Grundzüge der Sozialpolitik

Répertoire des administrateurs & commissaires de société, des banques, banquiers et agents de change de France et de Belgique

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Monograph

Identifikator:: 876559135

URN:: urn:nbn:de:zbw-retromon-1676

Document type:: Monograph

Author:: Borght, Richard van der http://d-nb.info/gnd/11625274X

Title:: Grundzüge der Sozialpolitik

Place of publication:: Leipzig

Publisher:: Verlag von C. L. Hirschfeld

Year of publication:: 1904

Scope:: 1 Online-Ressource (XII, 566 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: I.Teil. Allegeines

Collection:: Economics Books

IL.—CONSISTENCE. 21 possible. The conditions (1) and (2) therefore give all the con- ditions of consistence for the case of two attributes, conditions of an extremely simple and obvious kind. 11. Now consider the case of three attributes. There are eight ultimate frequencies. Expanding the ultimate in terms of the positive frequencies, and expressing the condition that each expansion is not less than zero, we have— or the frequency given below will Le negative. (a) (4BC)<0 4B0C)) L(4R) + (40) - (4) (4/3) FHS 2 (In) + = a (45) (4.3) | 4) C30 (480) a) FO) (aBC) B) P(AB)+(4C)+ (BC) - (4) - (B)- (C) +N (afy) These, again, are not conditions of a new form. We leave it as an exercise for the student to show that they may be derived from (1) (a) and (1) (4) by specifying the universe in turn as BC, By, 3C, and By. The two conditions holding in four universes give the eight inequalities above. 12. As in the last case, however, these conditions will be im- possible to fulfil if any one of the major limits (¢)—(%) be less than any one of the minor limits (a)-(d). The values on the right must be such as to make no major limit less than a minor. There are four major and four minor limits, or sixteen compari- sons in all to be made. But twelve of these, the student will find, only lead back to conditions of the form (2) for (4B), (40), and (BC) respectively. The four comparisons of expansions due to contrary frequencies ( (a) and (&), (6) and (g), (¢) and (f), (d) and (e) ) alone lead to new conditions, viz.— (a) (4B) + gio +(BC) 4(4) +(B) +(C) - N) (6) (4B)+(-.)=(LC)}(4) 4) (e) (AB)—(A0)+(LC)3(B) (d) - (4B) + (40) + (BC) » (C) 13. These are conditions of a wholly new type, not derivable in any way from those given under (1) and (2). They are con- ditions for the consistence of the second-order frequencies with each other, whilst the inequalities of the form (2) are only conditions for the consistence of the second-order frequencies with those of lower orders. Given any two of the second-order frequencies, e.g. Q.

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