Book, Paragraph

  1      I,  2 |            all events we do know by demonstration. By demonstration I mean
  2      I,  2 |           know by demonstration. By demonstration I mean a syllogism productive
  3      I,  2 |   scientific knowledge, will not be demonstration. The premisses must be true:
  4      I,  2 |         otherwise they will require demonstration in order to be known, since
  5      I,  2 |           means precisely to have a demonstration of them. The premisses must
  6      I,  2 |         truth. A "basic truth" in a demonstration is an immediate proposition.
  7      I,  2 |         such a syllogism as we call demonstration, and the ground of the syllogism
  8      I,  2 |       student whose belief rests on demonstration has not prior knowledge;
  9      I,  2 |        knowledge that comes through demonstration, he must not only have a
 10      I,  3 |            of knowing other than by demonstration, maintain that an infinite
 11      I,  3 |     unknowable because incapable of demonstration, which according to them
 12      I,  3 |         that it is only possible by demonstration, but they see no difficulty
 13      I,  3 |    demonstrated, on the ground that demonstration may be circular and reciprocal.~
 14      I,  3 |         premisses is independent of demonstration. (The necessity of this
 15      I,  3 |            premisses from which the demonstration is drawn, and since the
 16      I,  3 |      recognize the definitions.~Now demonstration must be based on premisses
 17      I,  3 |            one another: so circular demonstration is clearly not possible
 18      I,  3 |           the unqualified sense of "demonstration", but only possible if "
 19      I,  3 |               but only possible if "demonstration" be extended to include
 20      I,  3 |         however, the second form of demonstration, that which proceeds from
 21      I,  3 |          better known to us, is not demonstration in the unqualified sense
 22      I,  3 |           The advocates of circular demonstration are not only faced with
 23      I,  3 |           the upholders of circular demonstration are in the position of saying
 24      I,  3 |        Moreover, even such circular demonstration is impossible except in
 25      I,  3 |      conclusion rested, by circular demonstration in the first figure. But
 26      I,  3 |          and impossible to say that demonstration is reciprocal and that therefore
 27      I,  4 |         only present when we have a demonstration, it follows that demonstration
 28      I,  4 |      demonstration, it follows that demonstration is an inference from necessary
 29      I,  4 |            and universally, and the demonstration, in the essential sense,
 30      I,  4 |             to which it attaches is demonstration only in a secondary and
 31      I,  5 |          larger whole; for then the demonstration will be true of the individual
 32      I,  5 |             instance of it, yet the demonstration will not be true of this
 33      I,  5 |             and universally. When a demonstration is true of a subject primarily
 34      I,  5 |           the proper subject of the demonstration because being parallel is
 35      I,  5 |             of them all by a single demonstration. Because there was no single
 36      I,  6 |      premise that the conclusion of demonstration is necessary and that a
 37      I,  6 |            distinctive character of demonstration. That demonstration proceeds
 38      I,  6 |    character of demonstration. That demonstration proceeds from necessary
 39      I,  6 |           raise against a professed demonstration is that a premiss of it
 40      I,  6 |           the subject matter of the demonstration; and (2) not all truth is "
 41      I,  6 |      premisses is as follows. Where demonstration is possible, one who can
 42      I,  6 |              the middle term of the demonstration, is not necessarily connected
 43      I,  7 |         there are three elements in demonstration: (1) what is proved, the
 44      I,  7 |       axioms which are premisses of demonstration; (3) the subject-genus whose
 45      I,  7 |     properties, are revealed by the demonstration. The axioms which are premisses
 46      I,  7 |       axioms which are premisses of demonstration may be identical in two
 47      I,  7 |           cannot apply arithmetical demonstration to the properties of magnitudes
 48      I,  7 |         explain later.~Arithmetical demonstration and the other sciences likewise
 49      I,  7 |          own genera; so that if the demonstration is to pass from one sphere
 50      I,  8 |    temporary and special. If such a demonstration is made, one premiss must
 51      I,  8 |        premiss or a conclusion of a demonstration, or else only differs from
 52      I,  8 |            else only differs from a demonstration in the order of its terms.
 53      I,  8 |             the order of its terms. Demonstration and science of merely frequent
 54      I,  9 |         degree. But, as things are, demonstration is not transferable to another
 55      I,  10|            primary premisses of its demonstration; (3) the attributes, the
 56      I,  10|           the essential elements of demonstration are three: the subject,
 57      I,  10|            and therefore a fortiori demonstration, is addressed not to the
 58      I,  10|            assumed and used without demonstration.~The definition-viz. those
 59      I,  11|                               11~So demonstration does not necessarily imply
 60      I,  11|          term goes witb. it, and so demonstration becomes impossible. We conclude,
 61      I,  11|            expressly posited by any demonstration except when the conclusion
 62      I,  11|          subject is posited by such demonstration as uses reductio ad impossibile,
