Las máquinas aceleradas de Turing (ATMs) son dispositivos capaces de ejecutar súper-tareas. Sin embargo, el simple ejercicio de definirlas ha generado varias paradojas. En el presente artículo se definirán las nociones de súper-tarea y ATM de manera exhaustiva y se aclarará qué debe entenderse en un contexto lógico-formal cuando se pregunta por la existencia de un objeto. A partir de la distinción entre posibilidades lógicas y físicas se disolverán las paradojas y se concluirá que las ATMs son posibles y existen (...) como objetos abstractos. (shrink)

A ‘Black Box’ cannot be opened to reveal its mechanism. Rather, its operations are inferred through input from (and output to) an ‘observer’. All of us are observers, who attempt to understand the Black Boxes that are Minds. The Black Box and its observer constitute a system, differing from either component alone: a ‘greater’ Black Box to any further-external-observer. To Glanville (1982), the further-external-observer probes the greater-Black-Box by interacting directly with its core Black Box, ignoring that Box’s immediate observer. In (...) later accounts, however, Glanville’s greater-Black-Box inexplicably becomes unitary. Why the discrepancy? To resolve it, we start with von Foerster’s archetype ‘machines’, that are of two kinds: ‘Trivial’ (predictable) and ‘Non-Trivial’ (non-predictable). Early-on, Glanville treated the core Black Box and its observer as Trivial Machines, that gradually ‘whiten’ (reveal) each other though input and output, becoming ‘white boxes’. Later, however, Black Box and observer became Non-Trivial Machines, never fully ‘whitenable’. But Non-Trivial Machines can be concatenated from Trivial Machines, and are the only true Black Boxes; any greater-Black-Box (Non-Trivial Machine) may (within its core Black Box) involve white boxes (that are Trivial Machines). White boxes, therefore, could be the ultimate source of the greatest Black Box of all: the Mind. (shrink)

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)

Over the past thirty years, it is been common to hear the mind likened to a digital computer. This essay is concerned with a particular philosophical view that holds that the mind literally is a digital computer (in a specific sense of “computer” to be developed), and that thought literally is a kind of computation. This view—which will be called the “Computational Theory of Mind” (CTM)—is thus to be distinguished from other and broader attempts to connect the mind with computation, (...) including (a) various enterprises at modeling features of the mind using computational modeling techniques, and (b) employing some feature or features of production-model computers (such as the stored program concept, or the distinction between hardware and software) merely as a guiding metaphor for understanding some feature of the mind. This entry is therefore concerned solely with the Computational Theory of Mind (CTM) proposed by Hilary Putnam [1961] and developed most notably for philosophers by Jerry Fodor [1975, 1980, 1987, 1993]. The senses of ‘computer’ and ‘computation’ employed here are technical; the main tasks of this entry will therefore be to elucidate: (a) the technical sense of ‘computation’ that is at issue, (b) the ways in which it is claimed to be applicable to the mind, (c) the philosophical problems this understanding of the mind is claimed to solve, and (d) the major criticisms that have accrued to this view. (shrink)

Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. General interest and excitement in quantum computing was initially triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially “speed-up” classical computation and factor large numbers into primes far more efficiently than any (known) classical algorithm. Shor’s algorithm was soon followed by several (...) other algorithms that aimed to solve combinatorial and algebraic problems, and in the years since theoretical study of quantum systems serving as computational devices has achieved tremendous progress. Common belief has it that the implementation of Shor’s algorithm on a large scale quantum computer would have devastating consequences for current cryptography protocols which rely on the premise that all known classical worst-case algorithms for factoring take time exponential in the length of their input (see, e.g., Preskill 2005). Consequently, experimentalists around the world are engaged in attempts to tackle the technological difficulties that prevent the realisation of a large scale quantum computer. But regardless whether these technological problems can be overcome (Unruh 1995; Ekert and Jozsa 1996; Haroche and Raimond 1996), it is noteworthy that no proof exists yet for the general superiority of quantum computers over their classical counterparts. -/- The philosophical interest in quantum computing is manifold. From a social-historical perspective, quantum computing is a domain where experimentalists find themselves ahead of their fellow theorists. Indeed, quantum mysteries such as entanglement and nonlocality were historically considered a philosophical quibble, until physicists discovered that these mysteries might be harnessed to devise new efficient algorithms. But while the technology for harnessing the power of 50–100 qubits (the basic unit of information in the quantum computer) is now within reach (Preskill 2018), only a handful of quantum algorithms exist, and the question of whether these can truly outperform any conceivable classical alternative is still open. From a more philosophical perspective, advances in quantum computing may yield foundational benefits. For example, it may turn out that the technological capabilities that allow us to isolate quantum systems by shielding them from the effects of decoherence for a period of time long enough to manipulate them will also allow us to make progress in some fundamental problems in the foundations of quantum theory itself. Indeed, the development and the implementation of efficient quantum algorithms may help us understand better the border between classical and quantum physics (Cuffaro 2017, 2018a; cf. Pitowsky 1994, 100), and perhaps even illuminate fundamental concepts such as measurement and causality. Finally, the idea that abstract mathematical concepts such as computability and complexity may not only be translated into physics, but also re-written by physics bears directly on the autonomous character of computer science and the status of its theoretical entities—the so-called “computational kinds”. As such it is also relevant to the long-standing philosophical debate on the relationship between mathematics and the physical world. (shrink)

Are minds really dynamical or are they really symbolic? Because minds are bundles of computations, and because computation is always a matter of interpretation of one system by another, minds are necessarily symbolic. Because minds, along with everything else in the universe, are physical, and insofar as the laws of physics are dynamical, minds are necessarily dynamical systems. Thus, the short answer to the opening question is “yes.” It makes sense to ask further whether some of the computations that constitute (...) a human mind are constrained by functional, algorithmic, or implementational factors to be essentially of the discrete symbolic variety (even if they supervene on an apparently continuous dynamical substrate). I suggest that here too the answer is “yes” and discuss the need for such discrete, symbolic cognitive computations in communication-related tasks. (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)

The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit, for the reader's consideration, a tentative resolution to it. In particular, I argue, in this dissertation, that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product (...) states. I begin the dissertation by considering, in Chapter 2, the most popular of the candidate physical explanations for quantum speedup: the many worlds explanation of quantum computation. I argue that, although it is inspired by the neo-Everettian interpretation of quantum mechanics, unlike the latter it does not have the conceptual resources required to overcome objections such as the so-called `preferred basis objection'. I further argue that the many worlds explanation, at best, can serve as a good description of the physical process which takes place in so-called network-based computation, but that it is incompatible with other models of computation such as cluster state quantum computing. I next consider, in Chapter 3, a common component of most other candidate explanations of quantum speedup: quantum entanglement. I investigate whether entanglement can be said to be a necessary component of any explanation for quantum speedup, and I consider two major purported counter-examples to this claim. I argue that neither of these, in fact, show that entanglement is unnecessary for speedup, and that, on the contrary, we should conclude that it is. In Chapters 4 and 5 I then ask whether entanglement can be said to be sufficient as well. In Chapter 4 I argue that despite a result that seems to indicate the contrary, entanglement, considered as a resource, can be seen as sufficient to enable quantum speedup. Finally, in Chapter 5 I argue that entanglement is sufficient to explain quantum speedup as well. (shrink)

