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)

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)

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 ...

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)

Why do we remember the past and not the future? What does it mean for time to "flow"? Do we exist in time or does time exist in us? In lyric, accessible prose, Carlo Rovelli invites us to consider questions about the nature of time that continue to puzzle physicists and philosophers alike. For most readers this is unfamiliar terrain. We all experience time, but the more scientists learn about it, the more mysterious it remains. We think of it as (...) uniform and universal, moving steadily from past to future, measured by clocks. Rovelli tears down these assumptions one by one, revealing a strange universe where at the most fundamental level time disappears. He explains how the theory of quantum gravity attempts to understand and give meaning to the resulting extreme landscape of this timeless world. Weaving together ideas from philosophy, science and literature, he suggests that our perception of the flow of time depends on our perspective, better understood starting from the structure of our brain and emotions than from the physical universe. (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)

I am a theoretical physicist, and, following Aristotles' injunction (Aristotle, Physics III, 202b 34), I do consider it my responsibility to discuss the problem of the notion of infinity in the world--in particular, to "inquire whether there is such a thing or not." I will do so here by illustrating some aspects of the notion of infinity in the natural sciences.

All human civilizations have thought that the world was made of sky above and the Earth below. All except one. For the Greeks, the Earth was a rock floating in space, and under the earth there was no ground, no turtles, nor the gigantic columns of which the Bible speaks. How did the Greeks understand that the Earth is suspended in nothingness? Who understood this and how? It is this unique "scientific revolution" of Anaximander of which the author speaks, which (...) Karl Popper called "one of the most daring ideas, revolutionary and portentous in the entire history of human thought" The concern is with the conflict that was opened, still burning, with the nature of scientific thought, its critical and rebellious character, the force with which it subverts the order of things and our image of the world of scientific knowledge, and the highly effective "error" at the same time --as we teach physics in the twentieth century. Speaking of Anaximander, the author invites us to reflect on what his ideas mean to the scientific revolution opened by Einstein. (shrink)

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

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)

Expressivists claim that normative judgments (NJ) are non-cognitive states. But what kind of states are they, exactly? Expressivists need to provide us with an adequate account of their nature. Here, I argue that there are structural features that render this task rather daunting. The worry takes the form of a looming dilemma: NJ are either conative states (i.e. states with a world-to-mind direction of fit) or they are not. If they are, then they are either attitudes de se (i.e. attitudes (...) about oneself) or they are not. If they are, then they’re unable to account for disagreement. If they are not, then they're unable to account for agent-relative NJ. So NJ cannot be conative states (they cannot have a world-to-mind direction of fit). On the other hand, however, if NJ are not conative states (if they are states without a direction of fit, like affective or other sui generis non-cognitive, non-conative attitudes) then it remains a mystery how they support relations of disagreement. (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)

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)