Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every (...) definable function which is meromorphic on Kn is necessarily a rational function. We finally discuss definable analogues of complex analytic manifolds, with possible connections to the model theoretic work on compact complex manifolds, and present two examples of "nonstandard manifolds" in our setting. (shrink)

Children and adolescents are not indifferent to the dramatic impact of the COVID-19 pandemic, and the need to be forced to live in confinement. The change in life to which they have been abruptly subjected forces us to understand the state of their mental health in order to adequately address both their present and future needs. The present study was carried out with the intention of studying the consequences of confinement on anxiety, sleep routines and executive functioning of 1,028 children (...) and adolescents, aged from 6 to 18 years, residing in Spain to; assess if there are differences regarding these consequences in terms of sex and age; how anxiety affects executive functioning in males and females; and to examine the possible correlations between the measured variables. For this purpose, an online questionnaire containing five sections was designed: the first section gathers information on sociodemographic and health data, while the following sections gather information from different standardized scales which measure anxiety, sleep and executive functions, whose items were adapted in order to be completed by parents, and/or legal guardians. The statistical analyzes carried out highlights significant differences in executive functioning between males and females. In turn, in regards to age, greater difficulties were detected in anxiety in the 9 to 12 age group and greater sleep disturbances between 13 and 18 year olds. On the other hand, significant differences were found in intra-sexual executive functioning depending on whether they presented greater or lesser anxiety, with executive functioning being more tendentiously maladjusted in males than in females, revealing a significantly relevant effect size. Positive correlations are obtained between state anxiety and sleep and executive functioning alterations. Finally, through Path Analysis, it is verified that state anxiety is the variable with the greatest weight within the model that would explain the alteration in the executive functioning of the present sample. (shrink)

We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to (...) a real function of the form x cxr, c ≠ 0; in particular, this structure is polynomially bounded. Furthermore, given any definable function f:U → with U open in n, if α ε U and f is infinitely differentiable at α, then f is real analytic in a neighborhood of α. (shrink)

An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is (...) based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona. (shrink)

As driving functions become increasingly automated, motorists run the risk of becoming cognitively removed from the driving process. Psychophysiological measures may provide added value not captured through behavioral or self-report measures alone. This paper provides a selective review of the psychophysiological measures that can be utilized to assess cognitive states in real-world driving environments. First, the importance of psychophysiological measures within the context of traffic safety is discussed. Next, the most commonly used physiology-based indices of cognitive states are (...) considered as potential candidates relevant for driving research. These include: electroencephalography and event-related potentials, optical imaging, heart rate and heart rate variability, blood pressure, skin conductance, electromyography, thermal imaging, and pupillometry. For each of these measures, an overview is provided, followed by a discussion of the methods for measuring it in a driving context. Drawing from recent empirical driving and psychophysiology research, the relative strengths and limitations of each measure are discussed to highlight each measures’ unique value. Challenges and recommendations for valid and reliable quantification from lab to (less predictable) real-world driving settings are considered. Finally, we discuss measures that may be better candidates for a near real-time assessment of motorists’ cognitive states that can be utilized in applied settings outside the lab. This review synthesizes the literature on in-vehicle psychophysiological measures to advance the development of effective human-machine driving interfaces and driver support systems. (shrink)

In his writings about hypergeometric functions Gauss succeeded in moving beyond the restricted domain of eighteenth-century functions by changing several basic notions of analysis. He rejected formal methodology and the traditional notions of functions, complex numbers, infinite numbers, integration, and the sum of a series. Indeed, he thought that analysis derived from a few, intuitively given notions by means of other well-defined concepts which were reducible to intuitive ones. Gauss considered functions to be relations between continuous (...) variable quantities while he regarded integration and summation as appropriate operations with limits. He also regarded infinite and infinitesimal numbers as a façon de parler and used inequalities in order to prove the existence of certain limits. He took complex numbers to have the same legitimacy as real quantities. However, Gauss’s continuum was linked to a revised form of the eighteenth-century notion of continuous quantity: it was not reducible to a set of numbers but was immediately given. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between (...) their difference and the status quo, then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

We extend the notion of absolute convergence for real series in several variables to a notion of convergence for series in a power series field ℝ((t Γ)) with coefficients in ℝ. Subsequently, we define a natural notion of analytic function at a point of ℝ((t Γ))m. Then, given a real function f analytic on a open box I of ℝ m , we extend f to a function f ★ which is analytic on a subset of ℝ((t (...) Γ)) m containing I. We prove that the functions f ★ share with real analytic functions certain basic properties: they are , they have usual Taylor development, they satisfy the inverse function theorem and the implicit function theorem. (shrink)

In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of (...) the linguistic continuum we generally include the ends or to be more mathematical say it is a closed interval, where shortest denotes the shortest height of a person, maybe the born infant who is very short from usual and the tallest will denote the tallest one usually very tall; however this linguistic continuum [shortest, tallest] in the real continuum will be the closed interval say [1 foot, 8 feet] or [1, 8] the measurement in terms of feet. So, the real interval is a subinterval with which we have associated the real continuum in terms of qualifying unit feet and inches in this case. (shrink)

