In this paper we consider persuasion in the context of practical reasoning, and discuss the problems associated with construing reasoning about actions in a manner similar to reasoning about beliefs. We propose a perspective on practical reasoning as presumptive justification of a course of action, along with critical questions of this justification, building on the account of Walton. From this perspective, we articulate an interaction protocol, which we call PARMA, for dialogues over proposed actions based on this theory. We outline (...) an axiomatic semantics for the PARMA Protocol, and discuss two implementations which use this protocol to mediate a discussion between humans. We then show how our proposal can be made computational within the framework of agents based on the Belief-Desire-Intention model, and illustrate this proposal with an example debate within a multi agent system. (shrink)

Recent discussions in the philosophy of psychology have examined the use and legitimacy of such notions as ‘representation’, ‘content’, ‘computation’, and ‘inference’ within a scientific psychology. While the resulting assessments have varied widely, ranging from outright rejection of some or all of these notions to full vindication of their use, there has been notable agreement on the considerations deemed relevant for making an assessment. The answer to the question of whether the notion of, say, representational content may be admitted into (...) a scientific psychology has often been made to hinge upon whether the notion can be squared with our ‘ordinary’ or ‘folk’ style of psychological explanation, with its alleged commitment to the idiom of beliefs and desires. The emphasis on ‘folk psychology’ in arguments concerning the status of various concepts within scientific psychology is unfortunate, because it runs afoul of the ideal that the philosophy of psychology, by analogy with the philosophy of biology and the philosophy of physics, should have at its core the discussion of ongoing psychological theories. For while it may be admitted that the status of appeals to ‘folk psychology’ in order to justify a role for the belief-desire idiom within psychology proper is a matter that is of interest in its own right, it is not at all clear that mainstream experimental psychology has adopted either the language or the conceptions of ‘belief-desire’ psychology. (shrink)

Some modifications are suggested to recent (1985) generalised phrase-structure grammar which make the formalism more suitable to computational use, and at the same time provide a clear and elegant redefinition for parts of the formalism which are standardly complex and ill-defined. It is shown how the feature-instantiation principles can be represented as explicit rules in a format similar to metarules, and how a grammar of four parts, immediate-dominance rules, linear-precedence rules, metarules, and these new propagation rules, can be used (...) to produce the ordinary GPSG analyses of English. Methods of computational implementation are discussed, in particular it is suggested that the parts of the grammar are most conveniently interpreted as instructions as to how to produce a set of context-free phrase-structure rules which can be used with a simple left-corner parser. (shrink)

The purpose of this paper is to explore three alternative frameworks for understanding the nature of language and mentality, which accent syntactical, semantical, and pragmatical aspects of the phenomena with which they are concerned, respectively. Although the computational conception currently exerts considerable appeal, its defensibility appears to hinge upon an extremely implausible theory of the relation of form to content. Similarly, while the representational approach has much to recommend it, its range is essentially restricted to those units of language (...) that can be understood in terms of undefined units. Thus, the only alternative among these three that can account for the meaning of primitive units of language is one emphasizing the basic role of skills, habits, and tendencies in relating signs and dispositions. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 problems, by (...) contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding (...) biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery, are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case (...) of model-building by an engineer that led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account. (shrink)

This article describes research to build an embodied conversational agent as an interface to a question-and-answer system about a National Science Foundation program. We call this ECA the LifeLike Avatar, and it can interact with its users in spoken natural language to answer general as well as specific questions about specific topics. In an idealized case, the LifeLike Avatar could conceivably provide a user with a level of interaction such that he or she would not be certain as to whether (...) he or she is talking to the actual person via video teleconference. This could be considered a extended version of the seminal Turing test. Although passing such a test is still far off, our work moves the science in that direction. The Uncanny Valley notwithstanding, applications of such lifelike interfaces could include those where specific instructors/caregivers could be represented as stand-ins for the actual person in situations where personal representation is important. Possible areas that come to mind that might benefit from these lifelike ECAs include health-care support for elderly/disabled patients in extended home care, education/training, and knowledge preservation. Another more personal application would be to posthumously preserve elements of the persona of a loved one by family members. We apply this approach to a Q/a system for knowledge preservation and dissemination, where the specific individual who had this knowledge was to retire from the US National Science Foundation. The system is described in detail, and evaluations were performed to determine how well the system was perceived by users. (shrink)

How can computers distinguish the coherent from the unintelligible, recognize new information in a sentence, or draw inferences from a natural language passage? Computational semantics is an exciting new field that seeks answers to these questions, and this volume is the first textbook wholly devoted to this growing subdiscipline. The book explains the underlying theoretical issues and fundamental techniques for computing semantic representations for fragments of natural language. This volume will be an essential text for computer scientists, linguists, (...) and anyone interested in the development of computational semantics. (shrink)