Heuristics are often invoked in the philosophical, psychological, and cognitive science literatures to describe or explain methodological techniques or "shortcut" mental operations that help in inference, decision-making, and problem-solving. Yet there has been surprisingly little philosophical work done on the nature of heuristics and heuristic reasoning, and a close inspection of the way(s) in which "heuristic" is used throughout the literature reveals a vagueness and uncertainty with respect to what heuristics are and their role in cognition. This dissertation seeks to (...) remedy this situation by motivating philosophical inquiry into heuristics and heuristic reasoning, and then advancing a theory of how heuristics operate in cognition. I develop a positive working characterization of heuristics that is coherent and robust enough to account for a broad range of phenomena in reasoning and inference, and makes sense of empirical data in a systematic way. I then illustrate the work this characterization does by considering the sorts of problems that many philosophers believe heuristics solve, namely those resulting from the so-called frame problem. Considering the frame problem motivates the need to gain a better understanding of how heuristics work and the cognitive structures over which they operate. I develop a general theory of cognition which I argue underwrites the heuristic operations that concern this dissertation. I argue that heuristics operate over highly organized systems of knowledge, and I offer a cognitive architecture to accommodate this view. I then provide an account of the systems of knowledge that heuristics are supposed to operate over, in which I suggest that such systems of knowledge are concepts. The upshot, then, is that heuristics operate over concepts. I argue, however, that heuristics do not operate over conceptual content, but over metainformational relations between activated and primed concepts and their contents. Finally, to show that my thesis is empirically adequate, I consider empirical evidence on heuristic reasoning and argue that my account of heuristics explains the data. (shrink)

An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse)is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. From its (...) substrate of Mathematics, the knotted information processing loops determine emergent Physics and thence the evolution of super-emergent Life (biological and artificial intelligence). RGB-tricoloured information is processed in sequence in an Elemental feedback loop (R), then an Operational feedback loop (G), then a Structural feedback loop (B) and back to an Elemental feedback loop (R), and so on around the trefoil in deep learning macrocycles. It is postulated that hierarchical information correspondence from Mathematics through Physics to Life is mapped and conserved within each colour. The substrate of Mathematics has RGB-tricoloured feedback loops which are respectively Algebra (R), Algorithms (G) and Geometry (B). In Mathematics, the trefoil macrocycle is Algebraic Algorithmic Geometry and its correlation system is a Tensor Neural Knot Network enabling Qutrit Entanglement. Emergent Physics has corresponding RGB-tricoloured feedback loops of Quantum Mechanics (R), Quantum Deep Learning (G) and Quantum Geometrodynamics(B). In Physics, the trefoil macrocycle is Quantum Intelligent Geometrodynamics and its correlation system is Quantum Darwinism. Super-emergent Life has corresponding RGB-tricoloured loops of Variation (R), Selection (G) and Heredity (B). In the evolution of Life, the trefoil macrocycle is Variational Selective Heredity and its correlation ecosystem is Darwin’s ecologically “Entangled Bank”. (shrink)

The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based (...) on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant. (shrink)

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

Perhaps there has been no greater opportunity than in this “VOLUME FIFTEEN of our Death And Anti-Death set of anthologies” to write about how might think about life and how to avoid death. There are two reasons to discuss “life”, the first being enhancing our understanding of who we are and why we may be here in the Universe. The second is more practical: how humans meet the physical challenges brought about by the way they have interacted with their environment. (...) Many persons discussing “life” beg the question about what “life” is. Surely, when one discusses how to overcome its opposite, death, they are not referring to another “living” thing such as a plant. There seems to be a commonality, though, and it is this commonality is one needing elaboration. It ostensibly seems to be the boundary condition separating what is completely passive (inert) from what attempts to maintain its integrity, as well as fulfilling other conditions we think “life” has. In our present discussion, there will be a reminder that it by no means has been unequivocally established what life really is by placing quotes around the word, namely, “life”. Consider it a tag representing a bundle of philosophical ideas that will be unpacked in this paper. (shrink)

Según la versión estándar del juego de la imitación, la determinación del sexo de los participantes no desempeña ningún papel en el testeo de la inteligencia de máquina. Desafortunadamente, tal simplificación soslaya la teoría de la mente que fundamenta dicho juego. Teniendo en consideración este problema, en este ensayo argumento en contra de la simplificación del Test de Turing. En efecto, tal como sostengo, la determinación del sexo de los participantes no debe obviarse: la mente de una mujer y su (...) inteligencia son imitables y no dependen de realización física específica. Esto ocurre porque el funcionalismo de Turing supone un vínculo entre imitación, engaño y aprendizaje, tres claves para que el proyecto de la Inteligencia Artificial tenga éxito. (shrink)

