Aristotle
supposition of an interminable regress--he pronounces to be obviously
absurd: the second he declares tantamount to proving a thing by
itself; the circular demonstration, besides, having been shown to be
impossible, except in the First figure, with propositions in which
the predicate reciprocates or is co-extensive with the subject--a
very small proportion among propositions generally used in
demonstrating.[15]
[Footnote 15: Aristot. Analyt. Post. I. iii. p. 72, b. 5-p. 73, a.
20: [Greek: ô(/st' e)peidê\ _o)li/ga toiau=ta_ e)n tai=s
a)podei/xesin], &c.]
Demonstrative Science is attained only by syllogizing from necessary
premisses, such as cannot possibly be other than they are. The
predicate must be (1) _de omni_, (2) _per se_, (3) _quatenus ipsum_,
so that it is a _Primum Universale_; this third characteristic not
being realized without the preceding two. First, the predicate must
belong, and belong at all times, to everything called by the name of
the subject. Next, it must belong thereunto _per se_, or essentially;
that is, either the predicate must be stated in the definition
declaring the essence of the subject, or the subject must be stated
in the definition declaring the essence of the predicate. The
predicate must not be extra-essential to the subject, nor attached to
it as an adjunct from without, simply concomitant or accidental. The
like distinction holds in regard to events: some are accidentally
concomitant sequences which may or may not be realized (_e.g._, a
flash of lightning occurring when a man is on his journey); in
others, the conjunction is necessary or causal (as when an animal
dies under the sacrificial knife).[16] Both these two characteristics
(_de omni_ and _per se_) are presupposed in the third (_quatenus
ipsum_); but this last implies farther, that the predicate is
attached to the subject in the highest universality consistent with
truth; _i.e._, that it is a First Universal, a primary predicate and
not a derivative predicate. Thus, the predicate of having its three
angles equal to two right angles, is a characteristic not merely _de
omni_ and _per se_, but also a First Universal, applied to a
triangle. It is applied to a triangle, _quatenus_ triangle, as a
primary predicate. If applied to a subject of higher universality
(_e.g._, to every geometrical figure), it would not be always true.
If applied to a subject of lower universality (_e.g._, to a
right-angled triangle or an isosceles triangle), it would be
universally true and would be true _per se_, but it would be a
derivative predicate and not a First Universal; it would not be
applied to the isosceles _quatenus_ isosceles, for there is a still
higher Universal of which it is predicable, being true respecting
any triangle you please. Thus, the properties with which
Demonstration, or full and absolute Science, is conversant, are _de
omni_, _per se_, and _quatenus ipsum_, or _Universalia Prima_;[17]
all of them necessary, such as cannot but be true.]
[Footnote 16: Aristot. Analyt. Post. I. iv. p. 73, a. 21, b. 16.
[Greek: Ta\ a)/ra lego/mena e)pi\ tô=n a(plô=s e)pistêtô=n kath'
au(ta\ ou(/tôs ô(s e)nupa/rchein toi=s katêgoroume/nois ê)\
e)nupa/rchesthai di' au(ta/ te/ e)sti kai\ e)x a)na/gkês] (b. 16,
seq.). _Line_ must be included in the definition of the opposites
_straight_ or _curve_. Also it is essential to every line that it is
either straight or curve. _Number_ must be included in the definition
of the opposites _odd_ or _even_; and to be either odd or even is
essentially predicable of every number. You cannot understand what is
meant by _straight_ or _curve_ unless you have the notion of a
_line_.
The example given by Aristotle of _causal_ conjunction (the death of
an animal under the sacrificial knife) shows that he had in his mind
the perfection of Inductive Observation, including full application
of the Method of Difference.]
[Footnote 17: Aristot. Analyt. Post. I. iv. p. 73, b. 25-p. 74, a. 3.
[Greek: o(\ toi/nun _to\ tucho\n prô=ton_ dei/knutai du/o o)rtha\s
e)/chon ê)\ o(tiou=n a)/llo, tou/tô| prô/tô| u(pa/rchei katho/lou,
kai\ ê( _a)po/deixis kath' au(to\_ tou/tou katho/lou e)sti\, tô=n d'
a)/llôn tro/pon tina\ ou) kath' au(to/; ou)de\ tou= i)soske/lous ou)k
e)/sti katho/lou a)ll' e)pi\ ple/on.]
