Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics – the prevalent inductive logic of contemporary science. However, before working in statistics, K. Pearson had other interests in life, namely, in this order, philosophy, physics, and biological heredity. Key concepts of his philosophical and epistemological system of anti-Spinozism (a form of transcendental idealism) are carried over to his subsequent works on the (...) logic of scientific discovery. This article’s main goal is to analyze K. Pearson early philosophical and theological ideas and to investigate how the same ideas came to influence contemporary science, either directly or indirectly – by the use of variant theories, methods and dialects of statistics, corresponding to variant statistical inference procedures and their specific belief calculi. (shrink)

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to (...) the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectively. (shrink)

Corruption in public institutions is a significant problem that stifles economic, social and environmental development worldwide. This predominates when there is a lack of transparency, inadequate record-keeping, and low public accountability. Accordingly, the questions this paper intends to provide answers to are two-fold. Firstly, what are the recurring patterns of procurement corruption in the South Africa (SA) public sector? Secondly, how can digital technology deployment assist in checking this trend? Desktop method was adopted through literature examination of studies relating to (...) corruption, procurement, blockchain and digitization. We conclude by proposing a model/framework for adopting and using blockchain technology in public institutions to minimise corruption and the time taken for contract document preparation and acceptance. This study contributed to knowledge by evaluating the issues associated with public procurement and how blockchain and digitization can be adopted to help stern the tide of corruption in public institutions. (shrink)

Everyday media consumption leaves no doubt that the perception of moving images from various media is characterized by experience and understanding. Corresponding research in this field has shown that the stimulus patterns flooding in on us are not only processed mentally, but also bodily. Building on this, the following study argues that incoming stimuli are processed not only visually, but multimodally, with all senses, and moreover affectively. The classical binding of a sensory organ to a medium, on whose delimitation the (...) common understanding of multimodality is based, is thus abolished. Can arguments for this assumption be found? Building on the research of cultural anthropologist Ernst Cassirer and his successors, the two American philosophers Susanne K. Langer and John M. Krois, and supported by research from the life sciences in which, in parallel, the arts also play an important role in understanding image formation, as in the work of Heinz Werner and, following on from this, in the more recent research of the child psychologist Daniel N. Stern in collaboration with mirror neuron research by the group of neuroscientists around Giacomo Rizzolatti in Parma, justifications for this will be provided. What the multimodal processing of film images is concretely based on will finally be made clear by means of an exemplary analysis of a video film by the Swiss artist Pipilotti Rist. It aims to prove, that the prerequisites for the thesis can only lie in the fact, that both the modes of perception (visual, tactile, auditory, olfactory, gustatory) as well as the medially conditioned modes of image formation are based on non-discursive, formal-abstract structures that are also processed affectively. At the same time, the analysis thus shows how the selection and composition of the vital experienced forms can provide information about the socio-culturally shaped self-image of the producer and the viewer. (shrink)

The form of an action has a strong influence on the interaction between humans. According to their mood, people may perform the same gesture in different ways, such as gently or rudely. These aspects of social communication are named vitality forms by Daniel Stern, represent a mean to establish a direct and immediate connection with others. Indeed, the expression of different vitality forms enables us to communicate our affective states and at the same time the perception of these vitality (...) forms enables people around us to understand how we feel in that moment. In the last years of research, different fMRI studies have been carried out to investigate the neural correlates of vitality forms recognition and execution. Moreover, recent psychophysics studies conducted from our research group have demonstrated the presence of an affective contagion effect, during which vitality forms expressed by an agent affect the action perception and the motor response of the receiver. This means that vitality forms expressed by others can influence our mood positively or negatively, modulating as consequence our behavior. Note that vitality forms pervade our lives in a continuous manner and thus they are not expressed and perceived only during social interactions. For example, when we observe an artistic representation at the theatre, the dynamic postures of dancers, together with an alternation of acceleration and deceleration in their movements, communicate to us different affective states. Also when we are in a museum in front of a painting, lines, colors and shapes used by the artist can elicit in us different sensations and modify our attitude. In this view, with the aim to extend the concept of vitality forms from neuroscience and psychology to other disciplines of study, we dedicate part of this review to discuss how art, in all its forms, can be considered a pure expression of vitality forms. (shrink)

