The simulation hypothesis has recently excited renewed interest, especially in the physics and philosophy communities. However, the hypothesis specifically concerns {computers} that simulate physical universes, which means that to properly investigate it we need to couple computer science theory with physics. Here I do this by exploiting the physical Church-Turing thesis. This allows me to introduce a preliminary investigation of some of the computer science theoretic aspects of the simulation hypothesis. In particular, building on (...) Kleene's second recursion theorem, I prove that it is mathematically possible for us to be in a simulation that is being run on a computer \textit{by us}. In such a case, there would be two identical instances of us; the question of which of those is ``really us'' is meaningless. I also show how Rice's theorem provides some interesting impossibility results concerning simulation and self-simulation; briefly describe the philosophical implications of fully homomorphic encryption for (self-)simulation; briefly investigate the graphical structure of universes simulating universes simulating universes, among other issues. I end by describing some of the possible avenues for future research that this preliminary investigation reveals. (shrink)

What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). (...) Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gildel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest. (shrink)

In my 2013 article, “A New Theory of Free Will”, I argued that several serious hypotheses in philosophy and modern physics jointly entail that our reality is structurally identical to a peer-to-peer (P2P) networked computer simulation. The present paper outlines how quantum phenomena emerge naturally from the computational structure of a P2P simulation. §1 explains the P2P Hypothesis. §2 then sketches how the structure of any P2P simulation realizes quantum superposition and wave-function collapse (§2.1.), quantum indeterminacy (...) (§2.2.), wave-particle duality (§2.3.), and quantum entanglement (§2.4.). Finally, §3 argues that although this is by no means a philosophical proof that our reality is a P2P simulation, it provides ample reasons to investigate the hypothesis further using the methods of computer science, physics, philosophy, and mathematics. (shrink)

Hay and, then, Johnson extended the classic Rice and Rice-Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, equation image. Other cases are done for all transfinite notations in a very natural, proper subsystem equation image of equation image, where (...) equation image has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in equation image. (shrink)

The computational view of mind rests on certain intuitions regarding the fundamental similarity between computation and cognition. We examine some of these intuitions and suggest that they derive from the fact that computers and human organisms are both physical systems whose behavior is correctly described as being governed by rules acting on symbolic representations. Some of the implications of this view are discussed. It is suggested that a fundamental hypothesis of this approach is that there is a natural domain of (...) human functioning that can be addressed exclusively in terms of a formal symbolic or algorithmic vocabulary or level of analysis. Much of the paper elaborates various conditions that need to be met if a literal view of mental activity as computation is to serve as the basis for explanatory theories. The coherence of such a view depends on there being a principled distinction between functions whose explanation requires that we posit internal representations and those that we can appropriately describe as merely instantiating causal physical or biological laws. In this paper the distinction is empirically grounded in a methodological criterion called the " cognitive impenetrability condition." Functions are said to be cognitively impenetrable if they cannot be influenced by such purely cognitive factors as goals, beliefs, inferences, tacit knowledge, and so on. Such a criterion makes it possible to empirically separate the fixed capacities of mind from the particular representations and algorithms used on specific occasions. In order for computational theories to avoid being ad hoc, they must deal effectively with the "degrees of freedom" problem by constraining the extent to which they can be arbitrarily adjusted post hoc to fit some particular set of observations. This in turn requires that the fixed architectural function and the algorithms be independently validated. It is argued that the architectural assumptions implicit in many contemporary models run afoul of the cognitive impenetrability condition, since the required fixed functions are demonstrably sensitive to tacit knowledge and goals. The paper concludes with some tactical suggestions for the development of computational cognitive theories. (shrink)

