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matter, while ‘that for the sake of which’ is in the definition.
Necessity in mathematics is in a way similar to necessity in things which
come to be through the operation of nature. Since a straight line is what it is,
it is necessary that the angles of a triangle should equal two right angles. But
not conversely; though if the angles are not equal to two right angles, then the
straight line is not what it is either. But in things which come to be for an end,
the reverse is true. If the end is to exist or does exist, that also which precedes
it will exist or does exist; otherwise just as there, if-the conclusion is not true,
the premiss will not be true, so here the end or ‘that for the sake of which’ will
not exist. For this too is itself a starting-point, but of the reasoning, not of the
action; while in mathematics the starting-point is the starting-point of the
reasoning only, as there is no action. If then there is to be a house, such-and-
such things must be made or be there already or exist, or generally the matter
relative to the end, bricks and stones if it is a house. But the end is not due to
these except as the matter, nor will it come to exist because of them. Yet if
they do not exist at all, neither will the house, or the saw-the former in the
absence of stones, the latter in the absence of iron-just as in the other case the
premisses will not be true, if the angles of the triangle are not equal to two
right angles.
The necessary in nature, then, is plainly what we call by the name of
matter, and the changes in it. Both causes must be stated by the physicist, but
especially the end; for that is the cause of the matter, not vice versa; and the
end is ‘that for the sake of which’, and the beginning starts from the definition
or essence; as in artificial products, since a house is of such-and-such a kind,
certain things must necessarily come to be or be there already, or since health
is this, these things must necessarily come to be or be there already. Similarly
if man is this, then these; if these, then those. Perhaps the necessary is present
also in the definition. For if one defines the operation of sawing as being a
certain kind of dividing, then this cannot come about unless the saw has teeth
of a certain kind; and these cannot be unless it is of iron. For in the definition
too there are some parts that are, as it were, its matter.
431
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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