A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X \not\leq_T Y}$$\end{document}. A real X is relatively simple and above if there is a real Y (...) nonempty \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above. (shrink)

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s (...) more, I argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

The segregation of image parts into foreground and background is an important aspect of the neural computation of 3D scene perception. To achieve such segregation, the brain needs information about border ownership; that is, the belongingness of a contour to a specific surface represented in the image. This article presents psychophysical data derived from 3D percepts of figure and ground that were generated by presenting 2D images composed of spatially disjoint shapes that pointed inward or outward relative to the (...) continuous boundaries that they induced along their collinear edges. The shapes in some images had the same contrast (black or white) with respect to the background gray. Other images included opposite contrasts along each induced continuous boundary. Psychophysical results demonstrate conditions under which figure-ground judgment probabilities in response to these ambiguous displays are determined by the orientation of contrasts only, not by their relative contrasts, despite the fact that many border ownership cells in cortical area V2 respond to a preferred relative contrast. Studies are also reviewed in which both polarity-specific and polarity-invariant properties obtain perceptual figure-ground grouping results. The FACADE and 3D LAMINART models are used to explain these data. Keywords: figure-ground separation, border ownership, perceptual grouping, surface filling-in, V2, V4, FACADE Theory. (shrink)

I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

Significant variation in performance in motor imagery tasks impedes their wide adoption for brain-computer interface applications. Previous researchers have found that resting-state alpha-band power is positively correlated with MI-BCI performance. In this study, we designed a neurofeedback training protocol based on the up-regulation of the alpha band relative power to investigate its effect on MI-BCI performance. The principal finding of this study is that alpha NFT could successfully help subjects increase alpha-rhythm power and improve their MI-BCI performance. An individual (...) difference was also found in this study in that subjects who increased alpha power more had a better performance improvement. Additionally, the functional connectivity of the frontal-parietal network was found to be enhanced after alpha NFT. However, the enhancement failed to reach a significant level after multiple comparisons correction. These findings contribute to a better understanding of the neurophysiological mechanism of cognitive control through alpha regulation. (shrink)

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total information content (...) as special cases of this more general function. (shrink)

Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} (...) \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof. (shrink)

The question ‘What is computation?’ might seem a trivial one to many, but this is far from being in consensus in philosophy of mind, cognitive science and even in physics. The lack of consensus leads to some interesting, yet contentious, claims, such as that cognition or even the universe is computational. Some have argued, though, that computation is a subjective phenomenon: whether or not a physical system is computational, and if so, which computation it performs, is entirely a matter of (...) an observer choosing to view it as such. According to one view, which we dub bold anti-realist pancomputationalism, every physical object computes every computer program. According to another, more modest view, some computational systems can be ascribed multiple computational descriptions. We argue that the first view is misguided, and that the second view need not entail observer-relativity of computation. At least to a large extent, computation is an objective phenomenon. Construed as a form of information processing, we argue that information-processing considerations determine what type of computation takes place in physical systems. (shrink)

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers (...) that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself. (shrink)

This volume summarizes the ethical, social and cultural contexts of interfacing brains and computers. It is intended for the interdisciplinary community of BCI stakeholders. Insofar, engineers, neuroscientists, psychologists, physicians, care-givers and also users and their relatives are concerned. For about the last twenty years brain-computer-interfaces (BCIs) have been investigated with increasing intensity and have in principle shown their potential to be useful tools in diagnostics, rehabilitation and assistive technology. The central promise of BCI technology is enabling severely impaired people in (...) mobility, grasping, communication, and entertainment. Successful applications are for instance communication devices enabling locked-in patients in staying in contact with their environment, or prostheses enabling paralysed people in reaching and grasping. In addition to this, it serves as an introduction to the whole field of BCI for any interested reader. (shrink)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes and (...) pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (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)