The Epistemology Of Computer Simulation has developed as an epistemological and methodological analysis of simulative sciences using quantitative computational models to represent and predict empirical phenomena of interest. In this paper, Executable Cell Biology and Agent-Based Modelling are examined to show how one may take advantage of qualitative computational models to evaluate reachability properties of reactive systems. In contrast to the thesis, advanced by EOCS, that computational models are not adequate representations of the simulated empirical systems, it is (...) shown how the representational adequacy of qualitative models is essential to evaluate reachability properties. Justification theory, if not playing an essential role in EOCS, is exhibited to be involved in the process of advancing and corroborating model-based hypotheses about empirical systems in ECB and ABM. Finally, the practice of evaluating model-based hypothesis by testing the simulated systems is shown to constitute an argument in favour of the thesis that computer simulations in ECB and ABM can be put on a par with scientific experiments. (shrink)

An overview of my work arguing that peer-to-peer computer networking (the Peer-to-Peer Simulation Hypothesis) may be the best explanation of quantum phenomena and a number of perennial philosophical problems.

Historically, the hypothesis that our world is a computer simulation has struck many as just another improbable-but-possible “skeptical hypothesis” about the nature of reality. Recently, however, the simulation hypothesis has received significant attention from philosophers, physicists, and the popular press. This is due to the discovery of an epistemic dependency: If we believe that our civilization will one day run many simulations concerning its ancestry, then we should believe that we are probably in an ancestor simulation (...) right now. This essay examines a troubling but underexplored feature of the ancestor-simulation hypothesis: the termination risk posed by both ancestor-simulation technology and experimental probes into whether our world is an ancestor simulation. This essay evaluates the termination risk by using extrapolations from current computing practices and simulation technology. The conclusions, while provisional, have great implications for debates concerning the fundamental nature of reality and the safety of contemporary physics. (shrink)

The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it (...) is hoped will make this volume an invaluable resource for specialists and non-specialists alike. (shrink)

According to the age-of-acquisition hypothesis, words acquired early in life are processed faster and more accurately than words acquired later. Connectionist models have begun to explore the influence of the age/order of acquisition of items (and also their frequency of encounter). This study attempts to reconcile two different methodological and theoretical approaches (proposed by Lambon Ralph & Ehsan, 2006 and Zevin & Seidenberg, 2002) to age-limited learning effects. The current simulations extend the findings reported by Zevin and Seidenberg (2002) that (...) have shown that frequency trajectories (FTs) have limited and specific effects on word-reading tasks. Using the methodological framework proposed by Lambon Ralph and Ehsan (2006), which makes it possible to compare word-reading and picture-naming tasks in connectionist networks, we were able to show that FT has a considerable influence on age-limited learning effects in a picture naming task. The findings show that when the input–output mappings are arbitrary (simulating picture naming tasks), the links formed by the network become entrenched as a result of early experience and that subsequent variations in frequency of exposure of the items have only a minor impact. In contrast, when the mappings between input-output are quasi-systematic or systematic (simulating word-reading tasks), the training of new items was generalized and resulted in the suppression of age-limited learning effects. At a theoretical level, we suggest that FT, which simultaneously takes account of time and the level of exposure across time, represents a more precise and modulated measure compared with the order of introduction of the items and may lead to innovative hypotheses in the field of age-limited learning effects. (shrink)

Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access (...) to the empirical world. This expansion forms the basis for a new kind of empiricism, better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of epistemological correctness.Humphreys also includes arguments for the primacy of properties rather than objects, the need to consider technological constraints when appraising scientific methods, and a detailed account of how the path from computational template to scientific application is constructed. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on formal reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Extending Ourselves will be of interest to philosophers of science, epistemologists, and to anyone interested in the role played by computers in modern science. (shrink)

A Guide to Plato's Republic provides an integral interpretation of the Republic which is accessible even to readers approaching Plato's masterwork for the first time. Written at a level understandable to undergraduates, it is ideal for students and other readers who have little or no background in philosophy or political theory. Rice anticipates their inevitable reactions to the Republic and treats them seriously, opening the way to an appreciation of the complexities of the text without oversimplifying it. While many (...) books on the Republic never stray far from explicating Plato's text, this work contrasts Plato's responses to perennial issues in philosophy and political theory with those of several key subsequent thinkers. It uses engaging examples to show the continuing relevance of Plato's arguments and introduces some basic vocabulary of philosophy and political theory, going beyond terse dictionary definitions by illustrating what technical terms mean in the context of Plato's work. The author's interpretative posture is appreciative but respectfully critical of Plato's vision. Stressing the relationship between Plato's politics and metaphysics, Rice argues that Plato's reluctance to accept the reality and consequences of finitude accounts for much of what many readers find objectionable in his politics. Lively, relatively brief, and designed to provoke discussion in the classroom, A Guide to Plato's Republic is ideal for political theory and introduction to philosophy courses as well as other courses that assign the Republic as a primary text. (shrink)