"Time. Perception. Imagination. Phenomenological Studies on the Question of Time by Augustine, Kant and Husserl". (rus), SPb, 2013. Summary: The monograph is devoted to the key elements of the philosophy of time which determine the necessity of historicism in the analysis of subjectivity. The main idea which defined the composition and design of this work is to trace how the Kantian definition of time as the “form of inner sense” is revealed in Husserl’s phenomenology. The original intention was to understand (...) all three components of this definition. Firstly, what is the inner form, in terms of phenomenology, what are the principles of its constitution and how one can talk about the property of formation? Secondly, what is the meaning of the term "inner" in philosophy, where the division into internal and external has always been a formality, not affecting the essence of things? And finally, what sort of “sensibility” is assumed in transcendental science, bound to become the basis of understanding the history and culture. Presumably, these three Kantian concepts constituted the original plan to analyze the nature of cognitive capabilities of the subject, claiming the gnoseological stage on which the philosophy of time is unfolded. In other words, this work deals with the historical and philosophical analysis of the phenomenological principles by which the concept of time as developed in the twentieth century emerged in the framework of phenomenology. The analyze of the structure of the subject assumes that time, perception and imagination combine in a special type of inner synthesis, which may not be relevant to certain aspects of the method but maintain the basis for a kind of anthropology of time, in continuation of the traditional “inner” contemplation. I consider the inner structure of time with the account of philosophy of St. Augustine, who in many respects not only anticipated the conclusions of phenomenology, but also in his reflections encompassed deeper layers of inner experience. The first chapter is devoted to the doctrine of St. Augustine, in which the theory of time is analyzed in conjunction with the doctrine of “inner word”, specifics of memory representations and notion of inner sense. Additionally, I consider St. Augustine’s reflections about numbers that constitute the basis of aesthetic perception of music (De Musica). Thus, the philosophy of St. Augustine already covers the whole spectrum of anthropology of time, including the question of relation between time and eternity, which remains practically unexplored in phenomenology and serves as the proof of that in interactions between philosophy and theology the tradition remains important. The second chapter of this study is devoted to analysis of the transcendental aesthetic of Kant, which includes all the methodological possibilities of considering the category of time as a formal condition for any experience, consequentially serving as a foundation for further logical development by Husserl, which includes the critical disengagement of the founder of phenomenology from Kant's transcendentalism. Particular attention is paid to the origin of the concept of inner sense, as well as possible interpretations of the function of imagination, which as a transcendental ability remains the most interesting type of synthesis. Handwritten fragments of Kant’s works are also of interest to the character of the imagery as considered in detail by Husserl. Chapter three discusses the phenomenology of inner time consciousness, represented in those important aspects, without which it is impossible to speak about the internal structure of temporal experience - the subjectivity of time, retention, "living present", and the character of synthesis. Particular attention is paid to Husserl's polemics with those representatives of psychological branch in the studies of consciousness, whose ideas greatly influenced the very motivation for creating the method. Apart from the well-known criticism of Brentano, the third chapter highlights the rarely analyzed psychological ideas that motivated the choice of Husserl’s terminology - the "Präsenzzeit” by W. Stern, the "psychological analysis" by A. Meinong, and the “fusion” (Verschmelzung) by K. Stumpf. Chapter four deals with the need to analyze the specifics of image as an element of consciousness and imagery as such, which includes a system of objectified acts. Thus is revealed the very nature of synthetic connections in the acts of consciousness, as well as the presumably imaginative character of the constitution of temporal form. (shrink)

