Geometry of Interaction V: Logic in the hyperfinite factor

Geometry of Interaction (GoI) reacts against the absence of any satisfactory explanation for logic. The usual one is that of a symbolic calculus of truth values, which supposes that truth values preexist and formulas as well. This was later improved into a symbolic calculus of category-theoretic diagrams, what is still unsatisfactory: since this calculus rests upon an oriented rewriting, one side is more equal, more commutative, than the other. The aim of GoI is therefore to find a space where truth, commuting diagrams, etc. are no longer primitive and where dynamical processes (proof-search, rewriting, a.k.a. normalisation) are primitive: let us call such processes projects (or designs). The curious preexistence of formulas makes logic dependent over ad hoc syntactical choices: most convenient to write PhDs, but at the same time a severe morphological flaw. GoI should thus define formulas independently of any language: let us call such language-free formulas behaviours or conducts. We thus bestow a central status to deduction from which everything (esp. syntax) should proceed, whence the syntax-free approach, projects and behaviours. This is Philosophy of Science, but not the usual sterile and incompetent comment on (or rather: against) living science we are accustomed to.