Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

Much of what we know and love about music is based on implicitly acquired mental representations of musical pitches and the relationships between them. While previous studies have shown that these mental representations of music can be acquired rapidly and can influence preference, it is still unclear which aspects of music influence learning and preference formation. This article reports two experiments that use an artificial musical system to examine two questions: (1) which aspects of music matter most for (...) class='Hi'>learning, and (2) which aspects of music matter most for preference formation. Two aspects of music are tested: melody and harmony. In Experiment 1 we tested the learning and liking of a new musical system that is manipulated melodically so that only some of the possible conditional probabilities between successive notes are presented. In Experiment 2 we administered the same tests for learning and liking, but we used a musical system that is manipulated harmonically to eliminate the property of harmonic whole-integer ratios between pitches. Results show that disrupting melody (Experiment 1) disabled the learning of music without disrupting preference formation, whereas disrupting harmony (Experiment 2) does not affect learning and memory but disrupts preference formation. Results point to a possible dissociation between learning and preference in musical knowledge. (shrink)

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that clearly (...) does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. (shrink)

Social-emotional learning is a tendency in education and must be accounted for in all areas of study. Heritage education cannot ignore this reality and must include and its planning and delivery effective strategies to implement and promote social-emotional competencies. The following work, proves patrimonial visits are an innovative approach towards coping with emotions in society. The activity proposed and studied in this investigation demonstrated the opportunities for integer learning during these experiences are real and cause a significant impact (...) in students and society. This study demonstrated the most relevant aspects to consider in patrimonial visits. (shrink)

It is commonly believed that there is no equivalent of the Church–Turing thesis for computation over the reals. In particular, computational models on this domain do not exhibit the convergence of formalisms that supports this thesis in the case of integer computation. In the light of recent philosophical developments on the different meanings of the Church–Turing thesis, and recent technical results on analog computation, I will show that this current belief confounds two distinct issues, namely the extension of the notion (...) of effective computation to the reals on the one hand, and the simulation of analog computers by Turing machines on the other hand. I will argue that it is possible in both cases to defend an equivalent of the Church–Turing thesis over the reals. Along the way, we will learn some methodological caveats on the comparison of different computational models, and how to make it meaningful. (shrink)

Let G V, E be a simple undirected complete graph with vertex and edge sets V and E, respectively. In this paper, we consider the degree-constrained k -minimum spanning tree problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2. In particular, in this paper, we consider degree values of d ∈ (...) 2,3. Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2, it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization and variable neighborhood search algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements. (shrink)

Traditional theories of how children learn the positive integers start from infants' abilities in detecting the quantity of physical objects. Our target article examined this view and found no plausible accounts of such development. Most of our commentators appear to agree that no adequate developmental theory is presently available, but they attempt to hold onto a role for early enumeration. Although some defend the traditional theories, others introduce new basic quantitative abilities, new methods of transformation, or new types of (...) end states. A survey of these proposals, however, shows that they do not succeed in bridging the gap to knowledge of the integers. We suggest that a better theory depends on starting with primitives that are inherently structural and mathematical. (shrink)

According to Carey (2009), humans construct new concepts by abstracting structural relations among sets of partly unspecified symbols, and then analogically mapping those symbol structures onto the target domain. Using the development of integer concepts as an example, I give reasons to doubt this account and to consider other ways in which language and symbol learning foster conceptual development.