About the precise signification of [Greek: katho/lou] in Aristotle,
see a valuable note of Bonitz (ad Metaphys. Z. iii.) p. 299; also
Waitz (ad Aristot. De Interpr. c. vii.) I. p. 334. Aristotle gives it
here, b. 26: [Greek: katho/lou de\ le/gô o(\ a)\n kata\ panto/s te
u(pa/rchê| kai\ kath' au(to\ kai\ ê(=| au)to/.] Compare Themistius,
Paraphr. p. 19, Spengel. [Greek: To\ kath' au(to/] is described by
Aristotle confusedly. [Greek: To\ katho/lou], is that which is
predicable of the subject as a whole or _summum genus_: [Greek: to\
kata\ panto/s], that which is predicable of every individual, either
of the _summum genus_ or of any inferior species contained therein.
Cf. Analyt. Post. 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]--the subject is
itself the cause or _fundamentum_ of the properties _per se_. See the
explanation and references in Kampe, Die Erkenntniss-theorie des
Aristoteles, ch. v. pp. 160-165.]
Aristotle remarks that there is great liability to error about these
_Universalia Prima_. We sometimes demonstrate a predicate to be true,
universally and _per se_, of a lower species, without being aware
that it might also be demonstrated to be true, universally and _per
se_, of the higher genus to which that species belongs; perhaps,
indeed, that higher genus may not yet have obtained a current name.
That proportions hold by permutation, was demonstrated severally for
numbers, lines, solids, and intervals of time; but this belongs to
each of them, not from any separate property of each, but from what
is common to all: that, however, which is common to all had received
no name, so that it was not known that one demonstration might
comprise all the four.[18] In like manner, a man may know that an
equilateral and an isosceles triangle have their three angles equal
to two right angles, and also that a scalene triangle has its three
angles equal to two right angles; yet he may not know (except
sophistically and by accident[19]) that a triangle _in genere_ has
its three angles equal to two right angles, though there be no other
triangles except equilateral, isosceles, and scalene. He does not
know that this may be demonstrated of every triangle _quatenus_
triangle. The only way to obtain a certain recognition of _Primum
Universale_, is, to abstract successively from the several conditions
of a demonstration respecting the concrete and particular, until the
proposition ceases to be true. Thus, you have before you a brazen
isosceles triangle, the three angles whereof are equal to two right
angles. You may eliminate the condition brazen, and the proposition
will still remain true. You may also eliminate the condition
isosceles; still the proposition is true. But you cannot eliminate
the condition triangle, so as to retain only the higher genus,
geometrical figure; for the proposition then ceases to be always
true. Triangle is in this case the _Primum Universale_.[20]
[Footnote 18: Aristot. Analyt. Post I. v. p. 74, a. 4-23. [Greek:
a)lla\ dia\ to\ mê\ ei)=nai ô)nomasme/non ti pa/nta tau=ta e(/n,
a)rithmoi/, mê/kê, chro/nos, sterea/, kai\ ei)/dei diaphe/rein
a)llê/lôn, chôri\s e)lamba/neto.] What these four have in common is
that which he himself expresses by [Greek: Poso/n]--_Quantum_--in the
Categoriæ and elsewhere. (Categor. p. 4, b. 20, seq.; Metaph. [Greek:
D]. p. 1020, a. 7, seq.)]
[Footnote 19: Aristot. Analyt. Post. I. v. p. 74, a. 27: [Greek:
ou)/pô oi)=de to\ tri/gônon o(/ti du/o o)rthai=s, ei) mê\ _to\n
sophistiko\n tro/pon_ ou)de\ katho/lou tri/gônon, ou)/d' ei) mêde/n
e)sti para\ tau=ta tri/gônon e(/teron.] The phrase [Greek: to\n
sophistiko\n tro/pon] is equivalent to [Greek: to\n sophistiko\n
**tro/pon to\n kata\ sumbebêko/s], p. 71, b. 10. I see nothing
in it connected with Aristotle's characteristic of a Sophist (special
professional life purpose--[Greek: tou= bi/ou tê=| proaire/sei],
Metaphys. [Greek: G]. p. 1004, b. 24): the phrase means nothing more
than _unscientific_.]