One of us has previously argued that the Church-Turing Thesis (CTT), contra Elliot Mendelson, is not provable, and is — light of the mind’s capacity for effortless hypercomputation — moreover false (e.g., [13]). But a new, more serious challenge has appeared on the scene: an attempt by Smith [28] to prove CTT. His case is a clever “squeezing argument” that makes crucial use of Kolmogorov-Uspenskii (KU) machines. The plan for the present paper is as follows. After covering some necessary preliminaries (...) regarding the nature of CTT, and taking note of the fact that this thesis is “intrinsically cognitive” (§2), we: sketch out, for context, an open-minded position on CTT and related matters (§3); explain the formal structure of squeezing arguments (§4); after a review of KU-machines, formalize Smith’s case (§5); give our objections to certain assumptions in Smith’s argument (§6); support these objections with some evidence from general but limited-agent problem solving (§7); and explain why Smith’s argument is inconclusive (§8). We end with some brief, concluding remarks, some of which point toward near-future work that will build on the present paper (§9). (shrink)

In the beginning was the word, or grunt, or groan, or signal of some sort. This, however, hardly qualifies as an information revolution, at least in any standard technological sense. Nature is replete with meaningful signs, and we must imagine that our early ancestors noticed natural patterns that helped to determine when to sow and when to reap, which animal tracks to follow, what to eat, and so forth. Spoken words at first must have been meaningful in some similar sense. (...) But in time the word became flesh (corpus) and dwelt among us, as "inscription" (literally, to put into writing) inaugurated the dawn of human history. This did not happen instantly. One place to enter the story is with clay tokens to represent trade transactions that in time became accounting tablets and, then, the world's first literature (Enmerkar and the Lord of Aratta, The Epic of Gilgamesh, etc.) and codes of law (The Codes of Ur-Nammu, Lipit-Ishtar, Hammurabi, and so forth.) This event happened around the north shore of the Persian Gulf sometime in the 4th millennium BCE and was enshrouded in mystery as the role of the scribe trained in the art of inscribing and deciphering signs belonged to the priest (Deibert 1997). With the sanction of religion, writing gave birth to "civility" (literally, life in the city) and defined the line between "history" and "pre-history," the latter being a term designating everything that happened before. There is little doubt that the invention of writing was significant and that it deserves recognition as the first revolution in the history of information. Life as we live it today would have been impossible otherwise. Innovations in writing technologies happened with significant effects, but at various points in the history of information, changes in technology were so dramatic that they reshaped the course of human history in radical ways. The revolution in printing is well-studied; the invention of the printing press and movable type (c.. (shrink)

Kakšne možnosti obstajajo za reprezentacijo kapitalizma kot takega? To vprašanje se opira na predstavo o kognitivnem mapiranju, kot sta ga raziskovala Toscano in Kinkle v Cartographies of the Absolute, v nadaljevanju pa avtor glede na to vprašanje obravnava abstraktne potenciale računalnikov in Turingovega stroja, ki omogočajo izdelavo algoritmičnega modela kapitalizma.