Analysis of grip force signals tailored to hand and finger movement evolution and changes in grip force control during task execution provide unprecedented functional insight into somatosensory cognition. Somatosensory cognition is a basis of our ability to manipulate, move, and transform objects of the physical world around us, to recognize them on the basis of touch alone, and to grasp them with the right amount of force for lifting and manipulating them. Recent technology has permitted the wireless monitoring of grip (...) force signals recorded from biosensors in the palm of the human hand to track and trace human grip forces deployed in cognitive tasks executed under conditions of variable sensory (visual, auditory) input. Non-invasive multi-finger grip force sensor technology can be exploited to explore functional interactions between somatosensory brain mechanisms and motor control, in particular during learning a cognitive task where the planning and strategic execution of hand movements is essential. Sensorial and cognitive processes underlying manual skills and/or hand-specific (dominant versus non-dominant hand) behaviors can be studied in a variety of contexts by probing selected measurement loci in the fingers and palm of the human hand. Thousands of sensor data recorded from multiple spatial locations can be approached statistically to breathe functional sense into the forces measured under specific task constraints. Grip force patterns in individual performance profiling may reveal the evolution of grip force control as a direct result of cognitive changes during task learning. Grip forces can be functionally mapped to from-global-to-local coding principles in brain networks governing somatosensory processes for motor control in cognitive tasks leading to a specific task expertise or skill. Under the light of a comprehensive overview of recent discoveries into the functional significance of human grip force variations, perspectives for future studies in cognition, in particular the cognitive control of strategic and task relevant hand movements in complex real-world precision task, are pointed out. (shrink)

One of the main challenges in medicine is to guarantee an appropriate drug supply according to the real needs of patients. Closed-loop strategies have been widely used to develop automatic solutions based on feedback variables. However, when the variable of interest cannot be directly measured or there is a lack of knowledge behind the process, it turns into a difficult issue to solve. In this research, a novel algorithm to approach this problem is presented. The main objective of (...) this study is to provide a new general algorithm capable of determining the influence of a certain clinical variable in the decision making process for drug supply and then defining an automatic system able to guide the process considering this information. Thus, this new technique will provide a way to validate a given physiological signal as a feedback variable for drug titration. In addition, the result of the algorithm in terms of fuzzy rules and membership functions will define a fuzzy-based decision system for the drug delivery process. The method proposed is based on a Fuzzy Inference System whose structure is obtained through a decision tree algorithm. A four-step methodology is then developed: data collection, preprocessing, Fuzzy Inference System generation, and the validation of results. To test this methodology, the analgesia control scenario was analysed. Specifically, the viability of the Analgesia Nociception Index as a guiding variable for the analgesic process during surgical interventions was studied. Real data was obtained from fifteen patients undergoing cholecystectomy surgery. (shrink)

This uncommonly fine textbook of the modern theory of functions of a real variable is particularly well-suited for mathematically mature students in the fields of philosophy and foundations of mathematics, philosophy of physics, probability theory, and statistics. Those who wish to achieve first-hand acquaintance with the quantum theory will also need to have a grasp of the material presented in this book. The first chapter presents a capsule survey of topics in abstract set theory and algebra, including a (...) discussion of relations, functions, the axiom of choice, and the well-ordering theorem, and leading up to the construction of the fields of real and complex numbers. The second chapter is an introduction to topology and spaces of topological functions. The approach is set-theoretical. Chapter three deals with the theory of the Lebesgue integral and measure theory. This chapter is quite comprehensive, rigorous and embellished with many exercises for the student. Subsequent sections include the theories of function spaces, Banach spaces, abstract Hilbert spaces, and differentiation. This is clearly one of the more worthwhile texts in its field.—H. P. K. (shrink)

In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993 ) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Björling’s general view of real- and complexvalued functions. We argue that Björling had a tendency to sometimes consider mathematical objects in a naturalistic way. One (...) example is how Björling interprets Cauchy’s definition of the logarithm function with respect to complex variables, which is investigated in the paper. Furthermore, in view of an article written by Björling (Kongl Vetens Akad Förh Stockholm 166–228, 1852 ) we consider Cauchy’s theorem on power series expansions of complex valued functions. We investigate Björling’s, Cauchy’s and the Belgian mathematician Lamarle’s different conditions for expanding a complex function of a complex variable in a power series. We argue that one reason why Cauchy’s theorem was controversial could be the ambiguities of fundamental concepts in analysis that existed during the mid-nineteenth century. This problem is demonstrated with examples from Björling, Cauchy and Lamarle. (shrink)