Walter Reese-Schäfer, Karl-Otto Apel, Zur Einführung (with an Afterword by Jürgen Habermas), Junis Verlag GmbH, Hamburg 1990, 176pp. DM 17.80 -/- The author, presently a freelance writer published in the newspaper “Die Zeit” and the magazine “Stern,” pro­vides in this small book a clear and concise introduction to sources, themes and conclusions in the philosophy of Karl-Otto Apel. Apel, Emeritus Pro­fessor at Frank­furt, and close colleague of Habermas, characterizes his viewpoint as a “transcen­dental pragmatism” in which a Kantian concern (...) for question regarding “the conditions for the possi­bility of some­thing,” (p.10) mixes with deontological discourse-ethics, semeiotic themes from Peirce, an ap­proach to fallibilism, the demand for “final justifica­tions” (Letzt­begründung) and German her­meneutics. In view of the “den­sity and concentration” of Apel’s texts, which often have a “deterrent effect” upon those not already at home with “the phil­osophical language game,” it is the announced aim of this book to provide a work of translation and clarification of Apel’s special­ized efforts --in effect an orientation to Apel’s work. The book divides into an Introduction, 8 chapters and a summary conclusion --with Habermas’ appreciation, “A Master Builder with Hermeneutic Feeling --The Way of Philosopher Karl-Otto Apel,” bringing up the rear. There is also a bibliography of primary and secondary sources and a short table outlining highlights of Apel’s career. The “Introduction” provides a good overview of the aims of the book and gets one started on central themes. (shrink)

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s interventionist conception of causation. The viability of these responses has been challenged by Gebharter, who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs (...) for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s anti-reductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an anti-reductionist interventionist account of causation.1. (shrink)

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically (...) consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

ABSTRACT ABSTRACT: Nietzsche, we are often told, had an account of 'self' or 'mind' or a 'philosophical psychology', in which what he calls our 'drives' play a highly significant role. This underpins not merely his understanding of mind, in particular, of consciousness and action. but also his positive ethics, be they understood as authenticity, freedom, knowledge, autonomy, self-creation, or power. But Nietzsche did not have anything like a coherent account of 'the drives' according to which the self, the relationship between (...) thought and action, or consciousness could be explained; consequently, he did not have a stable account of drives on which his positive ethics could rest. By this, I do not mean that his account is incomplete or that it is philosophically indefensible: both would leave open, misleadingly, the possibility of a rational reconstruction of Nietzsche’s views; both would already assume more unity and coherence than we find in his texts. Specifically, as I show through detailed analysis, Nietzsche provides varied and inconsistent accounts of what a 'drive' is, how much we can know about drives, and the relationship between drives and conscious deliberations about action. I conclude by questioning the hunt for a Nietzschean theory: is this the best way to be reading him? (shrink)

The aim of this paper is to begin a conversation about how we read and write about Nietzsche and, related to this, other figures in the history of philosophy. The principle of charity can appear to be a way to bridge two dif-ferent interpretative goals: getting the meaning of the text right and offering the best philosophy. I argue that the principle of charity is multiply ambiguous along three different dimensions, which I call “unit,” “mode,” and “strength”: consequently, it is (...) not a single, neutral or independent principle to which we can helpfully appeal and it cannot, in itself, perform this bridging function. Nietzsche, I suggest, is particularly ill suited to some forms of charitable reading. I compare charity to what I call “misreporting” a philosopher’s words, in order to highlight some problematic structural similarities. Finally, I assess what charity might be doing instead, if it is not intended to bridge meaning and best philosophy. (shrink)

Inauguration speech at chair number 18 of the Brasilian Academy of Philosophy.

This article discusses some continuous limit cases of Susan Haack’s crossword puzzle metaphor for the coherent development and foundation of science. The main objective of this discussion is to build a bridge between Haack’s foundherentism and the epistemological framework of objective cognitive constructivism, including its key metaphor of objects as tokens for eigen-solutions. The historical development of chemical affinity tables is used to illustrate our arguments.

