ARISTOTLE AND THE EARLIER PERIPATETICS vol.I by Eduard Zeller, B.F.C.Costelloe 1897

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LOGIC 271
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progressive division is our surest method, while a correspondingly
gradual building up of concepts is equallyproper
to the upward process towards the universal. 1
And thus Plato's method, though Aristotle could not
accept it as a satisfactory process for deducing definitions,
was yet recognised and further worked out by him as a
means to their discovery. 2
Supposing, then, that we have defined and surveyed
the whole field
of the knowledge of concepts on this
method, we shall obtain a system of ideas such as Plato
looked for, 3 carrying us in an unbroken line from the
Summa Genera through all the intermediate members
down to the lowest species. And since scientific
deduction must consist in the specification of causes,
and since each specific difference in the upward scale
implies the introduction of a new cause, and every
added cause creates a corresponding differentia, it
results that our logical structure must exactly correspond
with the actual sequence and concatenation of
causes.
Plato never undertook actually to set forth that
derivation of everything knowable out of unity, which
he saw ahead as the end and goal of science.
Aristotle
1
Aristotle includes both, with- the object to be divided; and
out further separating them, in lastly (to which Plato devoted
the concept of Division. For less attention), that it should
this he gives full rules in Anal, not proceed by means of deduced
Pott. ii. 13, 96, b, 15-97, b, or contingent differences, but by
25 ;
Top. vi. 5, 6 ; Part. Anvm. the essential ones. Cf. preceding
i. 2, 3. Like Plato (Zellbb, note.
Ph. d. Gr. pt. i. p. 524 sq.), 2
Two further rules, contained
he also considers that the most especially in the sixth book of
important thing is that the di- the Topic)—wherehe enumerates
vision should be continuous, at length the mistakes made in
should omit no intermediate denning—are omitted here,
grade, and should totally exhaust 3
See Zell. ibid. p. 525, 588.
272 ARISTOTLE
considers such a demonstration to be quite impracticable.
The highest genera, according to him, are no more
capable of being derived from any one higher principle
than are the special postulates of each science, 1 They
are connected, not by any complete community of
nature, but only by a kind of analogy, 2 and the reason
1
Anal. Post. i. 32, 88, a, 31
sqq., &c. ; vid. supra p. 246. sqq.
Aristotle says, in Metaph. xii. 4,
1070, b, 1 {irapa yap t)\v ovtrlav Kal
TaAAa refc Karyyopovfieva ovBev %trri
koiv&v), that the categories especially
can be deduced neither from
one another nor from a higher
common genus: v. 28, 1024, b,
9 (where the same is said of
Form and Matter) ; xi. 9, 1065,
b, 8 ; Phys. iii. 1, 200, b, 34 ; De
An. i. 6, 410, a, 13 ; Mh. N. i. 4,
1096, a, 19, 23 sqq. ; of. TRENDE-
LENBURG, Hist. Beitr. i. 149 sq.
The concepts, which one would
be most inclined to consider the
highest genera,
'
Being ' and
'
One,' are no ydvri : Metaph. iii.
3, 998, b, 22 ; viii. 6, 1045, b, 5 ;
x. 2, 1053, b, 21 ; xi. 1, 1059, b,
27 sq. ; xii. 4, 1070, b. 7 ; Eth. JST.
ibid. ; Anal. Post. ii. 7, 92, b, 14 ;
Top. iv. 1, 121, a, 16, c. 6, 127,
a, 26 sqq. Cf. Trendelenburg,
loo. cit. 67 ; Bonitz and Schwegler
on Metaph. iii. 3 (more
on p. 276 infra'). Therefore the
principle ' that eventually everything
is contained in a single
highest concept as in a common
genus,' which Strumpell, Gesch.
d. theor. Phil. d. Gr. p. 193,
gives as an assertion of Aristotle,
is not really Aristotelian.
2 In Metaph. v. 6, 1016, b,
31, four kinds of Unity are distinguished
(somewhat different
is the other fourfold enumeration
in Metaph. x. 1, in which
the unity of analogy does not
occur) : the unity of number, of
species, of genus, and of analogy.
Each of these unities includes in
it the subsequent unities (i.e.
that which in number is one is
also one in species, &c.) ;
but not
vive versa. Hence the unity of
Analogy can occur even in those
things which belong to no
common genus (cf. Part. An. i.
5, 645, b, 26 : t& ficv yap exavat
to Kotvbv Kar avahoylav, ra Se
Kara yevos, Ta Sh /car' elSos). It
occurs in everything Sera £%« us
fiAAo vpbs SAAo. It consists in
identity of relation (io-oV»js \6yav~),
and hence supposes at least four
members {Eth. N. v. 6, 1131, a,
31). Its formula is : &s touto iv
tovtu % irpbs touto, to*8' ev T tV abri]v %x ov
5vvaii.iv, ibid. i. 4, 644, b, 11
ii. 6, 652, a, 3), and in fact in all
categories {Metaph. xiv. 6, 1093,
b, 18). Besi8es those in the
passages just mentioned, other
instances are given in De Part.