It is possible today to observe in hindsight the epistemological landscape of the twentieth century, and the work of Albert Lautman in mathematical philosophy appears as a profound turning point, opening to a true under- standing of creativity in mathematics and its relation with the real. Little understood in its time or even today, Lautman’s work explores the difficult but exciting intersection where modern mathematics, advanced mathe- matical invention, the structural or unitary relations of mathematical knowledge and, finally, the (...) metaphysical and dialectical tensions underly- ing mathematical activity converge. Well beyond other better-known names in philosophy of mathematics – who are focused above all on ques- tions concerning the logical problem of foundations, important but frag- mentary studies in the vast panorama of modern mathematics – Lautman broaches the emergence of inventiveness in the very broad spectrum of the development of the mathematical real. Group theory, differential geome- try, algebraic topology, differential equations, functional analysis, functions of complex variables and number fields are some of the domains of his preferred examples. He detects in them methods of construction, structu- ration and unification of modern mathematics that he connects to a precise Platonic interpretation in which powerful pairs of ideas serve to organize the edifice of effective mathematics. (shrink)

We present an initial and elementary investigation of the formal specification and mechanical verification of programs that interact with environments. We describe a formal, mechanically produced proof that a simple, real time control program keeps a vehicle on a straightline course in a variable crosswind. To formalize the specification we define a mathematical function which models the interaction of the program and its environment. We then state and prove two theorems about this function: the simulated vehicle never gets farther (...) than three units away from the intended course and homes to the course if the wind ever remains steady for at least four sampling intervals. (shrink)

We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles.

One’s first impression is that Brouwer’s Continuity Theorem of intuitionistic analysis, that every total, real-valued function of a real variable is continuous, stands in straightforward contradiction to a simple theorem of conventional real analysis, that there are discontinuous, real-valued func­tions. Here we argue that, despite philosophical views to the contrary, first impressions are not misleading; the Brouwer Theorem, together with its proof, presents mathematicians and philosophers of mathematics with an antimony, one that can only be resolved (...) by a close, foundational study of the structure of the intuitive continuum. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.3 (2002) 237-241 [Access article in PDF] Practical, Functional, and Natural Kinds Nick Haslam Keywords: Classification, essentialism, natural kinds, practical kinds. I am grateful to the two commentators for giving my paper their serious attention, and for writing such stimulating, clarifying, and challenging responses. In a brief response I can only begin to discuss a select few issues, although both commentaries could generate a great (...) deal of profitable exchange.Zachar's commentary elaborates his practical kinds model, discusses several of the graded series of kinds proposed in my taxonomy of psychiatric categories, and disputes some aspects of my treatment of natural kinds. Zachar and I have no quarrel on his first point. I recognize his practical kinds model as a general theory of psychiatric classification rather than simply as a description of one type of category, the "practical kind." It was perhaps bad form to pilfer a term from Zachar's model and give it a more circumscribed role in my own, although by doing so I intended both to acknowledge the importance of the concept and to situate it among some of its alternatives.All the same, I stand by the account of practical kinds developed in my paper, even if it reflects a narrower sense than Zachar's. In my sense, practical kinds are pragmatically drawn distinctions imposed on continuous dimensions, whereas to Zachar all psychiatric categories are at least to some degree practical. He therefore proposes a broad "continuum" of practical kinds. The difficulty that I have with this proposal is that such a continuum implies a fundamental unity among psychiatric categories: categories are all to be understood first and foremost in pragmatic terms and differences in kind between them in internal structure are to be neglected. In my view, although the pragmatic bases of psychiatric classification are vitally important, and perhaps inadequately formulated in my paper, the neglect of internal structure and of possible breaks in the continuum of kinds are real limitations of the practical kinds model. Although Zachar is partially justified in claiming that his view is pluralistic, allowing as it does for variability in degrees of practicality, by failing to acknowledge distinctly different kinds of categories in the psychiatric domain, his view is less pluralistic than I believe it should be.One example of what I take to be this neglect of structural differences is a conflation of two sorts of practicality in Zachar's work. On the one hand, certain categories such as hypertension or obesity are defined on pragmatic grounds, a binary distinction being drawn in the absence of an internal discontinuity, because individuals identified as category members are adjudged to [End Page 237] be at significantly elevated risk. On the other hand, some categories just happen to have high practical utility. Zachar argues that schizotaxia, for example, is practical because it affords a variety of scientific and clinical inferences.It seems to me that these sorts of practicality—or perhaps these sorts of relations to practicality—are importantly different. Hypertension is defined as a category because of its practical utility—because a certain blood pressure threshold marks an inflection in actuarial risk of other illnesses—and might therefore be said to have "front-end" or constitutive practicality. Schizotaxia, which taxometric research shows to be a discrete kind (Haslam, 2003), is not defined and identified primarily on the basis of its relation to an external criterion, but on the basis of its internal structure. Its features cohere in a way that indicates a category with a determinate prevalence. It has "back-end" or consequential practicality to the degree that this category enables useful predictions. These two proposed forms of practicality are equally important: both mean that categories will be pragmatically valuable. However, they are also different, being characteristic of different kinds of categories and perhaps even negatively related. Kinds with front-end practicality, that is, may tend to have a more restricted range of practical implications, defined as they are in relation to specific external criteria. Kinds with back-end practicality, in contrast, may enable a wider array of predictions to the extent that... (shrink)

