Book, Paragraph

  1      I,  1 |           no recognition through a middle of a minor term as subject
  2      I,  2 |          its own nature excludes a middle. The part of a contradiction
  3      I,  6 |           inheres in C, yet B, the middle term of the demonstration,
  4      I,  6 |           owe its necessity to the middle term; for though the conclusion
  5      I,  6 |       conclusion is necessary, the middle through which it was proved
  6      I,  6 |           the other hand, when the middle is necessary the conclusion
  7      I,  6 |     conclusion is nonnecessary the middle cannot be necessary either.
  8      I,  6 |       obtained through a necessary middle term; otherwise its possessor
  9      I,  6 |       infers the mere fact through middle terms or the reasoned fact
 10      I,  6 |           We may conclude that the middle must be consequentially
 11      I,  6 |             and the major with the middle.~
 12      I,  7 |        because the extreme and the middle terms must be drawn from
 13      I,  9 |         operate by taking as their middle a common character-a character,
 14      I,  9 |         that connexion through the middle term in virtue of which
 15      I,  9 |           subject: so that if that middle term also belongs essentially
 16      I,  9 |      essentially to the minor, the middle must belong to the same
 17      I,  9 |    theorems are proved by the same middle terms as arithmetical properties,
 18      I,  11|            the universal goes, the middle term goes witb. it, and
 19      I,  11|           is truly affirmed of the middle but falsely denied. It makes
 20      I,  11|          however, if we add to the middle, or again to the minor term,
 21      I,  11|         predicable not only of the middle, but of something other
 22      I,  11|           something other than the middle as well, being of wider
 23      I,  11|           not affected even if the middle is extended to cover the
 24      I,  11|     extended to cover the original middle term and also what is not
 25      I,  11|           what is not the original middle term.~The law that every
 26      I,  11|        such as the law of excluded middle, the law that the subtraction
 27      I,  12|          common, because it is the middle term in which the ambiguity
 28      I,  12|     predicated of the whole of the middle and the middle of the whole
 29      I,  12|        whole of the middle and the middle of the whole of the minor (
 30      I,  12|             so to speak, see these middle terms with an intellectual
 31      I,  12|         the interposition of fresh middle terms, but by the apposition
 32      I,  13|        reciprocals is taken as the middle; for of two reciprocally
 33      I,  13|            known and so become the middle term of the demonstration.
 34      I,  13|         not twinkle. The major and middle of the proof, however, may
 35      I,  13|           reasoned fact, since its middle term is the proximate cause.
 36      I,  13|            of the fact, but if the middle and major be reversed it
 37      I,  13|           also occurs (1) when the middle falls outside the major
 38      I,  13|   according to the position of the middle terms. But there is another
 39      I,  15|           be atomic. If there be a middle term, one or other of them
 40      I,  16|      conclusion inferred through a middle term C, that all B is A,
 41      I,  16|       false; for if all B is A, no middle term can be with truth universally
 42      I,  16|         but premisses in which the middle is affirmed of one extreme
 43      I,  17|          through the "appropriate" middle, only the major and not
 44      I,  17|          be false. By "appropriate middle" I mean the middle term
 45      I,  17|     appropriate middle" I mean the middle term through which the contradictory-i.
 46      I,  17|        attributable to B through a middle term C: then, since to produce
 47      I,  17|        true. Similarly (ii) if the middle is taken from another series
 48      I,  17|          through the "appropriate" middle. On the other hand, (b)
 49      I,  17|          through the "appropriate" middle - (i) when the middle is
 50      I,  17| appropriate" middle - (i) when the middle is subordinate to A but
 51      I,  17|            When, however, (ii) the middle D is not subordinate to
 52      I,  17|  subordinate to A, there can be no middle predicable of all of one
 53      I,  17|          through the "appropriate" middle term. In this case both
 54      I,  17|           equally true if (ii) the middle is taken from another series
 55      I,  17|            same as before.~(b) The middle may be inappropriate. Then (
 56      I,  17|         emerges, then, that if the middle term is not subordinate
 57      I,  19|            in B through some other middle term, and similarly that
 58      I,  19|          as possible: so that if a middle term between A and B is
 59      I,  20|          the more particular), the middle terms cannot be infinite
 60      I,  23|         them in virtue of a common middle term. Isosceles and scalene
 61      I,  23|       angles in virtue of a common middle; for they possess it in
 62      I,  23|            we take B as the common middle in virtue of which A inheres
 63      I,  23|            through a second common middle, and this in turn would
 64      I,  23|           be in virtue of a common middle term that a single attribute
 65      I,  23|          essential attributes, the middle terms involved must be within
 66      I,  23|         demonstrated if there is a middle term. Further, the "elements"
 67      I,  23|           premisses containing the middle in question, and they are
 68      I,  23|       identical in number with the middle terms, seeing that the immediate
 69      I,  23|            other hand, there is no middle term, demonstration ceases
 70      I,  23|         demonstrated if there is a middle term or a term prior to
 71      I,  23|            conclusion as there are middle terms, since it is propositions
