Book, Paragraph

 1      I,  2 |          it is not susceptible of proof by the teacher, yet ignorance
 2      I,  3 |         are taken. Thus by direct proof, if A is, B must be; if
 3      I,  4 |           of any predicate is the proof of it as belonging to this
 4      I,  4 |        and universally: while the proof of it as belonging to the
 5      I,  5 |         be thus exemplified. If a proof were given that perpendiculars
 6      I,  5 |  separately. To-day, however, the proof is commensurately universal,
 7      I,  6 |           appropriate".~A further proof that the conclusion must
 8      I,  8 |         in perishable things. The proof can only be accidental,
 9      I,  9 |      basic truths. Consequently a proof even from true, indemonstrable,
10      I,  10|         the case of the remainder proof is required.~Of the basic
11      I,  10|          That which is capable of proof but assumed by the teacher
12      I,  10|    assumed by the teacher without proof is, if the pupil believes
13      I,  11|           form; in which case the proof lays down as its major premiss
14      I,  11|         might attempt a universal proof of axioms such as the law
15      I,  12|      which form premisses for the proof of the theorems of geometry
16      I,  12|         diagram to be false.~If a proof has an inductive minor premiss,
17      I,  12|      instance of this is Caeneus’ proof that fire increases in geometrical
18      I,  13|           major and middle of the proof, however, may be reversed,
19      I,  13|         syllogism turns out to be proof of the fact, but if the
20      I,  13|           major be reversed it is proof of the reasoned fact; since
21      I,  14|           in this figure-a second proof that this figure is the
22      I,  15|           by syllogism;~ ~and the proof will be similar if both
23      I,  19|        they have been stated, and proof is bound to follow-proof
24      I,  21|         no C is B,..no C is A. If proof of this is required, plainly
25      I,  21|    proceed to display the second, proof by which will be as follows:
26      I,  21|           Even supposing that the proof is not confined to one method,
27      I,  22|  substances. On the other hand-in proof of the impossibility of
28      I,  22|  so-called proofs; an alternative proof follows. Predicates so related
29      I,  22|           dialectically, analytic proof has now been given.~
30      I,  23|       have seen that processes of proof cannot pass from one genus
31      I,  23|       beyond A is admitted in the proof: the interval is constantly
32      I,  24|        these. Since, then, such a proof is characteristically commensurate
33      I,  24|        this further argument:~(8) Proof becomes more and more proof
34      I,  24|       Proof becomes more and more proof of the commensurate universal
35      I,  24|        the basic truth. If, then, proof from the basic truth is
36      I,  24|       truth is more accurate than proof not so derived, demonstration
37      I,  25|      degree as A-E (in the second proof), but A-D is better known
38      I,  25|        prior to A-E (in the first proof); since A-E is proved through
39      I,  25|          premiss in each complete proof. Thus, suppose no B is A,
40      I,  25|         nature of a basic form of proof, because it is a sine qua
41      I,  32| middle-serve as premisses for the proof of all conclusions. For
42      I,  32|          some to qualia only; and proof is achieved by means of
43      I,  32|        case has been shown by our proof that the basic truths of
44     II,  6 |          is the truth that, since proof must be through the middle
45     II,  6 |    following type of hypothetical proof also begs the question.
46     II,  6 |       with the major.~Again, both proof by division and the syllogism
47     II,  8 |        thing’s existence, and the proof of this depends on the fact
48     II,  8 |    universal and affirmative, the proof is in the first figure.
49     II,  8 |         is actually a dialectical proof of it-so let us begin again
50     II,  11|           be the middle term of a proof, for (a) though the inference
51     II,  11|          reverse of what it is in proof through the efficient cause:
52     II,  12|         be shaped beforehand; and proof is through the middle in
53     II,  12|   reciprocity in the terms of the proof. This-the convertibility
54     II,  15|           connexions that require proof are identical in that they
55     II,  15|           connexions that require proof only differ in that the "
56     II,  16|    coincident and each capable of proof through the other. Let me
57     II,  17|   connexions demanding scientific proof. But if they are accepted
58     II,  17|       Again, connexions requiring proof which are identical by analogy