The study of social, ethical, and political issues from a naturalistic perspective has been pervasive in social sciences and the humanities in the last decades. This articulation of empirical research with philosophical and normative reflection is increasingly getting attention in academic circles and the public spheres, given the prevalence of urgent needs and challenges that society is facing on a global scale. The contemporary world is full of challenges or what some philosophers have called ‘existential risks’ to humanity. Nuclear wars, (...) natural and/or engineered pandemics, climate change, global totalitarianism, and emergent technologies, are some of the challenges mentioned by many authors devoted to the study of long-term potential risks for the survival of the human species. However, while there are many reasons to be a pessimist about the future of humanity, there is also a lot of ink wasted in showing that the world today is far better than we had in the past and also that there have been many instances of social and moral progress in the last centuries. Some authors have even claimed that “we have made more progress over the last 100 years than in the first 100,000”. According to ‘our world in data’, some of the most relevant advances of humanity in the last centuries have to do with the reduction of poverty and/or inequality, better health and security, the decline of violence and war, and the development of democracy and institutional mechanisms to guarantee individual freedom and rights. Yet, there is a more concrete concern that our world faces nowadays, and requires a particularly detailed analysis. In a few words, the advance in information and communication technologies, the huge volume of people migration because of prevalent instances of global inequality, and the reality of an interconnected world that just mirrors an extensive history of massive human intergroup relations open the question about the feasibility of social and moral progress in the contexts of diverse, multicultural, and unequal societies. This makes it crucial to reflect not only on whether human societies may keep advancing on a path of social progress, but how this can be achieved by addressing the challenges of inequality and potential intergroup conflict. This concern closely relates to the further consolidation of democratic values and the achievement of a more generalized consideration of the equal moral value of human individuals far from group, ethnic, or collective distinctions. This vision of progress follows the moral convictions that have been considered right and worthy to be pursued by most ethical theories explored by philosophers and social scientists so far. This work aims to contribute to the study of the mechanisms and feasibility of social and moral progress grounded on the precept of human equality and is guided by the idea that social and moral progress in a plural world requires the accomplishment of a more democratic and tolerant society. These forms of progress have already been defined by philosophers Allen Buchanan and Russel Powell as inclusivist forms of moral progress. According to these authors, inclusivist moral progress is featured by the transformation of moral judgments, motivations, and norms guided by the rejection of “group-based restrictions on moral standing and moral status” (2018). The work of Buchanan and Powell is fundamental for the argumentation developed in this work since they have pioneered a more complex debate in the field of evolutionary social sciences and philosophical anthropology. In brief, these authors have inquired how human nature, conceptualized by the advances in evolutionary thinking and the empirical sciences, is related to our moral convictions and the possibilities that we have to establish certain forms of social and moral progress. The work of Buchanan and Powell contributes to the debate on moral progress by incorporating empirically-informed concepts and arguments. With this objective in mind, they develop their discussion around a generalized tension between exclusivist and inclusivist forms of moral progress. This tension revolves around the question of whether and to what extent human moral concerns, motivations, and norms, are limited or bounded by social identities, group thinking, or collective values. This question is at the center of this work. In other words, I aim to answer whether and to what extent the nature of our social and moral cognition hinders or enables the development of inclusivist forms of morality and moral progress. As I mentioned so far, the distinction between exclusivist and inclusivist forms of morality has a practical implication and facilitates the reflection on the mechanisms and feasibility of concrete forms of progress based on the precept of human equality, which is the road to progress that we should follow according to most ethical theories. The distinction between exclusivist and inclusivist morality is not used here as a form of summarizing highly divergent descriptive approaches to morality, but as a way to address the practical implications of morality research, particularly around the question of the feasibility of social forms of progress based on the precept of equality and tolerance. My objective then has less to do with offering a conceptualization of human morality or with the proposition of a new ethical perspective. Instead, I aim to identify, from an empirically informed perspective, what enables the achievement of egalitarian forms of social progress, to subsequently offer a normative reflection about what we should do if we want to accomplish such inclusivist forms of progress. This task is of great relevance, having in mind that some theoretical proposals on the matter have claimed that human prosocial behavior and morality are constrained by exclusivist fixed tendencies as a product of our evolutionary history. According to these views, human morality is a group-centered cognitive and behavioral expression that has severe limits in its scope and extent, which hinders in the end the emergence of inclusivist forms of moral concerns and behaviors. These claims align with the philosophical intuition about the ‘dissociation of empathy’, or the fact that human individuals tend