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

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PHYSICS 431
must conclude that the infinite exists in one sense
and not in another: or in other words, that it has
a potential hut not an actual existence. The divisibility
of magnitudes in space is indefinite
;
yet we
may not therefore argue that there is an infinitely small
particle. The multiplication of numbers has no limit
yet there is no infinitely great number. 1 In a word,
the infinite can never be represented in actuality.
It is
always potential, and in its two manifestations takes
opposite directions—extension being capable of infinite
division, but not of infinite augmentation :
number, on
the other hand, of infinite augmentation, but not of
infinite division, since the unit is the smallest number. 2
Real infinity is only possible in incorporeal substance
Again, all change is excluded in
things indivisible, for change involves
division between an earlier
and a later condition {Phys. vi.
4 init.). In particular, when we
come to the indivisible elementary
bodies and surfaces of Democritus
and Plato, we shall find
these beset by a whole series of
new difficulties in addition to
the above. (3) Lastly, as there
is no highest number, number is
capable of infinite multiplication.
This, however, has never been
disputed, and therefore requires
no proof.
1
Phys. iii. 6, 206, a, 12 sqq.
troas fiev cCTi [to foreipov], ttus 5'
oS. \iyerat 5jj to elvvu rb /liv
Suvdfiet to 5e evreKexeitf, ko! rb
fciretpov eoTi /iht/ irpotrBeffet %ffri 5e
koX cupcupetrei. rb 8e fieyedos '6rt /j.kv
Kar' Mpyeiav ovk . airfipov,
etpTjrat, Staipetrei 6° Iffriv ov yap
'
Xa\evbv cwe\eiv Tas arSfiovs
ypafifids ' \eiirerai aitv Swdfiei chat
rb bmeipov. Only we must not
suppose that this potentiality can
ever become actual, Sktts rb
aireipov ov Set \afi$dveiv us To*5e
Ti . . . o\A' del 4v yev4ffei % (pdopa.
Sec. ; o. 7, 207, b, 11 (on the infinity
of number) : Sore Swa/dti
/teV cVtiv, ivtpyeiq b" off • dA\' del
{mepfidWei rb \anPav6iievov iravrbs
&pto , fi4vov Tr\4\Qovs. a\\' ov \upiarbs
6 aptOfibs ovros ttjs SixoTOfiias,
ovSe jiieVet t\ aireipta aKAa ylverai,
oxTirep teal 6 xp6vos KaX d apidpbs rov
Xpovov. It is shown also, Gen. et
Corr. i. 2, 316, a, 14 sqq., with respect
to infinite divisibility, that
it never can be actually realised
in fact and therefore exists only
potentially. It is just because it
is merely iv Svvdfiei that the
Infinite is reckoned among
material causes (see p. 350, n. 1,
swpra).
% Phys. iii. 7. Time, however,
even Aristotle holds to be infinite
in both directions.
432 ARISTOTLE
as an infinity of force.
This also, however, is manifested
only in a series which is never exhausted, and in the
endless motion of the world. 1
In proceeding to the notion of Space, we. may
remark, in the first
place, that Aristotle did not regard
it as the boundary-line or shape of individual bodies
for in this case bodies would not move in a space, but
with their space, and several bodies could not successively
enter the same space. No more can it be identified
with the matter of bodies, since this also is
inseparable from the body which is in space : nor is it
that which circumscribes, but that which is circumscribed.
In the third place, we may not regard it as
the distance between the boundaries of bodies, since
this distance changes with the bodies, whereas space
remains always the same, whatever may exist and move
within it. 2
Space may more properly be defined as the
limit of the surrounding body in respect to that which
it surrounds. 3 The place of each particular body 4 is
therefore formed by the (internal) limits of that which
surrounds it, and space in general by the limits of the
world. 5
1
See notes to p. 395, supra. It is strange that space should
2
Phys. iv. 1-4, cf. esp. 211, here be called as in c. i, 212, a,
b, 5 sqq., 209, b, 21 sqq. 20 (cf . n. 3, supra) rov oipavov ti to
3
To irepas rod irepUxovros %axaTOV Ka-l airr6fieyoy rov kivtjtov
awfiaros, or, more accurately, to o-t&naros irepas ripe/iovy ; for we are
toC irepiexopTos irepas aKivTjrov told (v. below and p. 377) that
irp&Tov. Cf. De Coelo, iv. 3, 310, the vault of heaven moves conb,
7. tinually in a circle. Aristotle
4 "ISios tcSttos, as it is called means, however (c. 4, 212, a, 18
Phys. iv. 2 init., as opposed to sqq. c. C, 212, a, 31 sqq., viii. 9,
toVos KOIVOS. It is also called o 265, b, 1 sqq.) that just as in the
irpuros rdiros iv Ss 4cttiv %Kaaroy case of a ball which spins round
ibid. c. 4, 211, a, 28. its own axis without otherwise
5
Phys. iv. 5, 212, a, 31, b, IS. moving the circumference is as