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552 Raymond Boudon
The notion of model. The present considerations wil be limited to the concept
of the mathematical model.
A model in this sense of the term is always a hypothetical-deductive theory.
In other words, it is a set of premises or axioms from which a set of consequences
is deduced.
In certain cases, these consequences may be checked by observation and in
that case the model is verifiable. But this property of verifiability, or more pre-
cisely falsifiability (since, as Popper has stressed, a universal proposition can be
proved false, but never proved true), is not indispensable, for there are models
which are not falsifiable.
This point gives us an initial distinction between the notion of the model and
that of the theory (in the sense in which the natural sciences use the latter word).
In effect, many examples can be cited of non-verifiable models such as the
multi-factorial analysis in psychology which always produces a solution, what-
ever the data available, the solution itself being rejected or accepted on criteria
other than that of congruence with the observed situation, which, by definition,
is always achieved. Similarly, a multitude of models in mathematical economics
could be cited where it is impossible to decide on unambiguous criteria whether
the model is true or false. Take for instance the models of Samuelson, Goodwin
or Phillips on economic cycle theory. These models show that, for certain hy-
potheses as to the immediate or deferred linkages between the global economic
quantities (investments, savings, consumption, etc.) and for certain classes of
value of the models’ parameters, the global quantities mentioned manifest
oscillations. Certain of these models can then be judged preferable to others
to the extent that they will reproduce more faithfully the general characteristics
of the real cycles. Thus Goodwin’s model, as against the Samuelson-Hicks
theory, has the advantage of giving theoretical cycles where the rising phase is
longer than the falling, as in the real cycles. The first will therefore be preferred
to the second. But it cannot be said that we are really in a position to verify
this type of model (show it to be either false or not false); in short, we can say
that Goodwin’s model is more ‘realistic’ than the Samuelson-Hicks model, but
we cannot say that it is more veridical.
It could easily be shown that many models are universally recognized to be
useful, although they are not strictly theories in the usual sense, meaning that no
criterion of falsifiability can be used directly on them, or that they cannot be
made the subject of an experimentum crucis. But this is not to say that they are
thereby reduced to the status of arbitrary constructs. No experimentum crucis
can be imagined which could invalidate, for example, game ‘theory’ or phonolog-
ical classification. Similarly, no falsifiability criterion can be worked out from
the psychoanalytic ‘theory’ of personality. To conclude that such ‘theories’ are
meaningless would run counter to the weight of opinion. What it does, on the
contrary, seem important to bring out is that these examples suggest the neces-
sity of rethinking the whole question of inductive logic in the social and human
sciences, since the logical principles inherited from the natural sciences, as de-
scribed for example by Karl Popper in his famous Logik der Forschung, are of no
service whatever for enabling us to understand why unverifiable models or