Attempts by 20th century philosophers of science to define inductive concepts and methods concerning the support provided to scientific theories by empirical data have been unsuccessful. Although 20th century philosophers of science largely ignored statistical methods for testing theories, when they did address them they argued against rather than for their use. In contrast, this study demonstrates that traditional statistical methods used for validating computer simulation models provide tests of the scientific theories that those models may (...) embody. This study shows that these statistical methods are applicable regardless of whether the scientific theory or model is deterministic, stochastic, or chaos-based in nature. Traditional statistical methods, such as hypothesis testing, test theories by providing measures of their goodness-of-fit with the portion of the world the theories describe. Nothing more is needed to portray the agreement between theory and the world. Furthermore, the statistical measures of goodness-of-fit are not ampliative inductive measures. Therefore, the ultimate value and direction of the 20 th century ampliative inductive program within philosophy of science is thrown into question. This study also suggests that advanced statistical, visualization, and hybrid quantitative qualitative methods hold promise for offering scientists additional methods for testing scientific theories through validating their computer model representations. As a prerequisite to the above discussions, this study proves that scientific theories, when applied to concrete physical systems, can indeed be represented by computer models. (shrink)

This volume presents the proceedings of the workshop CSL '91 (Computer Science Logic) held at the University of Berne, Switzerland, October 7-11, 1991. This was the fifth in a series of annual workshops on computer sciencelogic (the first four are recorded in LNCS volumes 329, 385, 440, and 533). The volume contains 33 invited and selected papers on a variety of logical topics in computer science, including abstract datatypes, bounded theories, complexity results, cut elimination, denotational (...) semantics, infinitary queries, Kleene algebra with recursion, minimal proofs, normal forms in infinite-valued logic, ordinal processes, persistent Petri nets, plausibility logic, program synthesis systems, quantifier hierarchies, semantics of modularization, stable logic, term rewriting systems, termination of logic programs, transitive closure logic, variants of resolution, and many others. (shrink)

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central (...) role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11-CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic. (shrink)

Introduction -- Sanctioning models : theories and their scope -- Methodology for a virtual world -- A tale of two methods -- When theories shake hands -- Models of climate : values and uncertainties -- Reliability without truth -- Conclusion.

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, (...) if X intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

Shapiro and Sober claim that Walsh, Ariew, Lewens, and Matthen give a mistaken, a priori defense of natural selection and drift as epiphenomenal. Contrary to Shapiro and Sober’s claims, we first argue that WALM’s explanatory doctrine does not require a defense of epiphenomenalism. We then defend WALM’s explanatory doctrine by arguing that the explanations provided by the modern genetical theory of natural selection are ‘autonomous-statistical explanations’ analogous to Galton’s explanation of reversion to mediocrity and an explanation of the diffusion ofgases. (...) We then argue that whereas Sober’s theory of forces is an adequate description of Darwin’s theory, WALM’s explanatory doctrine is required to understand how themodern genetical theory of natural selection explains large-scale statistical regularities. 1 Introduction2 Shapiro and Sober’s ‘Epiphenomenalism Do’s and Don’ts’3 WALM’s Explanatory Doctrine4 Galton’s Autonomous-Statistical Explanation5 A Second Example: The Statistical Explanation of the Diffusion of Gases6 Distinguishing Two Theories of Evolution by Natural Selection7 A Possible Objection: Are Statistical Laws Sufficient for Explanation?8 Conclusion. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic (...) computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