 72      I,  23|      propositions containing these middle terms that are the basic
 73      I,  23|            e.g. to prove through a middle C that A does not inhere
 74      I,  23|           proved that no C is A, a middle must be found between and
 75      I,  23|          not all E, is C; then the middle will never fall beyond E,
 76      I,  23|            In the third figure the middle will never fall beyond the
 77      I,  24|      commensurate universal as its middle term approaches nearer to
 78      I,  25|            in both cases alike the middle terms are known, and that
 79      I,  25|            to be again expanded, a middle must be interposed. Let
 80      I,  25|          affirmative syllogism the middle is always related affirmatively
 81      I,  29|           A-B—but also by taking a middle from another series. Thus
 82      I,  32|        predicable of C, but B, the middle, is false, both A-B and
 83      I,  32|         terms could only fit in as middle terms or as major or minor
 84      I,  32|           interposition of a fresh middle. Moreover, the number of
 85      I,  32|   indefinite, though the number of middle terms is finite; and lastly
 86      I,  33|           thought through the same middle terms until the immediate
 87      I,  33|        fact, and the reason is the middle term; so that, since the
 88      I,  34|        faculty of hitting upon the middle term instantaneously. It
 89      I,  34|            grasped the causes, the middle terms.~Let A represent "
 90     II,  2 |      connexion or the thing has a "middle"; and when we have ascertained
 91     II,  2 |            we are asking what the "middle" is.~(By distinguishing
 92     II,  2 |         either whether there is a "middle" or what the "middle" is:
 93     II,  2 |            a "middle" or what the "middle" is: for the "middle" here
 94     II,  2 |          the "middle" is: for the "middle" here is precisely the cause,
 95     II,  2 |        accident-are both alike the middle". By that which is without
 96     II,  2 |       ratio?".~Cases in which the "middle" is sensible show that the
 97     II,  2 |         our inquiry is always the "middle": we inquire, because we
 98     II,  2 |      whether there is or is not a "middle" causing, e.g. an eclipse.
 99     II,  3 |      questions are a search for a "middle". Let us now state how essential
100     II,  4 |           of a subject through the middle term; on the other hand (
101     II,  4 |            its definition, and the middle term connecting them must
102     II,  4 |            form will appear in the middle term before the conclusion
103     II,  6 |          proof must be through the middle term, the definable form
104     II,  8 |    possible, the cause must be the middle term, and, the conclusion
105     II,  8 |         must be inferred through a middle which is an essential nature
106     II,  8 |         must be inferred through a middle which is a "peculiar" property;
107     II,  9 |            of things which have a "middle", i.e. a cause of their
108     II,  11|           each of these can be the middle term of a proof, for (a)
109     II,  11|          they have a single common middle term. So it is from the
110     II,  11|          assumption of this single middle term that the conclusion
111     II,  11|       already been shown to be the middle. (c) "Why did the Athenians
112     II,  11|         the efficient cause-is the middle term. (d) This is no less
113     II,  11|            the efficient order the middle term must come to be first,
114     II,  12|    actually existent-for it is the middle which is the cause-except
115     II,  12|         water, A solidified, B the middle, which is the cause, namely
116     II,  12|         reason of this is that the middle must be homogeneous, past
117     II,  12|    existent; and there cannot be a middle term homogeneous with extremes
118     II,  12|            the manner in which the middle would be identical with
119     II,  12|           of such a series too the middle and major terms must form
120     II,  12|            occurred.~If we get our middle term in this way, will the
121     II,  12|          contiguous", will a fresh middle term always intervene because
122     II,  12|            premiss consisting of a middle and the present event as
123     II,  12|           and proof is through the middle in the same way, for the
124     II,  12|            is possible only if the middle and extreme terms are reciprocal,
125     II,  12|        case of such connexions the middle term too must be a general
126     II,  12|     general rule; consequently the middle term B must also be a general
127     II,  13|            the opposites exclude a middle; since if it is the differentia
128     II,  15|         they possess an identical "middle" e.g. a whole group might
129     II,  15|           only differ in that the "middle" of the one is subordinate
130     II,  15|         one is subordinate to the "middle" of the other. For example:
131     II,  16|        vine is deciduous), and the middle term B is the cause. But
132     II,  16|       commensurate connexions the "middle"" and its effect must reciprocate,
133     II,  17|            an accident-because the middle is then the definition of
134     II,  17|          are accepted as such, the middle will correspond to the extremes,
135     II,  17|        four right angles). And the middle likewise reciprocates, for
136     II,  17|     likewise reciprocates, for the middle is a definition of the major;
137     II,  17|      species. Then if you take the middle which is proximate, it is
138     II,  17|     because you will first reach a middle next the subject, and a
139     II,  17|         the connexion of the first middle with the major: but it is
140     II,  18|            there is not merely one middle but several middles, i.e.
141     II,  18|            the several species the middle which is proximate to the
142     II,  18|          primary universal, or the middle which is proximate to the