Aristotle
must be assumed as an immediate or undemonstrable principium, and
must be exposed or set out in the best manner practicable as an
existent reality, on Induction or on some other authority. The
arithmetician makes his first steps by assuming both what a monad is
and that there exists such a monad.[22]
[Footnote 22: Analyt. Post. II. ix. p. 93, b. 21. [Greek: e)/sti de\
tô=n me\n e(/tero/n ti ai)/tion, tô=n d' ou)k e)/stin. ô(/ste dê=lon
o(/ti kai\ tô=n ti/ e)sti ta\ me\n a)/mesa kai\ a)rchai/ ei)sin, a(\
kai\ ei)=nai kai\ ti/ e)stin u(pothe/sthai dei= ê)\ a)/llon tro/pon
phanera\ poiê=sai. o(/per o( a)rithmêtiko\s poiei=; kai\ ga\r ti/
e)sti tê\n mona/da u(poti/thetai, kai\ o(/ti e)/stin.]
Themistius, p. 80: [Greek: a(\ kai\ ei)=nai kai\ ti/ e)stin
u(pothe/sthai dei=, ê)\ a)/llon tro/pon phanera\ poiê=sai e)x
e)pagôgê=s ê)\ pi/steôs ê)\ e)mpeiri/as.] Rassow, De Notionis
Definitione, pp. 18-22.]
We may distinguish three varieties of Definition. 1. Sometimes it is
the mere explanation what a word signifies; in this sense, it has
nothing to do with essence or existence; it is a nominal definition
and nothing more.[23] 2. Sometimes it enunciates the Essence, cause,
or reason of the _definitum_; this will happen where the cause is
distinct or extraneous, and where there is accordingly an intervening
middle term: the definition will then differ from a demonstration
only by condensing into one enunciation the two premisses and the
conclusion which together constitute the demonstration.[24] 3.
Sometimes it is an immediate proposition, an indemonstrable
hypothesis, assuming Essence or Quiddity; the essence itself being
cause, and no extraneous cause--no intervening middle term--being
obtainable.[25]
[Footnote 23: Analyt. Post. II. x. p. 93, b. 29-37.]
[Footnote 24: Ibid. p. 93, b. 38, seq. [Greek: oi(=on a)po/deixis
tou= ti/ e)stin, tê=| the/sei diaphe/rôn tê=s
a)podei/xeôs;--sullogismo\s tou= ti/ e)sti, ptô/sei diaphe/rôn tê=s
a)podei/xeôs]--differing "situ et positione terminorum" (Julius
Pacius, p. 493).]
[Footnote 25: Ibid. p. 94, a. 9: [Greek: o( de\ tô=n a)me/sôn
o(rismo/s, the/sis e)sti\ tou= ti/ e)stin a)napo/deiktos.] Compare I.
xxiv. p. 85, b. 24: [Greek: ô(=| ga\r kath' au(to\ u(pa/rchei ti,
tou=to au)to\ au(tô=| ai)/tion.] See Kampe, Die Erkenntniss-theorie
des Aristoteles, p. 212, seq.]
To know or cognize is, to know the Cause; when we know the Cause, we
are satisfied with our cognition. Now there are four Causes, or
varieties of Cause:--
1. The Essence or Quiddity (Form)--[Greek: to\ ti/ ê)=n ei)=nai].
2. The necessitating conditions (Matter)--[Greek: to/ ti/nôn o)/ntôn
a)na/gkê tou=t' ei)=nai].
3. The proximate mover or stimulator of change (Efficient)--[Greek:
ê( ti/ prô=ton e)ki/nêse].
4. That for the sake of which (Final Cause or End)--[Greek: to\
ti/nos e(/neka].
All these four Causes (Formal, Material, Efficient, Final) appear as
middle terms in demonstrating. We can proceed through the medium
either of Form, or of Matter, or of Efficient, or of End. The first
of the four has already been exemplified--the demonstration by Form.
