Book, Paragraph

  1      I, 2 |                 are affirmative, others negative, in respect of each of the
  2      I, 2 |              again some affirmative and negative premisses are universal,
  3      I, 2 |            attribution the terms of the negative premiss should be convertible,
  4      I, 2 |           pleasure); but the particular negative need not convert, for if
  5      I, 2 |             First then take a universal negative with the terms A and B.
  6      I, 3 |                premisses. The universal negative converts universally; each
  7      I, 3 |         necessarily. But the particular negative does not convert, for the
  8      I, 3 |             been already proved. But in negative statements the case is different.
  9      I, 3 |                of conversion like other negative statements, e.g. if one
 10      I, 3 |             premiss converts like other negative statements. For if it is
 11      I, 3 |          already proved. The particular negative also must be treated like
 12      I, 3 |               define the possible), the negative premisses can no longer
 13      I, 3 |                negatives; the universal negative premiss does not convert,
 14      I, 4 |              man, horse; of a universal negative relation, the terms animal,
 15      I, 4 |           science, line, medicine: of a negative relation science, line,
 16      I, 4 |            major premiss is positive or negative, indefinite or particular:
 17      I, 4 |               good, state, wisdom: of a negative relation, good, state, ignorance.
 18      I, 4 |                  whether affirmative or negative, and the minor premiss is
 19      I, 4 |                and the minor premiss is negative and particular, can there
 20      I, 4 |               possible with a universal negative minor premiss. A similar
 21      I, 4 |                the universal premiss is negative.~Nor can there in any way
 22      I, 4 |               or negatively, or the one negative and the other affirmative,
 23      I, 4 |             particular, affirmative and negative. Such a figure I call the
 24      I, 5 |                not matter which has the negative relation), but in no other
 25      I, 5 |                 all O. Since, then, the negative relation is convertible,
 26      I, 5 |              been formed. But since the negative relation is convertible,
 27      I, 5 |               substance, animal, man; a negative relation, substance, animal,
 28      I, 5 |                are line, animal, man: a negative relation, line, animal,
 29      I, 5 |              the extremes, a particular negative syllogism must result whenever
 30      I, 5 |              the universal statement is negative, the particular is affirmative:
 31      I, 5 |          affirmative, the particular is negative. For if M belongs to no
 32      I, 5 |                to some O. For since the negative statement is convertible,
 33      I, 5 |              animal, substance, unit: a negative relation, animal, substance,
 34      I, 5 |            similar in form, I mean both negative or both affirmative, a syllogism
 35      I, 5 |               anyhow. First let them be negative, and let the major premiss
 36      I, 5 |                 Terms to illustrate the negative relation are black, snow,
 37      I, 5 |                 Terms to illustrate the negative relation are white, swan,
 38      I, 5 |                  animal, raven: for the negative relation, white, stone,
 39      I, 5 |              affirmative, terms for the negative relation are white, animal,
 40      I, 5 |                this figure, but all are negative, whether universal or particular.~
 41      I, 6 |             animal, horse, man: for the negative relation animal, inanimate,
 42      I, 6 |               horse, inanimate; for the negative relation man, horse, inanimate-inanimate
 43      I, 6 |                other; but when they are negative, no syllogism will be possible.
 44      I, 6 |               possible. But when one is negative, the other affirmative,
 45      I, 6 |            affirmative, if the major is negative, the minor affirmative,
 46      I, 6 |               is affirmative, the other negative, and if the affirmative
 47      I, 6 |               animal. For the universal negative relation it is not possible
 48      I, 6 |               possible here.~But if the negative term is universal, whenever
 49      I, 6 |        universal, whenever the major is negative and the minor affirmative
 50      I, 6 |        converted.~But when the minor is negative, there will be no syllogism.
 51      I, 6 |              animal, man, wild: for the negative relation, animal, science,
 52      I, 6 |             when both are stated in the negative, but one is universal, the
 53      I, 6 |             middle, take as terms for a negative relation raven, snow, white.
 54      I, 6 |                 of this figure, whether negative or affirmative.~
 55      I, 7 |                terms are affirmative or negative nothing necessary follows
 56      I, 7 |               is affirmative, the other negative, and if the negative is
 57      I, 7 |              other negative, and if the negative is stated universally, a
 58      I, 7 |               perfect by converting the negative premiss, each of the particular
 59      I, 7 |             possible in the case of the negative. For if A belongs to no
 60      I, 8 |      necessarily" to the terms. For the negative statement is convertible
 61      I, 8 |         affirmative, and the particular negative, and again in the third
 62      I, 8 |          affirmative and the particular negative, the demonstration will
 63      I, 8 |               subject of the particular negative proposition, to which the
