42 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
(54) 
E(vlz)=f(e(2), 2) 
Thanks to the isomorphism here briefly touched upon, eo ipso 
predictors are a most convenient tool for the analysis of cause- 
effect relationships. Since behavioural relations are cause-effect 
relationships, this last comment leads us to the second point, 
namely: 
(2) The rationale of making use of eo ipso predictors in 
the specification of behavioural relations. The main argument 
ts, of course, that unless a behavioural relation makes an eo 
1pso predictor it cannot provide forecasts that are unbiased in 
the sense of expected or average values. This point is brought 
in relief by (47) and (50), and the reader will have no diffi- 
culty to supply any number of similar illustrations. 
(3) Eo ipso predictors in multipurpose model building. 
Speaking broadly, the transition from deterministic to stochastic 
models makes no trouble, in principle, if the model involves 
just one relation of potential use for forecasting; all that is 
needed is to design the relation so as to make an eo ipso pre- 
dictor. It is quite another matter that the relation can be a 
bad forecasting device because of specification errors, but in 
this respect there is no difference between deterministic rela- 
tions and eo ipso predictors. The trouble begins when the 
model involves two or more predictive relations, inasmuch as 
the corresponding eo ipso predictors may be incompatible. It 
is important to note that the ensuing questions of compatibility 
or noncompatibility belong to the pure probability theory; no 
empirical or substance-matter considerations enter into these 
matters. Such is the situation in (48)-(49), where the inference 
from p to d and from d to p cannot be obtained by way of 
two eo ipso predictors that form a pair of inverse functions. 
This nonexistence theorem in probability theory was one of 
the cornerstones when KARL Pearson laid the foundations of 
correlation and regression analysis, but its implications for 
causal analysis by regression methods remained obscure for 
2] Wold - pag. 28