Computable limits and colimits are “recursive counterparts” of the suitable classical concepts from category theory. We present mainly some interesting problems related to computable products. Moreover, some “computable counterparts” of well-known classical facts from category theory are given. MSC: 03D45, 18A30.

Any attempt to conceptualize, categorize and constraint foundational issues in a living science, such as Computing, is bound to show its limitations and leave a number of open issues. Taking stock with some critical reviews of Primiero (On the foundations of computing, Oxford University Press, Oxford, 2019) published in this Journal, I overview potential new problems to be investigated by a foundational analysis of the science of computing.

Stanovich & West interpret errors in syllogistic reasoning in terms of computational limitations. I argue that the variety of strategies used by reasoners in solving syllogisms requires us to consider also performance errors. Although reasoners' performance from one trial to another is quite consistent, it can be different, in line with the definition of performance errors. My argument has methodological implications for reasoning theories.

Since the cognitive revolution, psychologists have developed formal theories of cognition by thinking about the mind as a computer. However, this metaphor is typically applied to individual minds. Humans rarely think alone; compared to other animals, humans are curiously dependent on stores of culturally transmitted skills and knowledge, and we are particularly good at collaborating with others. Rather than picturing the human mind as an isolated computer, we can imagine each mind as a node in a vast distributed (...) system. Viewing human cognition through the lens of distributed systems motivates new questions about how humans share computation, when it makes sense to do so, and how we can build institutions to facilitate collaboration. (shrink)

This paper reviews the contemporary discussion on the epistemological and ontological effects of Big Data within social science, observing an increased focus on relationality and complexity, and a tendency to naturalize social phenomena. The epistemic limits of this emerging computational paradigm are outlined through a comparison with the discussions in the early days of digitalization, when digital technology was primarily seen through the lens of dematerialization, and as part of the larger processes of “postmodernity”. Since then, the online landscape (...) has become increasingly centralized, and the “liquidity” of dematerialized technology has come to empower online platforms in shaping the conditions for human behavior. This contrast between the contemporary epistemological currents and the previous philosophical discussions brings to the fore contradictions within the study of digital social life: While qualitative change has become increasingly dominant, the focus has gone towards quantitative methods; while the platforms have become empowered to shape social behavior, the focus has gone from social context to naturalizing social patterns; while meaning is increasingly contested and fragmented, the role of hermeneutics has diminished; while platforms have become power hubs pursuing their interests through sophisticated data manipulation, the data they provide is increasingly trusted to hold the keys to understanding social life. These contradictions, we argue, are partially the result of a lack of philosophical discussion on the nature of social reality in the digital era; only from a firm metatheoretical perspective can we avoid forgetting the reality of the system under study as we are affected by the powerful social life of Big Data. (shrink)

In this chapter, I argue that some aspects of cognitive phenomena cannot be explained computationally. In the first part, I sketch a mechanistic account of computational explanation that spans multiple levels of organization of cognitive systems. In the second part, I turn my attention to what cannot be explained about cognitive systems in this way. I argue that information-processing mechanisms are indispensable in explanations of cognitive phenomena, and this vindicates the computational explanation of cognition. At the same time, it has (...) to be supplemented with other explanations to make the mechanistic explanation complete, and that naturally leads to explanatory pluralism in cognitive science. The price to pay for pluralism, however, is the abandonment of the traditional autonomy thesis asserting that cognition is independent of implementation details. (shrink)

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)

Humans constantly produce strings of characters in symbolic languages, e.g., sentences in natural languages. We show that for any given moment in human history, the set of character strings that have been produced up to that moment, i.e., the sum total of human symbolic output up to that moment, is finite and so Turing computable. We then prove a much stronger result: a Turing machine can produce any particular set of symbolic output that we could possibly have produced. We then (...) discuss metaphysical and/or theological systems, e.g., Spinoza’s, Leibniz’s, or Aquinas’s. We argue that any particular metaphysical system could be the output of a Turing machine. We then briefly discuss (i) automated theorem proving, the attempt to generate and/or prove theorems using computers, and (ii) computational metaphysics, the attempt to apply methods from computer science such as automated theorem proving to metaphysics. We conclude by arguing that: (i) computational metaphysics can succeed, at least in theory; indeed, all human metaphysical reasoning could be automated; (ii) computational metaphysics – and indeed metaphysical systems in general – will have the same limitations as Turing machines; and (iii) a number of different methods – not currently used in computational metaphysics – could be used to advance metaphysical research. (shrink)

