Aristotle
the Particular, the conclusion teaches you nothing more than you
might have learnt from a direct observation of sense; whereas in that
of the Universal the conclusion teaches you more than you could have
learnt from direct sensation, and comes into correlation with the
highest form of our intellectual nature.[76]
[Footnote 75: Analyt. Post. I. xxiv. p. 86**, a. 22: [Greek: a)lla\
tô=n me\n ei)rême/nôn e)/nia logika/ e)sti; _ma/lista_ de\ dê=lon
o(/ti ê( katho/lou kuriôte/ra, o(/ti--o( de\ tau/tên e)/chôn tê\n
pro/tasin] (the Particular) [Greek: _to\ katho/lou ou)damô=s oi)=den,
ou)/te duna/mei ou)/t' e)nergei/a|_.]]
[Footnote 76: Ibid. a. 29: [Greek: kai\ ê( me\n katho/lou noêtê/, ê(
de\ kata\ me/ros ei)s ai)/sthêsin teleuta=|.] Compare xxiii. p. 84,
b. 39, where we noticed the doctrine that [Greek: Nou=s] is the
_unit_ of scientific demonstration.]
Next, Aristotle compares the Affirmative with the Negative
demonstration, and shows that the Affirmative is the better. Of two
demonstrations (he lays it down) that one which proceeds upon a
smaller number of postulates, assumptions, or propositions, is better
than the other; for, to say nothing of other reasons, it conducts you
more speedily to knowledge than the other, and that is an advantage.
Now, both in the affirmative and in the negative syllogism, you must
have three terms and two propositions; but in the affirmative you
assume only that something _is_; while in the negative you assume
both that something _is_, and that something _is not_. Here is a
double assumption instead of a single; therefore the negative is the
worse or inferior of the two.[77] Moreover, for the demonstration of
a negative conclusion, you require one affirmative premiss (since
from two negative premisses nothing whatever can be concluded); while
for the demonstration of an affirmative conclusion, you must have two
affirmative premisses, and you cannot admit a negative. This, again,
shows that the affirmative is logically prior, more trustworthy, and
better than the negative.[78] The negative is only intelligible and
knowable through the affirmative, just as _Non-Ens_ is knowable only
through _Ens_. The affirmative demonstration therefore, as involving
better principles, is, on this ground also, better than the
negative.[79] _A fortiori_, it is also better than the demonstration
by way of _Reductio ad Absurdum_, which was the last case to be
considered. This, as concluding only indirectly and from
impossibility of the contradictory, is worse even than the negative;
much more therefore is it worse than the direct affirmative.[80]
[Footnote 77: Analyt. Post. I. xxv. p. 86, a. 31-b. 9.]
[Footnote 78: Ibid. b. 10-30.]
[Footnote 79: Ibid. b. 30-39.]
[Footnote 80: Ibid. I. xxvi. p. 87, a. 2-30. Waitz (II. p. 370),
says: "deductio (ad absurdum), quippe quæ per ambages cogat, post
ponenda, est demonstrationi rectæ."
Philoponus says (Schol. pp. 234-235**, Brand.) that the
Commentators all censured Aristotle for the manner in which he here
laid out the Syllogism [Greek: di' a)duna/tou]. I do not, however,
find any such censure in Themistius. Philoponus defends Aristotle
from the censure.]
If we next compare one Science with another, the prior and more
accurate of the two is, (1) That which combines at once the [Greek:
o(/ti] and the [Greek: dio/ti]; (2) That which is abstracted from
material conditions, as compared with that which is immersed
therein--for example, arithmetic is more accurate than harmonics;
(3) The more simple as compared with the more complex: thus,
arithmetic is more accurate than geometry, a monad or unit is a
substance without position, whereas a point (more concrete) is a
substance with position.[81] One and the same science is that which
belongs to one and the same generic subject-matter. The premisses of
a demonstration must be included in the same genus with the
conclusion; and where the ultimate premisses are heterogeneous, the
cognition derived from them must be considered as not one but a
compound of several.[82] You may find two or more distinct middle
terms for demonstrating the same conclusion; sometimes out of the
same logical series or table, sometimes out of different tables.[83]
[Footnote 81: Analyt. Post. I. xxvii. p. 87, a. 31-37. Themistius,
Paraphras. p. 60, ed. Speng.: [Greek: kat' a)/llon de\ (tro/pon),
e)a\n ê( me\n peri\ u(pokei/mena/ tina kai\ ai)sthêta\
pragmateu/êtai, ê( de\ peri\ noêta\ kai\ katho/lou.]
