The Annotation Game: On Turing (1950) on Computing, Machinery, and Intelligence

This quote/commented critique of Turing's classical paper suggests that Turing meant -- or should have meant -- the robotic version of the Turing Test (and not just the email version). Moreover, any dynamic system (that we design and understand) can be a candidate, not just a computational one. Turing also dismisses the other-minds problem and the mind/body problem too quickly. They are at the heart of both the problem he is addressing and the solution he is proposing

The Computability-Theoretic Content of Emergence

In dealing with emergent phenomena, a common task is to identify useful descriptions of them in terms of the underlying atomic processes, and to extract enough computational content from these descriptions to enable predictions to be made. Generally, the underlying atomic processes are quite well understood, and (with important exceptions) captured by mathematics from which it is relatively easy to extract algorithmic con- tent. A widespread view is that the difficulty in describing transitions from algorithmic activity to the emergence associated with chaotic situations is a simple case of complexity outstripping computational resources and human ingenuity. Or, on the other hand, that phenomena transcending the standard Turing model of computation, if they exist, must necessarily lie outside the domain of classical computability theory. In this article we suggest that much of the current confusion arises from conceptual gaps and the lack of a suitably fundamental model within which to situate emergence. We examine the potential for placing emer- gent relations in a familiar context based on Turing's 1939 model for interactive computation over structures described in terms of reals. The explanatory power of this model is explored, formalising informal descrip- tions in terms of mathematical definability and invariance, and relating a range of basic scientific puzzles to results and intractable problems in computability theory

Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?

Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general, scientific, discourse cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic is verifiably complete. We show how some paradoxical concepts of Quantum mechanics can be expressed, and interpreted, naturally under a constructive definition of mathematical truth.Comment: 73 pages; this is an updated version of the NQ essay; an HTML version is available at http://alixcomsi.com/Do_Goedel_incompleteness_theorems.ht

The Turing Test and the Zombie Argument

In this paper I shall try to put some implications concerning the Turing's test and the so-called Zombie arguments into the context of philosophy of mind. My intention is not to compose a review of relevant concepts, but to discuss central problems, which originate from the Turing's test - as a paradigm of computational theory of mind - with the arguments, which refute sustainability of this thesis. In the first section (Section I), I expose the basic computationalist presuppositions; by examining the premises of the Turing Test (TT) I argue that the TT, as a functionalist paradigm concept, underlies the computational theory of mind. I treat computationalism as a thesis that defines the human cognitive system as a physical, symbolic and semantic system, in such a manner that the description of its physical states is isomorphic with the description of its symbolic conditions, so that this isomorphism is semantically interpretable. In the second section (Section II), I discuss the Zombie arguments, and the epistemological-modal problems connected with them, which refute sustainability of computationalism. The proponents of the Zombie arguments build their attack on the computationalism on the basis of thought experiments with creatures behaviorally, functionally and physically indistinguishable from human beings, though these creatures do not have phenomenal experiences. According to the consequences of these thought experiments - if zombies are possible, then, the computationalism doesn't offer a satisfying explanation of consciousness. I compare my thesis from Section 1, with recent versions of Zombie arguments, which claim that computationalism fails to explain qualitative phenomenal experience. I conclude that despite the weaknesses of computationalism, which are made obvious by zombie-arguments, these arguments are not the last word when it comes to explanatory force of computationalism

On The Foundations of Digital Games

Computers have lead to a revolution in the games we play, and, following this, an interest for computer-based games has been sparked in research communities. However, this easily leads to the perception of a one-way direction of influence between that the field of game research and computer science. This historical investigation points towards a deep and intertwined relationship between research on games and the development of computers, giving a richer picture of both fields. While doing so, an overview of early game research is presented and an argument made that the distinction between digital games and non-digital games may be counter-productive to game research as a whole

Is thinking computable?

