Book, Paragraph

  1      I, 1 |            demonstrative, if it is true and obtained through the
  2      I, 2 |            were B, it would not be true that no B is A; for C is
  3      I, 4 |         some C is not B, and it is true that some C is not B, whether
  4      I, 5 |         statement. For since it is true that M does not belong to
  5      I, 9 |            syllogisms. The same is true of negative syllogisms.
  6      I, 10|         belong to some A, if it is true (as was assumed) that A
  7      I, 13|     possible of that of which B is true, one premiss is a simple
  8      I, 14|          to that of which B may be true means (as we saw) that none
  9      I, 15|    possible for all C (and this is true) and if the premiss AB remains
 10      I, 17|           be white), but it is not true to say that it is possible
 11      I, 17|          may belong to no A, it is true that it cannot belong to
 12      I, 17|           But if this is so, it is true that B necessarily belongs
 13      I, 17|   necessarily not B. For it is not true to say that that which necessarily
 14      I, 17|           any A, just as it is not true to say that what necessarily
 15      I, 23|         hypothesis. But if this is true, every demonstration and
 16      I, 30| demonstrations. For if none of the true attributes of things had
 17      I, 31|           belonging to it. Now the true conclusion is that every
 18      I, 32|             For everything that is true must in every respect agree
 19      I, 33|             C "Aristomenes". It is true then that A belongs to B.
 20      I, 33|        perishing to-morrow". It is true to predicate B of C: for
 21      I, 33|          the former; for it is not true universally that musical
 22      I, 34|            B disease, C man. It is true to say that A cannot belong
 23      I, 34|            disease". For it is not true to say that being healthy
 24      I, 36|       thing "is" may be said to be true. Take for example the statement
 25      I, 36|            in the sense that it is true to say of the contraries
 26      I, 37|           to that" and "this holds true of that" must be understood
 27      I, 38|         good, C for justice. It is true to predicate A of B. For
 28      I, 38|        that it is good. Also it is true to predicate B of C. For
 29      I, 38|          not follow: for A will be true of B, but B will not be
 30      I, 38|            of B, but B will not be true of C. For to predicate of
 31      I, 38|            stand for "good". It is true to predicate A of B: for
 32      I, 38|          it is something. B too is true of C: for that which C represents
 33      I, 38|       something. Consequently A is true of C: there will then be
 34      I, 41|          to something white, it is true to say that beauty belongs
 35      I, 46|            C belongs. For if it is true to say "it is a not-white",
 36      I, 46|          it is a not-white", it is true also to say "it is not white":
 37      I, 46|          that which is white it is true to say that it is not not-white.
 38      I, 46|            not-white. But A is not true of all D. For of that which
 39      I, 46|         not a log at all it is not true to say A, viz. that it is
 40      I, 46|       white log. Consequently D is true, but A is not true, i.e.
 41      I, 46|            D is true, but A is not true, i.e. that it is a white
 42      I, 46|        others, the negation may be true in a similar way, viz. that
 43      I, 46|           be white, and that it is true to call it not-white; for
 44      I, 46|            we may prove that it is true to call it white or not-white
 45      I, 46|          For the expression "it is true" stands on a similar footing
 46      I, 46|         For the negation of "it is true to call it white" is not "
 47      I, 46|            it white" is not "it is true to call it not-white" but "
 48      I, 46|          not-white" but "it is not true to call it white". If then
 49      I, 46|        white". If then it is to be true to say that whatever is
 50     II, 2 |   premisses of the syllogism to be true, or to be false, or to be
 51     II, 2 |            false, or to be the one true, the other false. The conclusion
 52     II, 2 |           The conclusion is either true or false necessarily. From
 53     II, 2 |            false necessarily. From true premisses it is not possible
 54     II, 2 |            false conclusion, but a true conclusion may be drawn
 55     II, 2 |        drawn from false premisses, true however only in respect
 56     II, 2 |            a false conclusion from true premisses, is made clear
 57     II, 2 |        when B is not. If then A is true, B must be true: otherwise
 58     II, 2 |          then A is true, B must be true: otherwise it will turn
 59     II, 2 |           premisses. If then it is true that A belongs to all that
 60     II, 2 |            a false conclusion from true premisses.~But from what
 61     II, 2 |           But from what is false a true conclusion may be drawn,
 62     II, 2 |            false the conclusion is true: for every man is an animal.
 63     II, 2 |       false the conclusion will be true. (2) A similar proof may
 64     II, 2 |         the conclusion will not be true, but if the premiss BC is
 65     II, 2 |      premiss BC is wholly false, a true conclusion will be possible.
 66     II, 2 |         premiss BC which I take is true, and the premiss AB is wholly
