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But in particular syllogisms there will be no necessity of inferring what is
subordinate to the conclusion (for a syllogism does not result when this
premiss is particular), but whatever is subordinate to the middle term may be
inferred, not however through the syllogism, e.g. if A belongs to all B and B
to some C. Nothing can be inferred about that which is subordinate to C;
something can be inferred about that which is subordinate to B, but not
through the preceding syllogism. Similarly in the other figures. That which is
subordinate to the conclusion cannot be proved; the other subordinate can be
proved, only not through the syllogism, just as in the universal syllogisms
what is subordinate to the middle term is proved (as we saw) from a premiss
which is not demonstrated: consequently either a conclusion is not possible in
the case of universal syllogisms or else it is possible also in the case of
particular syllogisms.
2
It is possible for the premisses of the syllogism to be true, or to be false, or
to be the one true, the other false. The conclusion is either true or false
necessarily. From true premisses it is not possible to draw a false conclusion,
but a true conclusion may be drawn from false premisses, true however only
in respect to the fact, not to the reason. The reason cannot be established from
false premisses: why this is so will be explained in the sequel.
First then that it is not possible to draw a false conclusion from true
premisses, is made clear by this consideration. If it is necessary that B should
be when A is, it is necessary that A should not be when B is not. If then A is
true, B must be true: otherwise it will turn out that the same thing both is and
is not at the same time. But this is impossible. Let it not, because A is laid
down as a single term, be supposed that it is possible, when a single fact is
given, that something should necessarily result. For that is not possible. For
what results necessarily is the conclusion, and the means by which this comes
about are at the least three terms, and two relations of subject and predicate or
premisses. If then it is true that A belongs to all that to which B belongs, and
that B belongs to all that to which C belongs, it is necessary that A should
belong to all that to which C belongs, and this cannot be false: for then the
same thing will belong and not belong at the same time. So A is posited as
one thing, being two premisses taken together. The same holds good of
negative syllogisms: it is not possible to prove a false conclusion from true
premisses.
But from what is false a true conclusion may be drawn, whether both the
premisses are false or only one, provided that this is not either of the
premisses indifferently, if it is taken as wholly false: but if the premiss is not
114
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The Complete Aristotle
- Title
- The Complete Aristotle
- Author
- Aristotle
- Date
- ~322 B.C.
- Language
- English
- License
- PD
- Size
- 21.0 x 29.7 cm
- Pages
- 2328
- Keywords
- Philosophy, Antique, Philosophie, Antike, Dialogues, Metaphysik, Metaphysics, Ideologie, Ideology, Englisch
- Categories
- Geisteswissenschaften
- International
Table of contents
- Part 1; Logic (Organon) 3
- Categories 4
- On Interpretation 34
- Prior Analytics, Book I 56
- Prior Analytics, Book II 113
- Posterior Analytics, Book I 149
- Posterior Analytics, Book II 193
- Topics, Book I 218
- Topics, Book II 221
- Topics, Book III 237
- Topics, Book IV 248
- Topics, Book V 266
- Topics, Book VI 291
- Topics, Book VII 317
- Topics, Book VIII 326
- On Sophistical Refutations 348
- Part 2; Universal Physics 396
- Physics, Book I 397
- Physics, Book II 415
- Physics, Book III 432
- Physics, Book IV 449
- Physics, Book V 481
- Physics, Book VI 496
- Physics, Book VII 519
- Physics, Book VIII 533
- On the Heavens, Book I 570
- On the Heavens, Book II 599
- On the Heavens, Book III 624
- On the Heavens, Book IV 640
- On Generation and Corruption, Book I 651
- On Generation and Corruption, Book II 685
- Meteorology, Book I 707
- Meteorology, Book II 733
- Meteorology, Book III 760
- Meteorology, Book IV 773
- Part 3; Human Physics 795
- On the Soul, Book I 796
- On the Soul, Book II 815
- On the Soul, Book III 840
- On Sense and the Sensible 861
- On Memory and Reminiscence 889
- On Sleep and Sleeplessness 899
- On Dreams 909
- On Prophesying by Dreams 918
- On Longevity and the Shortness of Life 923
- On Youth, Old Age, Life and Death, and Respiration 929
- Part 4; Animal Physics 952
- The History of Animals, Book I 953
- The History of Animals, Book II translated 977
- The History of Animals, Book III 1000
- The History of Animals, Book IV 1029
- The History of Animals, Book V 1056
- The History of Animals, Book VI 1094
- The History of Animals, Book VII 1135
- The History of Animals, Book VIII 1150
- The History of Animals, Book IX 1186
- On the Parts of Animals, Book I 1234
- On the Parts of Animals, Book II 1249
- On the Parts of Animals, Book III 1281
- On the Parts of Animals, Book IV 1311
- On the Motion of Animals 1351
- On the Gait of Animals 1363
- On the Generation of Animals, Book I 1381
- On the Generation of Animals, Book II 1412
- On the Generation of Animals, Book III 1444
- On the Generation of Animals, Book IV 1469
- On the Generation of Animals, Book V 1496
- Part 5; Metaphysics 1516
- Part 6; Ethics and Politics 1748
- Nicomachean Ethics, Book I 1749
- Nicomachean Ethics, Book II 1766
- Nicomachean Ethics, Book III 1779
- Nicomachean Ethics, Book IV 1799
- Nicomachean Ethics, Book V 1817
- Nicomachean Ethics, Book VI 1836
- Nicomachean Ethics, Book VII 1851
- Nicomachean Ethics, Book VIII 1872
- Nicomachean Ethics, Book IX 1890
- Nicomachean Ethics, Book X 1907
- Politics, Book I 1925
- Politics, Book II 1943
- Politics, Book III 1970
- Politics, Book IV 1997
- Politics, Book V 2023
- Politics, Book VI 2053
- Politics, Book VII 2065
- Politics, Book VIII 2091
- The Athenian Constitution 2102
- Part 7; Aesthetic Writings 2156