Book, Paragraph

  1      I, 7 |           on the assumption of the false statement the syllogism
  2      I, 9 | necessarily to some B. But this is false; for B may be such that
  3      I, 15|            it is evident that if a false and not impossible assumption
  4      I, 15|            assumption will also be false and not impossible: e.g.
  5      I, 15|           impossible: e.g. if A is false, but not impossible, and
  6      I, 15|   consequence of A, B also will be false but not impossible. For
  7      I, 15|          belongs to all C: this is false but not impossible. If then
  8      I, 15|          the assumption we made is false and not impossible, the
  9      I, 15|           C; for if at is supposed false, the consequence is an impossible
 10      I, 17|       belong to all A. But this is false: for if all this can be
 11      I, 17|   following argument: "since it is false that B may belong to no
 12      I, 17|            some D, he would make a false assumption: for it does
 13      I, 17|            can belong to all C, no false consequence results: for
 14      I, 23|            syllogistically what is false, and prove the original
 15      I, 29|         syllogism establishing the false conclusion may relate, so
 16      I, 33|           universally. But this is false, that every Aristomenes
 17      I, 33|             But to state A of C is false at any rate. This argument
 18      I, 38|           good that it is good" is false and not intelligible. Similarly
 19      I, 46|            or all are not-white is false. Similarly also "every animal
 20      I, 46|            is white" (for both are false): the proper negation is "
 21      I, 46|            D belongs": but this is false. "Assume that F stands for
 22      I, 46|        must follow D". But this is false: for as we proved the sequence
 23     II, 2 |     syllogism to be true, or to be false, or to be the one true,
 24     II, 2 |            the one true, the other false. The conclusion is either
 25     II, 2 |       conclusion is either true or false necessarily. From true premisses
 26     II, 2 |          is not possible to draw a false conclusion, but a true conclusion
 27     II, 2 |       conclusion may be drawn from false premisses, true however
 28     II, 2 |         cannot be established from false premisses: why this is so
 29     II, 2 |          is not possible to draw a false conclusion from true premisses,
 30     II, 2 |        belongs, and this cannot be false: for then the same thing
 31     II, 2 |            not possible to prove a false conclusion from true premisses.~
 32     II, 2 |        premisses.~But from what is false a true conclusion may be
 33     II, 2 |     whether both the premisses are false or only one, provided that
 34     II, 2 |           if it is taken as wholly false: but if the premiss is not
 35     II, 2 |     premiss is not taken as wholly false, it does not matter which
 36     II, 2 |         matter which of the two is false. (1) Let A belong to the
 37     II, 2 |      though both the premisses are false the conclusion is true:
 38     II, 2 |      though both the premisses are false the conclusion will be true. (
 39     II, 2 |          each premiss is partially false.~(3) But if one only of
 40     II, 2 |           only of the premisses is false, when the first premiss
 41     II, 2 |            first premiss is wholly false, e.g. AB, the conclusion
 42     II, 2 |           the premiss BC is wholly false, a true conclusion will
 43     II, 2 |        possible. I mean by "wholly false" the contrary of the truth,
 44     II, 2 |           the premiss AB is wholly false, viz. that A belongs to
 45     II, 2 |          BC is assumed, the wholly false premiss AB is also assumed,
 46     II, 2 |        here the conclusion must be false. For A will belong to all
 47     II, 2 |            first premiss is wholly false, whether affirmative or
 48     II, 2 |          the premiss is not wholly false, a true conclusion is possible.
 49     II, 2 |           the premiss BC is wholly false, a true syllogism will be
 50     II, 2 |           the premiss BC is wholly false. Similarly if the premiss
 51     II, 2 |           premiss BC is not wholly false but in part only, even so
 52     II, 2 |            first premiss is wholly false, and the other true, that
 53     II, 2 |          when the first premiss is false in part, and the other true;
 54     II, 2 |        true, and the particular is false; and when both are false. (
 55     II, 2 |           false; and when both are false. (7) For nothing prevents
 56     II, 2 |           the premiss BC is wholly false, the premiss BC true, and
 57     II, 2 |           the premiss AB is wholly false. (If the premiss AB is false
 58     II, 2 |       false. (If the premiss AB is false in part, the conclusion
 59     II, 2 |       premiss AB will be partially false, the premiss BC will be
 60     II, 2 |        true, and the premiss BC is false, the conclusion may be true.
 61     II, 2 |       although the statement BC is false. Similarly if the premiss
 62     II, 2 |            is true, the premiss BC false.~(10) Also if the premiss
 63     II, 2 |            premiss AB is partially false, and the premiss BC is false
 64     II, 2 |       false, and the premiss BC is false too, the conclusion may
 65     II, 2 |          though both premisses are false the conclusion may be true.
 66     II, 2 |          though both premisses are false. Similarly also if the premiss
 67     II, 2 |        true, but the premisses arc false.~
 68     II, 3 |            true conclusion through false premisses, whether the syllogisms
 69     II, 3 |          both premisses are wholly false; when each is partially
 70     II, 3 |             when each is partially false; when one is true, the other
 71     II, 3 |          is true, the other wholly false (it does not matter which
 72     II, 3 |            of the two premisses is false); if both premisses are
 73     II, 3 |            premisses are partially false; if one is quite true, the
 74     II, 3 |          true, the other partially false; if one is wholly false,
 75     II, 3 |            false; if one is wholly false, the other partially true.
 76     II, 3 |           the premisses are wholly false they will yield a true conclusion.
 77     II, 3 |           if one premiss is wholly false, the other wholly true:
 78     II, 3 |         one premiss will be wholly false, the other wholly true,
 79     II, 3 |           one premiss is partially false, the other wholly true.
 80     II, 3 |            premiss AB is partially false, the premiss AC wholly true,
