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| Alphabetical [« »] axiom 2 axioms 11 axioms-such 1 b 238 b-and 1 b-c 4 b-for 1 | Frequency [« »] 294 or 260 but 251 for 238 b 223 one 222 this 188 demonstration | Aristotle Posterior Analytics IntraText - Concordances b |
Book, Paragraph
1 I, 3 | by direct proof, if A is, B must be; if B is, C must 2 I, 3 | if A is, B must be; if B is, C must be; therefore 3 I, 3 | circular proof-if A is, B must be, and if B is, A 4 I, 3 | A is, B must be, and if B is, A must be, A may be 5 I, 3 | substituted for C above. Then "if B is, A must be"="if B is, 6 I, 3 | if B is, A must be"="if B is, C must be", which above 7 I, 3 | If, then, A is implied in B and C, and B and C are reciprocally 8 I, 3 | implied in B and C, and B and C are reciprocally implied 9 I, 4 | In another sense again (b) a thing consequentially 10 I, 6 | necessarily inheres in C, yet B, the middle term of the 11 I, 6 | necessarily predicated of B and B of C, then A is necessarily 12 I, 6 | necessarily predicated of B and B of C, then A is necessarily 13 I, 6 | of C but necessarily of B, and let B be a necessary 14 I, 6 | necessarily of B, and let B be a necessary predicate 15 I, 12| exist, which we may call B. I can now, since they reciprocate, 16 I, 12| reciprocate, infer A from B.~Reciprocation of premisses 17 I, 12| E.g. A is predicated of B, B of C, C of D, and so 18 I, 12| E.g. A is predicated of B, B of C, C of D, and so indefinitely. 19 I, 12| number taken indeterminately; B determinate odd number; 20 I, 13| twinkle: let C be the planets, B not twinkling, A proximity. 21 I, 13| twinkling, A proximity. Then B is predicable of C; for 22 I, 13| A is also predicable of B, since that which does not 23 I, 13| Thus: let C be the planets, B proximity, A not twinkling. 24 I, 13| proximity, A not twinkling. Then B is an attribute of C, and 25 I, 13| and A-not twinkling-of B. Consequently A is predicable 26 I, 13| spherical. (Let C be the moon, B spherical, and A waxing.) 27 I, 13| spherical, and A waxing.) Again (b), in cases where the cause 28 I, 13| Thus: let A be animal, B respiration, C wall. Then 29 I, 13| Then A is predicable of all B (for all that breathes is 30 I, 13| of no C; and consequently B is predicable of no C; that 31 I, 15| connected with a subject B, so its disconnexion may 32 I, 15| follows that if either A or B, or both A and B, have a 33 I, 15| either A or B, or both A and B, have a genus, their disconnexion 34 I, 15| proving A’s disconnexion from B thus:~all A is C,~no B is 35 I, 15| from B thus:~all A is C,~no B is C,~therefore no B is 36 I, 15| no B is C,~therefore no B is A.~ ~Or if it is B which 37 I, 15| no B is A.~ ~Or if it is B which has a genus D, we 38 I, 15| has a genus D, we have~all B is D,~no D is A,~therefore 39 I, 15| no D is A,~therefore no B is A, by syllogism;~ ~and 40 I, 15| be similar if both A and B have a genus. That the genus 41 I, 15| need not be the genus of B and vice versa, is shown 42 I, 15| will not be the genus of B; since, if it were, the 43 I, 15| mutually exclusive. So also if B has a genus, it will not 44 I, 15| other hand, neither A nor B has a genus and A does not 45 I, 15| and A does not inhere in B, this disconnexion must 46 I, 15| If it is in the first, B will have a genus-for the 47 I, 15| the second, either A or B indifferently, since syllogism 48 I, 16| atomically disconnected from all B: then the conclusion inferred 49 I, 16| middle term C, that all B is A, will be a case of 50 I, 16| a) both premisses, or (b) one premiss only, may be 51 I, 16| attribute of any C nor C of any B, whereas the contrary was 52 I, 16| well be so related to A and B that C is neither subordinate 53 I, 16| a universal attribute of B: for B, since A was said 54 I, 16| universal attribute of B: for B, since A was said to be 55 I, 16| primarily disconnected from B, cannot have a genus, and 56 I, 16| false.) On the other hand, (b) one of the premisses may 57 I, 16| only the major A-C since, B having