to express empathy and sympathy preferably for members of their group whereas their empathic and moral concern and recognition for outgroup individuals tend to be reduced or eliminated in real-life social interactions. Multiple theorists have expressed, however, that these assumptions are wrong for empirical and philosophical reasons, which results in a serious challenge to the conception of human morality as exclusivist by nature. Furthermore, simple intuition and practical experience constantly show us that human individuals can develop and endorse a broad spectrum of moral considerations and adopt an arguably inclusivist stance concerning the kind of persons or agents that deserve moral concern. Moreover, and adopting a historical perspective, the expansion of cultural and commercial exchanges, the consolidation of democracy, the development of welfare states, or the emergence of institutions based on the concept of universal human rights, have partially driven human progress based on the impartial concern for the well-being of persons. These historical instances of cultural evolution and institutional design have shown that it is feasible to promote behaviors and attitudes grounded in impersonal prosocial and inclusivist principles. This optimistic perspective, however, still begs the question of the exact relationship between social, cultural, and historical contexts, and the emergence of certain behavioral expressions of inclusivist morality. This is crucial since a great number of human individuals around the world still do not make part of these instances of social progress, and some authors have suggested that such instances of social and moral progress are particularly favored by the contexts of the WEIRD world, that is the world of Western, Educated, Industrialized, Rich, and Democratic societies. Some of these approaches consider moral inclusivity a ‘luxury good’ and follow the ‘dependency thesis’ according to which the expression of moral inclusivity depends on the presence of very concrete material conditions that trigger inclusivist and impersonal prosocial tendencies that human beings are not able to express in threatening contexts without physical security. This thesis is problematic for various reasons and has led to incomplete explanations about the enabling and causal factors of inclusivist moral progress, as well as unsatisfactory suggestions about what we should do to foster the accomplishment of more generalized instances of progress based on inclusivist concerns. In an attempt to contribute to this debate, the main objective of this thesis is to offer an alternative proposal about the nature of human morality and a more detailed reflection on what we should do if we want to further accomplish such instances of progress. More precisely, this work adopts a particular developmental and constructivist vision of human morality to answer the question of how feasible it is to reach generalized forms of social progress based on the precepts of moral inclusivity. Furthermore, it offers some ideas about what are the most adequate and favorable conditions to foster such progress both at the individual and the collective level. At this point, a preliminary clarification of some starting points is necessary. In the first place, and contrary to what other authors have proposed when debating moral progress from an empirically-based approach, my perspective adopts a radical developmental and constructivist perspective, following particularly the conceptual and empirical ideas of the social-domain theory in moral psychology. From this perspective, morality is a domain of normative and social knowledge that develops and emerges in human interactions. Moral concerns, judgments, and norms are not only the result of the expression of innate adaptive intuitions, nor the product of social conformity and a simple process of mirroring the normativity that communities have established to organize their social life. Human individuals, instead, construct moral concerns and judgments during their situated interactions. More specifically, the constructivist tradition claims that we need to research how moral concerns, judgments, and reasons emerge in social interactions and how human beings construct the content of their moral knowledge in the first place. Based on these ideas, morality is defined here as the result of a constructive process through which human individuals, by the means of constant interactions on a background of mutual respect and recognition, develop evaluative concerns about how we ought to treat others, and how to ‘care’ and ‘respect’ others’ well-being, needs, and vulnerabilities. This developmental-constructivist theory of human psychology contributes to an alternative understanding of the origins of moral variability and informs a very particular normative stance about the most desirable contexts needed for the urgent accomplishment of inclusivist forms of morality in contemporary societies. This is so given that the very same definition of morality adopted presupposes the feature of inclusivity. The main objective of this work is then to argue, based on a developmental perspective, what are the most favorable conditions to foster the development of moral inclusivity and what we should do to accomplish concrete instances of moral progress that truly help us to overcome our most urgent moral challenges. The whole thesis is organized as follows. In part I, I show how received visions about human social evolution have informed conceptions of morality as an adaptive function evolved to solve the challenges of cooperative life. Based on these assumptions, some theories argue that human morality is limited by the boundaries of group thinking, and always obeys the mandates of collective interests and the will of the majority. However, this conception has problematic implications from a normative and ethical perspective. The aim of Chapter 1 is to present this introductory debate in detail. In chapter 2, I consider a relevant amount of scientific evidence that helps to consolidate a more optimistic and inclusivist perspective about the starting conditions of human prosocial behavior. Later, I will summarize some ideas offered to explain the possible evolutionary mechanisms that