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also always limited in number. An immediately obvious consequence of this
is that demonstrations necessarily involve basic truths, and that the contention
of some-referred to at the outset-that all truths are demonstrable is mistaken.
For if there are basic truths, (a) not all truths are demonstrable, and (b) an
infinite regress is impossible; since if either (a) or (b) were not a fact, it would
mean that no interval was immediate and indivisible, but that all intervals
were divisible. This is true because a conclusion is demonstrated by the
interposition, not the apposition, of a fresh term. If such interposition could
continue to infinity there might be an infinite number of terms between any
two terms; but this is impossible if both the ascending and descending series
of predication terminate; and of this fact, which before was shown
dialectically, analytic proof has now been given.
23
It is an evident corollary of these conclusions that if the same attribute A
inheres in two terms C and D predicable either not at all, or not of all
instances, of one another, it does not always belong to them in virtue of a
common middle term. Isosceles and scalene possess the attribute of having
their angles equal to two right angles in virtue of a common middle; for they
possess it in so far as they are both a certain kind of figure, and not in so far
as they differ from one another. But this is not always the case: for, were it so,
if we take B as the common middle in virtue of which A inheres in C and D,
clearly B would inhere in C and D through a second common middle, and this
in turn would inhere in C and D through a third, so that between two terms an
infinity of intermediates would fall-an impossibility. Thus it need not always
be in virtue of a common middle term that a single attribute inheres in several
subjects, since there must be immediate intervals. Yet if the attribute to be
proved common to two subjects is to be one of their essential attributes, the
middle terms involved must be within one subject genus and be derived from
the same group of immediate premisses; for we have seen that processes of
proof cannot pass from one genus to another.
It is also clear that when A inheres in B, this can be demonstrated if there is
a middle term. Further, the ‘elements’ of such a conclusion are the premisses
containing the middle in question, and they are identical in number with the
middle terms, seeing that the immediate propositions-or at least such
immediate propositions as are universal-are the ‘elements’. If, on the other
hand, there is no middle term, demonstration ceases to be possible: we are on
the way to the basic truths. Similarly if A does not inhere in B, this can be
demonstrated if there is a middle term or a term prior to B in which A does
not inhere: otherwise there is no demonstration and a basic truth is reached.
180
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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