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4 and 5 exist.-Now none of these thinkers has said the units are inassociable
in this way, but according to their principles it is reasonable that they should
be so even in this way, though in truth it is impossible. For it is reasonable
both that the units should have priority and posteriority if there is a first unit
or first 1, and also that the 2’s should if there is a first 2; for after the first it is
reasonable and necessary that there should be a second, and if a second, a
third, and so with the others successively. (And to say both things at the same
time, that a unit is first and another unit is second after the ideal 1, and that a
2 is first after it, is impossible.) But they make a first unit or 1, but not also a
second and a third, and a first 2, but not also a second and a third. Clearly,
also, it is not possible, if all the units are inassociable, that there should be a
2-itself and a 3-itself; and so with the other numbers. For whether the units
are undifferentiated or different each from each, number must be counted by
addition, e.g. 2 by adding another 1 to the one, 3 by adding another 1 to the
two, and similarly. This being so, numbers cannot be generated as they
generate them, from the 2 and the 1; for 2 becomes part of 3 and 3 of 4 and
the same happens in the case of the succeeding numbers, but they say 4 came
from the first 2 and the indefinite which makes it two 2’s other than the 2-
itself; if not, the 2-itself will be a part of 4 and one other 2 will be added. And
similarly 2 will consist of the 1-itself and another 1; but if this is so, the other
element cannot be an indefinite 2; for it generates one unit, not, as the
indefinite 2 does, a definite 2.
Again, besides the 3-itself and the 2-itself how can there be other 3’s and
2’s? And how do they consist of prior and posterior units? All this is absurd
and fictitious, and there cannot be a first 2 and then a 3-itself. Yet there must,
if the 1 and the indefinite dyad are to be the elements. But if the results are
impossible, it is also impossible that these are the generating principles.
If the units, then, are differentiated, each from each, these results and others
similar to these follow of necessity. But (3) if those in different numbers are
differentiated, but those in the same number are alone undifferentiated from
one another, even so the difficulties that follow are no less. E.g. in the 10-
itself their are ten units, and the 10 is composed both of them and of two 5’s.
But since the 10-itself is not any chance number nor composed of any chance
5’s—or, for that matter, units—the units in this 10 must differ. For if they do
not differ, neither will the 5’s of which the 10 consists differ; but since these
differ, the units also will differ. But if they differ, will there be no other 5’s in
the 10 but only these two, or will there be others? If there are not, this is
paradoxical; and if there are, what sort of 10 will consist of them? For there is
no other in the 10 but the 10 itself. But it is actually necessary on their view
that the 4 should not consist of any chance 2’s; for the indefinite as they say,
received the definite 2 and made two 2’s; for its nature was to double what it
1724
zurĂĽck zum
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