 64      I, 9 |                also the positive or the negative relation to A will hold
 65      I, 9 |                 if the major premiss is negative; for the proof is the same.~
 66      I, 9 |                the universal premiss is negative or affirmative. First let
 67      I, 9 |                 the syllogism should be negative: for the proof will be the
 68      I, 9 |         syllogisms. The same is true of negative syllogisms. Try the terms
 69      I, 10|               the second figure, if the negative premiss is necessary, then
 70      I, 10|                necessary. First let the negative be necessary; let A be possible
 71      I, 10|             belong to C. Since then the negative statement is convertible,
 72      I, 10|               if the minor premiss were negative: for if A is possible be
 73      I, 10|                no C simply. If then the negative premiss is converted, the
 74      I, 10|                first figure that if the negative major premiss is not necessary
 75      I, 10|            syllogisms. For whenever the negative premiss is both universal
 76      I, 10|               premiss is universal, the negative particular, the conclusion
 77      I, 10|           necessary. First then let the negative premiss be both universal
 78      I, 10|             belong to some C. Since the negative statement is convertible,
 79      I, 10|           syllogisms. Nor again, if the negative statement is necessary but
 80      I, 11|                necessary. But if one is negative, the other affirmative,
 81      I, 11|               affirmative, whenever the negative is necessary the conclusion
 82      I, 11|                 some A.~Again let AC be negative, BC affirmative, and let
 83      I, 11|                affirmative, and let the negative premiss be necessary. Since
 84      I, 11|              and necessary, while AC is negative and not necessary. Since
 85      I, 11|               first figure, that if the negative premiss is not necessary,
 86      I, 11|               is affirmative, the other negative, whenever the universal
 87      I, 11|          whenever the universal is both negative and necessary the conclusion
 88      I, 11|         universal or particular, or the negative is particular, the conclusion
 89      I, 11|               some animal. But when the negative proposition being particular
 90      I, 12|           syllogisms are affirmative or negative, it is necessary that one
 91      I, 13|                are convertible into the negative, but that those which are
 92      I, 13|                 are affirmative and not negative; for "to be possible" is
 93      I, 14|               in both the premisses the negative is joined with "it is possible":
 94      I, 14|                 if the minor premiss is negative, or if both premisses are
 95      I, 14|                or if both premisses are negative, either no syllogism results,
 96      I, 14|               the particular premiss is negative, and the universal is affirmative,
 97      I, 14|                both are affirmative, or negative, or different in quality,
 98      I, 14|         affirmative is destroyed by the negative, and the negative by the
 99      I, 14|                by the negative, and the negative by the affirmative. There
100      I, 14|                 they are affirmative or negative, only a perfect syllogism
101      I, 15|          imperfect, and those which are negative will establish not possibility
102      I, 15|           Likewise if the premiss AB is negative, and the premiss BC is affirmative,
103      I, 15|             premiss AB be universal and negative, and assume that A belongs
104      I, 15|                 If the minor premiss is negative and indicates possibility,
105      I, 15|               if both the relations are negative, if the major premiss states
106      I, 15|               whether the premiss AB is negative or affirmative. As common
107      I, 15|   white-animal-snow: of a necessary and negative relation, white-animal-pitch.
108      I, 15|                  whether affirmative or negative, and the particular is affirmative
109      I, 15|              whether both premisses are negative or affirmative, or one is
110      I, 15|               or affirmative, or one is negative, the other affirmative,
111      I, 15|         assertoric, whether positive or negative, and the minor particular,
112      I, 15|               and the minor particular, negative, and problematic, e.g. if
113      I, 15|               premiss is assertoric and negative, there cannot be a syllogism.
114      I, 15|               white-animal-snow; of the negative, white-animal-pitch. For
115      I, 15|               whether either premiss is negative or affirmative, problematic
116      I, 15|  animal-white-man; of the necessary and negative relation, animal-white-garment.
117      I, 16|               is affirmative, the other negative, when the affirmative is
118      I, 16|                will be problematic, not negative assertoric; but when the
119      I, 16|                assertoric; but when the negative is necessary the conclusion
120      I, 16|          conclusion will be problematic negative, and assertoric negative,
121      I, 16|                negative, and assertoric negative, whether the premisses are
122      I, 16|              inference to the necessary negative proposition: for "not necessarily
123      I, 16|                  suppose first that the negative premiss is necessary, and
124      I, 16|               for any B. Since then the negative proposition is convertible,
125      I, 16|                 establish a problematic negative, not an assertoric negative.
