Intentionality and Foundations of Logic: a New Approach to Neurocomputation

Abstract

In this work we start from the idea that intentionality is the chief characteristic of intelligent behavior, both cognitive and deliberative. Investigating the ''originality of intelligent life'' from this standpoint means investigating ''intentional behavior'' in living organisms. In this work, we ask epistemological questions involved in making the intentional behavior the object of physical and mathematical inquiry. We show that the subjective component of intentionality can never become object of scientific inquiry, as related to self-consciousness. On the other hand, the inquiry on objective physical and logical components of intentional acts is central to scientific inquiry. Such inquiry concerns logical and semantic questions, like reference and truth of logical symbols constituted as such, as well as their relationship to the ''complexity'' of brain networking. These suggestions concern cognitive neuroscience and computability theory, so to constitute one of the most intriguing intellectual challenges of our age. Such metalogical inquiry suggests indeed some hypotheses about the amazing ''parallelism'', ''plasticity'' and ''storing capacity'' that mammalian and ever human brains might exhibit. Such properties, despite neurons are over five orders of magnitude slower than microchips, make biological neural nets much more efficient than artificial ones even in execution of simple cognitive and behavioral tasks.

Computing Nature – A Network of Networks of Concurrent Information Processes

“…There are authors such as Clark who maintain that mental representation are material [36] while others like Speaks think that thought processes use conventional linguistic symbols [37]. The question of digital representation involves the "problem of physical computation" [38] as well as the necessity of the notion of representation [39] so that we only have the problem of how to intend the very notion of representation [40,41]. But, there is also the possibility of understanding computation as a purely physical procedure where physical objects are symbols processed by physical laws on different levels of organization that include "every natural process" in a "computing universe" [42].…”

Intelligence and Reference

“…Two classes of logical symbols with their relations constituted via a common causal relation from the denoted object! It is evident that such a solution of the reference problem can be implemented only in a NC model where <v,w,z> can be interpreted as cognitive agents, particularly as (pseudo-)cycles of the same chaotic attractor, as we and others demonstrated elsewhere (See [30,18,31,32]; [33,34,35]). …”

“…Now in AC, any formal theory of reference and truth is faced with the Gödelian limits making impossible a recursive procedure of satisfaction in a semantically closed formal language. What we emphasized also elsewhere [18,19,20], as the core of the reference problem is that such a recursive procedure for being complete would imply the solution of the coding problem through a diagonalization procedure; that is, the solution of the so-called "Gödel numbering" problem. In computational terms, the impossibility of solving the coding problem through a diagonalization procedure means that no TM can constitute by itself the "basic symbols", the primitives, of its own computations.…”

Geometry for a brain. Optimal control in a network of adaptive memristors

“…We want to conclude with the Freeman reflections on the intentionality [7] It is known by now that the question of intentionality implies noisy long-range correlations in the brain [30,31]. The approach here defined in terms of global neuro geometry is compatible with these theories.…”