led to the consolidation of these inclusivist capacities. However, I will also show how evolutionary theories that share the same adaptationist foundations but initially seem relevant to explain the feasibility of moral inclusivity, result incomplete when considering the complexity of moral behavior and its ethical implications. Part II is devoted to presenting a developmental alternative to the adaptationist versions around the starting conditions of morality. In this section, I first summarize the epistemological, conceptual, and empirical basis of a constructivist perspective already proposed by several authors in the last decades. This is the goal of chapter 3. More precisely, I adopt the conceptualization of morality established by the social-domain theory school and clarify its conception of the situated development of moral concerns, motivations, and norms. All these ideas are essential for my argumentation on the feasibility of inclusivist moral progress offered later. Chapter 4 provides a more detailed idea of constructivist thinking about moral development, by analyzing one particular dimension: the development of moral concerns for fairness and the sense of justice in distributive dilemmas. In Part III, I assume a constructivist perspective on morality to contribute to the philosophy of moral progress. In particular, I discuss the implications of such a perspective for the conceptualization of human moral nature and discuss what are the most favorable conditions for moral inclusivity to emerge. Answering that question is of enormous relevance since favoring the transition of human societies towards more inclusivist forms of moral concern and behavior supposes a more generalized accomplishment of our most urgent moral convictions. Previous developmental or culturally-sensible attempts to explore this issue are already on the market. As mentioned before, most authors have approached the topic by situating the cultural evolution and development of (inclusivist) moral progress in the WEIRD world. For instance, some of these authors claim that very concrete material conditions (mostly present in the Western World) have been necessary for triggering inclusivist and impersonal prosocial tendencies that human beings are not able to express in threatening contexts without physical security. Despite their interest in explaining inclusivist morality and the feasibility of inclusivist forms of progress following a naturalistic and culturally situated approach, these theories are problematic for two main reasons. In the first place, most of the authors that explain moral progress tend to focus exclusively on the consolidation of liberal values in the Western world and the underlying adoption of laws, social-epistemic practices, and public narratives about tolerance and inclusivity, as unequivocal signs of inclusivist morality. Nevertheless, there is an enormous distance between the institutional and public support of inclusivist moral values or the construction of public images of tolerance and inclusivity, and the real materialization of impersonal moralities in situated social interactions. Secondly, the variability of human moral behavior is far bigger than most of the theories in moral psychology and moral progress tend to assume. Accordingly, inclusivist and exclusivist forms of morality may develop simultaneously in similar or divergent geographical and socio-ecological environments, including those with harsh conditions such as competition for scarce resources, potential intergroup conflict, and risks of disease transmission. In addition, harsh environmental conditions are usually present in almost all societies around the globe, and the presence of socio-ecological conditions such as physical security and prosperity, predominant in highly resourced populations, do not prevent the existence of exclusivist moral tendencies. My model explores a different perspective on the relationships between cultural, institutional, and historical factors, and the situated development of human morality. This supposes a clear distinction from previous approaches to the matter since it offers a different view on what we should do to pursue further instances of inclusivist social progress. In the fifth chapter, I first analyze the proposals of some defenders of the ‘dependency’ theory. The attention is focused on the ‘Evolutionary Developmental Model’ proposed by Buchanan and Powell (2018). Based on a critique of this approach, I will argue that to explain the evolution and development of human morality in its multiple manifestations, it is essential to put focus on social interactions. This also involves a different perspective on human-environment relations that in line with a constructivist worldview makes an innovative contribution to the philosophy of moral behavior and moral progress. Later, in the sixth chapter, I will define my alternative relational view of inclusivist morality and I will offer my view on how to establish favorable conditions that make inclusivist morality possible. Complementing the constructivist approach, my conception is based on the essential role of equality and individuality and on how moral inclusivity is favored if moral concerns do not develop driven by the accomplishment of group-centered, binding, and communitarian concerns and values. In brief, my relational model suggests that the accomplishment of moral inclusivity not only depends on the overall achievement of certain levels of physical security or economic prosperity. Instead, its development is favored by transforming the interactional contexts in which moral concerns towards autonomy and individuality emerge. In arguing so, I will need to start with a critique of contemporary situated and embodied approaches in ethics. Then, I will show how societies guided by the accomplishment of group-centered values of power, dominance, and relational inequality tend to express exclusivist moral behaviors, while individualistic societies tend to be more inclusivist. Starting from this diagnosis, my final attempt is then to reflect on which are the best conditions for the moral valuation of individuality to emerge and what we should do to promote the accomplishment of moral inclusivity at the societal level. (shrink)

