Logic of information theorizes a new approach to logic leading to momentous results. Some of them are sketched in the present abstract, whose odd numeration follows from the opportunity of preserving easy references to the chapters where the respective themes are treated.
1. Contemporary logic is seriously ill. The soundness of an approach to logic depends also on the adequateness of the language. The current languages are affected by two consequential lacks (§2 and §17).
2. The first lack concerns the scholastic distinction between supposition materialis and supposition formalis that is the distinction between use and mention of an expression. Such a distinction is too rough, because there are two and non-interchangeable modalities of mention: the syntactical and the semantic ones. Once these two modalities are formally admitted through the introduction of a second diacritical symbol, new horizons open out.
4. An immediate application of this stronger language allows us to recognize and to rule formally three kinds of definitions, all of them belonging to our everyday practice.
5. Another application analyses the objects of truth. To ask ourselves if they are sentences or propositions is is not a pseudo-problem. Only propositions can be the very objects of truth; two independent arguments prove that identifying such objects with sentences contradicts the usual meaning of "true";
7. The informational approach to logic is formalized by a powerful and elegant system of axioms.
8. Truth predicates are intrinsically relational: a piece of information can be true (or false et cetera) only with respect to a statute, that is to an informational structure assumed as a term of comparison. Arelational formulations appeal implicitly to some privileged statute.
15. A free variable is a sign adducing an incomplete information; it is fixed by filling that incompleteness. As such, no free variable can be fixed by an antecedent where the same variable continues occurring free.
16. Indexical terms act as variables. Reflexivity is a peculiar sort of indexicality.
17. The second lack is that symbolic languages, contrary to natural ones, do not possess reflexive variables. Current symbolic languages express reflexivity by repeating in the predicate the same term of the subject, but this technique entails the impossibility of symbolizing reflexive predicates singularly considered.
18. Logical paradoxes are born by a misrecognized indexicality. Overcoming such a fault is achieving their general solution and rejecting apagoges grounded upon defective dilemmas.
19. Indexicality concerns functions too. A formally strict theorization of the matter leads to the solution of some disconcerting results, as for instance Schoenfinkel's reduction.
20. Goedel's proof is vitiated by a formal and substantial mistake.