Main trends of research in the social and human ... - unesdoc - Unesco

General problems of interdisciplinary research and common mechanisms 487
psychological ‘subject’ as a matter of principle, having become a ‘logic without
subject’ so that the attributes it has mapped out for itself forbid it even to inquire
whether ‘subjects without logic’ even exist.
Yet the internal evolution of logic itself as well as the external evolution of
branches outside its field compel us to note the existence of numerous centrifu-
gal trends which inevitably give rise to problems of interdisciplinary connex-
ions.
The iirst of these trends arose from the discovery by K. Goedel in 1931 of
the limits of formalisation. In a series of celebrated theorems Goedel showed
that it is impossible for a theory of a certain richness (e.g. elementary as opposed
to transfinite arithmetic) to demonstrate its own non-contradiction solely by
its own means and by logical means weaker than those it implies; in this way it
must of necessity arrive at certain undecidable propositions, and in order to
decide these it is necessary to resort to ‘stronger’ means (e.g. transfinite arith-
metic). In other words logic is no longer an edifice resting on its base but a
construct whose consistency depends on higher levels which are never completed
because each in turn has need of the next. But as soon as there is a construct we
must ask: a construct of what and by whom? And if there are limits to formali-
sation we must ask why, to which J. Ladribre, for instance, replies by invoking
the impossibility for the subject to embrace in a single actual field the totality of
its possible operations (which in fact is an appeal to psychology to produce an
epistemology of logic; see below).
Another and equally remarkable internal trend is the concern shown by
certain logicians for establishing a connexion between formal logic and certain
systems of norms or rules used by subjects collectively. We have already quoted
(section 4) works like those by Weinberger, etc., which apply formal logic to
connexions between norms posed in the imperative. But mention should be
made especially of the important work of the Belgian logician Ch. Perelman in
the field of argumentation. Perelman sets out to study from a logical point of
view the many situations where a partner seeks to act upon another not through
sentiment or extrinsic arguments of authority, etc., that is to say not through
those sophisms which have so wrongly been grouped under the name of ‘logic
of sentiments’ (for the true logic of sentiments is morality, with which Perelman
is beginning to concern himself), but through an argumentation which is logi-
cally coherent although directed and organised so as to convince. Avast body
of works has appeared on this subject20 among which we find in particular a
study by L. Apostel on the presuppositions of such a theory and more particu-
larly on the relations between logical operations and the general co-ordination
of actions (Apostel shows in this respect the kinship between Perelman’s analyses
and the writer’s own research on the development of logical structures proceed-
ing from action). Starting from the theory of argumentation, Perelman has
naturally been led to study the logic of legal structures, and a very active collab-
oration on this issue between jurists and logicians has been established under
his direction and has already yielded a number of studies.
A third trend common to certain logicians consists in taking an interest in
psychology, not of course in order to find in it the internal foundations of logic