A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields that the realization (...) of hypercomputing devices is implausible, and that Thesis P is not essentially different from the standard Church-Turing Thesis. (shrink)

Function theorists routinely speculate that a viable function theory will be equally applicable to biological traits and artifacts. However, artifact function has received only the most cursory scrutiny in its own right. Closer scrutiny reveals that only a pluralist theory comprising two distinct notions of function--proper function and system function--will serve as an adequate general theory. The first section describes these two notions of function. The second section shows why both notions are necessary, by showing that attempts to do away (...) with one of them fail. This demonstration draws on examples from the artifactual realm to motivate major points of the argument. The third section is an outline of artifact function. It confirms the conclusions of the second section, and also begins the task of describing some of the special features of artifact function needing accommodation within the general theory. (shrink)

A complete sourcebook for philosophical discussion of the nature of function in biology.

Outlines the etiological theory of normative functionality. Analysis of the autonomous system; Function of systems-oriented approaches; Specifications of system identity.

Some philosophers have conflated functionalism and computationalism. I reconstruct how this came about and uncover two assumptions that made the conflation possible. They are the assumptions that (i) psychological functional analyses are computational descriptions and (ii) everything may be described as performing computations. I argue that, if we want to improve our understanding of both the metaphysics of mental states and the functional relations between them, we should reject these assumptions.

This volume provides a guide to the discussion among biologists and philosophersabout the role of concepts such as function and design in an evolutionary understanding oflife.

According to pancomputationalism, everything is a computing system. In this paper, I distinguish between different varieties of pancomputationalism. I find that although some varieties are more plausible than others, only the strongest variety is relevant to the philosophy of mind, but only the most trivial varieties are true. As a side effect of this exercise, I offer a clarified distinction between computational modelling and computational explanation.<br><br>.

Many areas of science develop by discovering mechanisms and role functions. Cummins' (1975) analysis of role functions-according to which an item's role function is a capacity of that item that appears in an analytic explanation of the capacity of some containing system-captures one important sense of "function" in the biological sciences and elsewhere. Here I synthesize Cummins' account with recent work on mechanisms and causal/mechanical explanation. The synthesis produces an analysis of specifically mechanistic role functions, one that uses the characteristic (...) active, spatial, temporal, and hierarchical organization of mechanisms to add precision and content to Cummins' original suggestion. This synthesis also shows why the discovery of role functions is a scientific achievement. Discovering a role function (i) contributes to the interlevel integration of multilevel mechanisms, and (ii) provides a unique, contextual variety of causal/mechanical explanation. (shrink)

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

A survey of the field of hypercomputation, including discussion of a variety of objections.

The concept of mechanism is analyzed in terms of entities and activities, organized such that they are productive of regular changes. Examples show how mechanisms work in neurobiology and molecular biology. Thinking in terms of mechanisms provides a new framework for addressing many traditional philosophical issues: causality, laws, explanation, reduction, and scientific change.

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)

After briefly discussing the relevance of the notions computation and implementation for cognitive science, I summarize some of the problems that have been found in their most common interpretations. In particular, I argue that standard notions of computation together with a state-to-state correspondence view of implementation cannot overcome difficulties posed by Putnam's Realization Theorem and that, therefore, a different approach to implementation is required. The notion realization of a function, developed out of physical theories, is then introduced as a replacement (...) for the notional pair computation-implementation. After gradual refinement, taking practical constraints into account, this notion gives rise to the notion digital system which singles out physical systems that could be actually used, and possibly even built. (shrink)

To compute is to execute an algorithm. More precisely, to say that a device or organ computes is to say that there exists a modelling relationship of a certain kind between it and a formal specification of an algorithm and supporting architecture. The key issue is to delimit the phrase of a certain kind. I call this the problem of distinguishing between standard and nonstandard models of computation. The successful drawing of this distinction guards Turing's 1936 analysis of computation against (...) a difficulty that has persistently been raised against it, and undercuts various objections that have been made to the computational theory of mind. (shrink)