 63      I,  11|            are used as premisses of demonstration, not the subjects nor the
 64      I,  13|       become the middle term of the demonstration. Thus (2) (a) you might
 65      I,  13|           be reversed, and then the demonstration will be of the reasoned
 66      I,  13|            is not given, and so the demonstration is of the fact, not of the
 67      I,  18|           either by induction or by demonstration, this knowledge cannot be
 68      I,  18|            cannot be acquired. Thus demonstration develops from universals,
 69      I,  21|          Further, if in affirmative demonstration the series terminates in
 70      I,  21|           terminate too in negative demonstration. Let us assume that we cannot
 71      I,  21|             in the case of negative demonstration, if it does so also in the
 72      I,  21|             the case of affirmative demonstration. That in fact the regress
 73      I,  22|           can one know them without demonstration. Secondly, if a consequent
 74      I,  22|           if it is possible through demonstration to know anything without
 75      I,  22|           we shall not know them by demonstration. If, therefore, we have
 76      I,  22|             them, we cannot through demonstration have unqualified but only
 77      I,  22|        object of our investigation. Demonstration proves the inherence of
 78      I,  23|            there is no middle term, demonstration ceases to be possible: we
 79      I,  23|       inhere: otherwise there is no demonstration and a basic truth is reached.
 80      I,  23|        basic premisses on which the demonstration rests; and as there are
 81      I,  23|           and in the knowledge that demonstration gives it is an intuition.
 82      I,  24|        regard to so-called "direct" demonstration and reductio ad impossibile.
 83      I,  24|         proceed to discuss "direct" demonstration and reductio ad impossibile.~
 84      I,  24|          minds to prefer particular demonstration.~(1) The superior demonstration
 85      I,  24|     demonstration.~(1) The superior demonstration is the demonstration which
 86      I,  24|       superior demonstration is the demonstration which gives us greater knowledge (
 87      I,  24|            for this is the ideal of demonstration), and we have greater knowledge
 88      I,  24|            commensurately universal demonstration, instead of proving that
 89      I,  24|             is x—whereas particular demonstration proves that the subject
 90      I,  24|            subject itself is x. The demonstration, then, that a subject, as
 91      I,  24|            demonstrates, particular demonstration is superior.~(2) The universal
 92      I,  24|        against groups of singulars. Demonstration nevertheless creates the
 93      I,  24|           figures, and numbers. But demonstration which touches the real and
 94      I,  24|            commensurately universal demonstration is of the latter kind: if
 95      I,  24|        reality than does particular demonstration, and creates a false opinion,
 96      I,  24|           is inferior to particular demonstration.~We may retort thus. (1)
 97      I,  24|        universal than to particular demonstration. If equality to two right
 98      I,  24|           qua triangle, that is not demonstration: but if it does possess
 99      I,  24|           is superior to particular demonstration.~(2) If there is a single
100      I,  24|            blame rests not with the demonstration but with the hearer.~(4)
101      I,  24|            but with the hearer.~(4) Demonstration is syllogism that proves
102      I,  24|            commensurately universal demonstration is superior as more especially
103      I,  24|            commensurately universal demonstration is superior.~(6) The more
104      I,  24|           is superior.~(6) The more demonstration becomes particular the more
105      I,  24|           manifold, while universal demonstration tends to the simple and
106      I,  24|   demonstrable there will be fuller demonstration. Hence the commensurate
107      I,  24|    universal form, being more truly demonstration, is the superior.~(7) Demonstration
108      I,  24| demonstration, is the superior.~(7) Demonstration which teaches two things
109      I,  24|             things is preferable to demonstration which teaches only one.
110      I,  24|            commensurately universal demonstration knows the particular as
111      I,  24|            who possesses particular demonstration does not know the universal.
112      I,  24|            commensurately universal demonstration. And there is yet this further
113      I,  24|          than proof not so derived, demonstration which depends more closely
114      I,  24|            it is more accurate than demonstration which is less closely dependent.
115      I,  24|            commensurately universal demonstration is characterized by this
116      I,  24|        higher term would render the demonstration which it mediated the more
117      I,  24|            commensurately universal demonstration is as follows: if of two
118      I,  24|            commensurately universal demonstration is through and through intelligible;
119      I,  24|            intelligible; particular demonstration issues in sense-perception.~
120      I,  25|             universal to particular demonstration. That affirmative demonstration
121      I,  25|     demonstration. That affirmative demonstration excels negative may be shown
122      I,  25|  superiority ceteris paribus of the demonstration which derives from fewer
123      I,  25|      implied in our contention that demonstration from fewer assumptions is
124      I,  25|          than the conclusion.~Hence demonstration by fewer premisses is ceteris
125      I,  25|            affirmative and negative demonstration operate through three terms
