Thus, you have learnt, and you know, the universal truth, that every
triangle has its three angles equal to two right angles; but you do
not yet know that A B C, D E F, G H I, &c., have their two angles
equal to two right angles; for you have not yet seen any of these
figures, and you do not know that they _are_ triangles. The moment
that you see A B C, or hear what figure it is, you learn at one and
the same time two facts: first, that it is a triangle; next, by
virtue of your previous cognition, that it possesses the
above-mentioned property. You knew this _in a certain way_ or
incompletely before, by having followed the demonstration of the
universal truth, and by thus knowing that _every_ triangle had its
three angles equal to two right angles; but you did not know it
absolutely, being ignorant that A B C was a triangle.[11]
[Footnote 11: Aristot. Analyt. Post. I. i. p. 71, a. 17-b. 8: [Greek:
e)/sti de\ gnôri/zein ta\ me\n pro/teron gnôri/zonta, tô=n de\ kai\
a)/ma lamba/nonta tê\n gnô=sin, oi(=on o(/sa tugcha/nei o)/nta u(po\
to\ katho/lou, ô(=n e)/chei tê\n gnô=sin. o(/ti me\n ga\r pa=n
tri/gônon e)/chei dusi\n o)rthai=s i)/sas, proê/|dei; o(/ti de\ to/de
to\ e)n tô=| ê(mikukli/ô| tri/gôno/n e)stin, a(/ma e)pago/menos
e)gnô/risen.--pri\n d' e)pachthê=nai ê)\ labei=n sullogismo/n,
tro/pon me/n tina i)/sôs phate/on e)pi/stasthai, tro/pon d' a)/llon
ou)/. o(\ ga\r mê\ ê)/|dei ei) e)/stin a(plô=s, tou=to pô=s ê)/|dei
o(/ti du/o o)rtha\s e)/chei a(plô=s? a)lla\ dê=lon ô(s _ô(di\ me\n
e)pi/statai, o(/ti katho/lou e)pi/statai, a(plô=s d' ou)k
e)pi/statai_.--ou)de\n (oi)=mai) kôlu/ei, o(\ mantha/nei, e)/stin ô(s
e)pi/stasthai, e)/sti d' ô(s a)gnoei=n; a)/topon ga\r ou)k ei)
oi)=de/ pôs o(\ mantha/nei, a)ll' ei) ô(di/, oi(=on ê(=| mantha/nei
kai\ ô(/s.] Compare also Anal. Post. I. xxiv. p. 86, a. 23, and
Metaph. A. ii. p. 982, a. 8; Anal. Prior. II. xxi. p. 67, a. 5-b.
10.)
Aristotle reports the solution given by others, but from which he
himself dissented, of the Platonic puzzle. The respondent was asked,
Do you know that every Dyad is even?--Yes. Some Dyad was then
produced, which the respondent did not know to be a Dyad; accordingly
he did not know it to be even. Now the critics alluded to by
Aristotle said that the respondent made a wrong answer; instead of
saying I know every Dyad is even, he ought to have said. Every Dyad
_which I know to be a Dyad_ is even. Aristotle pronounces that this
criticism is incorrect. The respondent knows the conclusion which had
previously been demonstrated to him; and that conclusion was, Every
triangle has its three angles equal to two right angles; it was not,
Every thing _which I know_ to be a triangle has its three angles
equal to two right angles. This last proposition had never been
demonstrated, nor even stated: [Greek: ou)demi/a ga\r pro/tasis
lamba/netai toiau/tê, o(/ti _o(\n su\ oi)=das_ a)rithmo/n, _ê)\ o(\
su\ oi)=das_ eu)thu/grammon, a)lla\ _kata\ panto/s_] (b. 3-5).
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