no genus, the premiss 58 I, 16| atomically to both C and B; because when the same term 59 I, 16| connected with both C and B, if it be then assumed that 60 I, 16| assumed that no C is and all B is C, both premisses are 61 I, 16| cannot be an attribute of B; for if C-B were true, the 62 I, 16| if both C and A contain B as genera, one of them must 63 I, 16| wholly false; for if all B is A, no middle term can 64 I, 16| actually some A is C and some B is C, then if it is premised 65 I, 16| premised that all A is C and no B is C, both premisses are 66 I, 16| also be an attribute of all B, then if C is yet taken 67 I, 16| universally non-attributable to B, C-A will be true but C-B 68 I, 16| which is an attribute of no B will not be an attribute 69 I, 16| also be an attribute of all B, which is contrary to supposition; 70 I, 16| but an attribute of no B, then the premiss C-B is 71 I, 16| not be an attribute of any B either; and if it be yet 72 I, 16| a universal attribute of B, the premiss C-A is true 73 I, 16| which is an attribute of all B is an attribute of no A, 74 I, 16| it be an attribute of all B, it must be an attribute 75 I, 16| to be an attribute of all B but of no A, C-B will be 76 I, 17| let A be attributable to B through a middle term C: 77 I, 17| but also predicable of all B. Then the premiss D-B must 78 I, 17| middle. On the other hand, (b) if the conclusion is not 79 I, 17| but is predicable of no B, both premisses must be 80 I, 17| actually all D is A but no B is D; then if these premisses 81 I, 17| entirely false; since if B is subordinate to A, there 82 I, 17| attribute of both A and B, but is assumed to be an 83 I, 17| attribute of A only and not of B, C-A will be true, C-B false: 84 I, 17| assumed to be attributable to B but to no A, C-B will be 85 I, 17| is the same as before.~(b) The middle may be inappropriate. 86 I, 17| attribute of no D, whereas all B is D, e.g. no science is 87 I, 17| attribute of no D, and D of no B. It emerges, then, that 88 I, 19| showing that A inheres in B and B in C; the other is 89 I, 19| that A inheres in B and B in C; the other is negative 90 I, 19| that A inheres in C through B, and again that A inheres 91 I, 19| again that A inheres in B through some other middle 92 I, 19| term, and similarly that B inheres in C. If our reasoning 93 I, 19| middle term between A and B is credible though not real, 94 I, 19| subject of the attribute B—i.e. so that B-C is immediate; 95 I, 19| immediately to F, and F to B. The first question is, 96 I, 19| similarly related to G and G to B; then must this series also 97 I, 19| that A inheres in C and B is intermediate between 98 I, 19| between them, but between B and A there are other middles, 99 I, 19| A is attributable to no B, then either this predication 100 I, 19| intermediate term prior to B to which a is not attributable-G, 101 I, 20| intermediates-call them BB’B"...-are infinite, then clearly 102 I, 20| whichever terms of the series B...I take, the number of 103 I, 21| figure it is proved thus: no B is A, all C is B. In packing 104 I, 21| thus: no B is A, all C is B. In packing the interval 105 I, 21| denied of a term D prior to B, D will have to be predicable 106 I, 21| to be predicable of all B, and if the major is denied 107 I, 21| the syllogism is, all A is B, no C is B,..no C is A. 108 I, 21| is, all A is B, no C is B,..no C is A. If proof of 109 I, 21| will be as follows: all B is D, no C is D..., since 110 I, 21| since it is required that B should be a subject of which 111 I, 21| shows it as follows: all B is A, some B is not C. Therefore 112 I, 21| follows: all B is A, some B is not C. Therefore some 113 I, 21| take as premisses, all E is B, some E is not C, and this 114 I, 22| 3) If A is a quality of B, B cannot be a quality of 115 I, 22| If A is a quality of B, B cannot be a quality of A-a 116 I, 22| quality. Therefore A and B cannot be predicated reciprocally 117 I, 22| predicated of one another, i.e. B would become the genus or 118 I, 22| there