Book, Paragraph

  1      I, 1 |             to make the consequence necessary.~I call that a perfect syllogism
  2      I, 1 |  propositions, which are indeed the necessary consequences of the terms
  3      I, 2 |            others indefinite. It is necessary then that in universal attribution
  4      I, 3 |             good also in respect of necessary premisses. The universal
  5      I, 3 |         into a particular. If it is necessary that no B is A, it is necessary
  6      I, 3 |     necessary that no B is A, it is necessary also that no A is B. For
  7      I, 3 |            is A of necessity, it is necessary also that some A is B: for
  8      I, 3 |             for we say that what is necessary and what is not necessary
  9      I, 3 |           necessary and what is not necessary and what is potential is
 10      I, 4 |            B, and B of all C, it is necessary that no C will be A.~But
 11      I, 4 |           the extremes; for nothing necessary follows from the terms being
 12      I, 4 |             universal conclusion is necessary. But if there is no necessary
 13      I, 4 |       necessary. But if there is no necessary consequence, there cannot
 14      I, 4 |          what was said above, it is necessary that some C is A. And if
 15      I, 4 |            A but some C is B, it is necessary that some C is not A. The
 16      I, 5 |            are otherwise related no necessary consequence follows.~If
 17      I, 5 |             N, but to some O, it is necessary that N does not belong to
 18      I, 5 |            but not to some O, it is necessary that N does not belong to
 19      I, 6 |             belong to some S, it is necessary that P does not belong to
 20      I, 7 |     affirmative or negative nothing necessary follows at all, but if one
 21      I, 7 |       premisses are converted it is necessary that C does not belong to
 22      I, 8 |             concluding from what is necessary, another from what is, a
 23      I, 8 |             between syllogisms from necessary premisses and syllogisms
 24      I, 8 |     conclusion will be proved to be necessary by means of conversion,
 25      I, 8 |            the same form, but it is necessary by the "exposition" of a
 26      I, 8 |              But if the relation is necessary in respect of the part taken,
 27      I, 9 |            that when one premiss is necessary the conclusion is necessary,
 28      I, 9 |         necessary the conclusion is necessary, not however when either
 29      I, 9 |      however when either premiss is necessary, but only when the major
 30      I, 9 |            the major premiss is not necessary, but the minor is necessary,
 31      I, 9 |         necessary, but the minor is necessary, the conclusion will not
 32      I, 9 |          the conclusion will not be necessary. For if it were, it would
 33      I, 9 |          that the conclusion not be necessary, e.g. if A were movement,
 34      I, 9 |            the universal premiss is necessary, then the conclusion will
 35      I, 9 |         then the conclusion will be necessary; but if the particular,
 36      I, 9 |          the conclusion will not be necessary, whether the universal premiss
 37      I, 9 |          First let the universal be necessary, and let A belong to all
 38      I, 9 |             belong to some C: it is necessary then that A belongs to some
 39      I, 9 |           the particular premiss is necessary, the conclusion will not
 40      I, 9 |          the conclusion will not be necessary: for from the denial of
 41      I, 10|             the negative premiss is necessary, then the conclusion will
 42      I, 10|         then the conclusion will be necessary, but if the affirmative,
 43      I, 10|             if the affirmative, not necessary. First let the negative
 44      I, 10|           First let the negative be necessary; let A be possible of no
 45      I, 10|          the affirmative premiss is necessary, the conclusion will not
 46      I, 10|          the conclusion will not be necessary. Let A belong to all B necessarily,
 47      I, 10|       negative major premiss is not necessary the conclusion will not
 48      I, 10|          the conclusion will not be necessary either. Therefore the same
 49      I, 10|       Further, if the conclusion is necessary, it follows that C necessarily
 50      I, 10|           all B. Consequently it is necessary that C does not belong to
 51      I, 10|          that the conclusion is not necessary without qualification, though
 52      I, 10|       qualification, though it is a necessary conclusion from the premisses.
 53      I, 10|   conditions the conclusion will be necessary, but it is not necessary
 54      I, 10|            necessary, but it is not necessary without qualification.~Similar
 55      I, 10|       premiss is both universal and necessary, then the conclusion will