Recently, information retrieval is shown to be a science by mapping information retrieval scientific study to scientific study abstracted from physics. The exercise was rather tedious and lengthy. Instead of dealing with the nitty gritty, this paper looks at the insights into how computer science can be made into a science by using that methodology. That is by mapping computer science scientific study to the scientific study abstracted from physics. To show the mapping between (...) computer science and physics, we need to define what is engineering science which computer science belongs to. Some principles and assumptions of engineering science theory are presented. To show computer science is a science, we presented two approaches. Approach 1 considers computer science as simulation of human behaviour similar to the goal of artificial intelligence. Approach 2 is closely related to the actual activities in computer science, and this approach considers computer science based on the theory of computation. Finally, we answer some of the common outstanding issues about computer science to convince our reader that computer science is a science. (shrink)

Catherine Elgin has recently argued that a nonfactive conception of understanding is required to accommodate the epistemic successes of science that make essential use of idealizations and models. In this paper, I argue that the fact that our best scientific models and theories are pervasively inaccurate representations can be made compatible with a more nuanced form of scientific realism that I call Understanding Realism. According to this view, science aims at (and often achieves) factive scientific understanding of natural (...) phenomena. I contend that this factive scientific understanding is provided by grasping a set of true modal information about the phenomenon of interest. Furthermore, contrary to Elgin’s view, I argue that the facticity of this kind of scientific understanding can be separated from the inaccuracy of the models and theories used to produce it. (shrink)

Computer simulation is shown to be philosophically interesting because it introduces a qualitatively new methodology for theory construction in science different from the conventional two components of "theory" and "experiment and/or observation". This component is "experimentation with theoretical models." Two examples from the physical sciences are presented for the purpose of demonstration but it is claimed that the biological and social sciences permit similar theoretical model experiments. Furthermore, computer simulation permits theoretical models for the evolution (...) of physical systems which use cellular automata rather than differential equations as their syntax. The great advantages of the former are indicated. (shrink)

Current critical pedagogical scholarship has theorized the epistemological and social intersection between globalization and educational technology according to two distinct positions. For some, this intersection offers new liberatory knowledges and opportunities that can subvert social homogenization and economic disparity. For others, this relationship is just another phase of neoimperialism that should be politically and ideologically resisted. In contrast, we argue that the intersection between globalization and educational technologies is rather a manifestation of larger economic and logical forces, and that resistance (...) to such circumstances can neither be purely ideological or social. Instead, we contend that such a theoretical and pedagogical foreclosure dialectically actualizes conditions for real change—particularly when it complicates educational research technologies and their impact on epistemological multiplicity. (shrink)

Computer simulations are widely used within the area of building science research. Building science research deals with the physical phenomena that affect buildings, including heat and mass transfer, lighting and acoustic transmission. This wide usage of computer simulations, however, is characterized by a divergence in thought on the composition of an epistemological framework that may provide guidance for their deployment in research. This paper undertakes a fundamental review of the epistemology of computer simulations within the (...) context of the philosophy of science. Thereafter, it reviews the epistemological framework within which computer simulations are used in practice within the area of building science research. A comparison between the insights obtained from the realms of theory and practice is made, which then interrogates the adequacy of the epistemological approaches that have been employed in previously published simulation-based research. These insights may help in informing a normative composition of an adequate epistemological framework within which computer simulation-based building science research may be conducted. (shrink)

