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taken as wholly false, it does not matter which of the two is false. (1) Let A
belong to the whole of C, but to none of the Bs, neither let B belong to C.
This is possible, e.g. animal belongs to no stone, nor stone to any man. If then
A is taken to belong to all B and B to all C, A will belong to all C;
consequently though both the premisses are false the conclusion is true: for
every man is an animal. Similarly with the negative. For it is possible that
neither A nor B should belong to any C, although A belongs to all B, e.g. if
the same terms are taken and man is put as middle: for neither animal nor man
belongs to any stone, but animal belongs to every man. Consequently if one
term is taken to belong to none of that to which it does belong, and the other
term is taken to belong to all of that to which it does not belong, though both
the premisses are false the conclusion will be true. (2) A similar proof may be
given if each premiss is partially false.
(3) But if one only of the premisses is false, when the first premiss is
wholly false, e.g. AB, the conclusion will not be true, but if the premiss BC is
wholly false, a true conclusion will be possible. I mean by ‘wholly false’ the
contrary of the truth, e.g. if what belongs to none is assumed to belong to all,
or if what belongs to all is assumed to belong to none. Let A belong to no B,
and B to all C. If then the premiss BC which I take is true, and the premiss
AB is wholly false, viz. that A belongs to all B, it is impossible that the
conclusion should be true: for A belonged to none of the Cs, since A belonged
to nothing to which B belonged, and B belonged to all C. Similarly there
cannot be a true conclusion if A belongs to all B, and B to all C, but while the
true premiss BC is assumed, the wholly false premiss AB is also assumed,
viz. that A belongs to nothing to which B belongs: here the conclusion must
be false. For A will belong to all C, since A belongs to everything to which B
belongs, and B to all C. It is clear then that when the first premiss is wholly
false, whether affirmative or negative, and the other premiss is true, the
conclusion cannot be true.
(4) But if the premiss is not wholly false, a true conclusion is possible. For
if A belongs to all C and to some B, and if B belongs to all C, e.g. animal to
every swan and to some white thing, and white to every swan, then if we take
as premisses that A belongs to all B, and B to all C, A will belong to all C
truly: for every swan is an animal. Similarly if the statement AB is negative.
For it is possible that A should belong to some B and to no C, and that B
should belong to all C, e.g. animal to some white thing, but to no snow, and
white to all snow. If then one should assume that A belongs to no B, and B to
all C, then will belong to no C.
(5) But if the premiss AB, which is assumed, is wholly true, and the
premiss BC is wholly false, a true syllogism will be possible: for nothing
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Buch The Complete Aristotle"
The Complete Aristotle
- Titel
- The Complete Aristotle
- Autor
- Aristotle
- Datum
- ~322 B.C.
- Sprache
- englisch
- Lizenz
- PD
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 2328
- Schlagwörter
- Philosophy, Antique, Philosophie, Antike, Dialogues, Metaphysik, Metaphysics, Ideologie, Ideology, Englisch
- Kategorien
- Geisteswissenschaften
- International
Inhaltsverzeichnis
- 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