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)

Computer models and simulations have provided enormous benefits to researchers in the natural and social sciences, as well as many areas of philosophy. However, to date, there has been little attempt to use computer models in the development and evaluation of metaphysical theories. This is a shame, as there are good reasons for believing that metaphysics could benefit just as much from this practice as other disciplines. In this paper I assess the possibilities and limitations of using (...) class='Hi'>computer models in metaphysics. I outline the way in which different kinds of model could be useful for different areas of metaphysics, and I illustrate in more detail how agent-based models specifically could be used to model two well-known theories of laws: David Lewis’s "Best System Account" and David Armstrong's "Nomic Necessitation" view. Some logically possible processes cannot be simulated on a standard computing device. I finish by assessing how much of a threat this is to the prospect of metaphysical modeling in general. (shrink)

What is computational explanation? Many accounts treat it as a kind of causal explanation. I argue against two more specific versions of this view, corresponding to two popular treatments of causal explanation. The first holds that computational explanation is mechanistic, while the second holds that it is interventionist. However, both overlook an important class of computational explanations, which I call limitative explanations. Limitative explanations explain why certain problems cannot be solved computationally, either in principle or in practice. I argue that (...) limitative explanations are not plausibly understood in either mechanistic or interventionist terms. One upshot of this argument is that there are causal and non-causal kinds of computational explanation. I close the paper by suggesting that both are grounded in the notion of computational implementation. (shrink)

Aicardi et al. look to neuroscience to mitigate the limitations of current robotics technology. They propose that robotics technology guided by neuroscience has the capacity to create intelligent robots that function with awareness and capacity for abstraction and reasoning. As neurorobotics extends the capability of robotics technology, it introduces new social and ethical concerns, in particular co-opting civilian applications for military use, conflicts between industry and the academy, and data security. However, here we argue that empirical evidence has shown that (...) human cognition is faulty; therefore there is not a clear motivation to build intelligent robots on a human model; representation of meaning in the brain is not well-understood; therefore neuro-robotics is limited; and to the extent that intelligent robots become a reality, the ethics of robot rights will be of central concern. (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)

Since the 1980s, several studies of visual perception have persuasively argued that important aspects of human vision are best accounted for not by recourse to inner mental representations but rather through socially observable actions and behaviors (e.g. Lynch 1985, Latour 1986, Lynch 1990, Goodwin 1994, Goodwin 1997, Sharrock & Coulter 1998). While there are clearly physiological mechanisms required for vision, psychological accounts of perception in terms of inner mental representations have been dislodged from their position as the basic term in (...) the interface between human beings and their environment and replaced with terms such as "social practice," and "vernacular intelligibility." The focus for these .. (shrink)

Social science research on the anthropomorphisms of computers and robots has been devoted to studying intellectual anthropomorphism, emotional anthropomorphism, bodily anthropomorphism, and the limits of computer and robot anthropomorphism. Although these represent important patterns for studying the anthropomorphisms of computers and robots, there are other important patterns. The limitation of anthropomorphism is one of these patterns. The limitation of anthropomorphism is a discursive practice which places limits on anthropomorphism. Discursive practices are interactional and practical activities for making (...) sense of who and what we encounter. In this article, I analyze the limitation of anthropomorphism as another important activity to investigate. Drawing on an ethnographic study of a robotics research group, I show the importance of the limitation of anthropomorphism by documenting how it contributes to research group identity. In the final section, I describe some implications for future studies of the anthropomorphisms of computers and robots. (shrink)

This article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy (...) of ordinal recursive functionals of arbitrary type that can be reduced by substitution to natural number functions. (shrink)

