Book, Paragraph

 1      I, 4 |       other way, a syllogism is impossible. I call that term the major
 2      I, 9 |       such a conclusion nothing impossible results, just as it does
 3      I, 13|     assumed, results in nothing impossible. We say indeed ambiguously
 4      I, 13|     possible to belong", "it is impossible to belong", and "it is necessary
 5      I, 13| possible to belong", "it is not impossible to belong", and "it is not
 6      I, 14|        possibility. But this is impossible. For it has been proved
 7      I, 15|         A is possible, and B is impossible. If then that which is possible,
 8      I, 15|    happen, and if that which is impossible, when it is impossible,
 9      I, 15|       is impossible, when it is impossible, could not happen, and if
10      I, 15|        time A is possible and B impossible, it would be possible for
11      I, 15|        is. But we must take the impossible and the possible not only
12      I, 15|         that if a false and not impossible assumption is made, the
13      I, 15|      will also be false and not impossible: e.g. if A is false, but
14      I, 15|     e.g. if A is false, but not impossible, and if B is the consequence
15      I, 15|      also will be false but not impossible. For since it has been proved
16      I, 15|        possible: for if it were impossible, the same thing would at
17      I, 15|       same time be possible and impossible.~Since we have defined these
18      I, 15|        C: this is false but not impossible. If then A is not possible
19      I, 15|        we made is false and not impossible, the conclusion is impossible.
20      I, 15|   impossible, the conclusion is impossible. It is possible also in
21      I, 15|       third figure: but this is impossible. Thus it will be possible
22      I, 15|    false, the consequence is an impossible one. This syllogism then
23      I, 16|         not belong to any B, no impossible relation between B and C
24      I, 17|     some of the Bs. But this is impossible." The argument cannot be
25      I, 23|         this to that. But it is impossible to take a premiss in reference
26      I, 23|   hypothetically when something impossible results from the assumption
27      I, 23|          viz. proving something impossible by means of an hypothesis
28      I, 27|        statement is useless and impossible, e.g. that every man is
29      I, 29|        Syllogisms which lead to impossible conclusions are similar
30      I, 34|        such a conclusion is not impossible: for it is possible that
31      I, 41|    sense, not as though it were impossible to demonstrate without these
32      I, 44|        the reduction to what is impossible can be analysed since it
33      I, 45|         by reduction to what is impossible.~It is clear from what we
34      I, 46|        is not white": for it is impossible that a thing should simultaneously
35      I, 46|     follows C; and so something impossible results. It is clear then
36     II, 2 |      the same time. But this is impossible. Let it not, because A is
37     II, 2 |         belongs to all B, it is impossible that the conclusion should
38     II, 4 |     former should be. But it is impossible that the same thing should
39     II, 4 |         for example, that it is impossible that B should necessarily
40     II, 4 |   itself is great. (But this is impossible.) For if B is not great,
41     II, 5 |     demonstrated. Clearly it is impossible to demonstrate the universal
42     II, 7 |     concerns the other extreme, impossible. Let A belong to all C and
43     II, 11|          but a reduction to the impossible takes place not because
44     II, 11|       not to all B. But this is impossible: consequently the supposition
45     II, 11|    belongs to no D. Let this be impossible: it is false then A belongs
46     II, 11|       not to all C. But this is impossible (for let it be true and
47     II, 11|         some B. But let this be impossible, so that the supposition
48     II, 11|         have a syllogism and an impossible conclusion, but the problem
49     II, 11|    belong to all B. But this is impossible, so that it is false that
50     II, 11|       and a conclusion which is impossible, but the hypothesis is not
51     II, 11|       all B; so that if this is impossible, the hypothesis is false.
52     II, 11|         some B. If then this is impossible, it is false that A belongs
53     II, 11|   belong to some B. Further the impossible does not result from the
54     II, 11|     would be false, since it is impossible to draw a false conclusion
55     II, 12|    belong to all B. But this is impossible (for suppose it to be clear
56     II, 12| syllogism and a result which is impossible: but the problem in hand
57     II, 12|         belong to no B. This is impossible; so that it is false that
58     II, 12|        Consequently, if this is impossible, A must belong to some B.
59     II, 12|     belong to no B. But this is impossible: so that it is true that
60     II, 13|         some C. If then this is impossible, it is false that A does
61     II, 13|       and a conclusion which is impossible: but the problem in hand
62     II, 14|      syllogism was made and the impossible conclusion reached. But
63     II, 14|        way we shall get what is impossible. But if A and B belong to
64     II, 14|       thus we shall get what is impossible. But if A belongs to all
65     II, 14|       thus we shall get what is impossible. And the original premisses
66     II, 15|        to part. Otherwise it is impossible: for the premisses cannot
67     II, 16|      assuming facts which it is impossible to demonstrate unless the
68     II, 16|       self-evident. But that is impossible.~If then it is uncertain
69     II, 17| hypothesis is so related to the impossible conclusion, that the conclusion
70     II, 17|         from middle terms to an impossible conclusion is independent
71     II, 17|        s theorem that motion is impossible, and so establish a reductio
72     II, 17|       Another case is where the impossible conclusion is connected
73     II, 17|       to A. In this way too the impossible conclusion would result,
74     II, 17|        were eliminated. But the impossible conclusion ought to be connected
75     II, 17|        connexion downwards, the impossible conclusion must be connected
76     II, 17|        hypothesis: for if it is impossible that A should belong to
77     II, 17|      the connexion upwards, the impossible conclusion must be connected
78     II, 17|        hypothesis: for if it is impossible that F should belong to
79     II, 17|         should belong to B, the impossible conclusion will disappear
80     II, 17|    belongs to C and C to D, the impossible conclusion would still stand.
81     II, 20|       will be possible and when impossible. A refutation is possible
82     II, 20|       conceded, a refutation is impossible: for no syllogism is possible (
83     II, 21|       think at all: but that is impossible.~In the former case, where
84     II, 22|    belong together. But this is impossible. When A belongs to the whole