Many pagan, Jewish, Christian and Muslim philosophers from Antiquity to the Enlightenment made no meaningful distinction between philosophy and religion. Instead they advocated a philosophical religion, arguing that God is Reason and that the historical forms of a religious tradition serve as philosophy's handmaid to promote the life of reason among non-philosophers. Carlos Fraenkel provides the first account of this concept and traces its history back to Plato. He shows how Jews and Christians appropriated it in Antiquity, follows (...) it through the Middle Ages in both Islamic and Jewish forms and argues that it underlies Spinoza's interpretation of Christianity. The main challenge to a philosophical religion comes from the modern view that all human beings are equally able to order their lives rationally and hence need no guidance from religion. Fraenkel's wide-ranging book will appeal to anyone interested in how philosophy has interacted with Jewish, Christian, and Muslim religious traditions. (shrink)

According to both contemporary intuitions and scholarly opinion, autonomy is something specifically modern. It is certainly taken to be incompatible with religions like Islam and Judaism, if these are invested with political power. Both religions are seen as centered on a divine Law (sharî'a, viz., torah) which prescribes what we may and may not do, promising reward for obedience and threatening punishment for disobedience. Not we, but God makes the rules. This picture is in important ways misleading. There is, I (...) argue, a substantive intellectual tradition, going back to Plato's Laws, which takes the purpose of a theocracy—a community governed by God through the intermediary of a divine Law—to be promoting rational autonomy, conceived as (1) the ability to rationally determine what is in one's best interest and (2) having the motivation to live accordingly.Among the most important representatives of this intellectual tradition are medieval Muslim and Jewish philosophers. (shrink)

À plusieurs égards, il est vrai d’avancer que Maïmonide et Averroès poursuivent le même projet philosophique et religieux. D’autant plus que tous deux ont été décrits comme des disciples d’al-Fârâbî, le fondateur de l’école de l’aristotélisme arabe . Cependant, à première vue, leur oeuvre ne pouvait pas être moins ressemblante: Averroès n’a écrit presque exclusivement que des commentaires sur Aristote, cependant que Maïmonide n’est l’auteur d’aucune oeuvre qui appartienne à un genre philosophique dans le sens strict. Il est, d’un autre (...) côté, un commentateur distingué lui aussi - sauf qu’il n’explique pas Aristote, mais commente et met de l’ordre dans la Loi de Moïse. La question principale dont je traite dans cet article, est celle de savoir si ce rapport tellement différent à la philosophie et à l’exégèse chez Averroès et Maïmonide peut être compris comme deux façons d’implémenter le cadre conceptuel établi par al-Fârâbî. Je commence par examiner le projet d’al-Fârâbî, que j’essaie d’expliquer par deux objectifs: reprendre et continuer le projet de la philosophie antique et définir sa place dans une société, dans laquelle l’autorité de la Loi divine n’est pas mise en question. Ensuite, je montre que, tandis que l’oeuvre d’Averroès peut être comprise, dans l’ensemble, comme une continuation du projet d’al-Fârâbî, cela n’est pas vrai de la même façon pour l’oeuvre de Maïmonide qui en partie transforme al-Fârâbî de manière créative et en partie utilise des prémisses dont on ne trouvera pas la source en al-Fârâbî. La position de Maïmonide en ce qui concerne la philosophie et l’exégèse se distingue significativement de la position habituelle adoptée par les falâsifa, ce qui a eu des conséquences importantes pour la philosophie juive médiévale après Maïmonide. (shrink)

In this paper I explain how Spinoza's ontological monism is related to the monotheism of a distinct tradition in medieval Aristotelianism exemplified by Maimonides. My main contention is that Maimonides' God, conceived as intellectual activity has the same structure as Spinoza's Deus sive Natura. The main difference between them is that Maimonides' God is confined to cognitive activity, whereas Spinoza's God is extensive activity as well. I trace the impact of the medieval doctrine of God on Spinoza's thought from the (...) Cogitata Metaphysica to the Ethics, establishing conceptual parallels, literary links, and an explanation of the steps leading from the former to the latter. (shrink)

This volume draws a balanced picture of the Rationalists by bringing their intellectual contexts, sources and full range of interests into sharper focus, without neglecting their core commitment to the epistemological doctrine that earned ...

Maimon once described the philosophical project underlying his Essay on Transcendental Philosophy as an attempt “to unify Kantian philosophy with Spinozism”. But in the only reference to Spinoza in the Essay, he stresses that Spinoza was not the source of his argument. In this paper I will argue that, notwithstanding the disclaimer, Maimon's solution for the problems that in his view haunted Kant's theory of knowledge was indeed significantly influenced by Spinoza, as well as by the medieval Jewish Aristotelian Maimonides. (...) Since the key concept in the solution proposed by Maimon is the metaphysical doctrine of the “infinite intellect”, my focus will be on clarifying how this doctrine is related to Maimonides' doctrine of the divine intellect and to Spinoza's doctrine of Deus sive Natura. My main contention is that important aspects of Maimon's doctrine of the “infinite intellect” are based on a Spinozistic interpretation of Maimonides' doctrine of the divine intellect. (shrink)

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system the (...) axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group. (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.

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of (...) the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians. (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)

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 Dual State, first published in 1941, remains one of the most erudite books on the legal origins of democracy and dictatorship. It provided the first comprehensive analysis of the rise and nature of National Socialism, and was the only such analysis written from within Hitler's Germany. Fraenkel's concept of the dual state, being the normative state and the the prerogative state. It retains its vital relevance for the theory of democracy in the twenty-first century. The Dual State considerably (...) influenced scholars studying and working on questions of political justice in the period following World War II, particularly in the context of political and legal theory; in the domain of legal history; in the area of constitutional theory; in the context of comparative politics; and in what has become known as the field of comparative constitutional law. This republication of Fraenkel's classic work makes it once again widely available to scholars and students in the field. It includes both Fraenkel's 1974 introduction to the German second edition, never before published in English, and a new introduction by Dr Jens Meierhenrich, examining the world in which The Dual State was originally published, and the lasting legacy of this classic work. (shrink)

The lack of access to gender-affirming surgery represents a significant unmet health care need within the transgender community, frequently resulting in depression and self-destructive behavior. While some transgender people may have access to gender reassignment surgery, an overwhelming majority cannot afford facial feminization surgery. The former may be covered as a “medical necessity,” but FFS is considered “cosmetic” and excluded from insurance coverage. This demarcation between “necessity” and “cosmetic” in transgender health care based on specific body parts is in direct (...) opposition to the scientific community’s understanding of gender dysphoria and professional guidelines for transgender health. GRS affects one’s ability to function in an intimate relationship, while FFS has the same impact on social interactions an, therefore may have a far greater implication for one’s quality of life. FFS is a cost-effective intervention that needs to be covered by insurance policies. The benefits of such coverage far exceed the insignificant costs. (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)