We present a computational evaluation of three hypotheses about sources of deficit in sentence comprehension in aphasia: slowed processing, intermittent deficiency, and resource reduction. The ACT-R based Lewis and Vasishth model is used to implement these three proposals. Slowed processing is implemented as slowed execution time of parse steps; intermittent deficiency as increased random noise in activation of elements in memory; and resource reduction as reduced spreading activation. As data, we considered subject vs. object relative sentences, presented in a (...) self-paced listening modality to 56 individuals with aphasia and 46 matched controls. The participants heard the sentences and carried out a picture verification task to decide on an interpretation of the sentence. These response accuracies are used to identify the best parameters that correspond to the three hypotheses mentioned above. We show that controls have more tightly clustered parameter values than IWA; specifically, compared to controls, among IWA there are more individuals with slow parsing times, high noise, and low spreading activation. We find that individual IWA show differential amounts of deficit along the three dimensions of slowed processing, intermittent deficiency, and resource reduction, overall, there is evidence for all three sources of deficit playing a role, and IWA have a more variable range of parameter values than controls. An important implication is that it may be meaningless to talk about sources of deficit with respect to an abstract verage IWA; the focus should be on the individual's differential degrees of deficit along different dimensions, and on understanding the causes of variability in deficit between participants. (shrink)

The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truth-table reducibility [6]). This reducibility measures both the relative randomness and the relative computational power of real numbers. This paper proves that the computable Lipschitz degrees of computably enumerable sets are not dense. An immediate corollary is that the Solovay degrees of strongly c.e. reals are not dense. There are similarities to Barmpalias and Lewis’ proof that the identity bounded Turing degrees (...) of c.e. sets are not dense [2]), however the problem for the computable Lipschitz degrees is more complex. (shrink)

We examine the interrelationships between analog computational modelling and analogue (physical) modelling. To this end, we attempt a regimentation of the informal distinction between analog and digital, which turns on the consideration of computing in a broader context. We argue that in doing so one comes to see that (scientific) computation is better conceptualised as an epistemic process relative to agents, wherein representations play a key role. We distinguish between two, conceptually distinct, kinds of representation that, we argue, are (...) both involved in each case of computing. Based on the semantic and syntactic properties of each of these representations, we put forward a new account of the distinction between analog and digital computing. We discuss how the developed account is able to explain various properties of different models of computation, and we finish by conceptually comparing analog computational modelling to analogue (scale) modelling. It is concluded that, contrary to the standard view, the two practices are orthogonal, differing both in their foundations and in the epistemic functions they fulfil. (shrink)

PurposeThe purpose of this paper is to present a four component model of ethical behavior (PRIMES) that integrates literature in moral psychology, computing ethics, and virtue ethics as informed by research on moral exemplars in computing. This is part 1 of a two‐part contribution.Design/methodology/approachThis psychologically based and philosophically informed model argues that moral action is: grounded in relatively stable PeRsonality characteristics (PR); guided by integration of morality into the self‐system; shaped by the context of the surrounding moral ecology; and facilitated (...) by morally relevant skills and knowledge (S).FindingsThe model seeks to explain the daily successful (and unsuccessful) performance of moral action by computing professionals and to provide groundwork for a pedagogy that emphasizes ethically effective performance.Practical implicationsThe model has significant implications for how ethical action might be taught to computer professionals and other design professionals. It also makes recommendations about what is needed to measure to construct a complete picture of sustained ethical action in a profession.Originality/valueMost accepted models of ethical behavior are unidimensional, emphasizing either principled reasoning or a simplistic model of integrity/character. This model brings together a variety of disparate literatures in the light of its emphasis on sustained moral action in the profession. It thereby provides researchers and educators with a picture of what is needed to construct a complete understanding of moral action in the profession. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