Strong artificial intelligence claims that conscious thought can arise in computers containing the right algorithms even though none of the programs or components of those computers understand which is going on. As proof, it asserts that brains are finite webs of neurons, each with a definite function governed by the laws of physics; this web has a set of equations that can be solved (or simulated) by a sufficiently powerful computer. Strong AI claims the Turing test as a criterion of success. A recent debate in Scientific American concludes that the Turing test is not sufficient, but leaves intact the underlying premise that thought is a computable process. The recent book by Roger Penrose, however, offers a sharp challenge, arguing that the laws of quantum physics may govern mental processes and that these laws may not be computable. In every area of mathematics and physics, Penrose finds evidence of nonalgorithmic human activity and concludes that mental processes are inherently more powerful than computational processes

Abstract Body, Abstract Machine: Alan Turing's Drama of Difference

In order to prove that mathematics cannot be exhausted by a finite set of procedures, Alan Turing conceives, in 1936, of an abstract machine 1. The machine makes its debut in “On Computable Numbers with an application to the Entscheidungsproblem,” his first major mathematical paper 2. A close reading of this machine’s dynamic will show that Turing’s thought in the field of mathematics is a consciously embodied thought that contemplates its own incompleteness. By examining Turing’s machine through the lens of incompleteness, this project will reveal how, through his extension into abstraction, Turing engages in a paradoxically intensive movement that reveals his body as inextricably enfolded in thought. To understand this radical act of contemplation, Turing must be situated within a history of thinkers working against totality, because in thinking his own incompleteness, he refutes the idea that systems are defined by completeness, or that the unfolding of something is circumscribed by that something as goal. This constellation of thinkers includes Kurt Gödel, before Turing, with his Incompleteness Theorem 3; it also includes Gilles Deleuze, with his explanation of how meaning gets made in The Logic of Sense ,4 and Michel Foucault, with his formulation of meaning’s dissolution in “The Thought of the Outside.”5 Brian Massumi then ushers this tradition into the present by defining the limit of a human being as immanent to that being in Parables for the Virtual.6 Massumi grounds his theory in Deleuzeian and Foucauldian concepts, themselves built from Turing’s legacy of lived thought, which in turn is grounded in Gödel’s theorem. Explaining these writers’ relation to Turing’s work on incompleteness will reveal the way in which systems of meaning are always torn between their own constitution and dissolution; this state of being torn will clarify, in turn, the movement of Turing’s mathematical body

The External Tape Hypothesis: a Turing machine based approach to cognitive computation

The symbol processing or "classical cognitivist" approach to mental computation suggests that the cognitive architecture operates rather like a digital computer. The components of the architecture are input, output and central systems. The input and output systems communicate with both the internal and external environments of the cognizer and transmit codes to and from the rule governed, central processing system which operates on structured representational expressions in the internal environment. The connectionist approach, by contrast, suggests that the cognitive architecture should be thought of as a network of interconnected neuron-like processing elements (nodes) which operates rather like a brain. Connectionism distinguishes input, output and central or "hidden" layers of nodes. Connectionists claim that internal processing consists not of the rule governed manipulation of structured symbolic expressions, but of the excitation and inhibition of activity and the alteration of connection strengths via message passing within and between layers of nodes in the network. A central claim of the thesis is that neither symbol processing nor connectionism provides an adequate characterization of the role of the external environment in cognitive computation. An alternative approach, called the External Tape Hypothesis (ETH), is developed which claims, on the basis of Turing's analysis of routine computation, that the Turing machine model can be used as the basis for a theory which includes the environment as an essential part of the cognitive architecture. The environment is thought of as the tape, and the brain as the control of a Turing machine. Finite state automata, Turing machines, and universal Turing machines are described, including details of Turing's original universal machine construction. A short account of relevant aspects of the history of digital computation is followed by a critique of the symbol processing approach as it is construed by influential proponents such as Allen Newell and Zenon Pylyshyn among others. The External Tape Hypothesis is then developed as an alternative theoretical basis. In the final chapter, the ETH is combined with the notion of a self-describing Turing machine to provide the basis for an account of thinking and the development of internal representations