As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were (...) replaced by pocket calculators and personal computers, but I stuck to my original decision.My computer phobia did not prevent me from taking an interest in the theoretical question: what is a computation? This question goes back to Hilbert's 10th problem, which asks for an algorithm, or computational procedure, to decide whether any given polynomial equation is solvable in integers. It quickly leads to the related question: which numerical functionsf: ℕn→ ℕ are computable?While Hilbert's 10th problem was only resolved in 1970, this related question had some earlier answers, of which I shall single out the following three:f is recursive,f is computable on an abstract machine,f is definable in the untyped λ-calculus.These tentative answers were shown to be equivalent by Church [1936] and Turing [1936–7].I shall discuss here some of the more recent developments of these notions of computability and their relevance to linguistics and logic. I hope to be forgiven for dwelling on some of the work I have been involved with personally, with greater emphasis than is justified by its historical significance. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Epigram into Lyric: Francis Bacon Translates from the Greek Anthology GORDON BRADEN If sir francis bacon did not exactly invent modern science and technology, he did predict it, with remarkable accuracy. The unfinished project of which the writings of his later years were to be component parts is a reformation of the life of the human mind from the ground up—“a complete Instauration of the arts and sciences and (...) all the learning of mankind, raised upon proper foundations ”1—and the most (arguably the only) successful such plan ever drafted. It foresaw both the previously unimaginable worldly triumph of the human race over nature in the centuries that followed and the intellectual means by which that triumph was to be achieved. He also wrote poetry. It is no surprise that someone of his time and place and station should have done so, and its existence is not in itself remarkable. Not much of it has survived, and we have no particular reason to think there was more; and, despite the extensive scholarly and critical scrutiny that Bacon’s work has received, very little attention has been given to this part of it. Still, one poem has achieved something of an afterlife and is worth attention, especially alongside the triumphalism of Bacon’s Magna Instauratio. It concerns hopelessness. Serious attention has been given to Bacon’s remarks on literature and the imagination, including his proposal, amid all his other plans, for what he calls “literary history” (historia literarum).2 But his poems are a different matter. They can be found in the great 19th-century edition of Bacon’s collected works, tucked in between his Prayers and his Christian Paradoxes.3 Most of the poems are from a small volume of psalm translations published under his own name the year before arion 27.1 spring/summer 2019 his death; these are now available in one of the published volumes of the new Oxford edition of Bacon’s works.4 There is also 12-line poem in hexameter couplets that begins sounding like a translation of Horace’s Integer vitae but goes on to be a fairly straightforward completion of its opening thesis and never gets around to sweetly laughing, sweetly speaking Lalage; a manuscript in the British Library attributes it to Bacon, though it is also printed in two of Thomas Campion’s books of airs as if it were one of his.5 My own interest is in the one remaining poem, a 32-line translation of a 10-line poem from the Greek Anthology (9.359 in the Palatine Anthology, though known in Bacon’s time from the Planudean). It first appears in print in 1626, anonymously, as “Certaine verses concerning the present estate of Man,” appended with other “characters, and many other witty conceits ” to an edition of Thomas Overbury’s poem “A Wife.”6 Three years later the classical scholar Thomas Farnaby prints it with an ascription to Bacon in a selection of poems from the Greek Anthology, along with the original text of the Greek poem, a Latin translation of it, and the editor’s facing translation of Bacon’s poem back into Greek.7 Bacon’s poem can also be found, both complete and in fragmentary form, in quite a few manuscripts, which are being collated for the first time for The Oxford Francis Bacon, though the editors have not yet decided where to put it. Isolated citations and quotations of the poem occur over the next several centuries; Francis Turner Palgrave includes it in his much-reprinted Golden Treasury, with the title “Life.”8 But there has been little discussion of the poem. It is the subject of an excellent scholarly article by Herbert Grierson, but that was over a hundred years ago.9 Paul Fussell has some sharp observations on Bacon’s use of his stanza form, but they fit onto a single page.10 Other comment is mostly incidental. I want to gather and slightly enhance what has been learned or said about the poem, and explore why it has snagged my interest. The Greek original is variously attributed; the most commonly mentioned name is Posidippus, probably the Mace50 epigram into... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Philosophic Foundations of Mimetic Theory and Cognitive Science(Including Artificial Intelligence)Jean-Pierre Dupuy (bio)In the mid 1970s I discovered at the same time cognitive science and mimetic theory. Being a philosopher with a scientific background, I immediately brought them together and tried to reconceptualize the latter in terms of the former. In a sense, I haven't stopped doing that in the last 45 years. That is why I feel fully (...) at home with the goals pursued by the organizers of this conference.I do not believe it is feasible or even desirable to operate the rapprochement between the two disciplines at a global level. The history of cognitive science is exceedingly involved, and the part played by artificial intelligence in it compared to the part played by the neurosciences has varied greatly over time.1 Only a piecemeal approach makes sense. I present here four short case studies that cover the whole period, from the beginnings in cybernetics to today's artificial intelligence (AI).In order to better situate these studies within a broader frame, I propose the diagram in Figure 1. To comment on it would require more time than available for my whole presentation. Let me just say the following. [End Page 1]It is essential to distinguish between two kinds of AI. The first to bear this name was launched by economist Herbert Simon and computer scientist Allan Newell at a Dartmouth conference in 1956. It was based on the premise that thinking is computing, with this computation bearing on sentences of a "language of thought" implementable in a digital computer. It turns out that this AI(1) was progressively substituted from the 1980s onward by an AI(2), which, to some extent, was a return to a fundamental result obtained by cybernetics in 1943. Neurophysiologist Warren McCulloch and mathematician Walter Pitts had constructed a mathematical model of a network of elementary calculators called "neurons" and explored its properties. The capacity to "think" was one of these. It was not situated at the elementary level, as was the case in AI(1), but it emerged at the collective level from the interactions between the neurons.This model was heavily criticized by the supporters of AI(1),2 and its first implementations, in the notorious "Perceptron" in particular (1957), were pitiful failures. However, the emergence of "second-order cybernetics" under the guidance of cybernetician Heinz von Foerster and the theory of complex, self-organizing systems that it helped develop, in cooperation and rivalry with similar efforts in the physical sciences, enabled the neural network model to come to a second life under different names: formal neurons, deep learning, big data, and the like. Together, they constitute AI(2).The following network of influences wouldn't have been possible without its stem, that is, the boxes containing the names of Kurt Gödel and Alan Turing. The former revolutionized logic by showing that reasoning about arithmetic and arithmetic are one and the same, insofar as it is possible to code in a 1-to-1 fashion propositions about integers (for instance, "7 is a prime number") by means of integers. The latter demonstrated that some mechanisms can self-transcend inasmuch as they generate an ensemble of outputs that cannot be defined mechanistically. Later, John von Neumann, who is credited along with Alan Turing with having invented the digital computer, would use this logical possibility to define complexity: A mechanism is complex if it is capable of generating one more complex than itself. The gate was open for the theories of complex, self-organizing systems to thrive and, by way of consequence, for AI(2) to emerge.fascination with modelsHerbert Simon (1916–2001), winner of the Nobel Prize in economics for his work on what he called "bounded rationality," is generally considered to be one [End Page 2] Click for larger view View full resolutionFigure 1.of the founders of artificial intelligence. Some cognitive scientists still rely on the computer program that he devised with Alan Newell to simulate the creative processes of human thought—a program aptly named "General Problem Solver." The title of one of his principal works, The Sciences of the... (shrink)