This Element explains Nietzsche's ethics in his late works, from 1886 onwards. The first three sections explain the basics of his ethical theory – its context and presuppositions, its scope and its central tension. The next three sections explore Nietzsche's goals in writing a history of Christian morality, the content of that history, and whether he achieves his goals. The last two sections take a broader look, respectively, at Nietzsche's wider philosophy in light of his ethics and at the prospects (...) for a Nietzschean ethics after Nietzsche. (shrink)

A critical comment on methods in Nietzsche scholarship, and some suggestions about how to improve things.

ABSTRACTAmor fati—the love of fate—is one of many Nietzschean terms which seem to point towards a positive ethics, but which appear infrequently and are seldom defined. On a traditional understanding, Nietzsche is asking us to love whatever it is that happens to have happened to us—including all sorts of horrible things. My paper analyses amor fati by looking closely at Nietzsche's most sustained discussion of the concept—in book four of The Gay Science—and at closely related passages in that book. I (...) argue that by ignoring the context in which Nietzsche writes about amor fati in The Gay Science, we are liable to ignore several exegetical and philosophical problems with the traditional understanding of the term. I'll argue for a different interpretation which locates Nietzsche's amor fati within the philosophical project of The Gay Science and which copes better with the objections that plague the traditional view. (shrink)

This chapter looks at Nietzsche's notion of the affirmation of life. It begins with the origins of the concept in Schopenhauer and in the Schopenhauerian philosophy known to Nietzsche. It then examines affirmation in three phases of Nietzsche's writing: early, middle and late. It relates affirmation to other key Nietzschean concepts like the Apollonian and the Dionysian, eternal recurrence, amor fati and will to power.

Decoupling is a general principle that allows us to separate simple components in a complex system. In statistics, decoupling is often expressed as independence, no association, or zero covariance relations. These relations are sharp statistical hypotheses, that can be tested using the FBST - Full Bayesian Significance Test. Decoupling relations can also be introduced by some techniques of Design of Statistical Experiments, DSEs, like randomization. This article discusses the concepts of decoupling, randomization and sparsely connected statistical models in the epistemological (...) framework of cognitive constructivism. (shrink)

An introduction to Nietzsche's life and works.

The central question in this paper is the following: how does Nietzsche use history in his critique of morality? The answer, in sum: interestingly, not how you (i.e. most Nietzsche scholars) think, and not well enough. My focus is on The Antichrist, not his Genealogy of Morality, which is more commonly used to answer this question. And I look, in particular, at Nietzsche’s use of good, contemporary scholarship on the origins of Judaism. The chapter also examines the so-called 'genetic fallacy', (...) arguing that Nietzsche has a provisional response to it, but that this response leads to further complications. (shrink)

Nietzsche writes a great deal about freedom throughout his work, but never more explicitly than in Twiling of the Idols, a book he described as 'my philosophy in a nutshell'. This paper offers an analysis of Nietzsche's conception freedom and the role it plays within Twilight.

Wittgenstein’s writings and lectures during the first half of the 1930s play a crucial role in any interpretation of the relationship between the Tractatus and the Philosophical Investigations . G. E. Moore’s notes of Wittgenstein’s Cambridge lectures, 1930-1933, offer us a remarkably careful and conscientious record of what Wittgenstein said at the time, and are much more detailed and reliable than previously published notes from those lectures. The co-authors are currently editing these notes of Wittgenstein’s lectures for a book to (...) be published by Cambridge University Press. We describe the materials that make up Moore’s notes, explain their unique value, review the principal editorial challenges that these materials present, and provide a brief outline of our editorial project. (shrink)

We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss–Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the “most general” module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. (...) The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems. (shrink)

The authors propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. The cycle basis corresponds to a fundamental null-space basis of the adjacency matrix. This problem is meant to model sparse null-space basis computations occurring in a variety of settings. An O(n3/2) bound is achieved on the nullspace basis size (i.e., the number of nonzero entries in the basis), and an O(n log n) bound on the size in the special case of grid graphs.