Philoponus illustrates this (Schol. p. 235, b. 41, Br.): [Greek:
oi(=on ta\ Theodosi/ou sphairika\ a)kribe/stera/ e)stin e)pistê/mê|
tê=s tô=n Au)tolu/kou peri\ kinoume/nês sphai/ras.] &c.]
[Footnote 82: Analyt. Post. I. xxviii. p. 87, a. 38-b. 5. Themistius,
p. 61: [Greek: dê=lon de\ tou=to gi/netai proi+ou=sin e)pi\ ta\s
a)napodei/ktous a)rcha/s; au(=tai ga\r ei) mêdemi/an e)/choien
sugge/neian, e(/terai ai( e)pistê=mai.]]
[Footnote 83: Analyt. Post. I. xxix. p. 87, b. 5-18. Aristotle gives
an example to illustrate this general doctrine: [Greek: ê(/desthai,
to\ kinei=sthai, to\ ê)remi/zesthai, to\ metaba/llein]. As he
includes these terms und this subject among the topics for
demonstration, it is difficult to see where he would draw a distinct
line between topics for Demonstration and topics for Dialectic.]
There cannot be demonstrative cognition of fortuitous events,[84] for
all demonstration is either of the necessary or of the customary. Nor
can there be demonstrative cognition through sensible perception. For
though by sense we perceive a thing as such and such (through its
sensible qualities), yet we perceive it inevitably as _hoc aliquid_,
_hic_, _et nunc_. But the Universal cannot be perceived by sense; for
it is neither _hic_ nor _nunc_, but _semper et ubique_.[85] Now
demonstrations are all accomplished by means of the Universal, and
demonstrative cognition cannot therefore be had through sensible
perception. If the equality of the three angles of a triangle to two
right angles were a fact directly perceivable by sense, we should
still have looked out for a demonstration thereof: we should have no
proper scientific cognition of it (though some persons contend for
this): for sensible perception gives us only particular cases, and
Cognition or Science proper comes only through knowing the
Universal.[86] If, being on the surface of the moon, we had on any
one occasion seen the earth between us and the sun, we could not have
known from that single observation that such interposition is the
cause universally of eclipses. We cannot directly by sense perceive
the Universal, though sense is the _principium_ of the Universal. By
multiplied observation of sensible particulars, we can hunt out and
elicit the Universal, enunciate it clearly and separately, and make
it serve for demonstration.[87] The Universal is precious, because it
reveals the Cause or [Greek: dio/ti], and is therefore more precious,
not merely than sensible observation, but also than intellectual
conception of the [Greek: o(/ti] only, where the Cause or [Greek:
dio/ti] lies apart, and is derived from a higher genus. Respecting
First Principles or _Summa Genera_, we must speak elsewhere.[88] It
is clear, therefore, that no demonstrable matter can be known,
properly speaking, from direct perception of sense; though there are
cases in which nothing but the impossibility of direct observation
drives us upon seeking for demonstration. Whenever we can get an
adequate number of sensible observations, we can generalize the fact;
and in some instances we may perhaps not seek for any demonstrative
knowledge (_i.e._ to explain it by any higher principle). If we could
see the pores in glass and the light passing through them, we should
learn through many such observations why combustion arises on the
farther side of the glass; each of our observations would have been
separate and individual, but we should by intellect generalize the
result that all the cases fall under the same law.[89]
[Footnote 84: Analyt. Post. I. xxx. p. 87, b. 19-27.]
[Footnote 85: Ibid. xxxi. p. 87, b. 28: [Greek: ei) ga\r kai\ e)/stin
ê( ai)/sthêsis tou= toiou=de kai\ mê\ tou=de/ tinos, a)ll'
ai)stha/nesthai/ ge a)nagkai=on to/de ti kai\ pou= kai\ nu=n.]]