 56      I, 10|         then the conclusion will be necessary: but whenever the affirmative
 57      I, 10|          the conclusion will not be necessary. First then let the negative
 58      I, 10|       premiss be both universal and necessary: let it be possible for
 59      I, 10|       premiss be both universal and necessary, and let the major premiss
 60      I, 10|           the negative statement is necessary but particular, will the
 61      I, 10|              will the conclusion be necessary. The point can be demonstrated
 62      I, 11|   affirmative, if one of the two is necessary, then the conclusion will
 63      I, 11|         then the conclusion will be necessary. But if one is negative,
 64      I, 11|            whenever the negative is necessary the conclusion also will
 65      I, 11|             conclusion also will be necessary, but whenever the affirmative
 66      I, 11|         whenever the affirmative is necessary the conclusion will not
 67      I, 11|          the conclusion will not be necessary. First let both the premisses
 68      I, 11|             to all C, and let AC be necessary. Since then B belongs to
 69      I, 11|            belongs to some B, it is necessary that A should belong to
 70      I, 11|         will be given also if BC is necessary. For C is convertible with
 71      I, 11|             the negative premiss be necessary. Since then C is convertible
 72      I, 11|           But if the affirmative is necessary, the conclusion will not
 73      I, 11|          the conclusion will not be necessary. For suppose BC is affirmative
 74      I, 11|       suppose BC is affirmative and necessary, while AC is negative and
 75      I, 11|        while AC is negative and not necessary. Since then the affirmative
 76      I, 11|             negative premiss is not necessary, neither will the conclusion
 77      I, 11|      neither will the conclusion be necessary. Further, the point may
 78      I, 11|       belong to no horse, and it is necessary that the term animal should
 79      I, 11|          every horse: but it is not necessary that some animal should
 80      I, 11|         when the conclusion will be necessary. But if one premiss is universal,
 81      I, 11|           whenever the universal is necessary the conclusion also must
 82      I, 11|             conclusion also must be necessary. The demonstration is the
 83      I, 11|          convertible. If then it is necessary that B should belong to
 84      I, 11|          and A falls under C, it is necessary that B should belong to
 85      I, 11|      Similarly also if AC should be necessary and universal: for B falls
 86      I, 11|           the particular premiss is necessary, the conclusion will not
 87      I, 11|          the conclusion will not be necessary. Let the premiss BC be both
 88      I, 11|           BC be both particular and necessary, and let A belong to all
 89      I, 11|            universal premiss is not necessary, but the particular is necessary.
 90      I, 11|    necessary, but the particular is necessary. But when the premisses
 91      I, 11|    conclusion (as we proved was not necessary: consequently it is not
 92      I, 11|          biped, and C animal. It is necessary that B should belong to
 93      I, 11|           should belong to B is not necessary. For there is no necessity
 94      I, 11|           AC be both particular and necessary.~But if one premiss is affirmative,
 95      I, 11|      universal is both negative and necessary the conclusion also will
 96      I, 11|             conclusion also will be necessary. For if it is not possible
 97      I, 11|            belongs to some C, it is necessary that A should not belong
 98      I, 11|          affirmative proposition is necessary, whether universal or particular,
 99      I, 11|          the conclusion will not be necessary. The proof of this by reduction
100      I, 11|            universal affirmative is necessary, take the terms "waking" - "
101      I, 11|       affirmative is particular and necessary, take the terms "waking"- "
102      I, 11|        animal" - "white": for it is necessary that animal should belong
103      I, 11|       belong to none, and it is not necessary that waking should not belong
104      I, 11|     proposition being particular is necessary, take the terms "biped", "
105      I, 12|            simple assertions, but a necessary conclusion is possible although
106      I, 12|            only of the premisses is necessary. But in both cases, whether
107      I, 12|      affirmative or negative, it is necessary that one premiss should
108      I, 12|        simple; if the conclusion is necessary, the premiss must be necessary.
109      I, 12|      necessary, the premiss must be necessary. Consequently this also
110      I, 12|          conclusion will be neither necessary nor simple unless a necessary