A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano arithmetics having a remarkable (...) symmetry to the axiom of choice. The quantity of information is interpreted as the number of elementary choices (bits). Quantum information is seen as the generalization of information to infinite sets or series. The equivalence of that model to a quantum computer is demonstrated. The condition for the Turing machines to be independent of each other is reduced to the state of Nash equilibrium between them. Two relative models of language as game in the sense of game theory and as ontology of metaphors (all mappings, which are not one-to-one, i.e. not representations of reality in a formal sense) are deduced. (shrink)

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational (...) content is extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing. (shrink)

There are two versions of the language-of-thought hypothesis (LOT): Representational LOT (roughly, structured representation), introduced by Ockham, and computational LOT (roughly, symbolic computation) introduced by Fodor. Like many others, I oppose the latter but not the former. Quilty-Dunn et al. defend representational LOT, but they do not defend the strong computational LOT thesis central to the classical-connectionist debate.

Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: (...) it studies entities as represented in certain ways, rather than entities detached from any means of representing them. (shrink)

The ‘received view’ about computation is that all computations must involve representational content. Egan and Piccinini argue against the received view. In this paper, I focus on Egan’s arguments, claiming that they fall short of establishing that computations do not involve representational content. I provide positive arguments explaining why computation has to involve representational content, and how that representational content may be of any type. I also argue that there is no need for computational psychology to be individualistic. Finally, (...) I draw out a number of consequences for computational individuation, proposing necessary conditions on computational identity and necessary and sufficient conditions on computational I/O equivalence of physical systems.Keywords: Computation; Representation; Computational identity; Explanation; Narrow content; Physical computation. (shrink)

Cognitive representations are typically analysed in terms of content, vehicle and format. While current work on formats appeals to intuitions about external representations, such as words and maps, in this paper we develop a computational view of formats that does not rely on intuitions. In our view, formats are individuated by the computational profiles of vehicles, i.e., the set of constraints that fix the computational transformations vehicles can undergo. The resulting picture is strongly pluralistic, it (...) makes space for a variety of different formats, and is intimately tied to the computational approach to cognition in cognitive science and artificial intelligence. (shrink)

Relative to digital computation, analogue computation has been neglected in the philosophical literature. To the extent that attention has been paid to analogue computation, it has been misunderstood. The received view—that analogue computation has to do essentially with continuity—is simply wrong, as shown by careful attention to historical examples of discontinuous, discrete analogue computers. Instead of the received view, I develop an account of analogue computation in terms of a particular type of analogue representation that allows for discontinuity. This account (...) thus characterizes all types of analogue computation, whether continuous or discrete. Furthermore, the structure of this account can be generalized to other types of computation: analogue computation essentially involves analogue representation, whereas digital computation essentially involves digital representation. Besides being a necessary component of a complete philosophical understanding of computation in general, understanding analogue computation is important for computational explanation in contemporary neuroscience and cognitive science. (shrink)

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give (...) rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

The received view is that computational states are individuated at least in part by their semantic properties. I offer an alternative, according to which computational states are individuated by their functional properties. Functional properties are specified by a mechanistic explanation without appealing to any semantic properties. The primary purpose of this paper is to formulate the alternative view of computational individuation, point out that it supports a robust notion of computational explanation, and defend it on the (...) grounds of how computational states are individuated within computability theory and computer science. A secondary purpose is to show that existing arguments for the semantic view are defective. (shrink)

In this paper a possible general framework for the representation of concepts in cognitive artificial systems and cognitive architectures is proposed. The framework is inspired by the so called proxytype theory of concepts and combines it with the heterogeneity approach to concept representations, according to which concepts do not constitute a unitary phenomenon. The contribution of the paper is twofold: on one hand, it aims at providing a novel theoretical hypothesis for the debate about concepts in cognitive sciences by (...) providing unexplored connections between different theories; on the other hand it is aimed at sketching a computational characterization of the problem of concept representation in cognitively inspired artificial systems and in cognitive architectures. (shrink)

Peter Godfrey-Smith recently introduced the idea of representational ‘organization’. When a collection of representations form an organized family, similar representational vehicles carry similar contents. For example, where neural firing rate represents numerosity (an analogue magnitude representation), similar firing rates represent similar numbers of items. Organization has been elided with structural representation, but the two are in fact distinct. An under-appreciated merit of representational organization is the way it facilitates computational processing. Representations from different organized families can interact, (...) for example to perform addition. Their being organized allows them to implement a useful computation. Many of the cases where organization has seemed significant, but which fall short of structural representation, are cases where representational organization underpins a computationally useful processing structure. (shrink)

