. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. = 0-4 X + y -{- z — 0-20 {a) X -\- y — s — 035 (^) X — y -\- z — 040 (r) X -{• y -\- z — 045 (8). The form of the surface is shown in fig, 4a opposite, and in figs. 46 and 4(3from photographs of a model. All the edges of the tetrahedron are now truncatedby planes representing the conditions of inferior congruence. No infinite series ofdefinite inferences are left, but only four special cases corresponding to the pointsKEGF of the figure :-— (1) X (2) y (3) y (4) X Given. 0-35 . Z 0-35 z 0 z 0-35 z
. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. = 0-4 X + y -{- z — 0-20 {a) X -\- y — s — 035 (^) X — y -\- z — 040 (r) X -{• y -\- z — 045 (8). The form of the surface is shown in fig, 4a opposite, and in figs. 46 and 4(3from photographs of a model. All the edges of the tetrahedron are now truncatedby planes representing the conditions of inferior congruence. No infinite series ofdefinite inferences are left, but only four special cases corresponding to the pointsKEGF of the figure :-— (1) X (2) y (3) y (4) X Given. 0-35 . Z 0-35 z 0 z 0-35 z 0-4 0 0-4 0 — 0-35 X— 0 X = 0 u 0. The corresponding syllogisms are- (1.) All As are B, all Bs are 0, .*. all As are C. (2.) All As are C, no Cs are B, . \ no As are B. (3.) (4.) All Bs are C, no Cs are A,no Bs are As are B,no Bs are C,no As are C. § 21. In extreme cases the congruence-surface presents the appearance of a rightsix-face with its corners truncated rather than a tetrahedron with its edges cut down. OF LOGICAL CLASS-FEEQUENOIES, ETC. 115 03. 03 \. J?
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