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266 Jean Piaget
that among any homogeneous population there was a ‘normal’ distribution of
intelligence and aptitude, rather like sizes. This was a realistic and not a nom-
inalist point of view; but conventionalism comes into its own again, without
it always being realized, in the sense that, for lack of objective unity of measure
(see the ‘Introduction’, section 4, n B), one is obviously (psychological ex-
perience offering only relations of order) bound to choose an arbitrary metrics
and it is then always possible to find somehow the presupposed and desired
‘normal’ distribution. The best proof that the ‘convenient idiom’ for describing
‘observables’ is not enough is that now the question is being asked what takes
place under ordinal observables and partly arbitrary measurements, so as to
establish whether in ‘reality’ the distribution is normal or not. A number of
studies on measurement as such have been carried out, but in 1963 Burtz3 col-
lected specifically psychological indices that tended to show that in the distri-
bution of levels of intelligence the lower end of the curve was probably more
stretched out than the other end.
As regards models that can be explained (a ‘normal’ curve also involves
searching for its own explanation, and the same applies even more so to more or
less systematic exceptions to it), the general tendency, is, of course, not to keep
to patterns that are regarded as merely convenient, if not for reasons of diplo-
matic presentation, and for the reasons given in section z there is a very
rapid tendency to pass on to causal interpretations.
~n.
If we then examine from this point of view the partblayed by abstract models,
we are bound to see that it has always involved furthering the advancement
of structuralism, and exactly to the extent to which it was attempted to make the
model coincide with the real processes of the mental life of behaviour of the
subject. And yet there are models which in theory could have been atomistic in
character, such as factorial models and certain stochastic models.
Factorial analysis originated from simple methods of calculation -correlations
of correlations or tetrad-differences - and initially its aim was merely to bring
out ‘factors’ that elude direct qualitative analysis. But in the first place everyone
knows that it was not always immediately understood what a given ‘factor’ that
had thus been found corresponded to or meant, like the well-known G factor or
‘general intelligence’ factor which was in turn taken to express intelligence itself
or to be a calculated artefact. Further, it is fairly clear that the meaning of
factors partly depends on the tests that are chosen and that if, for example,
spatial factors are linked to perceptive and not numerical factors, this may be
due to the choice of figurative rather than operative tests, which does not make
the facts uninteresting, but shows that they are dependent on prior classifica-
tions. It was then attempted to construct ‘hierarchies of factors’ or systems that
involved overall classifications and bore out the findings that were made. This
marked a tendency towards a certain form of structuralism.
There can be all kinds of stochastic models, some of which may at first seem
rather atomistic. But once we want to determine what they mean from the be-
haviour angle, we are bound to turn to an epistemology of probability - a
priori probabilities, frequencies and subjective probability, and especially the