The aim of this paper is to begin developing a version of Gualtiero Piccinini’s mechanistic account of computation that does not need to appeal to any notion of proper functions. The motivation for doing so is a general concern about the role played by proper functions in Piccinini’s account, which will be evaluated in the first part of the paper. I will then propose a potential alternative approach, where computing mechanisms are understood in terms of Carl Craver’s perspectival account of (...) mechanistic functions. According to this approach, the mechanistic function of ‘performing a computation’ can only be attributed relative to an explanatory perspective, but such attributions are nonetheless constrained by the underlying physical structure of the system in question, thus avoiding unlimited pancomputationalism. If successful, this approach would carry with it fewer controversial assumptions than Piccinini’s original account, which requires a robust understanding of proper functions. Insofar as there are outstanding concerns about the status of proper functions, this approach would therefore be more generally acceptable. (shrink)

One of the most significant challenges in the application of brain-computer interfaces is the large performance variation, which often occurs over time or across users. Recent evidence suggests that the physiological states may explain this performance variation in BCI, however, the underlying neurophysiological mechanism is unclear. In this study, we conducted a seven-session motor-imagery experiment on 20 healthy subjects to investigate the neurophysiological mechanism on the performance variation. The classification accuracy was calculated offline by common spatial pattern and support vector (...) machine algorithms to measure the MI performance of each subject and session. Relative Power values from different rhythms and task stages were used to reflect the physiological states and their correlation with the BCI performance was investigated. Results showed that the alpha band RP from the supplementary motor area within a few seconds before MI was positively correlated with performance. Besides, the changes of RP between task and pre-task stage from theta, alpha, and gamma band were also found to be correlated with performance both across time and subjects. These findings reveal a neurophysiological manifestation of the performance variations, and would further provide a way to improve the BCI performance. (shrink)

The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of computational (...) complexity of the Ramsey quantifier for which the phrase “A is big relatively to the universe” is interpreted as containing at least one representative of each equivalence class, for some given equvalence relation. In this work we consider quantifiers Rf, for which “A is big relatively to the universe” means “card(A) > f (n), where n is the size of the universe”. Following [Blass, Gurevich 1986] we call R mighty if Rx, yH(x, y) defines N P – complete class of finite models. Similarly we say that Rf is N P –hard if the corresponding class is N P –hard. We prove the following theorems. (shrink)

We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting (...) and resetting infinite-time register machines, and α-Turing machines for countable admissible ordinals α. (shrink)

Increasing working memory (WM) capacity is often cited as a major influence on children's development and yet WM capacity is difficult to examine independently of long‐term knowledge. A computational model of children's nonword repetition (NWR) performance is presented that independently manipulates long‐term knowledge and WM capacity to determine the relative contributions of each in explaining the developmental data. The simulations show that (a) both mechanisms independently cause the same overall developmental changes in NWR performance, (b) increase in long‐term knowledge (...) provides the better fit to the child data, and (c) varying both long‐term knowledge and WM capacity adds no significant gains over varying long‐term knowledge alone. Given that increases in long‐term knowledge must occur during development, the results indicate that increases in WM capacity may not be required to explain developmental differences. An increase in WM capacity should only be cited as a mechanism of developmental change when there are clear empirical reasons for doing so. (shrink)

Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently (...) close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe. (shrink)

We have previously established that [Formula: see text]-comprehension is equivalent to the statement that every dilator has a well-founded Bachmann–Howard fixed point, over [Formula: see text]. In this paper, we show that the base theory can be lowered to [Formula: see text]. We also show that the minimal Bachmann–Howard fixed point of a dilator [Formula: see text] can be represented by a notation system [Formula: see text], which is computable relative to [Formula: see text]. The statement that [Formula: see (...) text] is well founded for any dilator [Formula: see text] will still be equivalent to [Formula: see text]-comprehension. Thus, the latter is split into the computable transformation [Formula: see text] and a statement about the preservation of well-foundedness, over a system of computable mathematics. (shrink)