Alan M. Turing, pioneer of computing and WWII codebreaker, is one of the most important and influential thinkers of the twentieth century. In this volume for the first time his key writings are made available to a broad, non-specialist readership. They make fascinating reading both in their own right and for their historic significance: contemporary computational theory, cognitive science, artificial intelligence, and artificial life all spring from this ground-breaking work, which is also rich in philosophical and logical insight. An (...) introduction by leading Turing expert Jack Copeland provides the background and guides the reader through the selection. About Alan Turing Alan Turing FRS OBE, (1912-1954) studied mathematics at King's College, Cambridge. He was elected a Fellow of King's in March 1935, at the age of only 22. In the same year he invented the abstract computing machines - now known simply as Turing machines - on which all subsequent stored-program digital computers are modelled. During 1936-1938 Turing continued his studies, now at Princeton University. He completed a PhD in mathematical logic, analysing the notion of 'intuition' in mathematics and introducing the idea of oracular computation, now fundamental in mathematical recursion theory. An 'oracle' is an abstract device able to solve mathematical problems too difficult for the universal Turing machine. In the summer of 1938 Turing returned to his Fellowship at King's. When WWII started in 1939 he joined the wartime headquarters of the Government Code and Cypher School (GC&CS) at Bletchley Park, Buckinghamshire. Building on earlier work by Polish cryptanalysts, Turing contributed crucially to the design of electro-mechanical machines ('bombes') used to decipher Enigma, the code by means of which the German armed forces sought to protect their radio communications. Turing's work on the version of Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as 'Fish'. Based on binary teleprinter code, Fish was used during the latter part of the war in preference to morse-based Enigma for the encryption of high-level signals, for example messages from Hitler and other members of the German High Command. It is estimated that the work of GC&CS shortened the war in Europe by at least two years. Turing received the Order of the British Empire for the part he played. In 1945, the war over, Turing was recruited to the National Physical Laboratory (NPL) in London, his brief to design and develop an electronic computer - a concrete form of the universal Turing machine. Turing's report setting out his design for the Automatic Computing Engine (ACE) was the first relatively complete specification of an electronic stored-program general-purpose digital computer. Delays beyond Turing's control resulted in NPL's losing the race to build the world's first working electronic stored-program digital computer - an honour that went to the Royal Society Computing Machine Laboratory at Manchester University, in June 1948. Discouraged by the delays at NPL, Turing took up the Deputy Directorship of the Royal Society Computing Machine Laboratory in that year. Turing was a founding father of modern cognitive science and a leading early exponent of the hypothesis that the human brain is in large part a digital computing machine, theorising that the cortex at birth is an 'unorganised machine' which through 'training' becomes organised 'into a universal machine or something like it'. He also pioneered Artificial Intelligence. Turing spent the rest of his short career at Manchester University, being appointed to a specially created Readership in the Theory of Computing in May 1953. He was elected a Fellow of the Royal Society of London in March 1951 (a high honour). (shrink)

Current critical pedagogical scholarship has theorized the epistemological and social intersection between globalization and educational technology according to two distinct positions. For some, this intersection offers new liberatory knowledges and opportunities that can subvert social homogenization and economic disparity. For others, this relationship is just another phase of neoimperialism that should be politically and ideologically resisted. In contrast, we argue that the intersection between globalization and educational technologies is rather a manifestation of larger economic and logical forces, and that resistance (...) to such circumstances can neither be purely ideological or social. Instead, we contend that such a theoretical and pedagogical foreclosure dialectically actualizes conditions for real change—particularly when it complicates educational research technologies and their impact on epistemological multiplicity. (shrink)

Humans grasp discrete infinities within several cognitive domains, such as in language, thought, social cognition and tool-making. It is sometimes suggested that any such generative ability is based on a computational system processing hierarchical and recursive mental representations. One view concerning such generativity has been that each of the mind’s modules defining a cognitive domain implements its own recursive computational system. In this paper recent evidence to the contrary is reviewed and it is proposed that there is only one supramodal (...) computational system with recursion in the human mind. A recursion thesis is defined, according to which the hominin cognitive evolution is constituted by a recent punctuated genetic mutation that installed the general, supramodal capacity for recursion into the human nervous system on top of the existing, evolutionarily older cognitive structures, and it is argued on the basis of empirical evidence and theoretical considerations that the recursion thesis constitutes a plausible research program for cognitive science. (shrink)

