Ludics and Anti-Realism

In this chapter we try to give a flavour of Ludics, a frame developed by Jean-Yves Girard on the basis of Linear Logic (cf [8, 9, 10]). Ludics seems to be very on purpose in a book devoted to logics and anti-realism because it makes no assumptions on the existence of the external world, in the sense that it does not require any ”model-theoretic” assumption (like the evidence of a concept of ”Truth”) in order to enjoy good properties, like a special form of completeness. On the technical side, it may be seen as a new kind of ”semantics” for computer science : proofs (or designs as we shall see later on) may be seen as interacting processes, a view which is strongly relevant in today technology : computers do not have access to an external reality by means of a relation like ”denotation”, and this remark may be extended to the case of our minds which do not either access to such a ”reality” by some direct relation, like it is wrongly assumed in denotational semantics. On the philosophical side, it is the first radical attack against the traditional dualism which opposes the syntactic aspect of logics (the ”language”) to the denotational one (”the world”), or in other words : proof theory to model theory. One of the most famous claims made by Girard is his slogan according to which ”the meaning of rules is inside the rules themselves”. Of course, said like that, it seems very elliptic. In fact what Girard puts in evidence is the geometrical structure underlying logic, so that the meaning of rules is ”to be found in the well hidden geometrical structure of the rules themselves”. Some of the main geometrical properties a system can have are symmetry and orthogonality. To begin, we shall refer mainly to the first one because it happens that it plays an