Mathematical thought in the light of Matte Blanco’s work

Taking into account some basic epistemological considerations on psychoanalysis by Ignacio Matte Blanco, it is possible to deduce some first simple remarks on certain logical aspects of schizophrenic reasoning. Further remarks on mathematical thought are also made in the light of what established, taking into account the comparison with the schizophrenia pattern. Ignacio Matte Blanco (1908-1995) has been a notable psychiatrist and psychoanalyst who has devoted many years of his work in studying the mathematical thought, starting from his many-years experience with schizophrenic patients. His definitive results were published in the celebrated work entitled Unconscious as Infinite Sets: An Essay on Bilogic (1975), which has seen various editions. In this paper, we mainly follow the synthetic work [1] which explain the main psychoanalytic considerations, also from an epistemological viewpoint, on the logic of unconscious deduced by Matte Blanco from his already mentioned fundamental psychiatric experience on schizophrenic patients. First, the preface by Professor Adriano Ossicini to [1] argues on the general epistemological aspects of the psychological sciences, since the work of Matte Blanco is just directed toward these last, that is to say, he tries to establish fundamental relationships between the psychoanalysis and the exact sciences, in particular the mathematics. The work of Matte Blanco1 is an original, interpretative afterthought of the Freudian theory through the methods of elementary logic. He starts from certain Freudian postulates which characterize the dynamical structure of unconscious, namely 1) displacement, 2) condensation, 3) absence of time, 4) substitution of the external reality with the psychic one (literal interpretation of the metaphor) and 5) absence of mutual contradiction among the presentation of the various instincts (or drives). In particular, according to Freud2, the usual ordinary logic rules of conscious thought are no valid for the unconscious since it operates according to another logic system. The former is ruled by a classical, assertoric (i.e., not modal) logic founded on the material implication and having, as fundamental laws, the identity principle, the non-contradiction principle, the bivalent principle, the principle of sufficient reason and the principle of the excluded third (tertium non datur). Instead, according to the studies on schizophrenia made by Matte Blanco, the fundamental principles of the unconscious are the generalization principle3 and the symmetric principle4 (see [1, Chap. I, Section 2]), through which it carries out the primary process (whereas the secondary process concerns the modus operandi of conscious thought). Subsequently, through them, Matte Blanco tries to explain the previous Freudian characteristic principles of unconscious (see [1, Chap. II]). In particular, he re-examines (see [1, Chap. II, Section 2]) the classical Freudian agencies in the light of his 1 Of such a theoretical system, herein we give only a few hints, possibly reserving us to study in-depth the thought of this Author, in its relationships with the mathematics, in further papers. 2 We recall that the above mentioned primary unconscious logic mechanisms were deduced by Freud mainly by two his clinical cases, precisely the case of the Rat Man (of 1909) and that of the Wolf Man (of 1914-1915), thanks to which Freud reached the discovery of the neurotic-obsessive disorders (see [2]). Besides, from the Rat Man paper, Freud established some analogies between the neurosis mechanisms and the primitive mind (see [2]). 3 According to this principle, the unconscious treats a single thing (individual, object, concept, etc) as it were a member, or an element, of a class which contains other members or elements; in turn, this class is considered as a subclass of another more general class, and so forth. 4 According to which, in the realm of unconscious, every relation is symmetric (just in the mathematical sense of this term). 2 principles. According to Matte Blanco, the conscious and unconscious are two different modes of being respect to the psychophysics unity of the human individual, asymmetric and in becoming the first one, symmetric and static the second one: this terminology is due to the fact that the latter is regulated by the above mentioned symmetric principle, contrarily to the first one. Following [1, Chap. III], the symmetry and staticity, characterizing the unconscious, do not allow any finite-dimensional space-time idea as well as any sequential logic reasoning (which relies on asymmetry, as we will see later), so that the asymmetric conscious thought seems to be the result of a sort of ‘symmetry breaking’ of the infinite symmetric unconscious world (recalling, besides, that the symmetry breaking mechanisms, according to the modern physics, are at the basis of any fundamental physical phenomenology from the dynamical viewpoint). Nevertheless, according to Matte Blanco, the conscious becoming cannot do without the being unconscious, so that it may seem to be, in a certain sense, solved the secular vexata quæstio concerning the known ParmenidesHeraclitean dialectic between the logic of being and the logic of becoming (see also [3, Chap. 6, Section 6.2]). Indeed, according to this Author, the pair unconscious-conscious is inseparable. The symmetric thought is unthinkable without the asymmetric one, and the limit between normality and abnormality is given by the degree of reciprocal compenetration of these two modes of being. In [1, Chap. IV], it is discussed the Matte Blanco’s notion of unconscious as infinite set, resuming the distinction between set and class, as typical of formal set theory. The unconscious does not distinguish between partial and total object and, moreover, each element of any set is conceived as having only human qualities (anthropomorphization attempts). This last property is a fundamental epistemological assumption common to many theory of the history of human thought, even if Matte Blanco deduced it from psychoanalytic considerations. In [1, Chap. IV], it is also discussed the notion of infinite set in Mathematics, analogically compared with the symmetric mode of being of the unconscious, precisely with its property of indistinguishability between the part and the whole, in the sense that they both have the same cardinality, this just being the first notion of infinite set according to R. Dedekind (that, inter alia, has considered the notion of infinite set as a tool to explain the world of the human thought – see [1, Chap. IV, pp. 47-48, footnote 3]). Again according to Matte Blanco, many other mathematical concepts (like that of limit process) have their origins by the attempts to asymmetrically explain the properties of the symmetric one. In [1, Chap. V], it is explained some useful concepts about consciousness according to Matte Blanco. Exactly, it cannot do without the asymmetric thought, in the sense that a conscious act consists in a continuous setting-up of asymmetric relations around the cathexis object (that is to say, the not-well defined thing invested by the human desire). The main consciousness’ activity is essentially analytic because it fundamentally subdivides every analyzed object into its constitutive components or parts (partial objects), unlike by an emotion, or an affection, which is a globally conceived symmetric sentiment5. Nevertheless, the symmetric and asymmetric modes are inseparable amongst them, because an entirely symmetric mode is typical of any state of loss of consciousness whereas a complete asymmetric mode is also impossible since it would imply a total absence of any cathexis object, which is impossible for each human being. Every normal psychic state varies within an interval (or range) including a right mixing of both these modes, but whose ratio is continuously changing. Moreover, if we consider, for instance, a mathematical argument – hence a full asymmetric thought, at least in the involved theoretical principles and at the end of his formulation – then there is always an unavoidable emotional involvement which may be described as an involvement of asymmetrical type6. Therefore, albeit a certain human result – like a mathematical proof – may seem to be the 5 It will also be interesting to discuss the essential difference among emotions, sentiments and affects – as, for instance, made by the notable recent work of the neuroscientist Antonio R. Damasio – and their possible role in Mathematics (see also next footnote), and this also taking into account other remarkable works of Matte-Blanco himself on the same subject. 6 This phenomenon can be identified in many historical cases of fundamental creative innovation: for instance, the celebrated Einstein’s (as well as the main Riemannian) ideas on space-time, have been mainly based, at least in their initial theoretical