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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2° 
of a VR-system, And CC-systems, too, are of general scope 
in the same sense. Here the substitutional design referred to 
in 1.2 (2), is the salient point. Thanks to this design it is pos- 
sible to carry through the specifications (13) of the primary 
form and (17) of the reduced form in terms of conditional 
expectations, although this bi-expectational specification of 
CC-systems might seem highly restrictive at first sight. At the 
same time the substitutional design marks the limit beyond 
which the generalization from VR-systems in the direction of 
CC- and ID-systems cannot be pushed without losing the 
bi-expectational property. Hence, as noted in 1.4 (2), ID- 
systems in general are not bi-expectational. Another important 
property that goes lost in the generalization from CC- to ID- 
systems is the optimality with regard to minimum-delay of 
information. 
2. 
ENDS AND MEANS IN THE TRANSITION FROM DETERMINISTIC 
TO STOCHASTIC APPROACHES 
Whe shall in this section consider a number of situations 
that are special instances of the universal mathematical rule 
that generalization of a theoretical model is always accompanied 
by attenuation of inference from the model. The theorems rele- 
vant to the argument of this section belong to the foundations 
of probability theory; thus (50) goes back to the beginnings of 
correlation and regression analysis around 1900, and the origin 
of (41) is still more remote. 
2.1. A review of basic notions. 
The transition from deterministic to stochastic specification 
is a radical generalization of a theoretical model, and the 
ensuing attenuation of inference goes down to the very foun- 
dations of model building. To emphasize the basic arguments 
we shall start from scratch and give some few simple illustra- 
2] Wold - pag. 20