In the context of constructive reverse mathematics, we show that weak Kőnig's lemma () implies that every pointwise continuous function is induced by a code in the sense of reverse mathematics. This, combined with the fact that implies the Fan theorem, shows that implies the uniform continuity theorem: every pointwise continuous function has a modulus of uniform continuity. Our results are obtained in Heyting arithmetic in all finite types with quantifier‐free axiom of choice.

The use of wireless sensor networks and the Internet of things to detect forest fire outbreaks may help to reduce the response time and avoid natural disasters. This work proposes the deployment of WSN to enhance the real-time monitoring of dynamic variables such as polluting gases, temperature or the presence of fire flames by infrared. In addition, the activation of forest fire alerts if environmental status may involve evidence of a recent fire outbreak. A fuzzy-based controller is implemented (...) to manage the uncertainty related to estimating forest fire occurrence and dynamic update of fuzzy sets is developed to distinguish usual and unusual environmental conditions of every monitored forest area. Merkle trees, AES and hash functions are considered to protect the integrity of environmental data. (shrink)

Psychotic-like experiences are a phenomenon that occurs in the general population experiencing delusional thoughts and hallucinations without being in a clinical condition. PLEs involve erroneous attributions of inner cognitive events to the external environment and the presence of intrusive thoughts influenced by dysfunctional beliefs; for these reasons, the role played by metacognition has been largely studied. This study investigates PLEs in a non-clinical population and discriminating factors involved in this kind of experience, among which metacognition, as well as psychopathological features, (...) seems to have a crucial role. The aim of this study was to extend the knowledge about the relationship between metacognition, psychopathology, and PLEs, orienting the focus on metacognitive functioning. The sample consisted of 207 Italian participants voluntarily recruited online, who gave consent to participate in the study. The average age of the sample was 32.69 years. Subjects affected by psychosis, neurological disease, and drug addiction were excluded from the analyses. The following scales were used to investigate PLEs: Peters et al. Delusions Inventory, Launay-Slade Hallucinations Scale-Extended Revised, Prodromal Questionnaire-Brief, and Revised Hallucination Scale. To assess general psychopathological features, the Behavior and Symptom Identification Scale was administrated. The Metacognition Self-Assessment Scale was chosen to evaluate metacognitive functioning. From hierarchical regression analyses, it emerged that the presence of anxiety, depression, and impulsive/addictive symptoms constitute a remarkable vulnerability factor for PLEs, in line with previous evidence regarding the relationship between general psychopathology and PLEs. Metacognition negatively predicts PLEs, and its presence does not affect the significance of psychopathological variables, suggesting that metacognitive abilities seem to play a protective role for the occurrence of PLEs among non-clinical individuals, and such ability operates as an independent predictor along with other variables. These results are explained by the role of metacognitive functions, which allow individuals to operate many mental processes such as interpreting sensorial events as real or illusory, understanding behaviors, thoughts, and drives of others, and questioning the subjective interpretation of facts. (shrink)

An MV-algebra A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1−x and x⊕y=min(1,x+y). Therefore, the free n-generated MV-algebra Free n is the algebra of [0,1]-valued functions over the n-cube [0,1] n generated by the coordinate functions ξ i ,i=1, . . . ,n, with pointwise operations. Any such function (...) f is a McNaughton function, i.e., f is continuous, piecewise linear, and each piece has integer coefficients. Conversely, McNaughton proved that all McNaughton functions f: [0,1] n →[0,1] are in Free n . The elements of Free n are logical equivalence classes of n-variable formulas in the infinite-valued calculus of Łukasiewicz. The aim of this paper is to provide an alternative, representation-free, characterization of Free n. (shrink)

Briefly sketches a standard form of the development of analysis within the Constructibility Theory. Then develops an axiomatized theory of lengths, in terms of which a system of rational and real numbers is specified. These developments are used to provide the basis for a theory of functions of real and complex variables.

The notion of a continuously variable quantity can be regarded as a generalization of that of a particular quantity, and the properties of such quantities are then akin to, and derived from, the properties of constants. For example, the continuous, real-valued functions on a topological space behave like the field of real numbers in many ways, but instead form a ring. Topos theory permits one to apply this same idea to logic, and to consider continuously variable sets (...) . In this expository paper, such applications are explained to the non-specialist. Some recent results are mentioned, including a new completeness theorem for higher-order logic. (shrink)

With a certain graphic interpretation in mind, we say that a function whose value at every point in its domain is a nonempty set of real numbers is an Abacus. It is shown that to every collection C of abaci there corresponds a logic, called an abacus logic, i.e., a certain set of propositions partially ordered by generalized implication. It is also shown that to every collection C of abaci there corresponds a theory JC in a classical propositional calculus (...) such that the abacus logic determined by C is isomorphic to the poset of JC. Two examples are given. In both examples abacus logic is a lattice in which there happens to be an operation of orthocomplementation. In the first example abacus logic turns out to be the Lindenbaum algebra of JC. In the second example abacus logic is a lattice isomorphic to the ortholattice of subspaces of a Hilbert space. Thus quantum logic can be regarded as an abacus logic. Without suggesting "hidden variables" it is finally shown that the Lindenbaum algebra of the theory in the second example is a subalgebra of the abacus logic B of the kind studied in example 1. It turns out that the "classical observables" associated with B and the "quantum observables" associated with quantum logic are not unrelated. The value of a classical observable contains, in coded form, information about the "uncertainty" of a quantum observable. This information is retrieved by decoding the value of the corresponding classical observable. (shrink)

BackgroundTranscranial direct current stimulation targeting the primary motor hand area may induce lasting shifts in corticospinal excitability, but after-effects show substantial inter-individual variability. Functional magnetic resonance imaging can probe after-effects of TDCS on regional neural activity on a whole-brain level.ObjectiveUsing a double-blinded cross-over design, we investigated whether the individual change in corticospinal excitability after TDCS of M1-HAND is associated with changes in task-related regional activity in cortical motor areas.MethodsSeventeen healthy volunteers received 20 min of real or sham TDCS on (...) separate days in randomized order. Real and sham TDCS used the classic bipolar set-up with the anode placed over right M1-HAND. Before and after each TDCS session, we recorded motor evoked potentials from the relaxed left first dorsal interosseus muscle after single-pulse transcranial magnetic stimulation of left M1-HAND and performed whole-brain fMRI at 3 Tesla while participants completed a visuomotor tracking task with their left hand. We also assessed the difference in MEP latency when applying anterior-posterior and latero-medial TMS pulses to the precentral hand knob.ResultsReal TDCS had no consistent aftereffects on mean MEP amplitude, task-related activity or motor performance. Individual changes in MEP amplitude, measured directly after real TDCS showed a positive linear relationship with individual changes in task-related activity in the supplementary motor area and AP-LM MEP latency.ConclusionFunctional aftereffects of classical bipolar anodal TDCS of M1-HAND on the motor system vary substantially across individuals. Physiological features upstream from the primary motor cortex may determine how anodal TDCS changes corticospinal excitability. (shrink)