This paper is an updated translation of an article published in French in the Journal Lato Sensu (I, 2014, p. 70-80). We study here the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. The difficulty to understand (...) it lies in the close intertwining of different fields we found in it: philosophy, history and mathematics. But conversely, correctly understood, it gives some evidences both about the question of the origins of the irrationals in Greek mathematics and some points concerning Plato's thought. Taking into account the historical context and the philosophical background generally forgotten in mathematical analyses, we get a new interpretation of this text, which far from being a tribute to some mathematicians, is a radical criticism of their ways of thinking. And the mathematical lesson, far from being a tribute to some future mathematical achievements, is ending on an aporia, in accordance with the whole dialogue. Résumé. Cet article est une traduction anglaise révisée d'un article paru en français dans la revue Lato Sensu (I, 2014, p. 70-80). (shrink)

The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is with (...) computing, which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine. (shrink)

Informed consent is at the core of the clinical relationship. With the introduction of machine learning (ML) in healthcare, the role of informed consent is challenged. This paper addresses the issue of whether patients must be informed about medical ML applications and asked for consent. It aims to expose the discrepancy between ethical and practical considerations, while arguing that this polarization is a false dichotomy: in reality, ethics is applied to specific contexts and situations. Bridging this gap and considering (...) the whole picture is essential for advancing the debate. In the light of the possible future developments of the situation and the technologies, as well as the benefits that informed consent for ML can bring to shared decision-making, the present analysis concludes that it is necessary to prepare the ground for a possible future requirement of informed consent for medical ML. (shrink)

