One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. (...) Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. We show that every recursively enumerable random real dominates all other recursively enumerable reals. We conclude that the recursively enumerable random reals are exactly the Ω-numbers [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. Second, we show that the sets in a universal Martin-Lof test for randomness have random measure, and every recursively enumerable random number is the sum of the measures represented in a universal Martin-Lof test. (shrink)

Philosophy of mind and cognitive science have recently become increasingly receptive to the hypothesis of extended cognition, according to which external artifacts such as our laptops and smartphones can—under appropriate circumstances—feature as material realizers of a person's cognitive processes. We argue that, to the extent that the hypothesis of extended cognition is correct, our legal and ethical theorizing and practice must be updated by broadening our conception of personal assault so as to include intentional harm toward gadgets that have been (...) appropriately integrated. We next situate the theoretical case for extended personal assault within the context of some recent ethical and legal cases and close with critical discussion. (shrink)

Predictive processing approaches to the mind are increasingly popular in the cognitive sciences. This surge of interest is accompanied by a proliferation of philosophical arguments, which seek to either extend or oppose various aspects of the emerging framework. In particular, the question of how to position predictive processing with respect to enactive and embodied cognition has become a topic of intense debate. While these arguments are certainly of valuable scientific and philosophical merit, they risk underestimating the variety of approaches gathered (...) under the predictive label. Here, we first present a basic review of neuroscientific, cognitive, and philosophical approaches to PP, to illustrate how these range from solidly cognitivist applications—with a firm commitment to modular, internalistic mental representation—to more moderate views emphasizing the importance of ‘body-representations’, and finally to those which fit comfortably with radically enactive, embodied, and dynamic theories of mind. Any nascent predictive processing theory must take into account this continuum of views, and associated theoretical commitments. As a final point, we illustrate how the Free Energy Principle attempts to dissolve tension between internalist and externalist accounts of cognition, by providing a formal synthetic account of how internal ‘representations’ arise from autopoietic self-organization. The FEP thus furnishes empirically productive process theories by which to guide discovery through the formal modelling of the embodied mind. (shrink)

Much of the progress in the fields constituting cognitive science has been based upon the use of explicit information processing models, almost exclusively patterned after conventional serial computers. An extension of these ideas to massively parallel, connectionist models appears to offer a number of advantages. After a preliminary discussion, this paper introduces a general connectionist model and considers how it might be used in cognitive science. Among the issues addressed are: stability and noise‐sensitivity, distributed decision‐making, time and sequence problems, and (...) the representation of complex concepts. (shrink)

For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and (...) codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks. (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.

For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and (...) codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks. (shrink)

Even the simplest known living organisms are complex chemical processing systems. But how sophisticated is the behaviour that arises from this? We present a framework in which even bacteria can be identified as capable of representing information in arbitrary signal molecules, to facilitate altering their behaviour to optimise their food supplies, for example. Known asion/Representation theory, this framework makes precise the relationship between physical systems and abstract concepts. Originally developed to answer the question of when a physical system is computing, (...) AR theory naturally extends to the realm of biological systems to bring clarity to questions of computation at the cellular level. (shrink)

The medium‐independence of computational descriptions has shaped common conceptions of computational explanation. So long as our goal is to explain how a system successfully carries out its computations, then we only need to describe the abstract series of operations that achieve the desired input–output mapping, however they may be implemented. It is argued that this abstract conception of computational explanation cannot be applied to so‐called real‐time computing systems, in which meeting temporal deadlines imposed by the systems with which a device (...) interfaces are constitutive of the computing tasks that a device performs. Instead, real‐time computing reveals the need for alternative conceptions of computational explanation, as well as computational implementation, that eschew medium‐independence. (shrink)

Philosophy of mind and cognitive science (e.g., Clark and Chalmers 1998; Clark 2010; Palermos 2014) have recently become increasingly receptive tothe hypothesis of extended cognition, according to which external artifacts such as our laptops and smartphones can—under appropriate circumstances—feature as material realisers of a person’s cognitive processes. We argue that, to the extent that the hypothesis of extended cognition is correct, our legal and ethical theorising and practice must be updated, by broadening our conception of personal assault so as to (...) include intentional harm towards gadgets that have been appropriately integrated. We next situate the theoretical case for extended personal assault within the context of some recent ethical and legal cases and close with some critical discussion. (shrink)