must be an attribute (B) primarily predicable of 119 I, 22| which it was predicated (B), and of which no term prior 120 I, 22| truths are demonstrable, and (b) an infinite regress is 121 I, 22| since if either (a) or (b) were not a fact, it would 122 I, 23| were it so, if we take B as the common middle in 123 I, 23| inheres in C and D, clearly B would inhere in C and D 124 I, 23| clear that when A inheres in B, this can be demonstrated 125 I, 23| if A does not inhere in B, this can be demonstrated 126 I, 23| term or a term prior to B in which A does not inhere: 127 I, 23| predicate-suppose it C-of the subject B, and then suppose A similarly 128 I, 23| that A does not inhere in B the premisses required are, 129 I, 23| premisses required are, all B is C, no C is A. Then if 130 I, 24| D, and the middles were B and C, B being the higher 131 I, 24| the middles were B and C, B being the higher term would 132 I, 25| proving it through the middles B, C and D, the other through 133 I, 25| proof. Thus, suppose no B is A, and all C is B. Then 134 I, 25| no B is A, and all C is B. Then if both the premisses 135 I, 25| interpose D between A and B, and E between B and C. 136 I, 25| between A and B, and E between B and C. Then clearly E is 137 I, 25| affirmatively related to B and C, while D is affirmatively 138 I, 25| affirmatively related to B but negatively to A; for 139 I, 25| negatively to A; for all B is D, but there must be 140 I, 26| Let us suppose that no B is A, and that all C is 141 I, 26| is A, and that all C is B: the conclusion necessarily 142 I, 26| that does not inhere in B, we have to assume that 143 I, 26| inhere, and further that B inheres in C, with the resulting 144 I, 26| that A cannot inhere in B. Thus if the inherence of 145 I, 26| Thus if the inherence of B in C is not questioned, 146 I, 26| questioned, A’s inherence in B is impossible.~The order 147 I, 26| known, the one denying A of B or the one denying A of 148 I, 26| proposition denying A of B is, in the order of being, 149 I, 26| is the conclusion, "no B is A" one of its premisses. 150 I, 29| alteration of a property, B feeling pleasure, and G 151 I, 29| falsehood predicate D of B and A of D, for he who is 152 I, 29| without falsehood, and G of B; for to feel pleasure is 153 I, 32| truly predicable of C, but B, the middle, is false, both 154 I, 34| bright side turned sunward", B "lighted from the sun", 155 I, 34| the sun", C the moon. Then B, "lighted from the sun" 156 I, 34| light", is predicable of B. So A is predicable of C 157 I, 34| predicable of C through B.~ ~ 158 II, 4 | term; on the other hand (b) its definable nature is 159 II, 4 | obviously A is "peculiar" to B and B to C-in fact all three 160 II, 4 | A is "peculiar" to B and B to C-in fact all three terms 161 II, 4 | inheres in the essence of all B and B is predicated universally 162 II, 4 | the essence of all B and B is predicated universally 163 II, 4 | being of the essence of B, but B is not of the essence 164 II, 4 | of the essence of B, but B is not of the essence of 165 II, 4 | essence, and consequently B also will be predicated 166 II, 4 | must be predicated of all B. But this premiss will be 167 II, 4 | what it has to prove, since B too is the essential nature 168 II, 4 | as a mere consequent of B and B of C, A will not on 169 II, 4 | mere consequent of B and B of C, A will not on that 170 II, 4 | if A is predicated of all B inasmuch as B is identical 171 II, 4 | predicated of all B inasmuch as B is identical with a species 172 II, 4 | so take them, in assuming B one will have assumed, before 173 II, 8 | be eclipse, C the moon, B the earth’s acting as a 174 II, 8 | is to ask whether or not B has occurred. But that is 175 II, 8 | be the moon, A eclipse, B the fact that the moon fails 176 II, 8 | between us and her. Then if B, failure to produce shadows 177 II, 8 | eclipse, is attributable to B, it is clear that the moon 178 II, 8 | inquiring what is the nature of B: is it the earth’s acting 179 II, 8 | rotation or her extinction? But B is the definition of the 180 II, 8 | Let C be cloud, A thunder, B the quenching of fire. Then 181 II, 8 | quenching of fire. Then B is attributable to C, cloud, 182 II, 8 | noise, is attributable to B; and B is assuredly the 183 II, 8 | is attributable to B; and B is assuredly the definition 184 II, 8 | further mediating cause of B, it will be one of the remaining 185 II, 10| of essential nature, or (b) a syllogism of essential 186 II, 11| Thus, let A be right angle, B the half of two right angles, 187 II, 11| angle in a semicircle. Then B is the cause in virtue of 188 II, 11| angle in a semicircle, since B=A and the other, viz. C,= 189 II, 11| A and the other, viz. C,=B, for C is half of two right 190 II, 11| it is the assumption of B, the half of two right angles, 191 II, 11| a right angle. Moreover, B is identical with (b) the 192 II, 11| Moreover, B is identical with (b) the defining form of A, 193 II, 11| originated the war. Let A be war, B unprovoked raiding, C the 194 II, 11| raiding, C the Athenians. Then B, unprovoked raiding, is 195 II, 11| Athenians, and A is true of B, since men make war on the 196 II, 11| waged upon them, is true of B, the initial aggressors, 197 II, 11| initial aggressors, and B is true of C, the Athenians, 198 II, 11| be walking after supper, B the non-regurgitation of 199 II, 11| healthy; since it seems that B, the non-regurgitation of 200 II, 11| health, is attributable to B. What, then, is the cause 201 II, 11| cause, inheres in C? It is B, the non-regurgitation of 202 II, 11| non-regurgitation of food; but B is a kind of definition 203 II, 11| explained by it. Why is B the cause of A’s belonging 204 II, 11| be in a condition such as B is to be in health. The 205 II, 12| be water, A solidified, B the middle, which is the 206 II, 12| total failure of heat. Then B is attributed to C, and 207 II, 12| and A, solidification, to B: ice when B is occurring, 208 II, 12| solidification, to B: ice when B is occurring, has formed 209 II, 12| occurring, has formed when B has occurred, and will form 210 II, 12| occurred, and will form when B shall occur.~This sort of 211 II, 12| occurred, therefore an event B has occurred subsequently 212 II, 12| therefore it is true to say that B, the subsequent event, occurred; 213 II, 12| predicated universally of B and B of C, A too must be 214 II, 12| predicated universally of B and B of C, A too must be predicated 215 II, 12| consequently the middle term B must also be a general rule. 216 II, 13| exhaustively into A and B, and that the subject accepts 217 II, 14| properties. Let A be animal, B the properties of every 218 II, 14| virtue of what character B inheres in D-namely A-and 219 II, 16| be deciduous character, B the possession of broad 220 II, 16| vine. Now if A inheres in B (for every broad-leaved 221 II, 16| plant is deciduous), and B in C (every vine possessing 222 II, 16| deciduous), and the middle term B is the cause. But we can 223 II, 16| its primary subject, let B be a primary subject in 224 II, 16| and E primary subjects of B and C respectively. A will 225 II, 16| then inhere in D and E, and B will be the cause of A’s 226 II, 17| A be an attribute of all B, and B of every species 227 II, 17| attribute of all B, and B of every species of D, but 228 II, 17| but so that both A and B are wider than their respective 229 II, 17| respective subjects. Then B will be a universal attribute 230 II, 17| taken separately.~Thus, B is the cause of A’s inherence 231 II, 17| be of wider extent than B; otherwise why should B 232 II, 17| B; otherwise why should B be the cause of A’s inherence 233 II, 17| more than A the cause of B’s inherence in D? Now if 234 II, 17| common cause other than B: otherwise how shall we 235 II, 18| formally: C is the cause of B’s inherence in D; hence 236 II, 18| cause of A’s inherence in D, B of A’s inherence in C, while 237 II, 18| cause of A’s inherence in B is B itself.~ 238 II, 18| of A’s inherence in B is B itself.~