The second appears in demonstrating that the angle in a semi-circle
is always a right angle; where the middle term (or matter of the
syllogism, ([Greek: to\ e)x ou(=]) is, that such angle is always the
half of two right angles.[26] The Efficient is the middle term, when
to the question, Why did the Persians invade Athens? it is answered
that the Athenians had previously invaded Persia along with the
Eretrians. (All are disposed to attack those who have attacked them
first; the Athenians attacked the Persians first; _ergo_, the
Persians were disposed to attack the Athenians.) Lastly, the Final
Cause serves as middle term, when to the question, Why does a man
walk after dinner? the response is, For the purpose of keeping up his
health. In another way, the middle term here is digestion: walking
after dinner promotes digestion; digestion is the efficient cause of
health.[27]
[Footnote 26: Analyt. Post. II. xi. p. 94, a. 21-36. Themistius, p.
83: [Greek: ma/lista me\n ga\r e)pi\ pa/sês a)podei/xeôs o( me/sos
e)/stin oi(=on ê( u(/lê tô=| sullogismô=|; ou(/tos ga\r o( poiô=n
ta\s du/o prota/seis, e)ph' ai(=s to\ sumpe/rasma.]]
[Footnote 27: Analyt. Post. II. xi. p. 94, a. 36-b. 21.]
The Final Cause or End is prior in the order of nature, but posterior
to the terms of the conclusion in the order of time or generation;
while the Efficient is prior in the order of time or generation. The
Formal and Material are simultaneous with the effect, neither prior
nor posterior.[28] Sometimes the same fact may proceed both from a
Final cause, and from a cause of Material Necessity; thus the light
passes through our lantern for the purpose of guiding us in the dark,
but also by reason that the particles of light are smaller than the
pores in the glass. Nature produces effects of finality, or with a
view to some given end; and also effects by necessity, the necessity
being either inherent in the substance itself, or imposed by
extraneous force. Thus a stone _falls_ to the ground by necessity of
the first kind, but _ascends_ by necessity of the second kind. Among
products of human intelligence some spring wholly from design without
necessity; but others arise by accident or chance and have no final
cause.[29]
[Footnote 28: Analyt. Post. II. xi. p. 94, a. 21-26. Themistius, p.
83: [Greek: ê( ge/nesis ou)=n tou= me/sou kai\ ai)ti/ou tê\n au)tê\n
ou)k e)/chei ta/xin e)ph' a(pa/ntôn, a)ll' ou(= me\n prô/tên ô(s
e)pi\ tô=n kinêtikô=n, ou(= de\ teleutai/an ô(s e)pi\ tô=n telô=n
kai\ ô(=n e(/neka, ou(= d' a(/ma ô(s e)pi\ tô=n o(rismô=n kai\ tou=
ti/ ê)=n ei)=nai.]]
[Footnote 29: Analyt. Post. II. p. 94, b. 27-p. 95, a. 9.]
That the middle term is the Cause, is equally true in respect to
_Entia_, _Fientia_, _Præterita_, and _Futura_; only that in respect
to _Entia_, the middle term or Cause must be an _Ens_; in respect to
_Fientia_ it must be a _Fiens_; in respect to _Præterita_, a
_Præteritum_; and in respect to _Futura_, a _Futurum_; that is, in
each case, it must be generated at the corresponding time with the
major and minor terms in the conclusion.[30] What is the cause of an
eclipse of the moon? The cause is, that the earth intervenes between
moon and sun; and this is true alike of eclipses past, present, and
future. Such an intervention is the essence or definition of a lunar
eclipse: the cause is therefore Formal, and cause and effect are
simultaneous, occurring at the same moment of time. But in the other
three Causes--Material, Efficient, Final--where phenomena are
successive and not simultaneous, can we say that the antecedent is
cause and the consequent effect, time being, as seems to us, a
_continuum_? In cases like this, we can syllogize from the consequent
backward to the antecedent; but not from the antecedent forward to
the consequent. If the house has been built, we can infer that the
foundations have been laid; but, if the foundations have been laid,
we cannot infer that the house has been built.[31] There must always
be an interval of time during which inference from the antecedent
will be untrue; perhaps, indeed, it may never become true. Cause and
_causatum_ in these three last varieties of Cause, do not universally
and necessarily reciprocate with each other, as in the case of the
Formal cause. Though time is continuous, events or generations are
distinct points marked in a continuous line, and are not continuous
with each other.[32] The number of these points that may be taken is
indeed infinite; yet we must assume some of them as ultimate and
immediate _principia_, in order to construct our syllogism, and
provide our middle term.[33] Where the middle term reciprocates and
is co-extensive with the major and the minor, in such cases we have
generation of phenomena in a cycle; _e.g._, after the earth has been
made wet, vapour rises of necessity: hence comes a cloud, hence
water; which again falls, and the earth again becomes wet.[34]
Finally, wherever our conclusion is not universally and necessarily
true, but true only in most cases, our immediate _principia_ must
also be of the same character, true in most cases, but in most cases
only.[35]
[Footnote 30: Analyt. Post. II. xii. p. 95, a. 10, 36: [Greek: to\
ga\r me/son o(mo/gonon dei= ei)=nai], &c.]
