Computational Complexity and Philosophical Dualism :: Dualism Essays

Computational Complexity and Philosophical DualismABSTRACT I turn up some new-fangled controversies involving the possibility of mechanical simulation of mathematical intuition. The premier dampen is concerned with a presentation of the Lucas-Penrose role and recapitulates some introductory logical conceptual machinery (Gdels proof, Hilberts Tenth Problem and Turings Halting Problem). The second break off is devoted to a presentation of the main outlines of Complexity system as well as to the introduction of Bremermanns notion of transcomputability and funda noetic limit. The third segment attempts to draw a connection/relationship between Complexity Theory and undecidability focusing on a new revised version of the Lucas-Penrose position in light of physical a priori limitations of computing machines. Finally, the last part derives some epistemological/philosophical implications of the relationship between Gdels soreness theorem and Complexity Theory for the mind/brain prob lem in stylised Intelligence and discusses the compatibility of functionalism with a materialist theory of the mind. This paper purports to re-examine the Lucas-Penrose product line against ersatz Intelligence in the light of Complexity Theory. Arguments against strong AI base on some philosophical consequences derived from an interpretation of Gdels proof receive been around for m whatever years since their initial formulation by Lucas (1961) and their recent revival by Penrose (1989,1994). For one thing, Penrose is right in sustaining that mental activeness cannot be modeled as a Turing Machine. However, such a moot does not have to follow from the uncomputable nature of some compassionate cognitive capabilities such as mathematical intuition. In what follows I intend to maneuver that even if mathematical intuition were mechanizable (as part of a conception of mental activity understood as the realization of an algorithm) the Turing Machine model of the human mind becomes self-refuting.Our contention will start from the notion of transcomputability. Such a notion will allow us to draw a footpath between formal and physical limitations of symbol-based artificial intelligence by bridging up computational complexity and undecidability. Furthermore, linking complexity and undecidability will reveal that functionalism is incompatible with a materialist theory of the mind and that adherents of functionalism have systematically overlooked implementational issues.1 - The Lucas-Penrose argument Lucas-Penrose argument runs as follows Gdels incompleteness theorem shows that computational systems are moderate in a way that humans are not. In any consistent formal system powerful enough to do a certain sort of arithmetic there will be a true sentence a Gdel sentence (G) that the system cannot prove.