Can sentence comprehension impairments in aphasia be explained by difficulties arising from dependency completion processes in parsing? Two distinct models of dependency completion difficulty are investigated, the Lewis and Vasishth (2005) activation-based model and the direct-access model (DA; McElree, 2000). These models' predictive performance is compared using data from individuals with aphasia (IWAs) and control participants. The data are from a self-paced listening task involving subject and object relative clauses. The relative predictive performance of the models is evaluated (...) using k-fold cross-validation. For both IWAs and controls, the activation-based model furnishes a somewhat better quantitative fit to the data than the DA. Model comparisons using Bayes factors show that, assuming an activation-based model, intermittent deficiencies may be the best explanation for the cause of impairments in IWAs, although slowed syntax and lexical delayed access may also play a role. This is the first computational evaluation of different models of dependency completion using data from impaired and unimpaired individuals. This evaluation develops a systematic approach that can be used to quantitatively compare the predictions of competing models of language processing. (shrink)

Can sentence comprehension impairments in aphasia be explained by difficulties arising from dependency completion processes in parsing? Two distinct models of dependency completion difficulty are investigated, the Lewis and Vasishth (2005) activation‐based model and the direct‐access model (DA; McElree, 2000). These models' predictive performance is compared using data from individuals with aphasia (IWAs) and control participants. The data are from a self‐paced listening task involving subject and object relative clauses. The relative predictive performance of the models is evaluated (...) using k‐fold cross‐validation. For both IWAs and controls, the activation‐based model furnishes a somewhat better quantitative fit to the data than the DA. Model comparisons using Bayes factors show that, assuming an activation‐based model, intermittent deficiencies may be the best explanation for the cause of impairments in IWAs, although slowed syntax and lexical delayed access may also play a role. This is the first computational evaluation of different models of dependency completion using data from impaired and unimpaired individuals. This evaluation develops a systematic approach that can be used to quantitatively compare the predictions of competing models of language processing. (shrink)

Computer simulation modeling is an important part of contemporary scientific practice but has not yet received much attention from philosophers. The present project helps to fill this lacuna in the philosophical literature by addressing three questions that arise in the context of computer simulation of Earth's climate. Computer simulation experimentation commonly is viewed as a suspect methodology, in contrast to the trusted mainstay of material experimentation. Are the results of computer simulation experiments somehow deeply problematic in ways that the results (...) of material experiments are not? I argue against categorical skepticism toward the results of computer simulation experiments by revealing important parallels in the epistemologies of material and computer simulation experimentation. It has often been remarked that simple computer simulation models---but not complex ones---contribute substantially to our understanding of the atmosphere and climate system. Is this view of the relative contributions of simple and complex models tenable? I show that both simple and complex climate models can promote scientific understanding and argue that the apparent contribution of simple models depends upon whether a causal or deductive account of scientific understanding is adopted. When two incompatible scientific theories are under consideration, they typically are viewed as competitors, and we seek evidence that refutes at least one of the theories. In the study of climate change, however, logically incompatible computer simulation models are accepted as complementary resources for investigating future climate. How can we make sense of this use of incompatible models? I show that a collection of incompatible climate models persists in part because of difficulties faced in evaluating and comparing climate models. I then discuss the rationale for using these incompatible models together and argue that this climate model pluralism has both competitive and integrative components. (shrink)

I argue that Stich's Syntactic Theory of Mind (STM) and a naturalistic narrow content functionalism run on a Language of Though story have the same exact structure. I elaborate on the argument that narrow content functionalism is either irremediably holistic in a rather destructive sense, or else doesn't have the resources for individuating contents interpersonally. So I show that, contrary to his own advertisement, Stich's STM has exactly the same problems (like holism, vagueness, observer-relativity, etc.) that he claims plague content-based (...) psychologies. So STM can't be any better than the Representational Theory of Mind (RTM) in its prospects for forming the foundations of a scientifically respectable psychology, whether or not RTM has the problems that Stich claims it does. (shrink)