126      I, 16|             negative, not an assertoric negative. For the major premiss was
127      I, 16|                 if the minor premiss is negative, when it is problematic
128      I, 16|                 when both premisses are negative, and the minor is necessary.
129      I, 16| relation-white-animal-snow, and for the negative relation-white-animal-pitch.~
130      I, 16|                syllogisms. Whenever the negative proposition is necessary,
131      I, 16|                  the conclusion will be negative assertoric: e.g. if it is
132      I, 16|           particular affirmative in the negative syllogism, e.g. BC the minor
133      I, 16|                  whether affirmative or negative, and the major premiss is
134      I, 16|               where it is necessary and negative, e.g. animal-white-garment.
135      I, 16|        problematic, if the universal is negative we may take the terms animal-white-raven
136      I, 16|    animal-white-pitch to illustrate the negative; and if the universal is
137      I, 16|     animal-white-snow to illustrate the negative and necessary relation.
138      I, 16|     animal-white-man: to illustrate the negative, animal-white-inanimate.
139      I, 16|              positive and necessary and negative. Similarly if the relation
140      I, 16|             this exception, that if the negative premiss is assertoric the
141      I, 16|                 problematic, but if the negative premiss is necessary the
142      I, 16|                 is both problematic and negative assertoric. [It is clear
143      I, 17|            premisses are affirmative or negative, universal or particular.
144      I, 17|          possible, but if the universal negative is assertoric a conclusion
145      I, 17|                 must point out that the negative problematic proposition
146      I, 17|               be this: consequently the negative proposition is not convertible.
147      I, 17|             what has been said that the negative proposition is not convertible.~
148      I, 17|                be either affirmative or negative. But neither is possible.
149      I, 17|               Suppose the conclusion is negative: it will be proved that
150      I, 17|                 if the major premiss is negative, the minor affirmative,
151      I, 17|                 both are affirmative or negative. The demonstration can be
152      I, 18|       affirmative is assertoric and the negative problematic no syllogism
153      I, 18|                 is problematic, and the negative assertoric, we shall have
154      I, 18|                 belong to all C. If the negative proposition is converted,
155      I, 18|                 if the minor premiss is negative. But if both premisses are
156      I, 18|               But if both premisses are negative, one being assertoric, the
157      I, 18|             animal, man, and when it is negative, e.g. health, horse, man.~
158      I, 18|                 as above), but when the negative proposition is assertoric,
159      I, 18|               if both the relations are negative, and the assertoric proposition
160      I, 18|       affirmative as before. But if the negative proposition is assertoric,
161      I, 18|               premiss is affirmative or negative. Nor can a conclusion be
162      I, 18|                  whether affirmative or negative, or particular. The proof
163      I, 19|                problematic, then if the negative is necessary a syllogistic
164      I, 19|              can be drawn, not merely a negative problematic but also a negative
165      I, 19|         negative problematic but also a negative assertoric conclusion; but
166      I, 19|                 belong to all C. If the negative premiss is converted B will
167      I, 19|                 if the minor premiss is negative. Again let the affirmative
168      I, 19|           necessary, or at any rate the negative premiss. (3) Further it
169      I, 19|                conclusion cannot be the negative assertion, if the relation
170      I, 19|               in quality, when they are negative a syllogism can always be
171      I, 19|                 if the minor premiss is negative. But if the premisses are
172      I, 19|              the conclusion cannot be a negative assertoric or a negative
173      I, 19|                negative assertoric or a negative necessary proposition because
174      I, 19|        necessary proposition because no negative premiss has been laid down
175      I, 19|             conclusion be a problematic negative proposition. For if the
176      I, 19|            syllogisms. For whenever the negative proposition is universal
177      I, 19|                both a problematic and a negative assertoric proposition (
178      I, 19|                 when both premisses are negative, and the premiss that definitely
179      I, 19|               that if the universal and negative premiss is necessary, a
180      I, 19|          possible, proving not merely a negative problematic, but also a
181      I, 19|                 problematic, but also a negative assertoric proposition;
182      I, 20|                assertoric; but if it is negative the syllogism will result
183      I, 20|              syllogism will result in a negative assertoric proposition,
184      I, 20|                both premisses should be negative no necessary consequence
185      I, 20|                if the proposition AC is negative, and the proposition BC
186      I, 20|     animal-man-white; to illustrate the negative, take the terms horse-man-white—
187      I, 21|                problematic; or if AC is negative, BC affirmative, no matter
188      I, 21|                 the minor premiss BC is negative, or if both premisses are
189      I, 21|                or if both premisses are negative, no syllogistic conclusion