Moral reasoning traditionally distinguishes two types of evil:moral and natural. The standard view is that ME is the product of human agency and so includes phenomena such as war, torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomousagents in cyberspace, a new (...) class of interesting and importantexamples of hybrid evil has come to light. In this paper, it is called artificial evil and a case is made for considering it to complement ME and NE to produce a more adequate taxonomy. By isolating the features that have led to the appearance of AE, cyberspace is characterised as a self-contained environment that forms the essential component in any foundation of the emerging field of Computer Ethics. It is argued that this goes someway towards providing a methodological explanation of whycyberspace is central to so many of CE's concerns; and it isshown how notions of good and evil can be formulated incyberspace. Of considerable interest is how the propensity for anagent's action to be morally good or evil can be determined evenin the absence of biologically sentient participants and thusallows artificial agents not only to perpetrate evil but conversely to `receive' or `suffer from'it. The thesis defended is that the notion of entropy structure,which encapsulates human value judgement concerning cyberspace ina formal mathematical definition, is sufficient to achieve thispurpose and, moreover, that the concept of AE can be determinedformally, by mathematical methods. A consequence of this approachis that the debate on whether CE should be considered unique, andhence developed as a Macroethics, may be viewed, constructively,in an alternative manner. The case is made that whilst CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the approach of standard Macroethics such as Utilitarianism and Deontologism and hence to prompt the search for a robust ethical theory that can deal with them successfully. The name Information Ethics is proposed for that theory. Itis argued that the uniqueness of IE is justified by its beingnon-biologically biased and patient-oriented: IE is anEnvironmental Macroethics based on the concept of data entityrather than life. It follows that the novelty of CE issues suchas AE can be appreciated properly because IE provides a newperspective. In light of the discussion provided in this paper, it is concluded that Computer Ethics is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, Information Ethics. (shrink)

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...) main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

This essay considers what it means to understand natural language and whether a computer running an artificial-intelligence program designed to understand natural language does in fact do so. It is argued that a certain kind of semantics is needed to understand natural language, that this kind of semantics is mere symbol manipulation (i.e., syntax), and that, hence, it is available to AI systems. Recent arguments by Searle and Dretske to the effect that computers cannot understand natural language are discussed, and (...) a prototype natural-language-understanding system is presented as an illustration. (shrink)

There are many branches of philosophy called “the philosophy of X,” where X = disciplines ranging from history to physics. The philosophy of artificial intelligence has a long history, and there are many courses and texts with that title. Surprisingly, the philosophy of computer science is not nearly as well-developed. This article proposes topics that might constitute the philosophy of computer science and describes a course covering those topics, along with suggested readings and assignments.

This paper presents a version of neurophenomenology based on generative modelling techniques developed in computational neuroscience and biology. Our approach can be described as _computational phenomenology_ because it applies methods originally developed in computational modelling to provide a formal model of the descriptions of lived experience in the phenomenological tradition of philosophy (e.g., the work of Edmund Husserl, Maurice Merleau-Ponty, etc.). The first section presents a brief review of the overall project to naturalize phenomenology. The second section presents and evaluates (...) philosophical objections to that project and situates our version of computational phenomenology with respect to these projects. The third section reviews the generative modelling framework. The final section presents our approach in detail. We conclude by discussing how our approach differs from previous attempts to use generative modelling to help understand consciousness. In summary, we describe a version of computational phenomenology which uses generative modelling to construct a computational model of the inferential or interpretive processes that best explain this or that kind of lived experience. (shrink)

To clarify the notion of computation and its role in cognitive science, we need an account of implementation, the nexus between abstract computations and physical systems. I provide such an account, based on the idea that a physical system implements a computation if the causal structure of the system mirrors the formal structure of the computation. The account is developed for the class of combinatorial-state automata, but is sufficiently general to cover all other discrete computational formalisms. The implementation relation is (...) non-vacuous, so that criticisms by Searle and others fail. This account of computation can be extended to justify the foundational role of computation in artificial intelligence and cognitive science. (shrink)

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

In this reply to James H. Fetzer’s “Minds and Machines: Limits to Simulations of Thought and Action”, I argue that computationalism should not be the view that (human) cognition is computation, but that it should be the view that cognition (simpliciter) is computable. It follows that computationalism can be true even if (human) cognition is not the result of computations in the brain. I also argue that, if semiotic systems are systems that interpret signs, then both humans and computers are (...) semiotic systems. Finally, I suggest that minds can be considered as virtual machines implemented in certain semiotic systems, primarily the brain, but also AI computers. In doing so, I take issue with Fetzer’s arguments to the contrary. (shrink)

A critical survey of some attempts to define ‘computer’, beginning with some informal ones, then critically evaluating those of three philosophers, and concluding with an examination of whether the brain and the universe are computers.