[Footnote 86: Ibid. b. 35: [Greek: dê=lon o(/ti kai\ ei) ê)=n
ai)stha/nesthai to\ tri/gônon o(/ti dusi\n o)rthai=s i)/sas e)/chei
ta\s gôni/as, e)zêtou=men a)\n a)po/deixin, kai\ ou)ch (_ô(/sper
phasi/ tines_) ê)pista/metha; ai)stha/nesthai me\n ga\r a)na/gkê
kath' e(/kaston, ê( d' e)pistê/mê tô=| to\ katho/lou gnôri/zein
e)sti/n.]
Euclid, in the 20th Proposition of his first Book, demonstrates that
any two sides of a triangle are together greater than the third side.
According to Proklus, the Epikureans derided the demonstration of
such a point as absurd; and it seems that some contemporaries of
Aristotle argued in a similar way, judging by the phrase [Greek:
ô(/sper phasi/ tines].]
[Footnote 87: Analyt. Post. I. xxxi. p. 88, a. 2: [Greek: ou) mê\n
a)ll' e)k tou= theôrei=n tou=to polla/kis sumbai=non, to\ katho/lou
a)\n thêreu/santes a)po/deixin ei)/chomen; e)k ga\r tô=n kath'
e(/kasta pleio/nôn to\ katho/lou dê=lon.] Themistius, p. 62, Sp.:
[Greek: a)rchê\ me\n ga\r a)podei/xeôs ai)/sthêsis, kai\ to\
katho/lou e)nnoou=men dia\ to\ polla/kis ai)sthe/sthai.]]
[Footnote 88: Analyt. Post. I. xxxi. p. 88, a. 6: [Greek: to\ de\
katho/lou ti/mion, o(/ti dêloi= to\ ai)/tion; ô(/ste peri\ tô=n
toiou/tôn ê( katho/lou timiôte/ra tô=n ai)sthê/seôn kai\ tê=s
noê/seôs, o(/sôn e(/teron to\ ai)/tion; peri\ de\ tô=n prô/tôn
a)/llos lo/gos.]
By [Greek: ta\ prô=ta], he means the [Greek: a)rchai\] of
Demonstration, which are treated especially in II. xix. See Biese,
Die Philos. des Aristoteles, p. 277.]
[Footnote 89: Analyt. Post. I. xxxi. p. 88, a. 9-17. [Greek: e)/sti
me/ntoi e)/nia a)nago/mena ei)s ai)sthê/seôs e)/kleipsin e)n toi=s
problê/masin; e)/nia ga\r ei) e(ô/rômen, ou)k a)\n e)zêtou=men, ou)ch
ô(s ei)do/tes tô=| o(ra=|n, a)ll' ô(s e)/chontes to\ katho/lou e)k
tou= o(ra=|n.]
The text of this and the succeeding words seems open to doubt, as
well as that of Themistius (p. 63). Waitz in his note (p. 374)
explains the meaning clearly:--"non ita quidem ut ipsa sensuum
perceptio scientiam afferat; sed ita ut quod in singulis accidere
videamus, idem etiam in omnibus accidere coniicientes universe
intelligamus."]
Aristotle next proceeds to refute, at some length, the supposition,
that the _principia_ of all syllogisms are the same. We see at once
that this cannot be so, because some syllogisms are true, others
false. But, besides, though there are indeed a few Axioms essential
to the process of demonstration, and the same in all syllogisms, yet
these are not sufficient of themselves for demonstration. There must
farther be other premisses or matters of evidence--propositions
immediately true (or established by prior demonstrations) belonging
to each branch of Science specially, as distinguished from the
others. Our demonstration relates _to_ these special matters or
premisses, though it is accomplished _out of_ or by means of the
common Axioms.[90]
[Footnote 90: Analyt. Post. I. xxxii. p. 88, a. 18-b. 29. [Greek: ai(
ga\r a)rchai\ dittai/, e)x ô(=n te kai\ peri\ o(\; ai( me\n ou)=n e)x
ô(=n koinai/, ai( de\ peri\ o(/ i)/diai, oi(=on a)rithmo/s,
me/gethos.] Compare xi. p. 77, a. 27. See Barthélemy St. Hilaire,
Plan Général des Derniers Analytiques, p. lxxxi.]
Science or scientific Cognition differs from true Opinion, and the
_cognitum_ from the _opinatum_, herein, that Science is of the
Universal, and through necessary premisses which cannot be otherwise;
while Opinion relates to matters true, yet which at the same time may
possibly be false. The belief in a proposition which is immediate