The present paper intends to show that computer simulations used in science are akin to fiction. Starting from the problem of defining computer simulation, the paper discusses the uses and disadvantages of simulations in science. Computer simulations have a representational function, but they do not resemble the phenomena that they purport to represent. Computer simulations do not preserve the content of the models, input data, and theories from which they proceed, since the content (...) is modified by computational processes. Because of the complexities of these processes, we cannot control or test the methods used to process the content of computer simulations. Still, simulations may help to explain the behaviour of a possible aspect of the phenomenon under examination. Although their role in doing so may be limited, by conforming to and immersing us in the worldview of science, simulations, thus reinforce the intuitions of the existing body of scientific knowledge, and similarly to the “believable fiction” described by John Woods, provide genuine understanding. (shrink)

The Role of Dorsal Premotor Cortex in Resolving Abstract Motor Rules provides alternative hypotheses about the cognitive functions affected by the application of repetitive transcranial magnetic stimulation. Their model simulated the effect of stimulation of the left dorsal premotor cortex right as participants provide a Models were used to demonstrate that the increased variability in observed response times can result from interference in replanning during the process of responding to the uninstructed stimulus.

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

A Guide to Plato's Republic provides an integral interpretation of the Republic that is accessible even to readers approaching Plato's masterwork for the first time. Written at a level understandable to undergraduates, it is ideal for students and other readers who have little or no background in philosophy or political theory. Rice anticipates their inevitable reactions to the Republic and treats them seriously, opening the way to an appreciation of the complexities of the text without oversimplifying it. While many (...) books on the Republic never stray far from explicating Plato's text, this work contrasts Plato's responses to perennial issues in philosophy and political theory with those of several key subsequent thinkers. It uses engaging examples to show the continuing relevance of Plato's arguments and introduces some basic vocabulary of philosophy and political theory, going beyond terse dictionary definitions by illustrating what technical terms mean in the context of Plato's work. The author's interpretative posture is appreciative but respectfully critical of Plato's vision. Stressing the relationship between Plato's politics and metaphysics, Rice argues that Plato's reluctance to accept the reality and consequences of finitude accounts for much of what many readers find objectionable in his politics. Lively, relatively brief, and designed to provoke discussion in the classroom, A Guide to Plato's Republic is ideal for political theory and introduction to philosophy courses as well as other courses that assign the Republic as a primary text. (shrink)

Jewish Agrarian Movements (JAM hereafter) in North America express the many different shapes and iterations of Jewish farming on the continent, grounded in historical perspectives that influence current practices and activities. From within this diversity, common threads emerge with much to contribute to agrarian social movements and scholarship. Jewish values of returning (_t_’_shuvah_), releasing (_shmitah_), and repairing (_tikkun_), along with theories of _doikayt_ (an anti-zionist movement around “hereness”) and radical diasporism, animate JAM’s critical engagement with agri-food systems. As researchers who (...) have both studied and participated in Jewish agrarianism in a variety of U.S. and Canadian contexts, we solidify a series of themes and tensions that emerge from JAM: diaspora and indigeneity, modernity and tradition, Jewish agroecological knowledge production, and lived religion. We argue that, while JAM has not yet been examined thoroughly within critical food scholarship, it has the potential to contribute to broader debates and frameworks within sub-fields such as radical food geographies, critical agrarianism, and decoloniality. Without consideration of JAM as a part the study of food and agriculture, there are risks of marginalization of farmers, activists and researchers of Jewish identity. (shrink)

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, (...) as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. (shrink)

The present paper introduces "ontomimetic simulation" and argues that this class of models has enabled the investigation of hypotheses about complex systems in new ways that have epistemological relevance. Ontomimetic simulation can be differentiated from other types of modeling by its reliance on causal similarity in addition to representation. Phenomena are modeled not directly but via mimesis of the ontology (i.e. the "underlying physics", microlevel etc.) of systems and a subsequent animation of the resulting model ontology as a (...) dynamical system. While the ontology is clearly used for computing system states, what is epistemologically important is that it is viewed as a hypothesis about the makeup of the studied system. This type of simulation, where model ontologies are used as hypotheses, is here called inverse ontomimetic simulation since it reverses the typical informational path from the target to the model system. It links experimental and analytical techniques in being explicitly dynamical while at the same time capable of abstraction. Inverse ontomimetic simulation is argued to have a great impact on science and to be the tool for hypothesis-testing that has made systematic theory development for complex systems possible. (shrink)

