(2) If we have to show that E is not D by means of the premisses,
all D is C; no E, or not all E, is C; then the middle will never
fall beyond E, and E is the subject of which D is to be denied in
the conclusion.
(3) In the third figure the middle will never fall beyond the limits
of the subject and the attribute denied of it.
24
Since demonstrations may be either commensurately universal or
particular, and either affirmative or negative; the question arises,
which form is the better? And the same question may be put in regard
to so-called 'direct' demonstration and reductio ad impossibile. Let
us first examine the commensurately universal and the particular
forms, and when we have cleared up this problem proceed to discuss
'direct' demonstration and reductio ad impossibile.
The following considerations might lead some minds to prefer
particular demonstration.
(1) The superior demonstration is the demonstration which gives us
greater knowledge (for this is the ideal of demonstration), and we
have greater knowledge of a particular individual when we know it in
itself than when we know it through something else; e.
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