Aristotle
lowest species thus defined; they belong to the higher genera only
through those species.[39] It is in this way, and not in any other,
that the logical Division of genera, according to specific
differences, can be made serviceable for investigation of essential
attributes; that is, it can only be made to demonstrate what is
derivative from the essence. We have shown already that it cannot
help in demonstrating essence or Definition itself. We learn to
marshal in proper order the two constituent elements of our
definition, and to attach each specific difference to the genus to
which it properly belongs. Thus we must not attempt to distribute the
genus animal according to the difference of having the wing divided
or undivided: many animals will fall under neither of the two heads;
the difference in question belongs to the lower genus winged animal,
and distributes the same into two species. The characteristic or
specific difference must be enunciated and postulated by itself, and
must be attached to its appropriate genus in order to form the
definition. It is only by careful attention to the steps of
legitimate logical Division that we can make sure of including all
the particulars and leaving out none.[40]
[Footnote 38: Ibid. b. 18. The straight line is the first or lowest
of all lines: no other line can be understood, unless we first
understand what is meant by a straight line. In like manner the right
angle is the first of all angles, the circle the first of all
curvilinear figures (Julius Pacius, ad loc. p. 504).]
[Footnote 39: Analyt. Post. II. xiii. p. 96, b. 19-25: [Greek: meta\
de\ tou=to, la/bo/nta ti/ to\ ge/nos, oi(=on po/teron tô=n posô=n ê)\
tô=n poiô=n, ta\ i)/dia pa/thê theôrei=n dia\ tô=n koinô=n prô/tôn.
toi=s ga\r suntitheme/nois e)k tô=n a)to/môn] (speciebus infimis)
[Greek: ta\ sumbai/nonta e)k tô=n o(rismô=n e)/stai dê=la, dia\ to\
a)rchê\n ei)=nai pa/ntôn to\n o(rismo/n kai\ to\ a(plou=n, kai\ toi=s
a(ploi=s kath' au(ta\ u(pa/rchein ta\ sumbai/nonta mo/nois, toi=s d'
a)/llois kat' e)kei=na.]
Themistius illustrates this obscure passage, p. 89. The definitions
of [Greek: eu)thei=a grammê/, keklasme/nê grammê/, peripherê\s
grammê/], must each of them contain the definition of [Greek: grammê/
(= mê=kos a)plate/s)], since it is in the Category [Greek: Poso/n
(poso\n mê=kos a)plate/s)]. But the derivative properties of the
circle ([Greek: peripherê\s grammê/]) are deduced from the definition
of a circle, and belong to it in the first instance _quâ_ [Greek:
peripherê\s grammê/], in a secondary way _quâ_ [Greek: grammê/].]
[Footnote 40: Analyt. Post. II. xiii. p. 96, b. 25-p. 97, a. 6.]
Some contemporaries of Aristotle, and among them Speusippus,
maintained that it was impossible either to define, or to divide
logically, unless you knew all particulars without exception. You
cannot (they said) know any one thing, except by knowing its
differences from all other things; which would imply that you knew
also all these other things.[41] To these reasoners Aristotle
replies: It is not necessary to know _all_ the differences of every
thing; you know a thing as soon as you know its essence, with the
properties _per se_ which are derivative therefrom. There are many
differences not belonging to the essence, but distinguishing from
each other two things having the same essence: you may know the
thing, without knowing these accidental differences.[42] When you
divide a genus into two species, distinguished by one proximate
specific difference, such that there cannot be any thing that does
not fall under one or other of these _membra condividentia_, and when
you have traced the subject investigated under one or other of these
members, you can always follow this road until no lower specific
difference can be found, and you have then the final essence and
definition of the subject; even though you may not know how many
_other_ subjects each of the two members may include.[43] Thus does
Aristotle reply to Speusippus, showing that it is not necessary, for
the definition of one thing, that you should know _all_ other things.
His reply, as in many other cases, is founded on the distinction
between the Essential and the Accidental.
