This is the first English translation of the 12th-century philosophical and ethical classic that has been a key work in the development of medieval Jewish thought.

The article examines the first Hebrew Encyclopedia of Science, Yesodei ha-Tvunah u-Migdal ha-Emunah, by Medieval Jewish scholar Abraham Bar Hiyya from Saragossa (Iberian peninsula).

We examine one of the well-known mathematical works of Abraham bar Ḥiyya: Ḥibbur ha-Meshiḥah ve-ha-Tishboret, written between 1116 and 1145, which is one of the first extant mathematical manuscripts in Hebrew. In the secondary literature about this work, two main theses have been presented: the first is that one Urtext exists; the second is that two recensions were written—a shorter, more practical one, and a longer, more scientific one. Critically comparing the eight known copies of the Ḥibbur, we show (...) that contrary to these two theses, one should adopt a fluid model of textual transmission for the various manuscripts of the Ḥibbur, because neither of these two theses can account fully for the changes among the various manuscripts. We hence offer to concentrate on the typology of the variations among the various manuscripts, dealing with macro-changes (such as omissions or additions of proofs, additional appendices or a reorganization of the text itself), and micro-changes (such as textual and pictorial variants). (shrink)

In this paper, we analyze the astronomical tables for 1340 by Immanuel ben Jacob Bonfils who flourished 1340–1365, based on four Hebrew manuscripts. We discuss the relation of these tables principally with those of al-Battānī, Abraham Bar Ḥiyya, and Levi ben Gerson, as well as with Bonfils’s better known tables, called Six Wings. An unusual feature of this set of tables is that there are two kinds of mean motion tables, one arranged for Julian years from 1340 to 1380, (...) months, days, hours, and minutes of an hour, and the other arranged in the Hebrew calendar for the times of conjunctions and oppositions of the Sun and the Moon only, with subtables for 19-year cycles, single years in a 19-year cycle, and months. The latter arrangement is found in Bonfils’s Six Wings for solar and lunar motions only, whereas in his Tables for 1340, this arrangement applies to all planets. Notably absent are tables for the trigonometric functions, etc., that are generally found in such sets of astronomical tables. (shrink)

The ArgumentThe major part of the mathematical “classics” in Hebrew were translated from Arabic between the second third of the thirteenth century and the first third of the fourteenth century, within the northern littoral of the western Mediterranean. This movement occurred after the original works by Abraham bar Hiyya and Abraham ibn Ezra became available to a wide readership. The translations were intended for a restricted audience — the scholarly readership involved in and dealing with the theoretical (...) sciences. In some cases the translators themselves were professional scientists (e.g., Jacob ben Makhir); in other cases they were, so to speak, professional translators, dealing as well with philosophy, medicine, and other works in Arabic.In aketshing this portrait of the beginning of Herbrew scholarly mathematics, my aim has been to contribute to a better understanding of mathematical activity as such among Jewish communities during this period. (shrink)

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)

... A. Zvie BAR-ON The Hebrew University of Jerusalem Shmuel Hugo Bergman, one of the most prominent Jewish philosophers of the 20th century, ...

Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...) by R. Carnap.--Basic verifiability in the combinatory theory of restricted generality, by H. B. Curry.--Uniqueness ordinals in constructive number classes, by H. Putnam.--On the construction of models, by A. Robinson.--Interpretation of mathematical theories in the first order predicate calculus, by T. Skolem.--The elementary character of two notions from general algebra, by R. Vaught.--Foundations of arithmetic and analysis. Axiomatic method and intuitionism, by A. Heyting.--On rank-decreasing functions, by G. Kurepa.--On non-standard models for number theory, by E. Mendelson.--Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic, by A. Mostowski.--Non-standard models and independence of the induction axiom, by M. O. Rabin.--Sur les ensembles raréfiés de nombres naturels, par W. Sierpinski.--Philosophy of logic and mathematics. Remarks on the paradoxes of logic and set theory, by E. W. Beth.--Logique formalisée et raisonnement juridique, par R. Feys.--Im Umkreis der sogenannten Raumprobleme, von H. Freudenthal.--Process and existence in mathematics, by H. Wang. (shrink)