Hilary Putnam has argued that computational functionalism cannot serve as a foundation for the study of the mind, as every ordinary open physical system implements every finite-state automaton. I argue that Putnam's argument fails, but that it points out the need for a better understanding of the bridge between the theory of computation and the theory of physical systems: the relation of implementation. It also raises questions about the class of automata that can serve as a basis for understanding the (...) mind. I develop an account of implementation, linked to an appropriate class of automata, such that the requirement that a system implement a given automaton places a very strong constraint on the system. This clears the way for computation to play a central role in the analysis of mind. (shrink)

This systematic investigation of computation and mental phenomena by a noted psychologist and computer scientist argues that cognition is a form of computation, that the semantic contents of mental states are encoded in the same general way as computer representations are encoded. It is a rich and sustained investigation of the assumptions underlying the directions cognitive science research is taking. 1 The Explanatory Vocabulary of Cognition 2 The Explanatory Role of Representations 3 The Relevance of Computation 4 The Psychological Reality (...) of Programs: Strong Equivalence 5 Constraining Functional Architecture 6 The Bridge from Physical to Symbolic: Transduction 7 Functional Architecture and Analogue Processes 8 Mental Imagery and Functional Architecture 9 Epilogue: What is Cognitive Science the Science of? (shrink)

The purpose of this paper is to set forth a sense in which programs can and do explain behavior, and to distinguish from this a number of senses in which they do not. Once we are tolerably clear concerning the sort of explanatory strategy being employed, two rather interesting facts emerge; (1) though it is true that programs are "internally represented," this fact has no explanatory interest beyond the mere fact that the program is executed; (2) programs which are couched (...) in information processing terms may have an explanatory interest for a given range of behavior which is independent of physiological explanations of the same range of behavior. (shrink)

What psychological and philosophical significance should we attach to recent efforts at computer simulations of human cognitive capacities? In answering this question, I find it useful to distinguish what I will call "strong" AI from "weak" or "cautious" AI. According to weak AI, the principal value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion. (...) But according to strong AI, the computer is not merely a tool in the study of the mind; rather, the appropriately programmed computer really is a mind, in the sense that computers given the right programs can be literally said to. (shrink)

This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...) Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical
objection” to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it
should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human
mathematicians presumably do. (shrink)

Hilary Putnam, who may have been the first philosopher to advance the notion that the computer is an apt model for the mind, takes a radically new view of his...

The renowned philosopher Jerry Fodor, a leading figure in the study of the mind for more than twenty years, presents a strikingly original theory on the basic constituents of thought. He suggests that the heart of cognitive science is its theory of concepts, and that cognitive scientists have gone badly wrong in many areas because their assumptions about concepts have been mistaken. Fodor argues compellingly for an atomistic theory of concepts, deals out witty and pugnacious demolitions of rival theories, and (...) suggests that future work on human cognition should build upon new foundations. This lively, conversational, and superbly accessible book is the first volume in the Oxford Cognitive Science Series, where the best original work in this field will be presented to a broad readership. Concepts will fascinate anyone interested in contemporary work on mind and language. Cognitive science will never be the same again. (shrink)

Philosophers of science typically associate the causal-mechanical view of scientific explanation with the work of Railton and Salmon. In this paper I shall argue that the defects of this view arise from an inadequate analysis of the concept of mechanism. I contrast Salmon's account of mechanisms in terms of the causal nexus with my own account of mechanisms, in which mechanisms are viewed as complex systems. After describing these two concepts of mechanism, I show how the complex-systems approach avoids certain (...) objections to Salmon's account of causal-mechanical explanation. I conclude by discussing how mechanistic explanations can provide understanding by unification. (shrink)

Carl F. Craver investigates what we are doing when we use neuroscience to explain what's going on in the brain. When does an explanation succeed and when does it fail? Craver offers explicit standards for successful explanation of the workings of the brain, on the basis of a systematic view about what neuroscientific explanations are.