[Footnote 41: Ibid. p. 97, a. 6-10; Themistius, p. 92. Aristotle does
not here expressly name Speusippus, but simply says [Greek: phasi/
tines]. It is Themistius who names Speusippus; and one of the
Scholiasts refers to Eudemus as having expressly indicated Speusippus
(Schol. p. 248, a. 24, Br.).]
[Footnote 42: Analyt. Post. II. xiii. p. 97, a. 12: [Greek: pollai\
ga\r diaphorai\ u(pa/rchousi toi=s au)toi=s tô=| ei)/dei, a)ll' ou)
kat' ou)si/an ou)de\ kath' au(ta/.]]
[Footnote 43: Ibid. a. 18-22: [Greek: phanero\n ga\r o(/ti a)\n
ou(/tô badi/zôn e)/lthê| ei)s tau=ta ô(=n mêke/ti e)sti\ diaphora/,
e(/xei to\n lo/gon tê=s ou)si/as.]]
To obtain or put together a definition through logical Division,
three points are to be attended to.[44] Collect the predicates _in
Quid_; range them in the proper order; make sure that there are no
more, or that you have collected all. The essential predicates are
genera, to be obtained not otherwise than by the method (dialectical)
used in concluding accidents. As regards order, you begin with the
highest genus, that which is predicable of all the others, while none
of these is predicable of it, determining in like fashion the
succession of the rest respectively. The collection will be complete,
if you divide the highest genus by an exhaustive specific difference,
such that every thing must be included in one or other of the two
proximate and opposed portions; and then taking the species thus
found as your _dividendum_, subdivide it until no lower specific
difference can be found, or you obtain from the elements an exact
equivalent to the subject.[45]
[Footnote 44: Ibid. a. 23: [Greek: ei)s de\ to\ kataskeua/zein o(/ron
dia\ diaire/seôn]. The Scholiast, p. 248, a. 41, explains [Greek:
kataskeua/zein] by [Greek: eu(rei=n, sunthei=nai, a)podou=nai]. He
distinguishes it from [Greek: a)podeiknu/nai]; demonstration of the
definition being impracticable.]
[Footnote 45: Analyt. Post. II. xiii. p. 97, a. 23 seq. See Waitz,
Comm. p. 418.]
When the investigation must proceed by getting together a group of
similar particulars, you compare them, and note what is the same in
all; then turn to another group which are the same _in genere_ yet
differ _in specie_ from the first group, and have a different point
of community among themselves. You next compare the point of
community among the members of the first group, and that among the
members of the second group. If the two points of community can be
brought under one rational formula, that will be the definition of
the subject; but if at the end of the process, the distinct points of
community are not found resolvable into any final one, this proves
that the supposed _definiendum_ is not one but two or more.[46] For
example, suppose you are investigating, What is the essence or
definition of magnanimity? You must study various magnanimous
individuals, and note what they have in common _quâ_ magnanimous.[47]
Thus, Achilles, Ajax, Alkibiades were all magnanimous. Now, that
which the three had in common was, that they could not endure to be
insulted; on that account Alkibiades went to war with his countrymen,
Achilles was angry and stood aloof from the Greeks, Ajax slew
himself. But, again, you find two other magnanimous men, Sokrates and
Lysander. These two had in common the quality, that they maintained
an equal and unshaken temper both in prosperity and adversity. Now
when you have got thus far, the question to be examined is, What is
the point of identity between the temper that will not endure insult,
and the temper that remains undisturbed under all diversities of
fortune? If an identity can be found, this will be the essence or
definition of magnanimity; to which will belong equanimity as one
variety, and intolerance of insult as another. If, on the contrary,
no identity can be found, you will then have two distinct mental
dispositions, without any common definition.[48]
[Footnote 46: Analyt. Post. II. xiii. p. 97, b. 7-15. [Greek: pa/lin
skopei=n ei) tau)to\n e(/ôs a)\n ei)s e(/na e)/lthê| lo/gon; ou(=tos
ga\r e)/stai tou= pra/gmatos o(rismo/s. e)a\n de\ mê\ badi/zê| ei)s
e(/na a)ll' ei)s du/o ê)\ plei/ô, dê=lon o(/ti ou)k a)\n ei)/ê e(/n
ti ei)=nai to\ zêtou/menon, a)lla\ plei/ô.]]