 67     II, 2 |           the conclusion should be true: for A belonged to none
 68     II, 2 |        Similarly there cannot be a true conclusion if A belongs
 69     II, 2 |            to all C, but while the true premiss BC is assumed, the
 70     II, 2 |           and the other premiss is true, the conclusion cannot be
 71     II, 2 |           the conclusion cannot be true.~(4) But if the premiss
 72     II, 2 |     premiss is not wholly false, a true conclusion is possible.
 73     II, 2 |        which is assumed, is wholly true, and the premiss BC is wholly
 74     II, 2 |      premiss BC is wholly false, a true syllogism will be possible:
 75     II, 2 |             the conclusion will be true, although the premiss BC
 76     II, 2 |             the conclusion will be true.~(6) And if the premiss
 77     II, 2 |           so the conclusion may be true. For nothing prevents A
 78     II, 2 |           and this ex hypothesi is true. Similarly if the premiss
 79     II, 2 |           and this ex hypothesi is true.~In particular syllogisms
 80     II, 2 |        wholly false, and the other true, that the conclusion should
 81     II, 2 |           the conclusion should be true; also when the first premiss
 82     II, 2 |       false in part, and the other true; and when the first is true,
 83     II, 2 |        true; and when the first is true, and the particular is false;
 84     II, 2 |       wholly false, the premiss BC true, and the conclusion true.
 85     II, 2 |           true, and the conclusion true. Similarly if the premiss
 86     II, 2 |             the conclusion will be true although the premiss AB
 87     II, 2 |        part, the conclusion may be true. For nothing prevents A
 88     II, 2 |             the premiss BC will be true, and the conclusion true.
 89     II, 2 |           true, and the conclusion true. Similarly if the premiss
 90     II, 2 |         Again if the premiss AB is true, and the premiss BC is false,
 91     II, 2 |       false, the conclusion may be true. For nothing prevents A
 92     II, 2 |             the conclusion will be true, although the statement
 93     II, 2 |           C, which ex hypothesi is true. And the premiss AB is true,
 94     II, 2 |        true. And the premiss AB is true, the premiss BC false.~(
 95     II, 2 |         too, the conclusion may be true. For nothing prevents A
 96     II, 2 |             the conclusion will be true. Similarly if the premiss
 97     II, 2 |        false the conclusion may be true. For it is possible that
 98     II, 2 |             the conclusion will be true, though both premisses are
 99     II, 2 |             The conclusion then is true, but the premisses arc false.~
100     II, 3 |            in every way to reach a true conclusion through false
101     II, 3 |       partially false; when one is true, the other wholly false (
102     II, 3 |   partially false; if one is quite true, the other partially false;
103     II, 3 |         false, the other partially true. For (1) if A belongs to
104     II, 3 |            false they will yield a true conclusion. Similarly if
105     II, 3 |            false, the other wholly true: for nothing prevents A
106     II, 3 |            false, the other wholly true, and the conclusion will
107     II, 3 |         and the conclusion will be true whichever term the negative
108     II, 3 |            false, the other wholly true. For it is possible that
109     II, 3 |       false, the premiss AC wholly true, and the conclusion true.
110     II, 3 |           true, and the conclusion true. Similarly if the negative
111     II, 3 |         false, the negative wholly true, a true conclusion is possible.
112     II, 3 |            negative wholly true, a true conclusion is possible.
113     II, 3 |           the premiss AC is wholly true, and the conclusion is true.~(
114     II, 3 |        true, and the conclusion is true.~(4) And if both the premisses
115     II, 3 |       false, the conclusion may be true. For it is possible that
116     II, 3 |       false, but the conclusion is true. Similarly, if the negative
117     II, 3 |          the particular premiss is true, and the conclusion is true.
118     II, 3 |        true, and the conclusion is true. Similarly if the premiss
119     II, 3 |           false, the premiss AC is true, and the conclusion is true.
120     II, 3 |        true, and the conclusion is true. Also a true conclusion
121     II, 3 |         conclusion is true. Also a true conclusion is possible when
122     II, 3 |           the universal premiss is true, and the particular is false.
123     II, 3 |             the conclusion will be true, and the universal premiss
124     II, 3 |          and the universal premiss true, but the particular false.
125     II, 3 |           the universal premiss is true, the particular false, and
126     II, 3 |          false, and the conclusion true.~(6) It is clear too that
127     II, 3 |         are false they may yield a true conclusion, since it is
128     II, 3 |       false, but the conclusion is true. Similarly if the universal
129     II, 3 |        false but the conclusion is true.~
130     II, 4 |             4~In the last figure a true conclusion may come through
131     II, 4 |         when one premiss is wholly true, the other false, when one
132     II, 4 |            false, the other wholly true, and vice versa, and in