111      I, 12|       necessary nor simple unless a necessary or simple premiss is assumed.~
112      I, 13|      possible" of that which is not necessary but, being assumed, results
113      I, 13|           indeed ambiguously of the necessary that it is possible. But
114      I, 13|   impossible to belong", and "it is necessary not to belong" are either
115      I, 13|             belong", and "it is not necessary not to belong", will either
116      I, 13|           possible then will be not necessary and that which is not necessary
117      I, 13|     necessary and that which is not necessary will be possible. It results
118      I, 13|            which is possible is not necessary, and that which is not necessary
119      I, 13|    necessary, and that which is not necessary may possibly not belong,
120      I, 14|            to some of the Cs, it is necessary that A may possibly not
121      I, 14|           in this manner it is both necessary that the major should belong
122      I, 14|            the possibility; for the necessary (as we stated) is not possible.~
123      I, 15|            only result that if A is necessary B is necessary, but also
124      I, 15|         that if A is necessary B is necessary, but also that if A is possible,
125      I, 15|           possible for all C: it is necessary then that should be a possible
126      I, 15|          attribute for all B. It is necessary then that A is possible
127      I, 15|          before, but the conclusion necessary, not possible. For man is
128      I, 15| propositions being laid down, it is necessary that A possibly belongs
129      I, 15|       belongs to C, as above. It is necessary then that A belongs to some
130      I, 15|            But neither is it always necessary. Let A be "moving", B "science",
131      I, 15|          the conclusion will not be necessary. For it is not necessary
132      I, 15|            necessary. For it is not necessary that no man should move;
133      I, 15|       should move; rather it is not necessary that any man should move.
134      I, 15|    premisses actually taken nothing necessary results in any way; but
135      I, 15|         Through these comes nothing necessary. But if B is assumed to
136      I, 15|            As common instances of a necessary and positive relation we
137      I, 15|             white-animal-snow: of a necessary and negative relation, white-animal-pitch.
138      I, 15|          above. As instances of the necessary and positive relation we
139      I, 15|            animal-white-man; of the necessary and negative relation, animal-white-garment.
140      I, 16|             Whenever one premiss is necessary, the other problematic,
141      I, 16|           when the minor premiss is necessary. If the premisses are affirmative
142      I, 16|             when the affirmative is necessary the conclusion will be problematic,
143      I, 16|            but when the negative is necessary the conclusion will be problematic
144      I, 16|       cannot be an inference to the necessary negative proposition: for "
145      I, 16|     conclusion which follows is not necessary. Suppose A necessarily belongs
146      I, 16|             the negative premiss is necessary, and let necessarily A not
147      I, 16|           possible for all C. It is necessary then that A belongs to no
148      I, 16|          the affirmative premiss be necessary, and let A possibly not
149      I, 16|            as above; but when it is necessary no syllogism can be formed.
150      I, 16|          negative, and the minor is necessary. The same terms as before
151      I, 16|             negative proposition is necessary, the conclusion will be
152      I, 16|            to some of the Cs, it is necessary that A should not belong
153      I, 16|            AB the major premiss, is necessary, there will not be an assertoric
154      I, 16|           premiss is particular and necessary, there cannot be a syllogism.
155      I, 16|            relation is positive and necessary, e.g. animal-white-man,
156      I, 16|   animal-white-man, and where it is necessary and negative, e.g. animal-white-garment.
157      I, 16|           But when the universal is necessary, the particular problematic,
158      I, 16|         illustrate the negative and necessary relation. Nor again is a
159      I, 16|             some inanimate, is both necessary and positive and necessary
160      I, 16|          necessary and positive and necessary and negative. Similarly
161      I, 16|             the negative premiss is necessary the conclusion is both problematic
162      I, 17|       Similarly when one premiss is necessary, the other problematic.
163      I, 17|        necessarily not men, and the necessary (as we saw) other than the
164      I, 17|           it is not problematic but necessary. Let A be white, B man,
165      I, 17|            not to belong. For it is necessary that no horse should be