Philosophers of science typically associate the causal-mechanical view of scientific explanation with the work of Railton and Salmon. In this paper I shall argue that the defects of this view arise from an inadequate analysis of the concept of mechanism. I contrast Salmon's account of mechanisms in terms of the causal nexus with my own account of mechanisms, in which mechanisms are viewed as complex systems. After describing these two concepts of mechanism, I show how the complex-systems approach avoids certain (...) objections to Salmon's account of causal-mechanical explanation. I conclude by discussing how mechanistic explanations can provide understanding by unification. (shrink)

I offer an explication of the notion of computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hard-wired versus programmable, general-purpose versus special-purpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system's mechanistic (...) properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind. (shrink)

Stuart Glennan, and the team of Peter Machamer, Lindley Darden, and Carl Craver have recently provided two accounts of the concept of a mechanism. The main difference between these two versions rests on how the behavior of the parts of the mechanism is conceptualized. Glennan considers mechanisms to be an interaction of parts, where the interaction between parts can be characterized by direct, invariant, change-relating generalizations. Machamer, Darden, and Craver criticize traditional conceptualizations of mechanisms which are based solely on parts (...) interacting and introduce a new conceptactivity. This essay is an attempt at carving out a relationship between these two philosophical interpretations of a mechanism. I will claim that, rather than being in conflict, Glennan's concept of interaction and Machamer, Darden, and Craver's notion of activity actually complement one another, each emphasizing a missing element of the other. (shrink)

In exploring the nature of psychological explanation, this book looks at how psychologists theorize about the human ability to calculate, to speak a language and the like. It shows how good theorizing explains or tries to explain such abilities as perception and cognition. It recasts the familiar explanations of "intelligence" and "cognitive capacity" as put forward by philosophers such as Fodor, Dennett, and others in terms of a theory of explanation that makes established doctrine more intelligible to professionals and their (...) students.In particular, the book shows that vestigial adherence to the positivists' D-N model has distorted the view of philosophers of science about what psychologists (and biologists) do and has masked the real nature of explanation. Major sections in the book cover Analysis and Subsumption; Functional Analysis; Understanding Cognitive Capacities; and Historical Reflections.Robert Cummins is Associate Professor of Philosophy at the University of Illinois, Chicago Circle. A Bradford Book. (shrink)

Some philosophers have conflated functionalism and computationalism. I reconstruct how this came about and uncover two assumptions that made the conflation possible. They are the assumptions that (i) psychological functional analyses are computational descriptions and (ii) everything may be described as performing computations. I argue that, if we want to improve our understanding of both the metaphysics of mental states and the functional relations between them, we should reject these assumptions. # 2004 Elsevier Ltd. All rights reserved.

But what are functions? Here, 15 leading scholars of philosophy of psychology and philosophy of biology present new essays on functions.

This paper is the introduction to Function, Selection, and Design, consisting of the following sections: 1. Introduction 2. The Philosophical Problem 3. Recent Prehistory: The "State of the Art" in the 1960s 4. Wright and Cummins 5. Millikan 6. The Core Consensus and the Peripheral Disagreements 7. Unconclusion.

Wilfred Sieg and John Byrnes. K-Graph Machines: Generalizing Turing's Machines and Arguments.

The following three theses are inconsistent: (1) (Paradigmatic) connectionist systems perform computations. (2) Performing computations requires executing programs. (3) Connectionist systems do not execute programs. Many authors embrace (2). This leads them to a dilemma: either connectionist systems execute programs or they don't compute. Accordingly, some authors attempt to deny (1), while others attempt to deny (3). But as I will argue, there are compelling reasons to accept both (1) and (3). So, we should replace (2) with a more satisfactory (...) account of computation. Once we do, we can see more clearly what is peculiar to connectionist computation. (shrink)

Wilfred Sieg and John Byrnes. Generalizing Turing's Machine and Arguments.