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Some men 89. We may consider the analytical expression of those examples of general judgments, which Aristotle discusses in his book on Interpretation. 7TOS ov (TTIV TTOLS ecrriv 7TOS 4(TTiV ov Tras ecrrtv ai/0/9t07ros ov The common universe of these propositions is CCI and the quality considered is St /ccuos. The equations are respectively 1=3. ) iv=S. (2) i = i-S. (3) as expressing a General Proposition. 3 iv denotes all minus some, some being greater than nought which 1 ; equivalent to not all.
4 that . when x Second ; Let if Hence, By a x is is ; is, negative. x= single yx xx =x. x 2 =x. then i x ; x being = i =x = x. 2 x positive. by first part. by Rule of Signs. ; consideration of the figure X it is also evident that if zz^Xj x must be single and positive j x*= and that if x must be single and negative. x 2 =^ix Hence is x, the necessary and sufficient condition for x representing a single character. 119. and if More x is generally single : If x is single and xm =x ; and negative, x=( i) m~l x.
3, it not possible which repre sents a case of FIG. 3. can when The Signs x and-^ 24 that -- Hence indefinite. is the 00 proper reading of _xz is y It is true in the is equivalent to an case of . x 3 that fig. yz=x, z= hence which means z is equivalent to an . y For there are evidently several z s which can satisfy the condition yz=x, although COR. For x and y be kept is x if 00 constant. not in general were necessarily = = i i, . the truth of the equation xy=xz would necessarily involve that of But an inspection of the figure y=z.
Absolutely summing operators from the disc algebra