 81     II, 3 |   affirmative premiss is partially false, the negative wholly true,
 82     II, 3 |            premiss AB is partially false, the premiss AC is wholly
 83     II, 3 |            premisses are partially false, the conclusion may be true.
 84     II, 3 |            premisses are partially false, but the conclusion is true.
 85     II, 3 |        universal premiss is wholly false, the particular premiss
 86     II, 3 |       which is universal is wholly false, the premiss AC is true,
 87     II, 3 |        true, and the particular is false. For nothing prevents A
 88     II, 3 |           true, but the particular false. Similarly if the premiss
 89     II, 3 |            is true, the particular false, and the conclusion true.~(
 90     II, 3 |          though both premisses are false they may yield a true conclusion,
 91     II, 3 |             the premisses are both false, but the conclusion is true.
 92     II, 3 |          some C, the premisses are false but the conclusion is true.~
 93     II, 4 |           may come through what is false, alike when both premisses
 94     II, 4 |          both premisses are wholly false, when each is partly false,
 95     II, 4 |         false, when each is partly false, when one premiss is wholly
 96     II, 4 |          is wholly true, the other false, when one premiss is partly
 97     II, 4 |         when one premiss is partly false, the other wholly true,
 98     II, 4 |           premisses will be wholly false, but the conclusion true.
 99     II, 4 |           though the premisses are false.~(2) Also if each premiss
100     II, 4 |          if each premiss is partly false, the conclusion may be true.
101     II, 4 |            premisses are partially false, but the conclusion is true.
102     II, 4 |          both premisses are partly false, but the conclusion is true.~(
103     II, 4 |        premisses assumed is wholly false, the other wholly true.
104     II, 4 |        true, the premiss AC wholly false, and the conclusion true.
105     II, 4 |   Similarly if the statement BC is false, the statement AC true,
106     II, 4 |           the premiss AC is wholly false, and the conclusion is true.
107     II, 4 |      wholly true, the other partly false, the conclusion may be true.
108     II, 4 |        true, the premiss AC partly false, the conclusion true. Similarly
109     II, 4 |           AC is true and BC partly false, a true conclusion is possible:
110     II, 4 |         negative premiss is partly false, the other premiss wholly
111     II, 4 |          and the premiss BC partly false, it is possible that the
112     II, 4 |           the premiss BC is partly false.~(5) It is clear also in
113     II, 4 |           may come through what is false, in every possible way.
114     II, 4 |          that if the conclusion is false, the premisses of the argument
115     II, 4 |            of the argument must be false, either all or some of them;
116     II, 11|    consequently the supposition is false: its contradictory then
117     II, 11|            syllogistically what is false, but not the problem proposed.
118     II, 11|          this be impossible: it is false then A belongs to no B.
119     II, 11|          the universal negative is false. But if the premiss CA is
120     II, 11|            consequently if this is false, it is necessary that A
121     II, 11|            that the supposition is false: in that case it is true
122     II, 11|          impossible, so that it is false that A belongs to all B.
123     II, 11|      impossible, the hypothesis is false. Similarly if the other
124     II, 11|          this is impossible, it is false that A belongs to some B;
125     II, 11|            the hypothesis would be false, since it is impossible
126     II, 11|            is impossible to draw a false conclusion from true premisses:
127     II, 11|          the universal negative is false, the universal affirmative
128     II, 11|        accepted that if the one is false the other is true.~
129     II, 12|     consequently the hypothesis is false. It is true then that A
130     II, 12|          impossible; so that it is false that A belongs to no B.
131     II, 12|           no B. But though this is false, it does not follow that
132     II, 12|     consequently the hypothesis is false: A then will belong to no
133     II, 13|          this is impossible, it is false that A does not belong to
134     II, 13|          to all C. If then this is false, it is true that A belongs
135     II, 13|     belongs to no C, so that it is false that A belongs to some B.
136     II, 13|     assumed not to be so, so it is false that A belongs to all B.
137     II, 14|           statement admitted to be false; whereas ostensive proof
138     II, 15|          It is clear too that from false premisses it is possible
139     II, 17|           reason why the result is false", which we frequently make
140     II, 17|      proposition he will not say, "False cause", but urge that something
141     II, 17|            but urge that something false has been assumed in the
142     II, 17|         For we use the expression "false cause", when the syllogism
143     II, 17|          then that the expression "false cause" can only be used
144     II, 17|           to a conclusion which is false is when a syllogism drawn
145     II, 17|            impossibile: for Zeno’s false theorem has no connexion
146     II, 17|           C to D, and it should be false that B belongs to D: for
147     II, 17|       belongs to C and C to D, the false conclusion would not depend
148     II, 17|          to A and F to E, it being false that F belongs to A. In
149     II, 17|            should belong to D, the false conclusion will no longer
150     II, 17|            the original terms, the false conclusion does not result
151     II, 17|  understand the statement that the false conclusion results independently
152     II, 17|       perhaps absurd that the same false result should follow from
153     II, 18|                               18~A false argument depends on the
154     II, 18|      argument depends on the first false statement in it. Every syllogism
155     II, 18|        more premisses. If then the false conclusion is drawn from
156     II, 18|            or both of them must be false: for (as we proved) a false
157     II, 18|        false: for (as we proved) a false syllogism cannot be drawn
158     II, 18|        higher propositions must be false, and on this the argument
159     II, 21|             But presumably that is false, that any one could suppose
160     II, 26|          are contraries, and it is false that they are the subjects