. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. ked that the independence of the attributes, pair and pair in the second-order classes, does not connote independence for the groups of the third order. Ihope to return to the logic of independence on a future occasion. § 29. Case (2)— (AB)/(U) ^ (BC)/(U) = &a = g = 0 pairs of attributes are now all negatively associated. * 1 propose to use this term in lieu of the more lengthy equality of contraries OF LOGICAL CLASS-FREQUENCIES, ETC. 123 The planes representing conditions of inferior congru
. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. ked that the independence of the attributes, pair and pair in the second-order classes, does not connote independence for the groups of the third order. Ihope to return to the logic of independence on a future occasion. § 29. Case (2)— (AB)/(U) ^ (BC)/(U) = &a = g = 0 pairs of attributes are now all negatively associated. * 1 propose to use this term in lieu of the more lengthy equality of contraries OF LOGICAL CLASS-FREQUENCIES, ETC. 123 The planes representing conditions of inferior congruence are X == 0 y =: 0 Z ::=r, 0 x-= 0-1 y ~ Ol z =: 0-1 The conditions of superior congruence are represented by planes X Y y — z X -{- y — z X + y + ^ X — y -\- z X -\ y ?{- z X — y -\ z 0-1 ~ 0-2 = ^ X + y + z (a) 0-2 (A r, 8)Ol {L v^ 0). but on drawing the figure (fig. 11) it will be seen that the planes (^, y, S, {, t], 6) donot come into account, the surface being an octahedron bounded by (a) (e) and the sixplanes representing conditions of inferior congruence. f r 03-. Fig. n. There are no infinite series of definite inferences but only six special cases,corresponding to the points ABCDEF. They are all of the form or X X y Ol V -- 0= 01 R 2 — 0-1. 124 MR. G. UDNY YULE ON^ THE THEORY OF CONSISTENCE It must be noted that in the type of cases at present under discussion q cannot beless than |thj or 0166 . . , for, by the third-dGgTee conditions of consistence, (AB) + (AC) + (BC) < (A) + (B) + (C) - (U)that is it (AB) ^ (AC) ::= (BC) =: q „ (U) (A) .-. (B) r=: (C) =-- I . (U) For this value of q the planes (a) and (e) fall together into the origin ; the wholesurface, so to speak, closes up.§ 30. Case (3)--- (AB)/(U) rr: (BC)/(U) = &C. rz. 0-3., In this case the pairs of attributes are all positively associated. The first case istherefore intermediate between the second case and the present planes representing the conditions of in
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