[Footnote 31: Ibid. a. 24 seq., b. 32; Julius Pacius, ad loc.; Biese,
Die Philosophie des Aristot. pp. 302-303.]
[Footnote 32: Analyt. Post. II. xii. p. 95, a. 39-b. 8; Themistius,
p. 86.]
[Footnote 33: Analyt. Post. II. xii. p. 95, b. 14-31: [Greek: a)rchê\
de\ kai\ e)n tou/tois a)/mesos lêpte/a].]
[Footnote 34: Ibid. b. 38-p. 96, a**. 7.]
[Footnote 35: Ibid. p. 96, a. 8-19.]
How are we to proceed in hunting out those attributes that are
predicated _in Quid_,[36] as belonging to the Essence of the subject?
The subject being a lowest species, we must look out for such
attributes as belong to all individuals thereof, but which belong
also to individuals of other species under the same genus. We shall
thus find one, two, three, or more, attributes, each of which,
separately taken, belongs to various individuals lying out of the
species; but the assemblage of which, collectively taken, does not
belong to any individual lying out of the species. The Assemblage
thus found is the Essence; and the enunciation thereof is the
Definition of the species. Thus, the triad is included in the genus
number; in searching for its definition, therefore, we must not go
beyond that genus, nor include any attributes (such as _ens_, &c.)
predicable of other subjects as well as numbers. Keeping within the
limits of the genus, we find that every triad agrees in being an odd
number. But this oddness belongs to other numbers also (pentad,
heptad, &c.). We therefore look out for other attributes, and we find
that every triad agrees in being a prime number, in two distinct
senses; first, that it is not measured by any other number; secondly,
that it is not compounded of any other numbers. This last attribute
belongs to no other odd number except the triad. We have now an
assemblage of attributes, which belong each of them to every triad,
universally and necessarily, and which, taken all together, belong
_exclusively_ to the triad, and therefore constitute its essence or
definition. The triad is a number, odd, and prime in the two
senses.[37] The _definitum_ and the definition are here exactly
co-extensive.
[Footnote 36: Ibid. xiii. p. 96, a. 22: [Greek: pô=s dei=
_thêreu/ein_ ta\ e)n tô=| ti/ e)sti katêgorou/mena?]]
[Footnote 37: Analyt. Post. II. xiii. p. 96, a. 24-b. 14. [Greek: ei)
toi/nun mêdeni\ u(pa/rchei a)/llô| ê)\ tai=s a)to/mois tria/si,
tou=t' a)\n ei)/ê to\ tria/di ei)=nai. u(pokei/sthô ga\r kai\ tou=to,
ê( ou)si/a ê( e(ka/stou ei)=nai ê( e)pi\ tai=s a)to/mois e)/schatos
toiau/tê katêgori/a. ô(/ste o(moi/ôs kai\ a)/llô| o(tô|ou=n tô=n
ou(/tô deichthe/ntôn to\ _au)tô=| ei)=nai_ e)/stai.]]
Where the matter that we study is the entire genus, we must begin by
distributing it into its lowest species; _e.g._ number into dyad,
triad, &c.; in like manner, taking straight line, circle, right
angle, &c.[38] We must first search out the definitions of each of
these lowest species; and these having been ascertained, we must next
look above the genus, to the Category in which it is itself
comprised, whether _Quantum_, _Quale_, &c. Having done thus much we
must study the derivative attributes or propria of the lowest species
through the common generalities true respecting the larger. We must
recollect that these derivative attributes are derived from the
essence and definition of the lowest species, the complex flowing
from the simple as its _principium_: they belong _per se_ only to the