Forty years’ experience as a bacterial geneticist has taught me that bacteria possess many cognitive, computational and evolutionary capabilities unimaginable in the first six decades of the twentieth century. Analysis of cellular processes such as metabolism, regulation of protein synthesis, and DNA repair established that bacteria continually monitor their external and internal environments and compute functional outputs based on information provided by their sensory apparatus. Studies of genetic recombination, lysogeny, antibiotic resistance and my own work on transposable elements revealed multiple (...) widespread bacterial systems for mobilizing and engineering DNA molecules. Examination of colony development and organization led me to appreciate how extensive multicellular collaboration is among the majority of bacterial species. Contemporary research in many laboratories on cell–cell signaling, symbiosis and pathogenesis show that bacteria utilise sophisticated mechanisms for intercellular communication and even have the ability to commandeer the basic cell biology of ‘higher’ plants and animals to meet their own needs. This remarkable series of observations requires us to revise basic ideas about biological information processing and recognise that even the smallest cells are sentient beings. Previous article in issue. (shrink)

The proper treatment of computationalism, as the thesis that cognition is computable, is presented and defended. Some arguments of James H. Fetzer against computationalism are examined and found wanting, and his positive theory of minds as semiotic systems is shown to be consistent with computationalism. An objection is raised to an argument of Selmer Bringsjord against one strand of computationalism, namely, that Turing-Test± passing artifacts are persons, it is argued that, whether or not this objection holds, such artifacts will inevitably (...) be persons. (shrink)

This article reviews the strengths and limitations of five major paradigms of medical computer-assisted decision making (CADM): (1) clinical algorithms, (2) statistical analysis of collections of patient data, (3) mathematical models of physical processes, (4) decision analysis, and (5) symbolic reasoning or artificial intelligence (Al). No one technique is best for all applications, and there is recent promising work which combines two or more established techniques. We emphasize both the inherent power of symbolic reasoning and the promise of artificial intelligence (...) and the other techniques to complement each other. (shrink)

Turner argues that computer programs must have purposes, that implementation is not a kind of semantics, and that computers might need to understand what they do. I respectfully disagree: Computer programs need not have purposes, implementation is a kind of semantic interpretation, and neither human computers nor computing machines need to understand what they do.

More than a decade ago, philosopher John Searle started a long-running controversy with his paper “Minds, Brains, and Programs” (Searle, 1980a), an attack on the ambitious claims of artificial intelligence (AI). With his now famous _Chinese Room_ argument, Searle claimed to show that despite the best efforts of AI researchers, a computer could never recreate such vital properties of human mentality as intentionality, subjectivity, and understanding. The AI research program is based on the underlying assumption that all important aspects of (...) human cognition may in principle be captured in a computational model. This assumption stems from the belief that beyond a certain level, implementational details are irrelevant to cognition. According to this belief, neurons, and biological wetware in general, have no preferred status as the substrate for a mind. As it happens, the best examples of minds we have at present have arisen from a carbon-based substrate, but this is due to constraints of evolution and possibly historical accidents, rather than to an absolute metaphysical necessity. As a result of this belief, many cognitive scientists have chosen to focus not on the biological substrate of the mind, but instead on the abstract causal structure_ _that the mind embodies (at an appropriate level of abstraction). The view that it is abstract causal structure that is essential to mentality has been an implicit assumption of the AI research program since Turing (1950), but was first articulated explicitly, in various forms, by Putnam (1960), Armstrong (1970) and Lewis (1970), and has become known as _functionalism_. From here, it is a very short step to _computationalism_, the view that computational structure is what is important in capturing the essence of mentality. This step follows from a belief that any abstract causal structure can be captured computationally: a belief made plausible by the Church–Turing Thesis, which articulates the power. (shrink)

This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate (...) twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson 's "constructible falsity". (shrink)

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...) with the appropriate topologies. (shrink)

John Searle once said: "The Chinese room shows what we knew all along: syntax by itself is not sufficient for semantics. (Does anyone actually deny this point, I mean straight out? Is anyone actually willing to say, straight out, that they think that syntax, in the sense of formal symbols, is really the same as semantic content, in the sense of meanings, thought contents, understanding, etc.?)." I say: "Yes". Stuart C. Shapiro has said: "Does that make any sense? Yes: Everything (...) makes sense. The question is: What sense does it make?" This essay explores what sense it makes to say that syntax by itself is sufficient for semantics. (shrink)

A response to a recent critique by Cem Bozşahin of the theory of syntactic semantics as it applies to Helen Keller, and some applications of the theory to the philosophy of computer science.

