Universal vs. particular reasoning: a study with neuroimaging techniques

In the present talk I intend to discuss the validity of a model (or better, a class of models) of learning and deuterolearning processes in cognitive systems, constructed combining set-theoretical and proof-theoretical concepts. This class of models is based on ideas coming from different disciplines: 1) Gregory Bateson’s systemic-relational theory of learning and change; 2) G ̈odel’s incompleteness theorem, and in particular one of foundational consequences of the Incompleteness theorems, so-called thesis of incompletability of mathematics; 3) The modelization of cognitive systems by means of deductive systems, where a deductive system is defined (in Hilbert, Gentzen or algebraic style) by axioms and rules of inference. This model allows to define in a precise way the distinction between almost three levels of learning process: (1) the level of solving a single problem, (2) the level solving a class of problems and (3) the level of the creation of a new class of problems (and of related rules of solution). While the passage from (1) to (2) is generally continuous, the passage from (2) to (3) involves a discontinuity (e.g. change of character in a single person, or paradigmatic change in a scientific community). Definition will be given of a class of models in which a non-well-founded set or a paradoxical sentence are interpreted as undecidable statements of some deductive system, and the learning process, or the psychologicalchange process, is defined in term of a sequence of deductive systems, obtained by a process of generalization of the consequence relations of the systems involved. COGNITION AND SEMIOTIC ARTIFACTS: SITUATEDNESS IN PEIRCEAN COGNITIVE SEMIOTICS Pedro Atã and Joao Queiroz According to Peirce’s semiotic theory of mind, cognitive process fundamentally depend on sign process, in a sense that diverges radically from computationalism. For Peirce, thinking involves the process of sign action. Against any form of internalism, Peirce can be considered a precursor of situated mind and distributed cognition thesis. But differently from the anti-cartesianism defended by some embodied-situated cognitive science, which is predominantly anti-representationalist, as recently explored in a Merleau-Pontyan, Heidegerian, or a Gibsonian trend, for Peirce, mind is semiosis in a dialogical -hence communicational -materially embodied form, and cognition is the development of available semiotic material artifacts in which it is embodied as a power to produce interpretants. It takes the form of development of semiotic artifacts, such as writing tools, instruments of observation, notational systems, languages, and so forth. Our approach here centers on the consideration of relevant properties and aspects of Peirce’s concept of mind as semiosis, with special attention to the material/formal/structural properties of signs. In our argumentation, Peirce’s semiotic theory of mind is a branch with important implications and unprecedent consequences – it is at the same time situated, embodied, and representationalist, with focus on the properties of dependence of the material available in the semiotic environment. In a certain sense, it is closer to the ideas of wide computationalism, but does not restrict the inferences to transformation processes upon structured signs in a declarative symbolic systems. Our aim here is to examine the relationship between the notion of abductive inference and iconic semiotic artifacts in the context of his semiotic theory of mind. In order properly to develop our argument, we introduce: (i) the basic characteristics of abduction, (ii) the concept of semiosis and the morphological variety of semiotic processes, (iii) Peirce’s notion of distributed cognition thesis. The reader should bear in mind that our argument borders on recent developments in situated cognition and extended mind approach. MODELING DIGITAL ECOSYSTEMS AS SUPER-CONSTRUCTIONS AND THE ROLE OF CHANCE-SEEKING.