Advocates of the computational theory of mind claim that the mind is a computer whose operations can be implemented by various computational systems. According to these philosophers, the mind is multiply realisable because—as they claim—thinking involves the manipulation of syntactically structured mental representations. Since syntactically structured representations can be made of different kinds of material while performing the same calculation, mental processes can also be implemented by different kinds of material. From this perspective, consciousness plays a (...) minor role in mental activity. However, contemporary neuroscience provides experimental evidence suggesting that mental representations necessarily involve consciousness. Consciousness does not only enable individuals to become aware of their own thoughts, it also constantly changes the causal properties of these thoughts. In light of these empirical studies, mental representations appear to be intrinsically dependent on consciousness. This discovery represents an obstacle to any attempt to construct an artificial mind. (shrink)

Connectionism provides hope for unifying work in neuroscience, computer science, and cognitive psychology. This promise has met with some resistance from Classical Computionalists, which may have inspired Connectionists to retaliate with bold, inflationary claims on behalf of Connectionist models. This paper demonstrates, by examining three intimately connected issues, that these inflationary claims made on behalf of Connectionism are wrong. This should not be construed as an attack on Connectionism, however, since the inflated claims made on its behalf have the look (...) of cures for which there are no ailments. There is nothing wrong with Connectionism for its failure to solve illusory problems. (shrink)

By the Riesz representation theorem for the dual of C [0; 1], if F: C [0; 1] → ℝ is a continuous linear operator, then there is a function g: [0;1] → ℝ of bounded variation such that F = ∫ f dg . The function g can be normalized such that V = ‖F ‖. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows (...) to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S ′ mapping F and its norm to some appropriate g. (shrink)

This paper discusses essential motivational representations necessary for a comprehensive computational cognitive architecture. It hypothesizes the need for implicit drive representations, as well as explicit goal representations. Drive representations consist of primary drives — both low-level primary drives (concerned mostly with basic physiological needs) and high-level primary drives (concerned more with social needs), as well as derived (secondary) drives. On the basis of drives, explicit goals may be generated on the fly during an agent’s interaction (...) with various situations. These motivational representations help to make cognitive architectural models more comprehensive and provide deeper explanations of psychological processes. This work represents a step forward in making computational cognitive architectures better reflections of the human mind and all its motivational complexity and intricacy. (shrink)

The computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cut or Cauchy sequence representations are considered instead. In other words, the computability of reals is independent of their representations. However, as it is shown by Specker [19] and Ko [9], the primitive recursiveness and polynomial time computability of the reals do depend on the representation. In this paper, (...) we explore how the weak computability of reals depends on the representation. To this end, we introduce three notions of weak computability in a way similar to the Ershov's hierarchy of Δ02-sets of natural numbers based on the binary expansion, Dedekind cut and Cauchy sequence, respectively. This leads to a series of classes of reals with different levels of computability. We investigate systematically questions as on which level these notions are equivalent. We also compare them with other known classes of reals like c. e. and d-c. e. reals. (shrink)

Recently, Horsman et al. have proposed a new framework, Abstraction/Representation theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is not itself a semantic (...) account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini. Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation. (shrink)

One of the central issues in cognitive science is the nature of human representations. We argue that symbolic representations are essential for capturing human cognitive capabilities. We start by examining some common misconceptions found in discussions of representations and models. Next we examine evidence that symbolic representations are essential for capturing human cognitive capabilities, drawing on the analogy literature. Then we examine fundamental limitations of feature vectors and other distributed representations that, despite their recent successes (...) on various practical problems, suggest that they are insufficient to capture many aspects of human cognition. After that, we describe the implications for cognitive architecture of our view that analogy is central, and we speculate on roles for hybrid approaches. We close with an analogy that might help bridge the gap. (shrink)

Society is becoming increasingly reliant upon the dependability of computerbased systems. Achieving and demonstrating the dependability of systems requires the construction and review of valid and coherent arguments. This paper discusses the need for a variety of classes of arguments in dependable systems and reviews existing approaches to the representation of arguments in each of these classes. The issues surrounding the certification of safety critical systems demonstrate the current need for richer representations of dependability arguments which support tools for (...) their construction and review. The paper discusses how a meta-logical framework, informed by aspects of both formal and informal logic, offers a rich and unified means of representing dependability arguments and of thus addressing this need. (shrink)

This paper analyses the impact of representation and search operators on Computational Complexity. A model of computation is introduced based on a directed graph, and representation and search are defined to be the vertices and edges of this graph respectively. Changing either the representation or the search algorithm leads to different possible complexity classes. The final section explores the role of representation in reducing time complexity in Artificial Intelligence.

