Biological diversity would apparently seem the most intuitive and easily studied of all the ecological concepts. However, in practice biodiversity has suffered from great number of definitions that vary with the specific needs of the different researchers, thus making it extremely confusing as an ecological concept. In this paper, I shortly review the concept of biodiversity showing that there exists a substantial ambiguity among ecologists as far as biodiversity conceptualization and evaluation is concerned. I conclude that, due to this major (...) disagreement on its very nature, biodiversity may be defined simply as a set of multivariate summary statistics for quantifying different characteristics of community structure. (shrink)

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon''s entropy H or Simpson''s index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot (...) diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy''s generalized entropy of type . In this way, a parametric measure of -diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker''s -diversity for data on species relative abundances. (shrink)

Community diversity has been studied extensively in relation to its effects on ecosystem functioning. Testing the consequences of diversity on ecosystem processes will require measures to be available based on a rigorous conceptualization of their very meaning. In the last decades, literally dozens of measures of diversity have been proposed. However, rather than using unrelated metrics, we need to identify their separate components so that possible links between them and ecosystem functioning can be examined using an agreed-upon language. In this (...) paper, first, a short overview on new and old measures of community diversity is presented. Next, I propose a general framework in which most of the existing measures of diversity are sorted into four interrelated semantic classes: richness, abundance-weighted diversity, evenness and divergence. In this view, this paper constitutes an attempt to organize the very large number of existing diversity measures avoiding ambiguities in the meaning of the different facets of community diversity. (shrink)

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total information content as (...) special cases of this more general function. (shrink)

This reply paper includes two brief remarks in rejoinder to the commentary papers of Myers and Patil, Podani, and Sarkar. The first observation concerns the fundamental nature of ecological diversity measures, while the second one specifically addresses some interesting mathematical connections between α- and β-diversity.

The degree to which abundances are divided equitably among community species or evenness is a basic property of any biological community. Several evenness indices have been proposed to summarize community structure. However, despite their potential applicability in ecological research, none seems to be generally preferred. In this paper we show that, unlike other evenness indices without any clear information-theoretical meaning, Hill's parametric diversity measure E ,0 has an immediate relation to Rényi's generalized information. Therefore, E ,0 might be adequate for (...) summarizing community structure within the context of a general theoretical framework of diversity analysis based on information theory. (shrink)

Minding Time: A Philosophical and Theoretical Approach to the Psychology of Time offers an innovative philosophical account of the most fundamental kinds of time representation.

Traditional diversity indices are computed from the abundances of species present and are insensitive to taxonomic differences between species. However, a community in which most species belong to the same genus is intuitively less diverse than another community with a similar number of species distributed more evenly between genera. In this paper, we propose an information-theoretical measure of taxonomic diversity that reflects both the abundances and taxonomic distinctness of the species. Unlike previous measures of taxonomic diversity, such as Rao's quadratic (...) entropy, in this new measure the analyzed taxonomic properties are associated with the single species instead of species pairs. (shrink)

The degree to which abundances are evenly divided among the species of a given community is a basic property of any biological community. Several evenness indices have thus far been proposed in ecological literature. However, despite their vast potential applicability in ecological research, none seems to be generally preferred. In this paper, I first summarize the basic requirements that evenness measures should meet to adequately behave in ecological studies. Then, I discuss the major drawbacks of these requirements and propose an (...) alternative family of measures that are based on the notion of specificity used in fuzzy set theory for measuring the uncertainty associated with a fuzzy set. (shrink)

This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last (...) century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality. (shrink)

Many of the computing systems programmed using Machine Learning are opaque: it is difficult to know why they do what they do or how they work. Explainable Artificial Intelligence aims to develop analytic techniques that render opaque computing systems transparent, but lacks a normative framework with which to evaluate these techniques’ explanatory successes. The aim of the present discussion is to develop such a framework, paying particular attention to different stakeholders’ distinct explanatory requirements. Building on an analysis of “opacity” from (...) philosophy of science, this framework is modeled after accounts of explanation in cognitive science. The framework distinguishes between the explanation-seeking questions that are likely to be asked by different stakeholders, and specifies the general ways in which these questions should be answered so as to allow these stakeholders to perform their roles in the Machine Learning ecosystem. By applying the normative framework to recently developed techniques such as input heatmapping, feature-detector visualization, and diagnostic classification, it is possible to determine whether and to what extent techniques from Explainable Artificial Intelligence can be used to render opaque computing systems transparent and, thus, whether they can be used to solve the Black Box Problem. (shrink)