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation’ and ‘information processing’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In (...) this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism on the other. We defend the relevance to cognitive science of both computation, in a generic sense that we fully articulate for the first time, and information processing, in three important senses of the term. Our account advances some foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates’ empirical aspects. (shrink)

I propose a new approach to the constitutive problem of psychology ‘what is mind?’ The first section introduces modifications of the received scope, methodology, and evaluation criteria of unified theories of cognition in accordance with the requirements of evolutionary compatibility and of a mature science. The second section outlines the proposed theory. Its first part provides empirically verifiable conditions delineating the class of meaningful neural formations and modifies accordingly the traditional conceptions of meaning, concept and thinking. This analysis is part (...) of a theory of communication in terms of inter-level systems of primitives that proposes the communication-understanding principle as a psychological invariance. It unifies a substantial amount of research by systematizing the notions of meaning, thinking, concept, belief, communication, and understanding and leads to a minimum vocabulary for this core system of mental phenomena. Its second part argues that written human language is the key characteristic of the artificially natural human mind. Overall, the theory both supports Darwin’s continuity hypothesis and proposes that the mental gap is within our own species. (shrink)

While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more than a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given a coin which lands heads with probability pX it can compute any function recursive in X with arbitrarily high probability. We also show how (...) the assumption of a non-recursive bias can be weakened by using a.. (shrink)

This paper explores the role of the traditional computational metaphor in our thinking as computer scientists, its influence on epistemological styles, and its implications for our understanding of cognition. It proposes to replace the conventional metaphor--a sequence of steps--with the notion of a community of interacting entities, and examines the ramifications of such a shift on these various ways in which we think.

Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be less-incomplete than other. Neutrosophy is less-incomplete than many other systems because it contains them. But this does not mean that it is finished, and it can always be improved. The comments presented here are an attempt to make Neutrosophy even less-incomplete. I argue that less-incomplete ideas are more useful, since we cannot perceive truth or falsity or indeterminacy (...) independently of a context, and are therefore relative. Absolute being and relative being are defined. Also the "silly theorem problem" is posed, and its partial solution described. The issues arising from the incompleteness of our contexts are presented. We also note the relativity and dependance of logic to a context. We propose "metacontextuality" as a paradigm for containing as many contexts as we can, in order to be less-incomplete and discuss some possible consequences. (shrink)

The automation of many repetitive or dangerous human activities yields numerous advantages. In order to automate a physical task that requires a finite series of sequential steps, the translation of those steps in terms of a computational procedure is often required. Even apparently menial tasks like following a cooking recipe may involve complex operations that can’t be perfectly described in formal terms. Recently, several studies have explored the possibility to model cooking recipes as a computational procedure based on a set (...) of instructions. This vision is the foundation for the construction of robotics kitchen, as Moley. These kitchen robots have shown promising results. Moley, for instance, is the very first example of a new generation of bioinspired robotics, based on the reproduction of particular movement, cooking, through artificial arms and hands. It is entirely different from the current appliances present in our domestic domain because Moley is able to manipulate ingredients and interact with kitchen equipment in order to prepare a dish autonomously. Nonetheless, they have also shown several limitations. In particular, Moley is an entirely autonomous robot in a structured environment in which it knows precisely the object position and manipulates the ingredients based on a list of instructions and a training phase made by Machine Learning. In this contribution we contend that these limitations arise from an essential mismatch between computational procedures, as originally described by Turing in his seminal 1936 paper, and recipes. Computational procedures have been originally created to observe and modify formal symbols with formal operators. Thus, they are independent from time and they are ideally executed in a closed environment, in which the computer directly produces all the relevant changes required to produce the intended result. Recipes, instead, are followed in an open environment, in which, while time goes by, changes happen independently from the cook’s intervention: the cook puts the butter on the pan, starts the fire and then waits until the butter is melted. To operate effectively in the open environment a kitchen robot must couple computational procedures with sensors, e.g a sensor which provides a time signal. These sensors are de facto oracles for the procedures and yet are required to bridge the gap from the formal to the physical world. (shrink)

Which is the relation between logic and philosophy of mind? This work tries to answer that question by shortly examining, first, the place that is assigned to logic in three current views of the mind: Computationalism, Interpretativism and Naive Naturalism. Secondly, the classical debate between psychologism and antipsychologism is reviewed -the question about whether logic is or not a part of psychology- and it is indicated in which place of such debate the three mentioned conceptions of mind are located.