An influential view in cognitive science is that computation in cognitive systems is semantic, conceptually depending on representation: to compute is to manipulate representations. I argue that accepting the non-semantic teleomechanistic view of computation lays the ground for a promising alternative strategy, in which computation helps to explain and naturalise representation, rather than the other way around. I show that this computation-based approach to representation presents six decisive advantages over the semantic view. I claim that it can improve the (...) two most influential current theories of representation, teleosemantics and structural representation, by providing them with precious tools to tackle some of their main shortcomings. In addition, the computation-based approach opens up interesting new theoretical paths for the project of naturalising representation, in which teleology plays a role in individuating computations, but not representations. (shrink)

Lattice representations are an important tool for computability theorists when they embed nondistributive lattices into degree-theoretic structures. In this expository paper, we present the basic definitions and results about lattice representations needed by computability theorists. We define lattice representations both from the lattice-theoretic and computability-theoretic points of view, give examples and show the connection between the two types of representations, discuss some of the known theorems on the existence of lattice representations that are of interest (...) to computability theorists, and give a simple example of the use of lattice representations in an embedding result. (shrink)

Reformers urge that representation no longer earns its explanatory keep in cognitive science, and that it is time to discard this troublesome concept. In contrast, we hold that without representation cognitive science is utterly bereft of tools for explaining natural intelligence. In order to defend the latter position, we focus on the explanatory role of representation in computation. We examine how the methods of digital and analog computation are used to model a relatively simple target system, and show that representation (...) plays an in-eliminable explanatory role in both cases. We conclude that, to the extent that biologic systems engage in computation, representation is destined to play an explanatory role in cognitive science. (shrink)

Although Clark & Thornton's “trading spaces” hypothesis is supposed to require trading internal representation for computation, it is not used consistently in that fashion. Not only do some of the offered computation-saving strategies turn out to be nonrepresentational, others (e.g., cultural artifacts) are external representations. Hence, C&T's hypothesis is consistent with antirepresentationalism.

Most of this work is concerned with two theories that underlie cognitive science; theories which I call "the representational theory of intentionality" and "the computational theory of cognition" . While the representational theory of intentionality asserts that mental states are about the world in virtue of a representation relation between the world and the state, the computational theory of cognition asserts that humans and others perform cognitive tasks by computing functions on these representations. CTC draws upon a (...) rich analogy between the mind and digital computers, portraying cognizers as receiving input and generating outputs . ;Since researchers within cognitive science--especially within cognitive psychology, computer science, and philosophy of mind--share a common theoretic background in their adherence to the combination of RTI and CTC, what I call "computationalism" most of the work done in philosophy of mind has been aimed at either refuting or further articulating these two theories. This work is strongly within that tradition. ;RTI and CTC combine to create an explanatory framework for explanation in cognitive science. In this work, I seek to delineate the exact structure of this framework, to determine its components and their overall relationships. In my mind, this involves making implicit aspects of computational explanation explicit, providing an overall rationale for the various components and their relationships, and defending that rationale against criticism. ;In particular, the project of this work is to argue that computationalist explanations of cognition within cognitive science need to make appeals to both representation and knowledge; to distinguish the respective roles of knowledge and of representation in an overall picture of computational explanations, and to develop and argue for definitions of representation and knowledge that would allow those concepts to play their respective roles within computational explanations in cognitive science. ;The first half of this work , therefore, is devoted to theories of representation, especially to the need for, and role of representation in computational explanations. The first half of the work culminates in chapter three with a definition of representation and a picture of the structure of computational explanations. The second half of the project then becomes to generate a definition of knowledge that defines knowledge in non-epistemic language amenable to computationalism and that carries the epistemic burdens placed upon knowledge by its use in computational explanations, as well as to offer a limited defence of that definition within the framework of traditional epistemology. (shrink)

Most cognitive scientists believe that cognitive processing (e.g., thought, speech, perception, and sensori‐motor processing) is the hallmark of intelligent systems. Aside from modeling such processes, cognitive science is in the business of mechanistically explaining how minds and other intelligent systems work. As one might expect, mechanistic explanations appeal to the causal‐functional interactions among a system's component structures. Good explanations are the ones that get the causal story right. But getting the causal story right requires positing structures that are really in (...) the system. After all, within the context of a mechanistic explanation, to posit X is to claim not only that X exists but that X is doing some causal labor. Because most cognitive scientists believe that cognitive processing requires the use, manipulation, and storage of internal representations, they characteristically posit internal representations to explain how intelligent systems work. (shrink)

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: extending the representation to the process of setting the problem, relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is (...) completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution. Completing the physical representation shows that the number of computation steps required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution. (shrink)