190      I, 21|                or when the universal is negative, the particular affirmative,
191      I, 21|               premiss is universal, the negative particular, the proof will
192      I, 22|               is affirmative, the other negative, if the affirmative is necessary
193      I, 22|                 necessary a problematic negative can be inferred; but if
194      I, 22|                 be inferred; but if the negative proposition is necessary
195      I, 22|                a problematic and a pure negative conclusion are possible.
196      I, 22|               possible. But a necessary negative conclusion will not be possible,
197      I, 22|               is affirmative, the other negative, the affirmative being necessary:
198      I, 22|                once more: and-since the negative premiss is problematic-it
199      I, 22|                 problematic. But if the negative premiss is necessary, the
200      I, 22|               the first figure, and the negative premiss is necessary. But
201      I, 22|               when the minor premiss is negative, if it is problematic we
202      I, 22|                also when one premiss is negative, the other affirmative,
203      I, 22|                 necessary. But when the negative premiss is necessary, the
204      I, 22|          conclusion also will be a pure negative proposition; for the same
205      I, 22|               when the minor premiss is negative and universal, if it is
206      I, 24|                 in being affirmative or negative, but also in being necessary,
207      I, 26|                 one mood; the universal negative is proved both through the
208      I, 26|                the last. The particular negative is proved in all the figures,
209      I, 26|           destroyed: and the particular negative is proved in all the figures,
210      I, 26|              the figures, the universal negative in two. Similarly with universal
211      I, 27|                be selected, because the negative statement implied above
212      I, 28|               to establish a particular negative proposition, we must find
213      I, 28|             prosyllogism: for since the negative proposition is convertible,
214      I, 28|              belongs to no F, since the negative statement is convertible,
215      I, 28|           figure with its minor premiss negative. If attributes which cannot
216      I, 28|               and H, both premisses are negative, either in the first or
217      I, 36|              holds if the premisses are negative. But we must suppose the
218      I, 36|              good where the relation is negative. For "that does not belong
219      I, 37|               good of the corresponding negative expressions. We must consider
220      I, 45|               to another figure, e.g. a negative syllogism in the first figure
221      I, 45|                first figure; but if the negative statement is converted,
222      I, 45|                B to some C. Convert the negative statement and you will have
223      I, 45|               and to all C. Convert the negative statement, and you will
224      I, 45|           statement concerns B, and the negative C, C must be made first
225      I, 45|                belongs to no C: for the negative statement is convertible.~
226      I, 45|                particular, whenever the negative statement concerns the major
227      I, 45|              and to some C: convert the negative statement and you will have
228      I, 45|           Similarly if the syllogism is negative: for the particular affirmative
229      I, 45|                the first, viz. when the negative statement is not universal:
230      I, 45|             some B. If the syllogism is negative, when the terms are universal
231      I, 45|           middle term. Similarly if the negative statement is universal,
232      I, 45|              some of the Bs. But if the negative statement is particular,
233      I, 45|              the universal statement is negative, resolution is possible.
234      I, 45|             middle figure, whenever the negative statement is universal,
235      I, 45|               and to some B. But if the negative statement is particular,
236      I, 45|            possible: for the particular negative does not admit of conversion.~
237     II, 1 |                yield more than one, the negative yield only the stated conclusion.
238     II, 1 |                save only the particular negative: and the conclusion states
239     II, 1 |          syllogisms save the particular negative yield more than one conclusion,
240     II, 1 |           Similarly if the syllogism is negative. In the second figure it
241     II, 2 |                  The same holds good of negative syllogisms: it is not possible
242     II, 2 |              animal. Similarly with the negative. For it is possible that
243     II, 2 |                  whether affirmative or negative, and the other premiss is
244     II, 2 |        Similarly if the statement AB is negative. For it is possible that
245     II, 2 |          Similarly if the premiss AB is negative. For it is possible that
246     II, 2 |          Similarly if the premiss AB is negative. For it is possible that
247     II, 2 |          Similarly if the premiss AB is negative: for it is possible that
248     II, 2 |          Similarly if the premiss AB is negative. For the same terms will
249     II, 2 |          Similarly if the premiss AB is negative. For it is possible that
250     II, 2 |          Similarly if the premiss AB is negative: for the same terms arranged
251     II, 2 |               also if the premiss AB is negative. For nothing prevents A