Autonomy has been the central principle underpinning changes which have affected the practice of medicine in recent years. Medical education is undergoing changes as well, many of which are underpinned, at least implicitly, by increasing concern for autonomy. Some universities have embarked on graduate courses which utilize problem-based learning (PBL) techniques to teach all areas, including medical ethics. I argue that PBL is a desirable method for teaching and learning in medical ethics. It is desirable because the nature (...) of ethical enquiry is highly compatible with the learning processes which characterize PBL. But it is also desirable because it should help keep open the question of what autonomy really is, and how it should operate within the sphere of medical practice and medical education. (shrink)

The relatedness between a country or a firm and a product is a measure of the feasibility of that economic activity. As such, it is a driver for investments at a private and institutional level. Traditionally, relatedness is measured using networks derived by country-level co-occurrences of product pairs, that is counting how many countries export both. In this work, we compare networks and machine learning algorithms trained not only on country-level data, but also on firms, which is something not (...) much studied due to the low availability of firm-level data. We quantitatively compare the different measures of relatedness, by using them to forecast the exports at the country and firm level, assuming that more related products have a higher likelihood to be exported in the future. Our results show that relatedness is scale dependent: the best assessments are obtained by using machine learning on the same typology of data one wants to predict. Moreover, we found that while relatedness measures based on country data are not suitable for firms, firm-level data are very informative also for the development of countries. In this sense, models built on firm data provide a better assessment of relatedness. We also discuss the effect of using parameter optimization and community detection algorithms to identify clusters of related companies and products, finding that a partition into a higher number of blocks decreases the computational time while maintaining a prediction performance well above the network-based benchmarks. (shrink)

This paper provides a broad bibliometric overview of the important conceptual advances that have been published during COVID-19 within “e-learning in higher education.” E-learning as a concept has been widely used in the academic and professional communities and has been approved as an educational approach during COVID-19. This article starts with a literature review of e-learning. Diverse subjects have appeared on the topic of e-learning, which is indicative of the dynamic and multidisciplinary nature of the field. (...) These include analyses of the most influential authors, of models and networks for bibliometric analysis, and progress towards the current research within the most critical areas. A bibliometric review analyzes data of 602 studies published in the Web of Science database to fully understand this field. The data were examined using VOSviewer, CiteSpace, and KnowledgeMatrix Plus to extract networks and bibliometric indicators about keywords, authors, organizations, and countries. The study concluded with several results within higher education. Many converging words or sub-fields of e-learning in higher education included distance learning, distance learning, interactive learning, online learning, virtual learning, computer-based learning, digital learning, and blended learning. This research is mainly focused on pedagogical techniques, particularly e-learning and collaborative learning, but these are not the only trends developing in this area. The sub-fields of artificial intelligence, machine learning, and deep learning constitute new research directions for e-learning in light of COVID-19 and are suggestive of new approaches for further analysis. (shrink)

Jonathan Bennett engages with the thought of six great thinkers of the early modern period: Descartes, Spinoza, Leibniz, Locke, Berkeley, and Hume. While not neglecting the historical setting of each, his chief focus is on the words they wrote. What problem is being tackled? How exactly is the solution meant to work? Does it succeed? If not, why not? What can be learned from its success or failure? For newcomers to the early modern scene, this clearly written work is an (...) excellent introduction to it. Those already in the know can learn how to argue with the great philosophers of the past, treating them as colleagues, antagonists, students, teachers. In this second volume, Bennett focuses on the work of Locke, Berkeley, and Hume. (shrink)

Vanderschraaf develops a new theory of game theory equilibrium selection in this book. The new theory defends general correlated equilibrium concepts and suggests a new analysis of convention.

