Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability. 2 1. Introduction Neither Turing nor Post, in their descriptions of the devices we now call Turing machines, made much mention of time (Turing 1936, Post 1936). 1 They listed the primitive operations that their devices perform - read a square of the tape, write a single symbol on a square of the tape (first deleting any symbol already present), move one square to the right, and so forth - but they made no mention of the duration of each primitive operation. The crucial concept is that of whether or not the machine halts after a finite number of operations. Temporal considerations are not relevant to the functioning of the devices as described, nor - so we are clearly supposed to believe - to the soundness of the proofs that Turi...

A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine - a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by Turing machines. In point of fact Turing himself nowhere endorses, nor even states, this claim (nor does Church). I describe a number of notional machines, both analogue and digital, that can compute more than a universal Turing machine. These machines are exemplars of the class of nonclassical computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built, nor that the brain itself is such a machine. These theoretical considerations undercut a numb...

ABSTRACT. Recent findings in neuroscience strongly suggest that an object’s features (e.g., its color, texture, shape, etc.) are represented in separate areas of the visual cortex. Although represented in separate neuronal areas, somehow the feature representations are brought together as a single, unified object of visual consciousness. This raises a question of binding: how do neural activities in separate areas of the visual cortex function to produce a feature-unified object of visual consciousness? Several prominent neuroscientists have adopted neural synchrony and attention-based approaches to explain object feature binding. I argue that although neural synchrony and/or attentional mechanisms might function to disambiguate an object’s features, it is difficult to see how either of these mechanisms could fully explain the unity of an object’s features at the level of visual consciousness. After presenting a detailed critique of neural synchrony and attention-based approaches to object feature binding, I propose interactive hierarchical structuralism (IHS). This view suggests that a unified percept (i.e., a feature-unified object

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Abstract. Functional explanation, for long the mainstay of psychology’s autonomy, has recently come under attack. It is sometimes argued that higher-level generalizations are causally impotent, and do not really explain anything. Presumably only the reduction of higher-level patterns to underlying causal physical properties, and the specifying of lower-level, local causal mechanisms, provides genuine explanations. Two lines of argument are critically discussed: causal exclusion and multiple realization. These bear upon the credibility of functional explanation, and upon the presumed explanatory superiority of causal mechanisms over functional higher-level generalizations. It is argued that the causal exclusion argument conflates metaphysics with explanation, and that, rather than pointing towards reductionism, multiple realization indicates the indispensability of higher (functional) generalizations, alongside lower (causal) explanations; the choice for higher or lower level depends on context and explanatory interest. The notion of screening-off suggests a criterion for the legitimacy of higher-level characterizations. A brief example from the history of genetics is discussed to illustrate these ideas. This leads to a plea for pluralism in explanation.

In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'O-machines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind.

Since the cognitive revolution, it’s become commonplace that cognition involves both computation and information processing. Is this one claim or two? Is computation the same as information processing? The two terms are often used interchangeably, but this usage masks important differences. In this paper, we distinguish information processing from computation and examine some of their mutual relations, shedding light on the role each can play in a theory of cognition. We recommend that theorists of cognition be explicit and careful in choosing 1 notions of computation and information and connecting them together. Much confusion can be avoided by doing so.

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation ’ and ‘information processing ’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism/computational neuroscience on the other. We defend the relevance to cognitive science of both computation, at least in a generic sense, and information processing, in three important senses of the term. Our account advances several foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates ’ empirical aspects.