The general topic of this book is the theory of categories, its sources, meaning and development. The inquiry can be seen to proceed on two levels. On one, the history of the theory is traced from its alleged genesis in Aristotle, through its main subsequent stages of Kant and Hegel, up to a kind of consummation in two of its prominent twentieth century adherents, Alfred North White head and Nicolai Hartmann. Special attention has been paid to that aspect of the (...) Hegelian conception of the categorial analysis from which the principle of coherence emerged. On the second, deeper level, however, everything starts with Whitehead's metaphysical system, the central part of which con sists of a fascinating, though highly intricate, web of categorial notions and propositions. The historical perspective becomes a means for untangling that web. I am indebted to a number of people for advice, comment and criticism of various parts of this book. My greatest thanks go to my teachers and colleagues Nathan Rotenstreich, Nathan Spiegel, Yaakov Fleischman, as well as to the late Shmuel Hugo Bergman and Pepita Haezrachi. of this book was published in 1967 by An earlier, Hebrew version the Bialik Institute of Jerusalem. I am grateful to Mr Yehoshua Perel, Mr Arnold Schwartz and to my wife Varda for their cooperation in rendering the extensively revised text of the book into readable English. I also owe great appreciation to Miss Liat Dawe for an accurate and painstaking word-processing of the text. (shrink)

Brouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s (...) story, the philosophical roots of Brouwer’s intuitionism cannot be traced to any previously established philosophical traditions. The paper concludes by showing how the intuitionistic inclinations of Hermann Weyl and Abraham Fraenkel serve as telling cases of how individuals are involved in setting in motion, adopting, and resisting framework transitions during periods of disagreement within a discipline. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 63.2 (2002) 303-321 [Access article in PDF] "The Peak on Which Abraham Stands": The Pregnant Moment of Søren Kierkegaard's Fear and Trembling Lasse Horne Kjaeldgaard When Søren Kierkegaard in the 1840s began his one-man crusade against the predominant philosophy of his time and place—the right Hegelianism that was en vogue among his contemporaries in Copenhagen—he chose his weapons with great circumspection. The (...) indirect form of communication, which he later advocated in more direct terms in his "Point of View," 1 was not only a maieutic means that helped the reader conceive of the latent and strictly private messages of the texts; it was also a strategy for Kierkegaard's undercover assaults on the Hegelian turn of the Geistesleben around him. By interweaving many of the Hegelian platitudes and self-confident pronouncements that circulated in the intellectual life of the day into the pseudonymous writings, Kierkegaard contested them with parody rather than argumentation. This is the local background against which these texts are structured and to which they are addressed in multiple and very subtle ways. That also goes for that of the pseudonymous writings which has become the best known but which may also be regarded as the most private and most secretive of them all, Fear and Trembling, published pseudonymously in 1843.Secrecy, silence, and unspeakable messages are abundantly thematized in Fear and Trembling, as one could expect from the name of the narrator, Johannes de Silentio. Silentio is a prominent member of the choir of pseudonymous figures Kierkegaard invented to communicate indirectly with his audience and in [End Page 303] the name of which he published his most celebrated works. The silence that Silentio speaks of is that of Abraham of the Old Testament, who was commanded by God to sacrifice his only son on Mount Moriah. Although Genesis 22 includes fragments of the dialogue between Abraham and Isaac on their way to the mountain, Silentio insists that Abraham remained silent on the essential issue: the command he acts upon. The unmediated message Abraham had received from God could not be conveyed, and he was therefore barred from communication and bereft of his community as he journeyed to the Mountain. Yet Silentio's discourse upon this silence in Fear and Trembling has given impetus to innumerable pages of commentary. The questions and answers he poses in his reflections upon Abraham's ordeal have called for critical attention and controversy since the time of its publication. His obsession with the biblical narrative certainly seems to have been passed on to many readers of Fear and Trembling, which, a recent commentator has remarked, "continues to haunt us like no other of [Kierkegaard's] writings." 2 So far, it would seem, then, that Kierkegaard was right when he predicted, in an undated journal entry, that "Fear and Trembling will be enough to immortalise my name." It has indeed been "read and translated into foreign languages," as he foresaw it would. 3Even so, what has passed unnoticed in its long history of reception is the significance of the titles that the manuscript text bore before it came to be called Fear and Trembling. On the title page the definitive appellation is placed together with two alternatives with less suggestion of pathos: "Movements and Postures" (Bevægelser og Stillinger) and "Between-each-other" (Mellemhver-andre). 4 Not much can be discerned from these unpeculiar phrases in isolation. However, tracing their history and significance through Kierkegaard's writings and beyond, will make it clear that Fear and Trembling was also dispatched to the narrow Hegelian community in Copenhagen for the purpose of questioning their literary and visual aesthetics and philosophy of history. Into the guerrilla warfare against them Fear and Trembling introduces a weapon of such sophistication that it has remained undetected so far: the power of the "pregnant moment." My aim here will be to demonstrate the way in which Fear and Trembling appropriates a principle of selection intended for the... (shrink)