What might Adam Smith have learned from Jane Austen and other novelists of his moment? This paper finds and examines a serious problem at the center of Adam Smith’s moral psychology, stemming from an unacknowledged tension between the effort of the spectator to sympathize with the feelings of the agent and that of the agent to moderate her feelings. The agent’s efforts will result in her opacity to spectators, blocking their attempts to read her emotions. I argue that we can (...) resolve this tension by looking to developments in eighteenth-century literature, as perfected in the hands of Jane Austen. I focus on two techniques, focalization and free indirect style, and I show that the problems for spectatorship diminish when we see that good Smithian spectators are savvy readers. (shrink)

This work aims to explore the application of deep learning-based artificial intelligence technology in sentencing, to promote the reform and innovation of the judicial system. First, the concept and the principles of sentencing are introduced, and the deep learning model of intelligent robot in trials is proposed. According to related concepts, the issues that need to be solved in artificial intelligence sentencing based on deep learning are introduced. The deep learning model is integrated into the intelligent (...) robot system, to assist in the sentencing of cases. Finally, an example is adopted to illustrate the feasibility of the intelligent robot under deep learning in legal sentencing. The results show that the general final trial periods for cases of traffic accidents, copyright information, trademark infringement, copyright protection, and theft are 1,049, 796, 663, 847, and 201 days, respectively; while the final trial period under artificial intelligence evaluation based on the restricted Boltzmann deep learning model is 458, 387, 376, 438, and 247 days, respectively. The accuracy of trials is above 92%, showing a high application value. It can be observed that expect theft cases, the final trial period for others cases has been effectively reduced. The intelligent robot assistance under the restricted Boltzmann deep learning model can shorten the trial period of cases. The deep learning intelligent robot has a certain auxiliary role in legal sentencing, and this outcome provides a theoretical basis for the research of artificial intelligence technology in legal sentencing. (shrink)

IntroductionThe assessments of the motor symptoms in Parkinson’s disease are usually limited to clinical rating scales, and it depends on the clinician’s experience. This study aims to propose a machine learning technique algorithm using the variables from upper and lower limbs, to classify people with PD from healthy people, using data from a portable low-cost device. And can be used to support the diagnosis and follow-up of patients in developing countries and remote areas.MethodsWe used Kinect®eMotion system to capture the (...) spatiotemporal gait data from 30 patients with PD and 30 healthy age-matched controls in three walking trials. First, a correlation matrix was made using the variables of upper and lower limbs. After this, we applied a backward feature selection model using R and Python to determine the most relevant variables. Three further analyses were done using variables selected from backward feature selection model, movement disorders specialist, and all the variables from the dataset. We ran seven machine learning models for each model. Dataset was divided 80% for algorithm training and 20% for evaluation. Finally, a causal inference model using the DoWhy library was performed on Dataset B due to its accuracy and simplicity.ResultsThe Random Forest model is the most accurate for all three variable Datasets followed by the support vector machine. The CIM shows a relation between leg variables and the arms swing asymmetry and a proportional relationship between ASA and the diagnosis of PD with a robust estimator.ConclusionsMachine learning techniques based on objective measures using portable low-cost devices are useful and accurate to classify patients with Parkinson’s disease. This method can be used to evaluate patients remotely and help clinicians make decisions regarding follow-up and treatment. (shrink)

In order to build high-quality concrete, it is imperative to know the raw materials in advance. It is possible to accurately predict the quality of concrete and the amount of raw materials used using machine learning-enhanced methods. An automated process based on machine learning strategies is proposed in this paper for predicting the compressive strength of concrete. Fusion-learning-based optimization is used in the proposed approach to generate a strong learner by pooling support vector regression models. The SVR (...) technique proposes an optimization method for finding the kernel radial basis function parameters based on improving the innovative gunner algorithm. As a result of AIG's diverse solutions, local optima are effectively avoided. Therefore, the novelty of our research is that, in solving the uncertainty of predicted outputs based on integrated models, we use fusion-learning-based optimization to improve regression discrimination. We also collected a standard dataset to analyze the proposed algorithm, and subsequently, the dataset was designed from concrete laboratory tests on 244 samples, seven features, and three outputs. Different regression intensities are determined by correlation analysis of responses. Regression fusion is sufficiently accurate to estimate the number of desired outcomes examined based on the appropriate input data sample. The best quality concrete can be achieved with an error rate of less than 5%. (shrink)

The specific mechanisms whereby Pavlovian conditioning leads to adaptive behavior need to be elaborated. There is no evidence that it is via reduction in the “destabilizing effect that time lags have on feedback control” (Domjan et al. 2000, sect. 3.3). The adaptive value of Pavlovian conditioning goes well beyond the regulation of social behavior.