The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in several areas of computer science. We give a short overview, and focus on the theory of software systems and modules. An algebra of theories TA is presented, with a nonstandard interpretation of the existential quantifier ∃. In TA, the interpolation property of the underlying logic corresponds with the quantifier combination (...) property ∃Σ ∃П S ≡ ∃(Σ ∪ П) S. It is shown how the Modularization Theorem, the Factorization Lemma and the Normal Form Theorem for module expressions can be proved in TA. (shrink)

The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in several areas of computer science. We give a short overview, and focus on the theory of software systems and modules. An algebra of theories TA is presented, with a nonstandard interpretation of the existential quantifier . In TA, the interpolation property of the underlying logic corresponds with the quantifier combination (...) property . It is shown how the Modularization Theorem, the Factorization Lemma and the Normal Form Theorem for module expressions can be proved in TA. (shrink)

Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, (...) ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side. (shrink)

Depending on what one means by the main connective of logic, the -if..., then... -, several systems of logic result: classic and modal logics, intuitionistic logic or relevance logic. This book presents the underlying ideas, the syntax and the semantics of these logics. Soundness and completeness are shown constructively and in a uniform way. Attention is paid to the interdisciplinary role of logic: its embedding in the foundations of mathematics and its intimate connection with philosophy, in particular the philosophy of (...) language. Set theory is presented both as a conditio sine qua non for logic and as a interesting exact ontology. The study of infinite sets yields perplexing results. Formalization of informal number theory results in formal number theory; Godel's incompleteness is treated. At appropriate places attention is paid to paradoxes, intuitionism, conditionals, the historical development of logic, to logic programming and automated theorem proving for classical logic.". (shrink)

Recent events have highlighted large-scale systemic racial disparities in U.S. criminal justice based on race and other demographic characteristics. Although criminological datasets are used to study and document the extent of such disparities, they often lack key information, including arrestees’ racial identification. As AI technologies are increasingly used by criminal justice agencies to make predictions about outcomes in bail, policing, and other decision-making, a growing literature suggests that the current implementation of these systems may perpetuate racial inequalities. In this paper, (...) we argue that AI technologies should be investigated to understand how they recognize racial categories and whether they can be harnessed to fill missing race data. By bridging this gap, we can work towards better understanding racial inequalities in a wide range of contexts, most notably criminal justice. Using a multidisciplinary perspective, we rethink the design and methodology used in facial processing technology (FPT) based on supervised deep learning model (DLM) image classification. By modifying standard FPT pipelines to tackle multiple sources of DLM bias, we propose an experimental methodology based on ethical AI principles to generate binary (Black and White) racial categories using mugshots. We go beyond simply reporting DLM accuracies and address fundamental issues such as generalizability and interpretability by using a “self-auditing” approach. First, we evaluate the inference performances of 42 fine-tuned DLMs using unseen test images from the same dataset but subject to varying data augmentations. Next, to interpret and validate our methodological approach, we apply gradient-based saliency maps to assess the consistency of facial region relevance and attribution. Finally, drawing upon insights from three areas (computer science, sociology, and law), we investigate the efficacy of our DLM-based method as a tool for detecting racial inequalities in criminal justice. (shrink)

In this article, I focus on the role of computer simulations as exploratory strategies. I begin by establishing the non-theory-driven nature of simulations. This refers to their ability to characterize phenomena without relying on a predefined conceptual framework that is provided by an implemented mathematical model. Drawing on Steinle’s notion of exploratory experimentation and Gelfert’s work on exploratory models, I present three exploratory strategies for computer simulations: (1) starting points and continuation of scientific inquiry, (2) varying the parameters, (...) and (3) scientific prototyping. (shrink)

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s (...) results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines. (shrink)