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)

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)

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)

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...