133     II, 4 |          false, but the conclusion true. Similarly if one premiss
134     II, 4 |           B: and the conclusion is true, though the premisses are
135     II, 4 |       false, the conclusion may be true. For nothing prevents both
136     II, 4 |       false, but the conclusion is true. Similarly if the premiss
137     II, 4 |       false, but the conclusion is true.~(3) Similarly if one of
138     II, 4 |            false, the other wholly true. For it is possible that
139     II, 4 |          premiss BC will be wholly true, the premiss AC wholly false,
140     II, 4 |          false, and the conclusion true. Similarly if the statement
141     II, 4 |            false, the statement AC true, the conclusion may be true.
142     II, 4 |        true, the conclusion may be true. The same terms will serve
143     II, 4 | affirmative, the conclusion may be true. For nothing prevents B
144     II, 4 |           the premiss BC is wholly true, the premiss AC is wholly
145     II, 4 |       false, and the conclusion is true. Similarly if the premiss
146     II, 4 |     premiss AC which is assumed is true: the proof can be made through
147     II, 4 |           if one premiss is wholly true, the other partly false,
148     II, 4 |       false, the conclusion may be true. For it is possible that
149     II, 4 |           the premiss BC is wholly true, the premiss AC partly false,
150     II, 4 |       partly false, the conclusion true. Similarly if of the premisses
151     II, 4 |            premisses assumed AC is true and BC partly false, a true
152     II, 4 |        true and BC partly false, a true conclusion is possible:
153     II, 4 |         Also the conclusion may be true if one premiss is negative,
154     II, 4 |           the other premiss wholly true, and the conclusion is true.
155     II, 4 |        true, and the conclusion is true. Again since it has been
156     II, 4 |           the premiss AC is wholly true, and the premiss BC partly
157     II, 4 |           the conclusion should be true. For if it is assumed that
158     II, 4 |           the premiss AC is wholly true, and the premiss BC is partly
159     II, 4 |       particular syllogisms that a true conclusion may come through
160     II, 4 |         but when the conclusion is true, it is not necessary that
161     II, 4 |            the premisses should be true, either one or all, yet
162     II, 4 |           part of the syllogism is true, that the conclusion may
163     II, 4 |    conclusion may none the less be true; but it is not necessitated.
164     II, 11|     because it is clear that it is true. The terms are alike in
165     II, 11|           which was admitted to be true), it follows that C belongs
166     II, 11|          its contradictory then is true. Similarly in the other
167     II, 11|     affirmative is not necessarily true if the universal negative
168     II, 11|          impossible (for let it be true and clear that A belongs
169     II, 11|          false: in that case it is true that A belongs to no B.
170     II, 11|         some B; consequently it is true that A belongs to no B.
171     II, 11|            a false conclusion from true premisses: but in fact it
172     II, 11|       premisses: but in fact it is true: for A belongs to some B.
173     II, 11|            the affirmation must be true. Again if it is not admitted
174     II, 11|            that the affirmation is true, the claim that the negation
175     II, 11|         claim that the negation is true will be generally accepted.
176     II, 11|    universal affirmative should be true, nor is it generally accepted
177     II, 11|          one is false the other is true.~
178     II, 12|         hypothesis is false. It is true then that A belongs to all
179     II, 12|         does not follow that it is true that A belongs to all B.~
180     II, 12|          impossible: so that it is true that A does not belong to
181     II, 13|           to some B; so that it is true that A belongs to all B.
182     II, 13|          then this is false, it is true that A belongs to some B.~
183     II, 13|             But in that case it is true that A belongs not to all
184     II, 14|      suppose beforehand that it is true or not: in the other it
185     II, 14|          beforehand that it is not true. It makes no difference
186     II, 15|           it is possible to draw a true conclusion, as has been
187     II, 19|            is to be inferred to be true of F, B, C, D, and E being
188     II, 21|       other and think the opposite true. Suppose that A belongs
189     II, 21|        just as we saw that if B is true of all of which C is true,
190     II, 21|          true of all of which C is true, and A is true of all of
191     II, 21|          which C is true, and A is true of all of which B is true,
192     II, 21|          true of all of which B is true, A is true of C, similarly
193     II, 21|           of which B is true, A is true of C, similarly with the
194     II, 22|             And indeed the same is true of the other desires and
195     II, 26|            third figure: for it is true of C (the knowable and the
196     II, 27|         men, C for Pittacus. It is true then to affirm both A and
197     II, 27|            is irrefutable if it is true (for it is universal), that
198     II, 27|          even if the conclusion is true, since the syllogism is
199     II, 27|        generally accepted and most true.~It is possible to infer