How did life come into existence on Earth? Although many scientific theories and hypotheses have been drawn, we have not yet been able to provide a detailed answer to this fundamental question. What if intelligent computers would someday be in a condition to postulate their own evolution theory which would explain how they came into the world, how would this theory look like? And how would it stand in comparison to the humans’ theory? Let us suppose that a thousand years (...) from now, intelligent and self-aware computers who, for any reason whatsoever, had lost all contacts with humans, and had continued to self-develop and improve by themselves, slowly began to wonder about how they came into the world? These intelligent computers may eventually develop a coherent theory of evolution, which would seemingly explain their existence. How would their theory stand in comparison to our theory of evolution? Would it be less comprehensive or viable? Taking into consideration the inorganic nature of computers, their relative simplicity compared to the human body, and the closeness of their components to the surrounding inorganic environment, it would not be a surprise if their theory would be more plausible than that of the humans. So, what would this signify and mean to our scientific theories in general? (shrink)

Millions of scientific articles are published each year, making it difficult to stay abreast of advances within even the smallest subdisciplines. Traditional approaches to the study of science, such as the history and philosophy of science, involve closely reading a relatively small set of journal articles. And yet many questions benefit from casting a wider net: Is most scientific change gradual or revolutionary? What are the key sources of scientific novelty? Over the past several decades, a massive effort to digitize (...) the academic literature and equip computers with algorithms that can distantly read and analyze a digital database has taken us one step closer to answering these questions. The Dynamics of Science brings together a diverse array of contributors to examine the largely unexplored computational frontiers of history and philosophy of science. Together, they reveal how tools and data from automated textual analysis, or machine "reading," combined with methods and models from game theory and cultural evolutionary theory, can begin to answer fundamental questions about the nature and history of science. (shrink)

An important, but relatively neglected, aspect of human theory of mind is emotion inference: understanding how and why a person feels a certain why is central to reasoning about their beliefs, desires and plans. The authors review recent work that has begun to unveil the structure and determinants of emotion inference, organizing them within a unified probabilistic framework.

Makkai [10] produced an arithmetical structure of Scott rank $\omega _{1}^{\mathit{CK}}$. In [9]. Makkai's example is made computable. Here we show that there are computable trees of Scott rank $\omega _{1}^{\mathit{CK}}$. We introduce a notion of "rank homogeneity". In rank homogeneous trees, orbits of tuples can be understood relatively easily. By using these trees, we avoid the need to pass to the more complicated "group trees" of [10] and [9]. Using the same kind of trees, we obtain one of rank (...) $\omega _{1}^{\mathit{CK}}$ that is "strongly computably approximable". We also develop some technology that may yield further results of this kind. (shrink)

We begin with the history of the discovery of computability in the 1930’s, the roles of Gödel, Church, and Turing, and the formalisms of recursive functions and Turing automatic machines . To whom did Gödel credit the definition of a computable function? We present Turing’s notion [1939, §4] of an oracle machine and Post’s development of it in [1944, §11], [1948], and finally Kleene-Post [1954] into its present form. A number of topics arose from Turing functionals including continuous functionals (...) on Cantor space and online computations. Almost all the results in theoretical computability use relative reducibility and o-machines rather than a-machines and most computing processes in the real world are potentially online or interactive. Therefore, we argue that Turing o-machines, relative computability, and online computing are the most important concepts in the subject, more so than Turing a-machines and standard computable functions since they are special cases of the former and are presented first only for pedagogical clarity to beginning students. At the end in §10–§13 we consider three displacements in computability theory, and the historical reasons they occurred. Several brief conclusions are drawn in §14. (shrink)

Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r \in R}$$\end{document}, there exists an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i \in I}$$\end{document} so that i ≤ r < i + 1. Mourgues and Ressayre (J Symb Logic 58:641–647, 1993) showed that every real closed field has an integer part. The procedure of Mourgues and (...) Ressayre appears to be quite complicated. We would like to know whether there is a simple procedure, yielding an integer part that is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2(R)}$$\end{document} —limit computable relative to R. We show that there is a maximal Z-ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I \subseteq R}$$\end{document} which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2(R)}$$\end{document}. However, this I may not be an integer part for R. By a result of Wilkie (Logic Colloquium ’77), any Z-ring can be extended to an integer part for some real closed field. Using Wilkie’s ideas, we produce a real closed field R with a Z-ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I \subseteq R}$$\end{document} such that I does not extend to an integer part for R. For a computable real closed field, we do not know whether there must be an integer part in the class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2}$$\end{document}. We know that certain subclasses of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2}$$\end{document} are not sufficient. We show that for each \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \in \omega}$$\end{document}, there is a computable real closed field with no n-c.e. integer part. In fact, there is a computable real closed field with no n-c.e. integer part for any n. (shrink)

Computer ethics is a relatively young discipline,hence it needs time both for reflection and forexploring alternative ethical standpoints in buildingup its own theoretical framework. Feminist ethics isoffered as one such alternative particularly to informissues of equality and power. We argue that feministethics is not narrowly confined to ‘women's issues’ but is an approach with wider egalitarianapplications. The rise of feminist ethics in relationto feminist theory in general is described and withinthat the work of Gilligan and others on an ‘ethic of (...) care’. We argue for the need to connect theory toempirical evidence. Empirical studies of gender andbusiness and computer ethics are reviewed. We noteconcerns with surveying a student audience, the issueof how far questionnaires and interviews can get tothe heart of ethical beliefs and problems ofperforming statistical analyses of quantitative data.Although we recognize them, our own small surveycannot avoid all these problems. Nevertheless byrefining our scenarios we are able to offer analternative reading of a hacking problem in terms ofan ethic of care thereby pointing a way forward forfuture research in computer ethics inspired byfeminist theory. (shrink)

PurposeThe purpose of this paper is to present a four component model of ethical behavior that integrates literature in moral psychology, computing ethics, and virtue ethics as informed by research on moral exemplars in computing. This is part 2 of a two part contribution, part 1 having appeared in Vol. 6 No. 3.Design/methodology/approachThis psychologically based and philosophically informed model argues that moral action is grounded in relatively stable personality characteristics, guided by integration of morality into the self‐system, shaped by the (...) context of the surrounding moral ecology, and facilitated by morally relevant skills and knowledge.FindingsThe model seeks to explain the daily successful (and unsuccessful) performance of moral action by computing professionals and to provide groundwork for a pedagogy that emphasizes ethically effective performance.Practical implicationsThe model has significant implications for how ethical action to computer professionals and other design professionals might be taught. It also makes recommendations about what need to be measured to construct a complete picture of sustained ethical action in a profession.Originality/valueMost accepted models of ethical behavior are unidimensional, emphasizing either principled reasoning or a simplistic model of integrity/character. This model brings together a variety of disparate literatures in the light of its emphasis on sustained moral action in the profession. It thereby provides researchers and educators with a picture of what is needed to construct a complete understanding of moral action in the profession. (shrink)

Recall that B is PA relative to A if B computes a member of every nonempty $\Pi ^0_1(A)$ class. This two-place relation is invariant under Turing equivalence and so can be thought of as a binary relation on Turing degrees. Miller and Soskova [23] introduced the notion of a $\Pi ^0_1$ class relative to an enumeration oracle A, which they called a $\Pi ^0_1{\left \langle {A}\right \rangle }$ class. We study the induced extension of the relation B is (...) PA relative to A to enumeration oracles and hence enumeration degrees. We isolate several classes of enumeration degrees based on their behavior with respect to this relation: the PA bounded degrees, the degrees that have a universal class, the low for PA degrees, and the ${\left \langle {\text {self}\kern1pt}\right \rangle }$ -PA degrees. We study the relationship between these classes and other known classes of enumeration degrees. We also investigate a group of classes of enumeration degrees that were introduced by Kalimullin and Puzarenko [14] based on properties that are commonly studied in descriptive set theory. As part of this investigation, we give characterizations of three of their classes in terms of a special sub-collection of relativized $\Pi ^0_1$ classes—the separating classes. These three can then be seen to be direct analogues of three of our classes. We completely determine the relative position of all classes in question. (shrink)