Behaviour is often described as the computation of a response to a stimulus. This description is incomplete in an important way because it only examines what occurs between the reception of stimulus information and the generation of an action. Behaviour is more correctly described as a control process where actions are performed in order to affect perceptions. This closed-loop nature of behaviour is de-emphasized in modern discussions of brain function, leading to a number of artificial mysteries. A notable example is (...) the ‘symbol grounding problem'. When behaviour is viewed as a control process, it is natural to explain how internal representations, even symbols, can have meaning for an organism, and how actions can be motivated by organic needs. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine - a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by (...) Turing machines. In point of fact Turing himself nowhere endorses, nor even states, this claim (nor does Church). I describe a number of notional machines, both analogue and digital, that can compute more than a universal Turing machine. These machines are exemplars of the class of _nonclassical_ computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built, nor that the brain itself is such a machine. These theoretical considerations undercut a number of foundational arguments that are commonly rehearsed in cognitive science, and gesture towards a new class of cognitive models. (shrink)

Some practical criteria for free-will are suggested where free-will is a matter of degree. It is argued that these are more appropriate than some extremely idealised conceptions. Thus although the paper takes lessons from philosophy it avoids idealistic approaches as irrelevant. A mechanism for allowing an agent to meet these criteria is suggested: that of facilitating the gradual emergence of free-will in the brain via an internal evolutionary process. This meets the requirement that not only must the choice of action (...) be free but also choice in the method of choice, and choice in the method of choice of the method of choice etc. This is directly analogous to the emergence of life from non-life. Such an emergence of indeterminism with respect to the conditions of the agent fits well with the `Machiavellian Intelligence Hypothesis' which posits that our intelligence evolved (at least partially) to enable us to deal with social complexity and modelling `arms races'. There is a clear evolutionary advantage in being internally coherent in seeking to fulfil ones goals and unpredictable by ones peers. To fully achieve this vision several other aspects of cognition are necessary: open-ended strategy development; the meta-evolution of the evolutionary process; the facility to anticipate the results of strategies; and the situating of this process in a society of competitive peers. Finally the requirement that reports of the deliberations that lead to actions need to be socially acceptable leads to the suggestion that the language that the strategies are developed within be subject to a normative process in parallel with the development of free-will. An appendix outlines a philosophical position in support of my position. (shrink)

In many fields of biology, researchers explain a phenomenon by characterizing the responsible mechanism. This requires identifying the candidate mechanism, decomposing it into its parts and operations, recomposing it so as to understand how it is organized and its operations orchestrated to generate the phenomenon, and situating it in its environment. Mechanistic researchers have developed sophisticated tools for decomposing mechanisms but new approaches, including modeling, are increasingly being invoked to recompose mechanisms when they involve nonsequential organization of nonlinear operations. The (...) results often are dynamical mechanistic explanations. The steps in mechanistic research are illustrated using research on circadian rhythms. (shrink)

Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...) claim to any notion of reality. This foundation begins with Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and the relationship of language to formal logic. Ultimately, we arrive at an answer to the question of why people believe the things they do. This is effectively a modification of Alfred Tarski’s semantic theory of truth. The second major issue addressed is the ‘dreaded’ Hard Problem of Consciousness as first stated by David Chalmers in 1995. The solution is found in the unification of consciousness, information theory and notions of physicalism. The physical world is shown to be an isomorphic representation of the phenomenological conscious experience. New concepts in understanding how language operates help to explain why this relationship has been so difficult to appreciate. The inclusion of concepts from information theory shows how a digital mechanics resolves heretofore conflicting theories in physics, cognitive science and linguistics. Scientific orthodoxy is supported, but viewed in a different light. Mainstream science is not challenged, but findings are interpreted in a manner that unifies consciousness without contradiction. Digital mechanics and formal systems of logic play central roles in combining language, consciousness and the physical world into a unified theory where all can be understood within a single consistent framework. (shrink)

