For one
does not know that triangle as such has this property, nor even that
'all' triangles have it-unless 'all' means 'each taken singly': if
'all' means 'as a whole class', then, though there be none in which
one does not recognize this property, one does not know it of 'all
triangles'.
When, then, does our knowledge fail of commensurate universality,
and when it is unqualified knowledge? If triangle be identical in
essence with equilateral, i.e. with each or all equilaterals, then
clearly we have unqualified knowledge: if on the other hand it be not,
and the attribute belongs to equilateral qua triangle; then our
knowledge fails of commensurate universality. 'But', it will be asked,
'does this attribute belong to the subject of which it has been
demonstrated qua triangle or qua isosceles? What is the point at which
the subject. to which it belongs is primary? (i.e. to what subject can
it be demonstrated as belonging commensurately and universally?)'
Clearly this point is the first term in which it is found to inhere as
the elimination of inferior differentiae proceeds. Thus the angles
of a brazen isosceles triangle are equal to two right angles: but
eliminate brazen and isosceles and the attribute remains.
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