[Footnote 47: Ibid. b. 16: [Greek: skepte/on e)pi/ tinôn
megalopsu/chôn, ou(\s i)/smen, ti/ e)/chousin e(\n pa/ntes ê(=|
_toiou=toi_.]]
[Footnote 48: Ibid. b. 17-25. [Greek: tau=ta du/o labô\n skopô= ti/
to\ au)to\ e)/chousin ê(/ te a)pa/theia ê( peri\ ta\s tu/chas kai\ ê(
mê\ u(pomonê\ a)timazome/nôn. ei) de\ mêde/n, du/o ei)/dê a)\n ei)/ê
tê=s megalopsuchi/as.]
Æquam memento rebus in arduis
Servare mentem: non secus in bonis
Ab insolenti temperatam
Lætitiâ.--Horace. _Ode_, ii. 3.
Aristotle says that there will be two species of magnanimity. But
surely if the two so-called species connote nothing in common they
are not rightly called species, nor is magnanimity rightly called a
genus. Equanimity would be distinct from magnanimity; Sokrates and
Lysander would not properly be magnanimous but equanimous.]
Every definition must be an universal proposition, applicable, not
exclusively to one particular object, but to a class of greater or
less extent. The lowest species is easier to define than the higher
genus; this is one reason why we must begin with particulars, and
ascend to universals. It is in the higher genera that equivocal terms
most frequently escape detection.[49] When you are demonstrating,
what you have first to attend to is, the completeness of the form of
syllogizing: when you are defining, the main requisite is to be
perspicuous and intelligible; _i.e._ to avoid equivocal or
metaphorical terms.[50] You will best succeed in avoiding them, if
you begin with the individuals, or with examples of the lowest
species, and then proceed to consider not their resemblances
generally, but their resemblances in certain definite ways, as in
colour or figure. These more definite resemblances you will note
first; upon each you will found a formula of separate definition;
after which you will ascend to the more general formula of less
definite resemblance common to both. Thus, in regard to the acute or
sharp, you will consider the acute in sound, and in other matters
(tastes, pains, weapons, angles, &c.), and you will investigate what
is the common point of identity characterizing all. Perhaps there may
be no such identity; the transfer of the term from one to the other
may be only a metaphor: you will thus learn that no common definition
is attainable. This is an important lesson; for as we are forbidden
to carry on a dialectical debate in metaphorical terms, much more are
we forbidden to introduce metaphorical terms in a definition.[51]
[Footnote 49: Analyt. Post. II. xiii. p. 97, b. 29: [Greek: kai\ ga\r
ai( o(mônumi/ai **lantha/nousi ma=llon e)n toi=s katho/lou
ê)\ e)n toi=s a)diapho/rois.]]
[Footnote 50: Analyt. Post. II. xiii. p. 97, b. 31: [Greek: ô(/sper
de e)n tai=s a)podei/xesi dei= to/ ge sullelogi/sthai u(pa/rchein,
ou(/tô kai\ e)n toi=s o(/rois _to\ saphe/s_.]
By [Greek: to\ saphe/s], he evidently means the avoidance of
equivocal or metaphorical terms, and the adherence to true genera and
species. Compare Biese, Die Philosophie des Aristot. pp. 308-310.]
[Footnote 51: Analyt. Post. II. xiii. p. 97, b. 35-39.--([Greek:
diale/gesthai/ phêsi, to\ dialektikô=s o(milei=n].--Schol. p. 248, b.
23, Brand.). Aristotle considers it metaphorical when the term
_acute_ is applied both to a sound and to an angle.