The present article attempts to investigate the 'philosophical foundations' of psychology and thereby of the social sciences in general with regard to a central problem, viz. the question of the 'inner'. It does this with special critical reference to an authoritative psychological theory, viz. the so-called 'mediation theory', and tries to show the necessity of interdisciplinary clarification. In the first part mediation theory was introduced as a variant of psychological behaviorism which attempts to substitute for the untenable total neglect of (...) 'inner' events a way of talking about them which is secured methodologically and retains a behavioral foundation. Of the three crucial questions raised by the project the second, viz. question, which concerns the theoretical status of the assumed inner mediators could be answered to the effect that they must be "hypothetical constructs" having the nature of real, phenomenally verifiable events, if, indeed, they are to figure as links in S-R-chains. Conceiving of them as "intervening variables", such a conception would exclude this function. The discussion of 'internalization' of behavior sequences as assumed by mediation theory has led to the conclusion that the relevant phenomena cannot, in this case, justify the necessity of a non-dispositional explanation which goes beyond 'external' performances ). Likewise the subject matter of question remained undecided; that is, the possibilities of phenomenally verifying the assumed 'inner' mediation processes which are only asserted to exist by the theory but are unspecified in content. Therefore, the observable performances in the case of sequential behaviour do not support the mediation theoretic solution of the problem of the 'inner'. (shrink)

Given a class ℱ oft otal functions in the set oft he natural numbers, one could study the real numbers that have arbitrarily close rational approximations explicitly expressible by means of functions from ℱ. We do this for classes ℱsatisfying certain closedness conditions. The conditions in question are satisfied for example by the class of all recursive functions, by the class of the primitive recursive ones, by any of the Grzegorczyk classes ℰnwith n ≥ 2, by (...) the class of all functions recursive in a given function and by the class of the functions primitive recursive in it, as well as by the class of all total functions in the set of the natural numbers. (shrink)

We owe most scientific knowledge to methods of inquiry that are never formally analyzed. The analysis of behavior does not call for hypothetico-deductive methods. Statistics, taught in lieu of scientific method, is incompatible with major features of much laboratory research. Squeezing significance out of ambiguous data discourages the more promising step of scrapping the experiment and starting again. As a consequence, psychologists have taken flight from the laboratory. They have fled to Real People and the human interest of “ (...) class='Hi'>real life,” to Mathematical Models and the elegance of symbolic treatments, to the Inner Man and the explanatory preoccupation with inferred internal mechanisms, and to Laymanship and its appeal to “common sense.” An experimental analysis provides an alternative to these divertissements.The “theories” to which objection is raised here are not the basic assumptions essential to any scientific activity or statements that are not yet facts, but rather explanations which appeal to events taking place somewhere else, at some other level of observation, described in different terms, and measured, if at all, in different dimensions. Three types of learning theories satisfy this definition: physiological theories attempting to reduce behavior to events in the nervous system; mentalistic theories appealing to inferred inner events; and theories of the Conceptual Nervous System offered as explanatory models of behavior. It would be foolhardy to deny the achievements of such theories in the history of science. The question of whether they are necessary, however, has other implications.Experimental material in three areas illustrates the function of theory more concretely. Alternatives to behavior ratios, excitatory potentials, and so on demonstrate the utility of rate or probability of response as the basic datum in learning. Functional relations between behavior and environmental variables provide an account of why learning occurs. Activities such as preferring, choosing, discriminating, and matching can be dealt with solely in terms of behavior, without referring to processes in another dimensional system. The experiments are not offered as demonstrating that theories are not necessary but to suggest an alternative. Theory is possible in another sense. Beyond the collection of uniform relationships lies the need for a formal representation of the data reduced to a minimal number of terms. A theoretical construction may yield greater generality than any assemblage of facts; such a construction will not refer to another dimensional system. (shrink)

One’s first impression is that Brouwer’s Continuity Theorem of intuitionistic analysis, that every total, real-valued function of a real variable is continuous, stands in straightforward contradiction to a simple theorem of conventional real analysis, that there are discontinuous, real-valued func­tions. Here we argue that, despite philosophical views to the contrary, first impressions are not misleading; the Brouwer Theorem, together with its proof, presents mathematicians and philosophers of mathematics with an antimony, one that can only be resolved (...) by a close, foundational study of the structure of the intuitive continuum. (shrink)