126      I,  25|             additional rule: as the demonstration expands, the affirmative
127      I,  25|             vice versa, affirmative demonstration, being prior and better
128      I,  25|      premiss asserts in affirmative demonstration and in negative denies:
129      I,  25|        basic premiss of affirmative demonstration is superior to that of negative
130      I,  25|        superior to that of negative demonstration, and the demonstration which
131      I,  25|     negative demonstration, and the demonstration which uses superior basic
132      I,  25|           superior.~(4) Affirmative demonstration is more of the nature of
133      I,  25|            sine qua non of negative demonstration.~
134      I,  26|                26~Since affirmative demonstration is superior to negative,
135      I,  26|         difference between negative demonstration and reductio ad impossibile.
136      I,  26|             therefore, the negative demonstration that no C is A is direct.
137      I,  26|         more obvious, we use direct demonstration. All the same the proposition
138      I,  26|           another. Now the superior demonstration is that which proceeds from
139      I,  26|           other. Therefore negative demonstration will have an unqualified
140      I,  26|        impossibile, and affirmative demonstration, being superior to negative,
141      I,  30|            There is no knowledge by demonstration of chance conjunctions;
142      I,  30|            distinct from these. Now demonstration is concerned only with one
143      I,  31|   commensurate universal, possess a demonstration, for the commensurate universal
144      I,  31|        scientific knowledge through demonstration. Nevertheless certain points
145      I,  32|        those which are premisses of demonstration and the subject-genus; and
146     II,  3 |            way it can be reduced to demonstration; what definition is, and
147     II,  3 |           both by definition and by demonstration. It might, I mean, be urged
148     II,  3 |             this difference between demonstration and definition is that to
149     II,  3 |         identical with possessing a demonstration of it: hence if demonstration
150     II,  3 |       demonstration of it: hence if demonstration of such conclusions as these
151     II,  3 |   definition without possessing the demonstration of it; for there is nothing
152     II,  3 |    scientifically is to possess the demonstration of it, an impossible consequence
153     II,  3 |          its definition without its demonstration will give knowledge of the
154     II,  3 |             because there can be no demonstration of the definable? There
155     II,  3 |           likewise. Moreover, every demonstration proves a predicate of a
156     II,  3 |           reveals essential nature, demonstration reveals that a given attribute
157     II,  3 |       demonstrations-unless the one demonstration is related to the other
158     II,  3 |             both a definition and a demonstration. It follows obviously that
159     II,  3 |       obviously that definition and demonstration are neither identical nor
160     II,  5 |         induction. For in a genuine demonstration the conclusion must not
161     II,  5 |          induction, perhaps, is not demonstration any more than is division,
162     II,  7 |           to be facts-the method of demonstration: we may not proceed as by
163     II,  7 |       exhibits one single thing and demonstration another single thing, and
164     II,  7 |           too we hold that it is by demonstration that the being of everything
165     II,  7 |      anything as fact is matter for demonstration; and this is the actual
166     II,  7 |             be a definition: (3) no demonstration can prove that any particular
167     II,  7 |          either by definition or by demonstration.~
168     II,  8 |        thing’s essential nature and demonstration is possible, the cause must
169     II,  8 |          method could not amount to demonstration of essential nature-it is
170     II,  8 |             itself be known without demonstration, nor can it be demonstrated;
171     II,  9 |       explained) to exhibit through demonstration the essential nature of
172     II,  10|    essential nature, differing from demonstration in the arrangement of its
173     II,  10|           one form it is continuous demonstration, in the other definition.
174     II,  10|            is the conclusion of the demonstration embodying essential nature.
175     II,  10|     essential nature differing from demonstration in grammatical form, or (
176     II,  10|              c) the conclusion of a demonstration giving essential nature.~
177     II,  10|           relation of definition to demonstration, and how far the same thing
178     II,  13|           set out in the terms of a demonstration, and the sense in which
179     II,  16|            interposition)-if, then, demonstration through the cause is of
180     II,  16|            of the reasoned fact and demonstration not through the cause is
181     II,  17|         term-though possible if the demonstration is not essential. Now it
182     II,  19|            As regards syllogism and demonstration, the definition of, and
183     II,  19|             since it is the same as demonstration. As to the basic premisses,
184     II,  19|        scientific knowledge through demonstration is impossible unless a man
185     II,  19|    apprehensions more accurate than demonstration and fail to notice them.
186     II,  19|         used to find in the case of demonstration. So it emerges that neither
187     II,  19|          follows from the fact that demonstration cannot be the originative
188     II,  19|           the originative source of demonstration, nor, consequently, scientific