Reasoning is Necessarily Informal,
		     or: A Critique of Formalisation

	           Baudouin Le Charlier, UCL, Belgium
		Pierre Flener, Uppsala University, Sweden

After reviewing a few key points about  first-order  logic, we try and show
why formal languages cannot serve to usefully  express problem  statements:
the  poverty of their  concepts  and  notations  entails  that  practically
nothing can be expressed in them, and that one can only  represent  in them
the intuitive  assertions and concepts  according to necessarily  arbitrary
and unformalisable  conventions.  We defend the idea that the best language
for expressing problem statements is natural language augmented with ad hoc
notations  (note that the usual language of  mathematics  is of this kind).
Next, we discuss the  problem of  paradoxes  and refute the claim that they
are a reason for  justifying  the  recourse to  formalisation.  Finally, we
show why the  rigour of  reasoning  cannot  be  founded  on  formal  logic:
justifying the validity of a reasoning process by the existence of a formal
proof that ``details'' it amounts to doing another  reasoning  process that
is longer and more  complicated  than the former  and  therefore  even more
error-prone.  There is thus no absolute  means of ensuring the  validity of
reasoning  processes  and one has to try and learn how not to make mistakes
while reasoning.