252     II, 3 |                 true whichever term the negative statement concerns.~(3)
253     II, 3 |       conclusion true. Similarly if the negative statement is transposed:
254     II, 3 |                 is partially false, the negative wholly true, a true conclusion
255     II, 3 |                 true. Similarly, if the negative premiss is transposed, the
256     II, 3 |          affirmative and the particular negative. For it is possible that
257     II, 4 |             Similarly if one premiss is negative, the other affirmative.
258     II, 4 |                 premiss AC is stated as negative. For nothing prevents A
259     II, 4 |               be true if one premiss is negative, the other affirmative.
260     II, 4 |                of C, and A to no C, the negative premiss is partly false,
261     II, 4 |                 in positive syllogisms, negative terms in negative. For it
262     II, 4 |           syllogisms, negative terms in negative. For it makes no difference
263     II, 4 |                all. The same applies to negative statements.~It is clear
264     II, 5 |               for the demonstration.~In negative syllogisms reciprocal proof
265     II, 5 |                 But if the syllogism is negative, it is not possible to prove
266     II, 5 |               the particular premiss is negative.~
267     II, 6 |          proposition in this way, but a negative proposition may be proved.
268     II, 6 |      affirmative (for the conclusion is negative) but an affirmative proposition
269     II, 6 |               are both affirmative. The negative is proved as follows. Let
270     II, 6 |               But if the premiss AB was negative, and the other affirmative,
271     II, 6 |                the universal premiss is negative, the premiss AC will not
272     II, 6 |                 one of the premisses is negative; consequently a syllogism
273     II, 7 |                is affirmative the other negative, and the affirmative is
274     II, 7 |              being middle. But when the negative premiss is universal, the
275     II, 7 |             first; if the conclusion is negative through the last. For it
276     II, 8 |           Similarly if the syllogism is negative. Suppose it has been proved
277     II, 8 |           Similarly if the syllogism is negative. For if A belongs to some
278     II, 8 |           Similarly if the syllogism is negative: for if it should be assumed
279     II, 10|               the original syllogism is negative. Suppose it has been proved
280     II, 10|             being affirmative, AC being negative: for it was thus that, as
281     II, 10|                AC becomes universal and negative, the other premiss particular
282     II, 11|       necessarily true if the universal negative is false. But if the premiss
283     II, 11|        proposition CA has been taken as negative. But if the premiss assumed
284     II, 11|             original proposition CA was negative: for thus also we get a
285     II, 11|                 a syllogism. But if the negative proposition concerns B,
286     II, 11|         necessary that if the universal negative is false, the universal
287     II, 14|            conclusion is affirmative or negative; the method is the same
288     II, 14|           middle or the last figure, if negative in the middle, if affirmative
289     II, 14|                affirmative in first, if negative in the middle. Suppose that
290     II, 14|                the premiss CA should be negative: for thus also we have the
291     II, 14|             some B. If the syllogism is negative, the hypothesis must have
292     II, 14|              all C. If the syllogism is negative, the hypothesis must have
293     II, 15|                affirmative to universal negative, universal affirmative to
294     II, 15|               affirmative to particular negative, particular affirmative
295     II, 15|                affirmative to universal negative, and particular affirmative
296     II, 15|               affirmative to particular negative: but really there are only
297     II, 15|               opposed to the particular negative. Of the genuine opposites
298     II, 15|           affirmative and the universal negative, e.g. "every science is
299     II, 15|        syllogism whether affirmative or negative can be made out of opposed
300     II, 15|              one affirmative, the other negative: no negative syllogism is
301     II, 15|                  the other negative: no negative syllogism is possible because
302     II, 15|                 the first figure; but a negative syllogism is possible whether
303     II, 15|               universal affirmative and negative, or universal affirmative
304     II, 15|              affirmative and particular negative, or particular affirmative
305     II, 15|               affirmative and universal negative, and the relations between
306     II, 16|            figures. If the syllogism is negative, the question is begged
307     II, 16|           figure), because the terms in negative syllogisms are not convertible.
308     II, 17|                 when the syllogisms are negative.~It is clear then that when
309     II, 20|            being affirmative, the other negative). For as has been shown
310     II, 20|               is affirmative, the other negative: consequently, if what is
311     II, 20|                  when all the terms are negative: therefore no refutation
312     II, 22|          Similarly if the conclusion is negative, e.g. if B belongs to C,
313     II, 26|               universal or a particular negative; the former is proved from
314     II, 26|              the premiss objected to is negative. For if a man maintains
315     II, 26|              from the first figure or a negative objection from the second.~