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for N to belong either to all O or to no O. Terms for the positive relation are
white, animal, raven: for the negative relation, white, stone, raven. If the
premisses are affirmative, terms for the negative relation are white, animal,
snow; for the positive relation, white, animal, swan. Evidently then, whenever
the premisses are similar in form, and one is universal, the other particular, a
syllogism can, not be formed anyhow. Nor is one possible if the middle term
belongs to some of each of the extremes, or does not belong to some of either,
or belongs to some of the one, not to some of the other, or belongs to neither
universally, or is related to them indefinitely. Common terms for all the above
are white, animal, man: white, animal, inanimate. It is clear then from what
has been said that if the terms are related to one another in the way stated, a
syllogism results of necessity; and if there is a syllogism, the terms must be so
related. But it is evident also that all the syllogisms in this figure are
imperfect: for all are made perfect by certain supplementary statements,
which either are contained in the terms of necessity or are assumed as
hypotheses, i.e. when we prove per impossibile. And it is evident that an
affirmative conclusion is not attained by means of this figure, but all are
negative, whether universal or particular.
6
But if one term belongs to all, and another to none, of a third, or if both
belong to all, or to none, of it, I call such a figure the third; by middle term in
it I mean that of which both the predicates are predicated, by extremes I mean
the predicates, by the major extreme that which is further from the middle, by
the minor that which is nearer to it. The middle term stands outside the
extremes, and is last in position. A syllogism cannot be perfect in this figure
either, but it may be valid whether the terms are related universally or not to
the middle term.
If they are universal, whenever both P and R belong to S, it follows that P
will necessarily belong to some R. For, since the affirmative statement is
convertible, S will belong to some R: consequently since P belongs to all S,
and S to some R, P must belong to some R: for a syllogism in the first figure
is produced. It is possible to demonstrate this also per impossibile and by
exposition. For if both P and R belong to all S, should one of the Ss, e.g. N, be
taken, both P and R will belong to this, and thus P will belong to some R.
If R belongs to all S, and P to no S, there will be a syllogism to prove that P
will necessarily not belong to some R. This may be demonstrated in the same
way as before by converting the premiss RS. It might be proved also per
impossibile, as in the former cases. But if R belongs to no S, P to all S, there
will be no syllogism. Terms for the positive relation are animal, horse, man:
63
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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