First Attempts to Formalize Some Main Aspects of Psychoanalysis

In this chapter, we have tried to join Lévi-Strauss' ideas with Matte Blanco's ones, in that they have in common from the structuralistic standpoint and psychoanalytically aimed. To this end, we have mainly made use of some notions and methods drawn from elementary mathematics and theoretical physics, in particular the notions of groupoid and symmetry breaking, which are suitable, from a conceptual-analogical viewpoint, to formalize together Lévi-Strauss' and Matte Blanco's ideas. Besides to have mentioned as well other formalizations attempts turned towards psychoanalytic domain, what we have originally reached is that, the typical feature of human consciousness, is that of oppositional dichotomy, a basic distinguishing binary task typical of humans, formalized in the notion of ordering, in which besides falls the temporal dimension, another distinguishing feature of human psyche with its possible different senses. This basic oppositional feature is then in agreement with the unavoidable presence of phallic logic.

Some Basic Elements of Psychoanalysis According to Sigmund Freud

After having briefly but exhaustively recalled the main lines of Freudian psychoanalytic thought, we have discussed a possible psychoanalytic theoretical model for human symbolic function mainly centred on the action of a set of primary psychic mechanisms rejoined around the negative, in its widest sense according to the works of André Green. A chief aspect of this pattern has turned out to be an underlying, irreducible dialecticity that reflects on the one hand, the typical feature of human symbolic function, and, on the other hand, the main outcome of the unavoidable presence of a basic dichotomy formalized the so-called phallic logic, that is, that primordial, ancestral and irreducible logical nucleus inevitably present in the deepest meanders of human psyche as an inborn structure phylogenetically preformed and ontogenetically re-established during the psychic evolution of any human being.

The Role of Unconscious Constructs in Logic and Their Applications to Informatics

Since phallic logic is the ancestral, irreducible and primordial logical nucleus of human psyche, phylogenetically implemented in its deepest unconscious meanders (we hypothesize that structural unconscious, according to Lévi-Strauss and Matte Blanco, springs out during homination process in concomitance with human brain formation and evolution) and afterwards ontogenetically re-enacted individually as a binary logic in the human consciousness, we may consider structural unconscious features as useful from a computational standpoint, so that we have compared this psychoanalytic construct with certain notions of computer sciences, like those of concurrent/parallel processes, synchronous/asynchronous circuits, temporal/modal logics, with the main purpose to formalize the main features of structural unconscious, like timelessness and the presence of logical contradictions. This has been mainly pursued from the standpoint of logic and its various trends.

A Brief Account of Ignacio Matte Blanco Theory and Other Related Psychoanalytic Themes

Besides the crucial work achieved by Claude Lévi-Strauss on the structural aspects of human mind, among which is the so-called structural unconscious (according to Lévi-Strauss) as a main psychic component of human being, also Ignacio Matte Blanco has greatly contributed to determine those structural features of human psyche which could be suitably formalized, reaching to an his own notion of structural unconscious (according to Matte Blanco), which he wants to lay out within Freudian framework. He has also identified other interesting formal aspects of Freudian theory, above all those regarding the central passage from primary process to secondary one. In doing so, he has introduced the notion of symmetry and asymmetry, then rejoined into the most general notion of bi-logic, as the overlying logic system presiding the overall functioning of human psyche. So, in this chapter, we have briefly recalled the main notions of Matte Blanco's psychoanalytic theory.

Foundations of Classical Logic and Its Applications to Informatics

This is a brief chapter recalling the essential elements of classical Boolean logic, its foundations and the first possible relationships with certain basic notions of psychoanalysis, in view of the wider discussions of the next chapters. We have also basically recalled, in a very sketchily fashion, the usual applications of Boolean logic in informatics, which are well-known. This, because the truly important aim of this chapter is simply to prepare the logic ground for a possible psychoanalytic interpretation of the basic elements of Aristotelian logics, to be identified in the unconscious realm, as we shall see better in the next chapters.

An Epistemological Introduction and a General Overview

We mention the main foundations and elements of philosophy of sciences to have a rough yet quite complete view of the epistemological framework in which to lay out our discussion on the possible formalizations attempts of psychoanalysis. In particular, we have highlighted the possible relations between exact/natural sciences and humanities, with a special emphasis on those intertwinements already established between humanities and informatics. We have however chosen to assume a new epistemological stance mainly based on a structuralistic view coming from Claude Lévi-Strauss' pioneering work, which, as reconsidered by the French school of psychoanalysis (above all, Jacques Lacan and Jean Laplanche), has led to identify a universally shared logical structure, irreducible per se, which basically rules human thought; this is the phallic logic (or Ur-logic).

Further Formalization Attempts of Matte Blanco's Theory, of Other Psychoanalytic Ideas, and Their Possible Applications to Informatics

We deepen the relationships between main Matte Blanco's ideas and Aristotelian logic, calling into question also phallic logic, after having premised some discussions on the possible intertwinements between logic and psychoanalysis again. Hence, further possible applications to informatics are also considered. In particular, we have outlined possible, first formalizations attempts of the processes involved in the passage from primary to secondary process according to Freudian theory, from a logical viewpoint, with the involvement of phallus logic and the usual Boolean one. Besides this, we conclude the chapter making mention to the so-called affect logic according to Luc Ciompi, with its relationships with natural sciences, as well as to other formalizations of the main psychoanalytic concepts from the topological and quasi-topological perspective, so reaching to identify possible pathways leading to fuzzy logic and other domains of application.