Context: Constructivist approaches to cognition have mostly been descriptive, and now face the challenge of specifying the mechanisms that may support the acquisition of knowledge. Departing from cognitivism, however, requires the development of a new functional framework that will support causal, powerful and goal-directed behavior in the context of the interaction between the organism and the environment. Problem: The properties affecting the computational power of this interaction are, however, unclear, and may include partial information from the environment, exploration, distributed processing (...) and aggregation of information, emergence of knowledge and directedness towards relevant information. Method: We posit that one path towards such a framework may be grounded in these properties, supported by dynamical systems. To assess this hypothesis, we describe computational models inspired from swarm intelligence, which we use as a metaphor to explore the practical implications of the properties highlighted. Results: Our results demonstrate that these properties may serve as the basis for complex operations, yielding the elaboration of knowledge and goal-directed behavior. Implications: This work highlights aspects of interaction that we believe ought to be taken into account when characterizing the possible mechanisms underlying cognition. The scope of the models we describe cannot go beyond that of a metaphor, however, and future work, theoretical and experimental, is required for further insight into the functional role of interaction with the environment for the elaboration of complex behavior. Constructivist content: Inspiration for this work stems from the constructivist impetus to account for knowledge acquisition based on interaction. (shrink)

The cognitive sciences tell us that the self is a construct. The visual arts illustrate this fact. Mathematics give it full expression, abstracting the self to a Grothendieck site. This self is a haecceity, an ephemeral this-ness and now-ness. We make up our minds and our histories. That our acts are public, that they communicate effectively, becomes a dialetheic paradox, a deep paradox for our times.

When modelling complex systems one can not include all the causal factors, but one has to settle for partial models. This is alright if the factors left out are either so constant that they can be ignored or one is able to recognise the circumstances when they will be such that the partial model applies. The transference of knowledge from the point of application to the point of learning utilises a combination of recognition and inference ­ a simple model of (...) the important features is learnt and later situations where inferences can be drawn from the model are recognised. Context is an abstraction of the collection of background features that are later recognised. Different heuristics for recognition and model formulation will be effective for different learning tasks. Each of these will lead to a different type of context. Given this, there are (at least) two ways of modelling context: one can either attempt to investigate the contexts that arise out of the heuristics that a particular agent actually applies (the `internal' approach); or (if this is feasible) one can attempt to model context using the external source of regularity that the heuristics exploit. There are also two basic methodologies for the investigation of context: a top-down (or `foundationalist') approach where one tries to lay down general, a priori principles and a bottom-up (or `scientific') approach where one can try and find what sorts of context arise by experiment and simulation. A simulation is exhibited which is designed to illustrate the practicality of the bottom-up approach in elucidating the sorts of internal context that arise in an artificial agent which is attempting to learn simple models of a complex environment. It ends with a plea for the cooperation of the AI and Machine Learning communities as both learning and inference is needed if context is to make complete sense. (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates choices (...) by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latters. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

We present a simple example that disproves the universality principle. Unlike previous counter-examples to computational universality, it does not rely on extraneous phenomena, such as the availability of input variables that are time varying, computational complexity that changes with time or order of execution, physical variables that interact with each other, uncertain deadlines, or mathematical conditions among the variables that must be obeyed throughout the computation. In the most basic case of the new example, all that is used is a (...) single pre-existing global variable whose value is modified by the computation itself. In addition, our example offers a new dimension for separating the computable from the uncomputable, while illustrating the power of parallelism in computation. (shrink)

En este ensayo respondo negativamente a la pregunta del título al sostener que el enunciado “La suma de los ángulos internos de un triángulo es igual a 180°” es contingentemente verdadero. Para ello, intento refutar la tesis de Ramsey de que las verdades geométricas necesariamente son verdades necesarias, así como la tesis de Kripke de que no puede haber proposiciones matemáticas contingentemente verdaderas. Además, recurriendo a la concepción fregeana sobre lo a priori y lo a posteriori, sostengo que hay verdades (...) geométricas que pueden ser a priori sin tener que serlo. -/- . (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)