We exploit properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy. Families of sets with such enumeration features were previously built by Selivanov, Goncharov, and Wehner. For a computable successor ordinal α, we transform a countable directed graph into a structure such that has a isomorphic copy if and only if has a computable isomorphic copy.A computable structure is (...) categorical if for all computable isomorphic copies of , there is an isomorphism from onto , which is . We prove that for every computable successor ordinal α, there is a computable, categorical structure, which is not relatively categorical. This generalizes the result of Goncharov that there is a computable, computably categorical structure, which is not relatively computably categorical.An additional relation R on the domain of a computable structure is intrinsically on if in all computable isomorphic copies of , the image of R is . We prove that for every computable successor ordinal α, there is an intrinsically relation on a computable structure, which not relatively intrinsically . This generalizes the result of Manasse that there is an intrinsically computably enumerable relation on a computable structure, which is not relatively intrinsically computably enumerable.The dimension of a structure is the number of computable isomorphic copies, up to isomorphisms. We prove that for every computable successor ordinal α and every n≥1, there is a computable structure with dimension n. This generalizes the result of Goncharov that there is a structure of computable dimension n for every n≥1.Finally, we prove that for every computable successor ordinal α, there is a countable structure with isomorphic copies in just the Turing degrees of sets X such that relative to X is not . In particular, for every finite n, there is a structure with isomorphic copies in exactly the non- Turing degrees. This generalizes the result obtained by Wehner, and independently by Slaman, that there is a structure with isomorphic copies in exactly the nonzero Turing degrees. (shrink)

The computer is a relatively new invention in the history of man. It has found application in many sectors, and will undoubtedly influence our society. As we shall show, however, the computer is linked to a chain of development that started 10,000 years ago, when a society of hunters and gatherers changed into an agricultural society. The computer is completely dependent on this development towards a more and more formalized society.

In 1982, when computers were just becoming widely available, I was a graduate student beginning my work with Clark Glymour on a PhD thesis entitled: “Causality in the Social Sciences.” Dazed and confused by the vast philosophical literature on causation, I found relative solace in the clarity of Structural Equation Models (SEMs), a form of statistical model used commonly by practicing sociologists, political scientists, etc., to model causal hypotheses with which associations among measured variables might be explained. The statistical (...) literature around SEMs was vast as well, but Clark had extracted from it a particular kind of evidential constraint first studied by Charles Spearman at the beginning of the 20th century, the “vanishing tetrad difference.”1 As it turned out, certain kinds of causal structures entailed these constraints, and others did not. Spearman used this lever to argue for the existence of a single, general intelligence factor, the infamous g (Spearman, 1904). (shrink)

Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))? Two applications are given: first, a constructive quantifier elimination relative to the (...) leading terms, suggesting a relative decision procedure; second, a presentation of every definable subset of K as the pullback of a definable set in the leading terms subjected to a linear translation. (shrink)

Different characterizations of classes of shift dynamical systems via labeled digraphs, languages, and sets of forbidden words are investigated. The corresponding naming systems are analyzed according to reducibility and particularly with regard to the computability of the topological entropy relative to the presented naming systems. It turns out that all examined natural representations separate into two equivalence classes and that the topological entropy is not computable in general with respect to the defined natural representations. However, if a specific (...) labeled digraph representation - namely primitive, right-resolving labeled digraphs - of some class of shifts is considered, namely the shifts having the specification property, then the topological entropy gets computable. (shrink)

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)