Artificial intelligence is increasingly being developed for use in medicine, including for diagnosis and in treatment decision making. The use of AI in medical treatment raises many ethical issues that are yet to be explored in depth by bioethicists. In this paper, I focus specifically on the relationship between the ethical ideal of shared decision making and AI systems that generate treatment recommendations, using the example of IBM’s Watson for Oncology. I argue that use of this type of system creates (...) both important risks and significant opportunities for promoting shared decision making. If value judgements are fixed and covert in AI systems, then we risk a shift back to more paternalistic medical care. However, if designed and used in an ethically informed way, AI could offer a potentially powerful way of supporting shared decision making. It could be used to incorporate explicit value reflection, promoting patient autonomy. In the context of medical treatment, we need value-flexible AI that can both respond to the values and treatment goals of individual patients and support clinicians to engage in shared decision making. (shrink)

This chapter contains section titled: Kin Selection Reciprocity Group Selection Coercion Mutualism Byproduct Mutualism Local Interactions References.

Here we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over Q, and ZS is the class of models of Th(Z, S). Similarly, (...) we show that there is no computable embedding of ACF into ZS, where ACF is the class of algebraically closed fields of characteristic 0. (shrink)

Lectures, scientific papers, top secret wartime material, correspondence, and broadcasts are introduced and set in context by Jack Copeland, Director of the Turing Archive for the History of Computing."--Jacket.

Forty years’ experience as a bacterial geneticist has taught me that bacteria possess many cognitive, computational and evolutionary capabilities unimaginable in the first six decades of the twentieth century. Analysis of cellular processes such as metabolism, regulation of protein synthesis, and DNA repair established that bacteria continually monitor their external and internal environments and compute functional outputs based on information provided by their sensory apparatus. Studies of genetic recombination, lysogeny, antibiotic resistance and my own work on transposable elements revealed multiple (...) widespread bacterial systems for mobilizing and engineering DNA molecules. Examination of colony development and organization led me to appreciate how extensive multicellular collaboration is among the majority of bacterial species. Contemporary research in many laboratories on cell–cell signaling, symbiosis and pathogenesis show that bacteria utilise sophisticated mechanisms for intercellular communication and even have the ability to commandeer the basic cell biology of ‘higher’ plants and animals to meet their own needs. This remarkable series of observations requires us to revise basic ideas about biological information processing and recognise that even the smallest cells are sentient beings. (shrink)

Intellectual autonomy has long been identified as an epistemic virtue, one that has been championed influentially by (among others) Kant, Hume and Emerson. Manifesting intellectual autonomy, at least, in a virtuous way, does not require that we form our beliefs in cognitive isolation. Rather, as Roberts and Wood (Intellectual virtues: an essay in regulative epistemology, OUP Oxford, Oxford, pp. 259–260, 2007) note, intellectually virtuous autonomy involves reliance and outsourcing (e.g., on other individuals, technology, medicine, etc.) to an appropriate extent, while (...) at the same time maintaining intellectual self-direction. In this essay, I want to investigate the ramifications for intellectual autonomy of a particular kind of epistemic dependence: cognitive enhancement. Cognitive enhancements (as opposed to therapeutic cognitive improvements) involve the use of technology and medicine to improve cognitive capacities in healthy individuals, through mechanisms ranging from smart drugs to brain-computer interfaces. With reference to case studies in bioethics, as well as the philosophy of mind and cognitive science, it is shown that epistemic dependence, in this extreme form, poses a prima facie threat to the retention of intellectual autonomy, specifically, by threatening to undermine our intellectual self-direction. My aim will be to show why certain kinds of cognitive enhancements are subject to this objection from self-direction, while others are not. Once this is established, we’ll see that even some extreme kinds of cognitive enhancement might be not merely compatible with, but constitutive of, virtuous intellectual autonomy. (shrink)