166      I, 17|            should be a man, but the necessary we found to be different
167      I, 19|             one of the premisses is necessary, the other problematic,
168      I, 19|             then if the negative is necessary a syllogistic conclusion
169      I, 19|          the affirmative premiss is necessary, no conclusion is possible.
170      I, 19|          affirmative proposition be necessary, and the other problematic;
171      I, 19|       conclusion; for that which is necessary is admittedly distinct from
172      I, 19|             Nor again can we draw a necessary conclusion: for that presupposes
173      I, 19|             that both premisses are necessary, or at any rate the negative
174      I, 19|            assertoric or a negative necessary proposition because no negative
175      I, 19|            the assertoric or in the necessary mode. Nor can the conclusion
176      I, 19|        proposition is universal and necessary, a syllogism will always
177      I, 19|        proposition is universal and necessary, no syllogistic conclusion
178      I, 19|          two terms is universal and necessary, though nothing follows
179      I, 19|             and negative premiss is necessary, a syllogism is always possible,
180      I, 19|          the affirmative premiss is necessary no conclusion can be drawn.
181      I, 19|          premisses is assertoric or necessary. And it is clear that all
182      I, 20|           when the other premiss is necessary, if it is affirmative the
183      I, 20|          conclusion will be neither necessary or assertoric; but if it
184      I, 20|     premisses should be negative no necessary consequence will follow
185      I, 22|             one of the premisses is necessary, the other problematic,
186      I, 22|     negative, if the affirmative is necessary a problematic negative can
187      I, 22|             negative proposition is necessary both a problematic and a
188      I, 22|      conclusion are possible. But a necessary negative conclusion will
189      I, 22|            if the proposition BC is necessary, and AC is problematic.
190      I, 22|     negative, the affirmative being necessary: i.e. suppose A may possibly
191      I, 22|             the negative premiss is necessary, the conclusion will be
192      I, 22|             the negative premiss is necessary. But when the premisses
193      I, 22|             as before; but if it is necessary no syllogism can be formed.
194      I, 22|       affirmative, the latter being necessary. But when the negative premiss
195      I, 22|             the negative premiss is necessary, the conclusion also will
196      I, 22|            conversion; but if it is necessary a syllogism is not possible.
197      I, 23|             of these figures.~It is necessary that every demonstration
198      I, 23|      several middle terms should be necessary to establish the relation
199      I, 24|         negative, but also in being necessary, pure, problematic. We must
200      I, 25|     premisses A, B, C, and D. It is necessary then that of these one should
201      I, 25|           has assumed more than was necessary to establish its thesis.~
202      I, 27|          the predicate "man". It is necessary indeed, if animal follows
203      I, 28|       should belong to all E is not necessary, but it must belong to some
204      I, 28|             some other way than the necessary way because they have failed
205      I, 29|         problem the same inquiry is necessary whether one wishes to use
206      I, 29|            rest. In all cases it is necessary to find some common term
207      I, 29|             whether the relation is necessary or possible. For the inquiry
208      I, 31|             immortal, but it is not necessary that man should be a mortal
209      I, 31|         animal); consequently it is necessary that man should be either
210      I, 31|      footless animal; but it is not necessary that man should be footed:
211      I, 31|            clear, and show it to be necessary, that this is man or whatever
212      I, 32|           been assumed, or anything necessary has been omitted, and we
213      I, 32|       syllogisms, because something necessary results from what has been
214      I, 32| propositions being laid down, it is necessary that any part of substance
215      I, 32|             wanting. Again if it is necessary that animal should exist,
216      I, 32|        exist, if animal does, it is necessary that substance should exist
217      I, 32|             cases because something necessary results from what is assumed,
218      I, 32|         since the syllogism also is necessary. But that which is necessary
219      I, 32|        necessary. But that which is necessary is wider than the syllogism:
220      I, 32|              for every syllogism is necessary, but not everything which
