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48 Jean Piaget
sciences, the search for causality has three stages, only the last two of which
throw light on explanation :
a) First comes the establishment of facts and laws, although these are not
two separate problems, for a fact is only a relation that can be repeated. The
establishment of a law is therefore nothing more than the recognition of the
generality of the fact, and of itself does not constitute an explanation. It is
true that people often refer - though incorrectly - to ‘causal laws’ in the sense
of regular successions in time; but this so-called causal law is nothing but a
law which, like any other, provides a basis for the search for causality; in itself it
provides no explanation. Moreover, any law makes forecasting possible simply
because it expresses statistical or completely determined regularity; but the
forecasting is merely an anticipation of a new fact in accordance with the
general applicability of the law in question, and it, too, provides no explanation;
it merely tells us that the fact is generally true. On the other hand, while the
criterion of causality is the presence of necessary and sufficient conditions,
there is an intermediate stage, within the sphere of laws, which leads to these
relationships of necessity - the stage of functional dependence y = f(x) or the
determination of the variants of y in terms of the variants of x. In the case of
multiple variants, therefore, we may legitimately acknowledge that there is a
certain degree of causality in the r61e ascribed to the determining factors.
b) The second stage begins with this establishment of relationships - that is,
with the deduction of laws. The difference between the necessity proper to
explanation and the generality that is characteristic of laws as such is that the
generality relates only to facts (no matter how complex are the inductive methods
or, in other words, the probabilist or statistical methods that enable it to be
established), whereas necessity is characteristic of logical or mathematical links ;
therefore, if we try to deduce laws instead of merely recognizing them, we are
introducing an element of necessity which brings us nearer to explanation.
There are, however, two kinds of deduction. One is merely inclusive or syl-
logistic, and is based solely on the relationship of ‘all’ and ‘some’; from this
sort of standpoint, a law A (for example, the law of perceptive or optico-geo-
metric illusion as in Muller-Lyer’s figure) may be deduced from a law B (the
law of all optico-geometric illusions belonging to the category of ‘field effects’
or what we have called relative centrations), simply because this law B is more
general. In this case we are not going beyond the field of laws, and the deduc-
tion is nothing but a generalization, which brings us nearer to the explanation, but
simply moves the problem further away. The other form of deduction, the only
one that is explanatory, may be called constructive. It consists in introducing
laws into a mathematical structure which has its own norms of composition, not
by a simple interlocking process, as in a syllogism, but as a result of more or less
complex transformations - for instance, a ‘network‘ structure, a ‘group’ struc-
ture, or a loop system (regulations or feedbacks) and so on. In this case, the
necessity for transformations joins the generality of laws and moves towards
explanation.
c) Even a constructive logico-mathematical deduction, however, is only
logical or mathematical, and does not deal with facts, except by means of a