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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 possible
 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), IDsystems
 in general are not bi-expectational. Another important
property that goes lost in the generalization from CC- to IDsystems
 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 relevant
 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 foundations
 of model building. To emphasize the basic arguments
we shall start from scratch and give some few simple illustra-2]

 Wold - pag. 20