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)

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)

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)

Fodor and others who think that scientific, computational psychology will vindicate commonsense belief-desire psychology have maintained that belief can be identified with the explicit storage of a token with appropriate content. I review and develop problems for the explicit storage view and show that a more plausible account identifies belief with the disposition to use a token with appropriate content in explicit reasoning and planning processes and as a basis for action. I argue that this type of inner disposition account (...) will also apply to most other common sense attitudes. The result is a realism about commonsense belief-desire psychology that is more modest than Fodor's: While such inner dispositions probably do exist, these states will probably not be the main focus of scientific psychological theories. (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)

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)

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)

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)

The question of where, between theory and experiment, computer simulations (CSs) locate on the methodological map is one of the central questions in the epistemology of simulation (cf. Saam Journal for General Philosophy of Science, 48, 293–309, 2017). The two extremes on the map have them either be a kind of experiment in their own right (e.g. Barberousse et al. Synthese, 169, 557–574, 2009; Morgan 2002, 2003, Journal of Economic Methodology, 12(2), 317–329, 2005; Morrison Philosophical Studies, 143, 33–57, 2009; Morrison (...) 2015; Massimi and Bhimji Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 51, 71–81, 2015; Parker Synthese, 169, 483–496, 2009) or just an argument executed with the aid of a computer (e.g. Beisbart European Journal for Philosophy of Science, 2, 395–434, 2012; Beisbart and Norton International Studies in the Philosophy of Science, 26, 403–422, 2012). There exist multiple versions of the first kind of position, whereas the latter is rather unified. I will argue that, while many claims about the ‘experimental’ status of CSs seem unjustified, there is a variant of the first position that seems preferable. In particular I will argue that while CSs respect the logic of (deductively valid) arguments, they neither agree with their pragmatics nor their epistemology. I will then lay out in what sense CSs can fruitfully be seen as experiments, and what features set them apart from traditional experiments nonetheless. I conclude that they should be seen as surrogate experiments, i.e. experiments executed consciously on the wrong kind of system, but with an exploitable connection to the system of interest. Finally, I contrast my view with that of Beisbart (European Journal for Philosophy of Science, 8, 171–204, 2018), according to which CSs are surrogates for experiments, arguing that this introduces an arbitrary split between CSs and other kinds of simulations. (shrink)

Cloud Computing paradigm has reached a high degree of popularity among all kinds of computer users, but it may not be suitable for mobile devices as they need computing power to be as close as possible to data sources in order to reduce delays. This paper focuses on achieving mathematical models for users moving around and proposes an overlay mobility model for Fog Data Centres based on traditional wireless mobility models aimed at better allocating edge computing resources to client demands. (...) Additionally, the focus is also on providing a model as to how the computing assets related to each user follow it through the fog infrastructure so as to minimise the distance to the user according to a Fat-Tree based Data Centre topology. (shrink)

Collecting, comparing, and computing molecular sequences are among the most prevalent practices in contemporary biological research. They represent a specific way of producing knowledge. This paper explores the historical development of these practices, focusing on the work of Margaret O. Dayhoff, Richard V. Eck, and Robert S. Ledley, who produced the first computer-based collection of protein sequences, published in book format in 1965 as the Atlas of Protein Sequence and Structure. While these practices are generally associated with the rise of (...) molecular evolution in the 1960s, this paper shows that they grew out of research agendas from the previous decade, including the biochemical investigation of the relations between the structures and function of proteins and the theoretical attempt to decipher the genetic code. It also shows how computers became essential for the handling and analysis of sequence data. Finally, this paper reflects on the relationships between experimenting and collecting as two distinct “ways of knowing” that were essential for the transformation of the life sciences in the twentieth century. (shrink)

In this paper, we pursue three general aims: (I) We will define a notion of fundamental opacity and ask whether it can be found in High Energy Physics (HEP), given the involvement of machine learning (ML) and computer simulations (CS) therein. (II) We identify two kinds of non-fundamental, contingent opacity associated with CS and ML in HEP respectively, and ask whether, and if so how, they may be overcome. (III) We address the question of whether any kind of opacity, contingent (...) or fundamental, is unique to ML or CS, or whether they stand in continuity to kinds of opacity associated with other scientific research. (shrink)

To provide an introduction to this book, we explain the motivation to publish this volume, state its main goal, characterize its intended readership, and give an overview of its content. To this purpose, we briefly summarize each chapter and put it in the context of the whole volume. We also take the opportunity to stress connections between the chapters. We conclude with a brief outlook.The main motivation to publish this volume was the diagnosis that the validation of computer simulation needs (...) more attention in practice and in theory. The aim of this volume is to improve our understanding of validation. To this purpose, computer scientists, mathematicians, working scientists from various fields, as well as philosophers of science join efforts. They explain basic notions and principles of validation, embed validation in philosophical frameworks such as Bayesian epistemology, detail the steps needed during validation, provide best practice examples, reflect upon challenges to validation, and put validation in a broader perspective. As we suggest in our outlook, the validation of computer simulations will remain an important research topic that needs cross- and interdisciplinary efforts. A key issue is whether, and if so, how very rigorous approaches to validation that have proven useful in, e.g., engineering can be extended to other disciplines. (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 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)

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.

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.

A brain-computer interface is a rapidly evolving neurotechnology connecting the human brain with a computer. In its classic form, brain activity is recorded and used to control external devices like protheses or wheelchairs. Thus, BCI users act with the power of their thoughts. While the initial development has focused on medical uses of BCIs, non-medical applications have recently been gaining more attention, for example in automobiles, airplanes, and the entertainment context. However, the attitudes of the general public towards BCIs have (...) hardly been explored. Among the general population in Germany aged 18–65 years, a representative online survey with 20 items was conducted in summer 2018 and analysed by descriptive statistics. The survey assessed: affinity for technology; previous knowledge and experience concerning BCIs; the attitude towards ethical, social and legal implications of BCI use and demographic information. Our results indicate that BCIs are a unique and puzzling way of human–machine interaction. The findings reveal a positive view and high level of trust in BCIs on the one hand but on the other hand a wide range of ethical and anthropological concerns. Agency and responsibility were clearly attributed to the BCI user. The participants’ opinions were divided regarding the impact BCIs have on humankind. In summary, a high level of ambivalence regarding BCIs was found. We suggest better information of the public and the promotion of public deliberation about BCIs in order to ensure responsible development and application of this potentially disruptive technology. (shrink)

In addition, this book contains tools that, in principle, can search a set of algorithms to see whether a problem is solvable, or more specifically, if it can be solved by an algorithm whose computations are efficient.

The author has surveyed a quarter of the accredited undergraduate computer science programs in the United States. More than half of these programs offer a “social and ethical implications of computing” course taught by a computer science faculty member, and there appears to be a trend toward teaching ethics classes within computer science departments. Although the decision to create an “in house” computer ethics course may sometimes be a pragmatic response to pressure from the accreditation agency, this paper argues that (...) teaching ethics within a computer science department can provide students and faculty members with numerous benefits. The paper lists topics that can be covered in a computer ethics course and offers some practical suggestions for making the course successful. (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)

It is the unique business of agents to act. But what does it take for an agent to act, and what unique conditions render an agent capable of acting? A remark of Wittgenstein’s proves useful in crys...

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between (...) thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed. (shrink)