Fraïssé studied countable structures S through analysis of the age of S i.e., the set of all finitely generated substructures of S. We investigate the effectiveness of his analysis, considering effectively presented lists of finitely generated structures and asking when such a list is the age of a computable structure. We focus particularly on the Fraïssé limit. We also show that degree spectra of relations on a sufficiently nice Fraïssé limit are always upward closed unless the relation is definable by (...) a quantifier-free formula. We give some sufficient or necessary conditions for a Fraïssé limit to be spectrally universal. As an application, we prove that the computable atomless Boolean algebra is spectrally universal. (shrink)

In addressing the shortcomings of computationalism, we should not throw the baby out with the bathwater. That consciousness is not merely an epiphenomenon with optional access to unconscious computations does not imply that unconscious computations, in the limited domain where they do occur (e.g., occipital transformations of visual data), cannot be reformulated in a way consistent with a self-organizational view.

The purpose of this paper is to describe some limitations on scientific behaviorist and computational models of the mind. These limitations stem from the inability of either model to account for the integration of experience and behavior. Behaviorism fails to give an adequate account of felt experience, whereas the computational model cannot account for the integration of our behavior with the world. Both approaches attempt to deal with their limitations by denying that the domain outside their limits is a (...) part of psychology. These attempts to turn the shortcomings of the two models into virtues would be more convincing if their limitations were not diametrically opposed. I will argue that in each case the limitations are too restrictive unless the theories are augmented by physiology. (shrink)

Much of the literature on the question “Is a human essentially distinct from every possible machine?” proceeds on the assumption that we know what a man essentially is, namely a living body with such attributes as consciousness, freedom, feeling and linguistic competence. Is a man essentially that? The paper contrasts that picture of man with Kierkegaard’s account of man as essentially self. Hard limits of machine subjectivity begin to appear in the failure of certain everyday concepts involving ‘self’ to (...) engage at all with the concept ‘machine’. (shrink)

Much of the literature on the question “Is a human essentially distinct from every possible machine?” proceeds on the assumption that we know what a man essentially is, namely a living body with such attributes as consciousness, freedom, feeling and linguistic competence. Is a man essentially that? The paper contrasts that picture of man with Kierkegaard’s account of man as essentially self. Hard limits of machine subjectivity begin to appear in the failure of certain everyday concepts involving ‘self’ to (...) engage at all with the concept ‘machine’. (shrink)

Perhaps no technological innovation has so dominated the second half of the twentieth century as has the introduction of the programmable computer. It is quite difficult if not impossible to imagine how contemporary affairs—in business and science, communications and transportation, governmental and military activities, for example—could be conducted without the use of computing machines, whose principal contribution has been to relieve us of the necessity for certain kinds of mental exertion. The computer revolution has reduced our mental labors (...) by means of these machines, just as the Industrial Revolution reduced our physical labor by means of other machines. (shrink)

Exclusively focused on data that are consistent with the proposed ideas, the target article misses an opportunity to review data that are inconsistent with them. Weaknesses of the emulation theory become especially evident when one tries to incorporate physiologically realistic muscle and reflex mechanisms into it. In particular, it fails to resolve the basic posture-movement controversy.

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 problems, by (...) contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding (...) biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

An increasing number of philosophers have promoted the idea that mechanism provides a fruitful framework for thinking about the explanatory contributions of computational approaches in cognitive neuroscience. For instance, Piccinini and Bahar :453–488, 2013) have recently argued that neural computation constitutes a sui generis category of physical computation which can play a genuine explanatory role in the context of investigating neural and cognitive processes. The core of their proposal is to conceive of computational explanations in cognitive neuroscience as a subspecies (...) of mechanistic explanations. This paper identifies several challenges facing their mechanistic account and sketches an alternative way of thinking about the epistemic roles of computational approaches used in the study of brain and cognition. Drawing on examples from both low-level and systems-level computational neuroscience, I argue that at least some computational explanations of neural and cognitive processes are partially independent from mechanistic constraints. (shrink)