[Footnote 20: Aristot. Analyt Post I. v. p. 74, a. 32-b. 4.]
In every demonstration the _principia_ or premisses must be not only
true, but necessarily true; the conclusion also will then be
necessarily true, by reason of the premisses, and this constitutes
Demonstration. Wherever the premisses are necessarily true, the
conclusion will be necessarily true; but you cannot say, _vice
versâ_, that wherever the conclusion is necessarily true, the
syllogistic premisses from which it follows must always be
necessarily true. They may be true without being necessarily true, or
they may even be false: if, then, the conclusion be necessarily true,
it is not so by reason of these premisses; and the syllogistic proof
is in this case no demonstration. Your syllogism may have true
premisses and may lead to a conclusion which is true by reason of
them; but still you have not demonstrated, since neither premisses
nor conclusion are _necessarily_ true.[21] When an opponent contests
your demonstration, he succeeds if he can disprove the _necessity_ of
your conclusion; if he can show any single case in which it either is
or may be false.[22] It is not enough to proceed upon a premiss which
is either probable or simply true: it may be true, yet not
appropriate to the case: you must take your departure from the first
or highest universal of the genus about which you attempt to
demonstrate.[23] Again, unless you can state the _why_ of your
conclusion; that is to say, unless the middle term, by reason of
which the conclusion is necessarily true, be itself necessarily
true,--you have not demonstrated it, nor do you know it absolutely.
Your middle term not being necessary may vanish, while the conclusion
to which it was supposed to lead abides: in truth no conclusion was
known through that middle.[24] In the complete demonstrative or
scientific syllogism, the major term must be predicable essentially
or _per se_ of the middle, and the middle term must be predicable
essentially or _per se_ of the minor; thus alone can you be sure that
the conclusion also is _per se_ or necessary. The demonstration
cannot take effect through a middle term which is merely a Sign; the
sign, even though it be a constant concomitant, yet being not, or at
least not known to be, _per se_, will not bring out the _why_ of the
conclusion, nor make the conclusion necessary. Of non-essential
concomitants altogether there is no demonstration; wherefore it might
seem to be useless to put questions about such; yet, though the
questions cannot yield necessary premisses for a demonstrative
conclusion, they may yield premisses from which a conclusion will
necessarily follow.[25]
[Footnote 21: Ibid. vi. p. 74, b. 5-18. [Greek: e)x a)lêthô=n me\n
ga\r e)/sti kai\ mê\ a)podeiknu/nta sullogi/sthai, e)x a)nagkai/ôn d'
ou)k e)/stin a)ll' ê)\ a)podeiknu/nta; tou=to ga\r ê)/dê
a)podei/xeô/s e)stin.] Compare Analyt. Prior. I. ii. p. 53, b. 7-25.]
[Footnote 22: Aristot. Analyt. Post. I. vi. p. 74, b. 18: [Greek:
sêmei=on d' o(/ti ê( a)po/deixis e)x a)nagkai/ôn, o(/ti kai\ ta\s
e)nsta/seis ou(/tô phe/romen pro\s tou\s oi)ome/nous a)podeiknu/nai,
o(/ti ou)k a)na/gkê], &c.]
[Footnote 23: Ibid. vi. p. 74, b. 21-26: [Greek: dê=lon d' e)k
tou/tôn kai\ o(/ti eu)ê/theis oi( lamba/nein oi)o/menoi kalô=s ta\s
a)rcha/s, e)a\n e)/ndoxos ê)=| ê( pro/tasis kai\ a)lêthê/s, oi(=on
oi( sophistai\ o(/ti to\ e)pi/stasthai to\ e)pistê/mên e)/chein;],
&c.]
[Footnote 24: Aristot. Analyt. Post. I. vi. p. 74, b. 26-p. 75, a.