376 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
Clearly, there exists an infinity of different mathematical 
functions which in a restricted field give analogous results, 
and this characteristic simply derives from the nature of things. 
The point is that everything takes place as if the theory 
presented and the model which illustrates that theory were cor- 
rect. As far as I know no other theory, no other model, have 
aver been put forward in order to explain the same facts. 
It may therefore reasonably be suggested that the theory 
and the model presented here can be accepted and used, at least 
as working tools, so long as no alternative theory or model is 
advanced which leads to results which concord still better with 
the real situation. 
In any event, the theory and the model which have been 
discussed here have the advantages that they represent ana- 
lytical tools and that they oblige the economist to reflect on a 
large number of issues which hitherto have been insufficiently 
studied, not to say completely neglected (1). 
Finally, it may be observed that every theory has a twin 
aim; on the one hand to describe and explain reality (2), but 
at the same time to constitute a guide to efficient action. For 
a given degree of approximation, the best theory at any given 
moment is the one which fulfils the condition of being the most 
convenient, or in other words, the simplest of all those which 
represent reality with that degree of approximation. If this 
criterion be admitted, and personally I know of no other (3, 
the theory given here has the double advantage of being on 
the one hand very simple, but also of describing and explain- 
ing reality, so far as it can be comprehended with the infor- 
mation presently available to us, i.e. of being compatible with 
observed facts and simultaneously establishing coherent and 
simple links between these facts. 
(') Doubtless precisely because they were too difficult. 
(3) In other words, to find relationships between the different aspects 
of reality, expressing the most complex in terms of the most simple. 
(3) See for instance HENRI POINCARE. The Value of Science (Flammarion) 
:1] Allais - pag. 1R0