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If the number of the 3-itself is not greater than that of the 2, this is
surprising; and if it is greater, clearly there is also a number in it equal to the
2, so that this is not different from the 2-itself. But this is not possible, if there
is a first and a second number.
Nor will the Ideas be numbers. For in this particular point they are right
who claim that the units must be different, if there are to be Ideas; as has been
said before. For the Form is unique; but if the units are not different, the 2’s
and the 3’s also will not be different. This is also the reason why they must
say that when we count thus-’1,2’-we do not proceed by adding to the given
number; for if we do, neither will the numbers be generated from the
indefinite dyad, nor can a number be an Idea; for then one Idea will be in
another, and all Forms will be parts of one Form. And so with a view to their
hypothesis their statements are right, but as a whole they are wrong; for their
view is very destructive, since they will admit that this question itself affords
some difficulty-whether, when we count and say —1,2,3-we count by
addition or by separate portions. But we do both; and so it is absurd to reason
back from this problem to so great a difference of essence.
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8
First of all it is well to determine what is the differentia of a number-and of
a unit, if it has a differentia. Units must differ either in quantity or in quality;
and neither of these seems to be possible. But number qua number differs in
quantity. And if the units also did differ in quantity, number would differ from
number, though equal in number of units. Again, are the first units greater or
smaller, and do the later ones increase or diminish? All these are irrational
suppositions. But neither can they differ in quality. For no attribute can attach
to them; for even to numbers quality is said to belong after quantity. Again,
quality could not come to them either from the 1 or the dyad; for the former
has no quality, and the latter gives quantity; for this entity is what makes
things to be many. If the facts are really otherwise, they should state this quite
at the beginning and determine if possible, regarding the differentia of the
unit, why it must exist, and, failing this, what differentia they mean.
Evidently then, if the Ideas are numbers, the units cannot all be associable,
nor can they be inassociable in either of the two ways. But neither is the way
in which some others speak about numbers correct. These are those who do
not think there are Ideas, either without qualification or as identified with
certain numbers, but think the objects of mathematics exist and the numbers
1726
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book The Complete Aristotle"
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