221      I, 32|             not everything which is necessary is a syllogism. Consequently,
222      I, 32|             the remisses: for it is necessary that the middle should be
223      I, 33|            because the inference is necessary, as has been said above;
224      I, 33|             stand thus: but nothing necessary results, nor does a syllogism.
225      I, 41|             belongs to C, it is not necessary that A should belong, I
226      I, 46|           the same thing, but it is necessary that one of them should
227      I, 46|          negation of C and D. It is necessary then that either A or F
228      I, 46|           because perhaps it is not necessary that A or F should belong
229     II, 1 |         belong to some B, it is not necessary that B should not belong
230     II, 2 |             consideration. If it is necessary that B should be when A
231     II, 2 |          should be when A is, it is necessary that A should not be when
232     II, 2 |           to which C belongs, it is necessary that A should belong to
233     II, 4 |       conclusion is true, it is not necessary that the premisses should
234     II, 4 |            the latter is, it is not necessary that the former should be.
235     II, 4 |             this, A, is white it is necessary that that, B, should be
236     II, 4 |            not be white, then it is necessary if is white that C should
237     II, 4 |           white. And whenever it is necessary, since one of two things
238     II, 4 |          the other should be, it is necessary, if the latter is not, that
239     II, 4 |          when A is not white, it is necessary that B should be great,
240     II, 5 |            e.g. suppose it has been necessary to prove that A belongs
241     II, 5 |      belongs to C. Or suppose it is necessary to prove that B belongs
242     II, 5 |             AB converted. But it is necessary to prove both the premiss
243     II, 5 |           of the Cs. If again it is necessary to prove that A belongs
244     II, 5 |       premiss is reversed. If it is necessary to prove that B belongs
245     II, 5 |           of which A belongs. It is necessary then that B should belong
246     II, 6 |             belongs to all A, it is necessary that A should belong to
247     II, 7 |          been proved. And yet it is necessary, if C belongs to some B,
248     II, 7 |            B and A to some B, it is necessary that A should belong to
249     II, 7 |             belongs to all B, it is necessary that A should not belong
250     II, 7 |        which does not belong, it is necessary that C should belong to
251     II, 8 |            the last term. For it is necessary, if the conclusion has been
252     II, 8 |       through the third since it is necessary to take both premisses in
253     II, 11|            or to some C. Then it is necessary that A should belong to
254     II, 11|             if this is false, it is necessary that A should belong to
255     II, 11|             belongs to all A. It is necessary then that C should belong
256     II, 11|             belongs to all A. It is necessary then that C should belong
257     II, 11|         have not yet shown it to be necessary that A belongs to no B,
258     II, 11|             contrary: for it is not necessary that if the universal negative
259     II, 12|            A belong to all C. It is necessary then that C should belong
260     II, 12|             A belong to no C. It is necessary then that C should not belong
261     II, 12|           all B, and to no C. It is necessary then that C should belong
262     II, 13|        belongs to all B. Then it is necessary that A should belong to
263     II, 14|           ostensive proof it is not necessary that the conclusion should
264     II, 14|             not: in the other it is necessary to suppose beforehand that
265     II, 19|           syllogisms, they take the necessary premisses and leave the
266     II, 21|        opine". Perhaps then this is necessary if a man will grant the
267     II, 22|      extremes are convertible it is necessary that the middle should be
268     II, 22|   incorruptible is uncreated, it is necessary that what is created should
269     II, 22|             belongs to all C, it is necessary that A and B should be convertible:
270     II, 22|           convertible with B, it is necessary that A should belong to
271     II, 23|           wider in extension, it is necessary that A should belong to
272     II, 27|           demonstrative proposition necessary or generally approved: for
273     II, 27|           good, it is not therefore necessary that all other wise men
274     II, 27|             also is pale, it is not necessary that she should be with
275     II, 27|             courage to lions, it is necessary that there should be a sign
276     II, 27|           has its sign, since it is necessary that it should have a single