This contribution defends two claims. The first is about why thought experiments are so relevant and powerful in mathematics. Heuristics and proof are not strictly and, therefore, the relevance of thought experiments is not contained to heuristics. The main argument is based on a semiotic analysis of how mathematics works with signs. Seen in this way, formal symbols do not eliminate thought experiments (replacing them by something rigorous), but rather provide a new stage for them. The formal world resembles the (...) empirical world in that it calls for exploration and offers surprises. This presents a major reason why thought experiments occur both in empirical sciences and in mathematics. The second claim is about a looming aporia that signals the limitation of thought experiments. This aporia arises when mathematical arguments cease to be fully accessible, thus violating a precondition for experimenting in thought. The contribution focuses on the work of Vladimir Voevodsky (1966–2017, Fields medalist in 2002) who argued that even very pure branches of mathematics cannot avoid inaccessibility of proof. Furthermore, he suggested that computer verification is a feasible path forward, but only if proof is not modeled in terms of formal logic. (shrink)

Topics in Cognitive Science, Volume 14, Issue 3, Page 550-573, July 2022.

Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Δn+10 basic sequence with respect to which no Δn0 real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and justify (...) the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)

Hydranencephaly is a developmental malady, where the cerebral hemispheres of the brain are reduced partly or entirely too membranous sacs filled with cerebrospinal fluid. Infants with this malady are presumed to have reduced life expectancy with a survival of weeks to few years and which solely depends on care and fostering of these individuals. During their life span these individuals demonstrate behaviours that are termed “vegetative” by neuroscientists but can be comparable to the state of being “aware” or “conscious”. Based (...) on the most simplified definition for consciousness i.e. “awareness” or “to be aware”, these individuals are undeniably aware of their existence and therefore should be termed “conscious”. The bigoted approach of neuroscience towards understanding consciousness is usually linked with the cortex of the brain and therefore a malady as hydranencephaly poses a great challenge to this field. This paper is a compilation of behaviours and aptitudes observed in several cases of hydranencephaly which suggests, that consciousness is not just a brain process, but is a highly quantum computed process that follows laws of quantum physics, giving rise to the subjective experience of consciousness in these individuals. (shrink)

In this paper, we analyzed the periodicity of discrete Logistic and Tent sequences with different computational precision in detail. Further, we found that the process of iterations of the Logistic and Tent mapping is composed of transient and periodic stages. Surprisingly, for the different initial iterative values, we first discovered that all periodic stages have the same periodic limit cycles. This phenomenon has seriously affected the security of chaotic cipher. To solve this problem, we designed a novel discrete chaotic sequence (...) generator based on m-sequence and discrete chaotic mapping. The experimental results indicated that the chaotic sequence generator can generate pseudorandom chaotic sequences with large periodicity and good performance under the condition of limited computational precision. (shrink)

Jerry Fodor argues against the widely held view that mental processes are largely computations, that the architecture of cognition is massively modular, and...

We introduce an implication-free fragment image of ω-arithmetic, having Exchange rule for sequents dropped. Exchange rule for formulas is, instead, an admissible rule in image. Our main result is that cut-free proofs of image are isomorphic with recursive winning strategies of a set of games called “1-backtracking games” in [S. Berardi, Th. Coquand, S. Hayashi, Games with 1-backtracking, Games for Logic and Programming Languages, Edinburgh, April 2005].We also show that image is a sound and complete formal system for the implication-free (...) fragment of LCM , Seventh International Conference on Typed Lambda Calculi and Applications, in: Lecture Notes in Computer Science, vol. 3461, 2005, pp. 11–22. Invited paper]). A simple syntactical description of this fragment was still missing. No sound and complete formal system is known for LCM itself. (shrink)

Open peer commentary on the article “Exploration of the Functional Properties of Interaction: Computer Models and Pointers for Theory” by Etienne B. Roesch, Matthew Spencer, Slawomir J. Nasuto, Thomas Tanay & J. Mark Bishop. Upshot: Why computer models of constructivist processes can enhance constructivist matters even though the models will always “seem incomplete.”.