Book, Paragraph

 1      I,  10|          the geometer’s hypotheses false, as some have held, urging
 2      I,  12|         shown by the diagram to be false.~If a proof has an inductive
 3      I,  12|      possibility is overlooked. If false premisses could never give
 4      I,  16|           one premiss only, may be false. (a) If neither A is an
 5      I,  16|             both premisses will be false. (C may quite well be so
 6      I,  16| Consequently both premisses may be false.) On the other hand, (b)
 7      I,  16|         premiss C-B will always be false, while A-C may be true.
 8      I,  16|            when both premisses are false; e.g. supposing A atomically
 9      I,  16|           is C, both premisses are false.~(d) It is also possible
10      I,  16|          also possible when one is false. This may be either premiss
11      I,  16|       attribute of all things, C-B false because C, which never has
12      I,  16|            C-B may be true and A-C false; e.g. if both C and A contain
13      I,  16|         form No C is A, it will be false. This makes it clear that
14      I,  16|       either or both premisses are false, the conclusion will equally
15      I,  16|         conclusion will equally be false.~In the second figure the
16      I,  16|    premisses cannot both be wholly false; for if all B is A, no middle
17      I,  16|          this way, they are wholly false, their contraries conversely
18      I,  16|          premisses being partially false; e.g. if actually some A
19      I,  16|           is C, both premisses are false, yet partially, not wholly,
20      I,  16|         yet partially, not wholly, false. The same is true if the
21      I,  16|          one premiss may be wholly false, and it may be either of
22      I,  16|           C-A will be true but C-B false. Again, actually that which
23      I,  16|           is true but the major is false. The case is similar if
24      I,  16|          true but the minor wholly false. Again, in fact it is false
25      I,  16|        false. Again, in fact it is false to assume that that which
26      I,  16|           C-B will be true but C-A false.~It is thus clear that in
27      I,  16|            when both premisses are false but also when only one is
28      I,  16|          but also when only one is false.~
29      I,  17|              a) (i) as long as the false conclusion is inferred through
30      I,  17|          not both premisses can be false. By "appropriate middle"
31      I,  17|      changed. But the major A-C is false, for it is by a change in
32      I,  17|            always true, A-D always false. Such error is practically
33      I,  17|             both premisses must be false, because if there is to
34      I,  17|         and so posited both become false: e.g. suppose that actually
35      I,  17|          the new premisses will be false. When, however, (ii) the
36      I,  17|          not subordinate to D, D-B false because if it had been true,
37      I,  17|             but it is ex hypothesi false.~When the erroneous inference
38      I,  17|       premisses cannot be entirely false; since if B is subordinate
39      I,  17|           premiss, however, may be false, and it may be either of
40      I,  17|           B, C-A will be true, C-B false: or again if C be assumed
41      I,  17|           A, C-B will be true, C-A false.~We have stated when and
42      I,  17|           both premisses cannot be false since, as we said before,
43      I,  17|            changed, will always be false. This is equally true if (
44      I,  17|          A-D will be true, but D-B false; since A may quite well
45      I,  17|           affirmed, will always be false, while D-B may be either
46      I,  17|          D-B may be either true or false; for A may very well be
47      I,  17|           but either singly may be false.~Thus we have made it clear
48      I,  24|       demonstration, and creates a false opinion, it will follow
49      I,  32|       syllogisms are true and some false: for though a true inference
50      I,  32|         inference is possible from false premisses, yet this occurs
51      I,  32|           C, but B, the middle, is false, both A-B and B-C being
52      I,  32|             both A-B and B-C being false; nevertheless, if middles
53      I,  32|            premisses, they will be false because every conclusion
54      I,  32|           which is a falsehood has false premisses, while true conclusions
55      I,  32|           have true premisses, and false and true differ in kind.
56      I,  33|          that which may be true or false, and can be otherwise: opinion
57      I,  33|          as the object of true and false opinion is in a sense identical.
58      I,  33|        some maintain that true and false opinion can have the same
59      I,  33|       sense the object of true and false opinion can be the same,
60     II,  12|           latter statement will be false. And the same argument applies
61     II,  12|           it the inference will be false. We have also to inquire