In his new book, Carlos Alberto Torres, an internationally renowned critical theorist of education, explores the early writings of Paulo Freire whose ideas have had a tremendous and long-lasting impact on the world of pedagogy and politics. Torres analyzes Freire's works, from the 1960s and 1970s, before Freire gained worldwide recognition for his Pedagogy of the Oppressed. Offering an in-depth look into the formative thinking of Freire, Torres identifies how his ideas produced frameworks for educating global citizens, building community and (...) mutual respect, creating social responsibility, instilling an appreciation for diversity, promoting multiple literacies, and social justice education. This volume is the result of more than 3 decades of research with access to Freire's personal library and the archives of the Paulo Freire Institute, as well as the author's extensive conversations with Paulo Freire over two decades--Dr. Torres was Freire's adviser during his tenure as Secretary of Education in the Municipality of São Paulo, Brazil, 1989-1991. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

v. 1. Ensino secundário e médio -- v. 2. Estudos sobre o ensino primário -- Planejamento educacional e contribuições à educação do futuro.

The received view of dynamical explanation is that dynamical cognitive science seeks to provide covering law explanations of cognitive phenomena. By analyzing three prominent examples of dynamicist research, I show that the received view is misleading: some dynamical explanations are mechanistic explanations, and in this way resemble computational and connectionist explanations. Interestingly, these dynamical explanations invoke the mathematical framework of dynamical systems theory to describe mechanisms far more complex and distributed than the ones typically considered by philosophers. Therefore, contemporary dynamicist (...) research reveals the need for a more sophisticated account of mechanistic explanation. (shrink)

Models developed using machine learning are increasingly prevalent in scientific research. At the same time, these models are notoriously opaque. Explainable AI aims to mitigate the impact of opacity by rendering opaque models transparent. More than being just the solution to a problem, however, Explainable AI can also play an invaluable role in scientific exploration. This paper describes how post-hoc analytic techniques from Explainable AI can be used to refine target phenomena in medical science, to identify starting points for future (...) investigations of causal relationships, and to generate possible explanations of target phenomena in cognitive science. In this way, this paper describes how Explainable AI—over and above machine learning itself—contributes to the efficiency and scope of data-driven scientific research. (shrink)

The definitive account of Aristotle's life and school This definitive biography shows that Aristotle's philosophy is best understood on the basis of a firm knowledge of his life and of the school he founded. First published in Italian, and now translated, updated, and expanded for English readers, this concise chronological narrative is the most authoritative account of Aristotle's life and his Lyceum available in any language. Gathering, distilling, and analyzing all the evidence and previous scholarship, Carlo Natali, one of (...) the world's leading Aristotle scholars, provides a masterful synthesis that is accessible to students yet filled with evidence and original interpretations that specialists will find informative and provocative. Cutting through the controversy and confusion that have surrounded Aristotle's biography, Natali tells the story of Aristotle's eventful life and sheds new light on his role in the foundation of the Lyceum. Natali offers the most detailed and persuasive argument yet for the view that the school, an important institution of higher learning and scientific research, was designed to foster a new intellectual way of life among Aristotle's followers, helping them fulfill an aristocratic ideal of the best way to use the leisure they enjoyed. Drawing a wealth of connections between Aristotle's life and thinking, Natali demonstrates how the two are mutually illuminating. For this edition, ancient texts have been freshly translated on the basis of the most recent critical editions; indexes have been added, including a comprehensive index of sources and an index to previous scholarship; and scholarship that has appeared since the book's original publication has been incorporated. (shrink)

Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is much less to (...) be found about mathematics in his published works. Besides Brentano’s own work, it is quite remarkable to see that practically all of his better-known students sooner or later produced a work on the philosophy of mathematics. This also encourages the supposition not just of a common interest in the matter, but of a common theoretical core. All this prompts the question: Can we speak of a Brentanist philosophy of mathematics? (shrink)

In a context of pervasive digitalization of the social world, both before and during the COVID-19 pandemic, the field of education has undergone major changes with the development of digital practices and settings. However, the physical presence of the subjects and the body remain something primordial and irreplaceable in traditional educational processes. Thus, it is often assumed that virtuality is opposed to the corporeal reality of the subjects involved in teaching, learning and studying. In this paper we aim to critically (...) challenge this assumption by addressing the phenomenon of virtuality in a more original sense: as a fundamental dimension of corporeality itself. Drawing on Merleau-Ponty’s phenomenological insights, we argue that the experience of the virtual is inherently embodied and fully real. We understand corporeality and virtuality as entangled and multidimensional phenomena. At the same time, this leads us to rethink the digital as only one possible medium in which virtuality can appear as inherent to embodied experience. We develop our phenomenological approach in three instances. First, we question and bracket two common assumptions about corporeality. From our critical perspective, assumptions about a disembodied digitality and a devirtualized corporeality represent extremes within which educational discourses currently move. Second, we address the inherent virtuality of embodied experience. We outline the heuristic concept of the virtual body to describe corporeality and virtuality as entangled and multidimensional phenomena that encompass extension, intercorporeality and intermediality. Finally, we make some remarks on the relationships of corporeality and virtuality considering the challenges of digital education. (shrink)

In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...) role diagrams play as means of discovery and understanding. Alternatively, this paper purports to show that the view that the method of mathematics is the analytic method is capable of dealing with diagrams qua diagrams, and of accounting for such role. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some (...) general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach. (shrink)

The philosophical conception of mechanistic explanation is grounded on a limited number of canonical examples. These examples provide an overly narrow view of contemporary scientific practice, because they do not reflect the extent to which the heuristic strategies and descriptive practices that contribute to mechanistic explanation have evolved beyond the well-known methods of decomposition, localization, and pictorial representation. Recent examples from evolutionary robotics and network approaches to biology and neuroscience demonstrate the increasingly important role played by computer simulations and mathematical (...) representations in the epistemic practices of mechanism discovery and mechanism description. These examples also indicate that the scope of mechanistic explanation must be re-examined: With new and increasingly powerful methods of discovery and description comes the possibility of describing mechanisms far more complex than traditionally assumed. (shrink)

The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic notations, (...) notations may play a crucial role in mathematical discovery in different ways. Some examples are given to illustrate these ways. (shrink)

This paper provides a commentary on Truth and Method III.1.

This article argues for a new interpretation of the realist claim that politics is autonomous from morality and involves specific political values. First, this article defends an original normative source: functional normativity. Second, it advocates a substantive functional standard: political institutions ought to be assessed by their capacity to select and implement collective decisions. Drawing from the ‘etiological account’ in philosophy of biology, I will argue that functions yield normative standards, which are independent from morality. For example, a ‘good heart’ (...) is one that pumps blood well, and a good army is one that it is effective at exerting military force. I then interpret realism’s naturalistic conception of politics as an etiological function of social groups: namely making binding collective decisions under persistent disagreement. I conclude that political institutions should be evaluated realistically by how well they perform this task. Finally, I assess trade-offs between this functional political normativity and other moral values. I conclude that justice, fairness, freedom and equality remain obviously important concerns, but only once the basic political function is secured. (shrink)

This chapter subsumes David Marr’s levels of analysis account of explanation in cognitive science under the framework of mechanistic explanation: Answering the questions that define each one of Marr’s three levels is tantamount to describing the component parts and operations of mechanisms, as well as their organization, behavior, and environmental context. By explicating these questions and showing how they are answered in several different cognitive science research programs, this chapter resolves some of the ambiguities that remain in Marr’s account, and (...) shows that many different areas and traditions of cognitive scientific research can be unified under the mechanistic framework. (shrink)