We study active set methods for optimization problems in Block Angular Form (BAF). We begin by reviewing some standard basis factorizations, including Saunders' orthogonal factorization and updates for the simplex method that do not impose any restriction on the pivot sequence and maintain the basis factorization structured in BAF throughout the algorithm. We then suggest orthogonal factorization and updating procedures that allow coarse grain parallelization, pivot updates local to the affected blocks, and independent block reinversion. A simple parallel environment appropriate (...) to the description and complexity analysis of test procedures is defined in Section 5. The factorization and updating procedures are presented in Sections 6 and 7. Our update procedure outperforms conventional Updating procedures even in a purely sequential environment. (shrink)

This article considers distinct ways of understanding the world, referred to in psychology as Functions of Consciousness or as Cognitive Modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung's Simile of the Spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an Hexagon of Opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that (...) are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

Comments presented at the 35th International Seminar on the -- New Institutional Economics -- Empirical Methods for the Law; Syracuse, 2018.

The main goal of this article is to use the epistemological framework of a specific version of Cognitive Constructivism to address Piaget’s central problem of knowledge construction, namely, the re-equilibration of cognitive structures. The distinctive objective character of this constructivist framework is supported by formal inference methods of Bayesian statistics, and is based on Heinz von Foerster’s fundamental metaphor of objects as tokens for eigen-solutions. This epistemological perspective is illustrated using some episodes in the history of chemistry concerning the definition (...) or identification of chemical elements. Some of von Foerster’s epistemological imperatives provide general guidelines of development and argumentation. (shrink)

Now that she is old enough to be taken to boring, so-called “cultural” events by her aging, academic relatives, we have just taken Anya to see a performance of Julius Caesar. When it’s over, we discuss the acting, the poetry, the famous lines. At some point, Anya asks: “I wonder if it happened like that?” Anya has not radically misunderstood what we just watched; she did not, for example, rush down and yell at Caesar that he’d better read that scroll. (...) Her question is not uncommon as a response to a history play, from audience members both young and old. It is perfectly intelligible; I would like to give her an answer. Before I sketch some possible answers, it is worth saying something more about Anya’s. (shrink)

It is a consequence of the theory of imprecise credences that there exist situations in which rational agents inevitably become less opinionated toward some propositions as they gather more evidence. The fact that an agent's imprecise credal state can dilate in this way is often treated as a strike against the imprecise approach to inductive inference. Here, we show that dilation is not a mere artifact of this approach by demonstrating that opinion loss is countenanced as rational by a substantially (...) broader class of normative theories than has been previously recognised. Specifically, we show that dilation-like phenomena arise even when one abandons the basic assumption that agents have (precise or imprecise) credences of any kind, and follows directly from bedrock norms for rational comparative confidence judgements of the form `I am at least as confident in p as I am in q'. We then use the comparative confidence framework to develop a novel understanding of what exactly gives rise to dilation-like phenomena. By considering opinion loss in this more general setting, we are able to provide a novel assessment of the prospects for an account of inductive inference that is not saddled with the inevitability of rational opinion loss. (shrink)

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic (...) versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais. (shrink)

This paper offers a reading of Thus Spoke Zarathustra, arguing that there is a conflict between Zarathustra's hope for something greater (in the form of the Übermensch) and his conception of the eternal recurrence.

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses (...) the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective. (shrink)

In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative insights, (...) and giving form to heuristic arguments. At the other hand, it is inherently difficult to control, lacking effective mechanisms needed for rigorous manipulation. Our discussion is illustrated with many examples from the Hebrew Bible, and some final examples from modern science. (shrink)

In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

This paper presents affirmation as the central normative category of Nietzsche’s positive ethics. The paper argues in particular for two interpretive claims: first, that from Beyond Good and Evil onwards, we find a new variety of Nietzschean affirmation (‘natural affirmation’), which is crucial to the strategy of his later works; and second, for reasons internal to his own philosophical aims, Nietzsche’s new variety of affirmation is seriously flawed. The author argues for the second claim on the basis that Nietzsche himself (...) requires that affirmation not perform exactly the role he requires that it perform. The author contends that we are thus faced with a major challenge to Nietzsche’s late philosophical project—that (late) Nietzschean affirmation fails by Nietzsche’s own standards. (shrink)

