not equal", C for " 433 I, 46| In general whenever A and B are such that they cannot 434 I, 46| reversed, then D must follow B and the relation cannot 435 I, 46| belong to the same thing, but B and C cannot. First it is 436 I, 46| consideration that D follows B. For since either C or D 437 I, 46| belong to that to which B belongs, because it carries 438 I, 46| along with it and A and B cannot belong to the same 439 I, 46| clear that D must follow B. Again since C does not 440 I, 46| belong to the same thing. But B and C cannot belong to the 441 I, 46| results. It is clear then that B does not reciprocate with 442 I, 46| may reason that "if A and B cannot belong at the same 443 I, 46| follows: it will result that B belongs necessarily to everything 444 I, 46| for the negation of A and B, and again that H stands 445 I, 46| Again since either F or B belongs to everything, and 446 I, 46| and since H follows F, B must follow D: for we know 447 I, 46| this. If then A follows C, B must follow D". But this 448 I, 46| everything, or that F or B should belong to everything: 449 II, 1 | proved to to all or to some B, then B must belong to some 450 II, 1 | to all or to some B, then B must belong to some A: and 451 II, 1 | been proved to belong to no B, then B belongs to no A. 452 II, 1 | to belong to no B, then B belongs to no A. This is 453 II, 1 | does not belong to some B, it is not necessary that 454 II, 1 | it is not necessary that B should not belong to some 455 II, 1 | whatever is subordinate to B or C must accept the predicate 456 II, 1 | for if D is included in B as in a whole, and B is 457 II, 1 | in B as in a whole, and B is included in A, then D 458 II, 1 | e.g. if A belongs to no B and to all C; we conclude 459 II, 1 | all C; we conclude that B belongs to no C. If then 460 II, 1 | subordinate to C, clearly B does not belong to it. But 461 II, 1 | not belong to it. But that B does not belong to what 462 II, 1 | of the syllogism. And yet B does not belong to E, if 463 II, 1 | through the syllogism that B belongs to no C, it has 464 II, 1 | assumed without proof that B does not belong to A, consequently 465 II, 1 | through the syllogism that B does not belong to E.~But 466 II, 1 | e.g. if A belongs to all B and B to some C. Nothing 467 II, 1 | if A belongs to all B and B to some C. Nothing can be 468 II, 1 | which is subordinate to B, but not through the preceding 469 II, 2 | If it is necessary that B should be when A is, it 470 II, 2 | that A should not be when B is not. If then A is true, 471 II, 2 | not. If then A is true, B must be true: otherwise 472 II, 2 | belongs to all that to which B belongs, and that B belongs 473 II, 2 | which B belongs, and that B belongs to all that to which 474 II, 2 | none of the Bs, neither let B belong to C. This is possible, 475 II, 2 | is taken to belong to all B and B to all C, A will belong 476 II, 2 | taken to belong to all B and B to all C, A will belong 477 II, 2 | possible that neither A nor B should belong to any C, 478 II, 2 | although A belongs to all B, e.g. if the same terms 479 II, 2 | none. Let A belong to no B, and B to all C. If then 480 II, 2 | Let A belong to no B, and B to all C. If then the premiss 481 II, 2 | viz. that A belongs to all B, it is impossible that the 482 II, 2 | belonged to nothing to which B belonged, and B belonged 483 II, 2 | to which B belonged, and B belonged to all C. Similarly 484 II, 2 | conclusion if A belongs to all B, and B to all C, but while 485 II, 2 | A belongs to all B, and B to all C, but while the 486 II, 2 | belongs to nothing to which B belongs: here the conclusion 487 II, 2 | belongs to everything to which B belongs, and B to all C. 488 II, 2 | to which B belongs, and B to all C. It is clear then 489 II, 2 | belongs to all C and to some B, and if B belongs to all 490 II, 2 | C and to some B, and if B belongs to all C, e.g. animal 491 II, 2 | premisses that A belongs to all B, and B to all C, A will 492 II, 2 | A belongs to all B, and B to all C, A will belong 493 II, 2 | A should belong to some B and to no C, and that B 494 II, 2 | B and to no C, and that B should belong to all C, 495 II, 2 | assume that A belongs to no B, and B to all C, then will 496 II, 2 | that A belongs to no B, and B to all C, then will belong 497 II, 2 | prevents A belonging to all B and to all C, though B belongs 498 II, 2 | all B and to all C, though B belongs to no C, e.g. these 499 II, 2 | assumed that A belongs to all B and B to all C, the conclusion 500 II, 2 | that A belongs to all B and B to all C, the conclusion