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. (...) However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

Heinz Von Forester characterizes the objects “known” by an autopoietic system as eigen-solutions, that is, as discrete, separable, stable and composable states of the interaction of the system with its environment. Previous articles have presented the FBST, Full Bayesian Significance Test, as a mathematical formalism specifically designed to access the support for sharp statistical hypotheses, and have shown that these hypotheses correspond, from a constructivist perspective, to systemic eigen-solutions in the practice of science. In this article several issues related to (...) the role played by language in the emergence of eigen-solutions are analyzed. The last sections also explore possible connections with the semiotic theory of Charles Sanders Peirce. (shrink)

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using (...) the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

Sortition, i.e. random appointment for public duty, has been employed by societies throughout the years as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case. Therefore, these random procedures play an important role in the course of a case, and should comply with (...) some principles, such as transparency and complete auditability. Nevertheless, these principles are neglected by random procedures in some judicial systems, which are performed in secrecy and are not auditable by the involved parties. The assignment of cases in the Brazilian Supreme Court is an example of such a procedure, for it is performed using procedures unknown to the parties involved in the judicial cases. This article presents a review of how sortition has been historically employed by societies and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. A statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court. As final remarks, guidelines for the development of good randomization procedures are outlined. (shrink)

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It is (...) shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (shrink)

Bayesians standardly claim that there is rational pressure for agents’ credences to cohere across time because they face bad (epistemic or practical) consequences if they fail to diachronically cohere. But as David Christensen has pointed out, groups of individual agents also face bad consequences if they fail to interpersonally cohere, and there is no general rational pressure for one agent's credences to cohere with another’s. So it seems that standard Bayesian arguments may prove too much. Here, we agree with Christensen (...) that there is no general rational pressure to diachronically cohere, but we argue that there are particular cases in which there is rational pressure to diachronically cohere, as well as particular cases in which interpersonal probabilistic coherence is rationally required. More generally, we suggest that Bayesian arguments for coherence apply whenever a collection (of agents or time slices) has a shared dimension of value and an ability to coordinate their actions in a range of cases relevant to that value. Typically, this shared value and ability to coordinate is very strong across the time slices of one human being, and very weak across different human beings, but there are special cases where these can switch—i.e., some groups of humans will have as much reason for their beliefs to cohere across a particular range of cases as the time slices of one human usually do, but some time slices of a human will have as much freedom to differ in their beliefs from the others as the members of a group usually do. (shrink)

The reader of RTP is granted just a few paragraphs before habit is introduced: Habit! That able but slow-moving arranger who begins by letting our minds sufer for weeks on end in temporary quarters, but whom our mind is nonetheless only too happy to fnd, for without it, reduced to its own devices, it would be powerless to make any room habitable. (SW, 9, translation altered; I 8) Implied is a view of mind: powerless to interfere with habit’s course, but (...) equally powerless to reconcile us even to something as innocuous as a room, were it not for habit’s work. Corresponding to this is a view of the world: hostile. The objects are nasty, imposing, menacing: a ‘mentally poisoning’ smell, malicious curtains and a cruel mirror (SW, 9; I 8). Habit, unbidden but welcome, steps in. The mirror becomes compassionate. Habit is a central aspect of the narrator’s worldview. It appears both at major plot points and in signifcant theoretical passages. Proust had already thematised habit in some of his earliest published work – notably in ‘Violante ou la Mondanité’ (1892) (‘Violante, or High Society’) – as well as in unpublished material (see II 1352 fn. 2). His ideas have their roots in his philosophical education, where habit formed a key part of the syllabus. Indeed, in retrospect, we can say that Proust may have been taught philosophy at a time and place where habit, as a philosophical topic, was approaching its high watermark, as a major theme in French philosophical thought. Another major theme, of course, was time. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

This article considers distinct ways of understanding the world, referred to in psychology as functions of consciousness or as cognitive modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung’s simile of the spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an hexagon of opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)