The aim of the paper is to investigate the role of allegory in Philo and spe­cifically in his text On the Migration of Abraham. This involves the twofold move of arguing that even though Philo remains a Platonist and that his language is Platonic in orientation what occurs is a transformation of seeing, which is an immediate activity, into reading, which is always mediate. The second elements stems from this insistence on mediation. It results in freeing allegory from the (...) hold of the allegorical/literal op­position. Allegory is transformed as a result in the name of an ineliminable allegoresis. (shrink)

This article deals with the incompatibility of Christian and Jewish stereotypes in asceticism and tries to establish new models for approaching ascetic tendencies within the latter. In the context of halachic regulations we examine different ascetic aspects within Judaism, with a special focus on medieval Spain. In this area we observe a certain interaction between Jewish and Sufi trends, esp. in the works of Bachja ibn Paquda, Abraham bar Chijja and Abraham Maimonides. In the works of these authors (...) we find tripartite models of asceticism which signify the path to the deity. In a comparison with Sufi texts such as those of Al-Gazali, the three levels of repentance/law, meditation/path and the recognition of the divine truth are shown to be intertwined in a similar way, and all describe the way of the philosopher or mystic to the highest knowledge. In a further section this tripartite schema is compared to kabbalistic texts with their ideas of ascent and union with the divine within ecstatic kabbalah. In the first example we observe how an erotic impulse may lead to an ascetic way of life and how the horizontal move out of society leads to a vertical ascent of the soul and the foundation of a new, mobile society. In the second text we also detect the three intertwined stages of our model and see how ascetic preparations lead to an erotic union of the mystic’s soul with the divine intellect. Asceticism is described in both texts as a mode of transformation and the path between two extremes, which finally leads to intimate knowledge of the deity. (shrink)

Das Verhältniss des Thomas von Aquino zum Judenthum und zur jüdischen Litteratur.--Eine bisher unbekannte dem Bachja ibn Pakuda zugeeignete Schrift.--Die philosophischen und ethischen Anschauungen in Abraham bar Chijja's Hegjon ha-Nefesch.--Ueber Abraham bar Chijja's "Buch der Enthüllung".--Die Familie Schemtob in ihren Beziehungen zur Philosophie.--Die Stellung des Simon ben Zemach Duran in der Geschichte der jüdischen Religionsphilosophie.--Die philosophischen Lehren des Isaak ben Salomon Israeli.

The question of which areas of the earth are fit for human habitation and which ones are not is dealt with in several Hebrew scientific texts of the twelfth and thirteenth century. Medieval Jewish scholars such as Abraham bar [Hdotu]iyya, Samuel ibn Tibbon, and the three thirteenth-century Hebrew encyclopedists were familiar with theories of the oikoumene and its boundaries through Arabic sources. These Hebrew texts display a variety of views on the earth's habitability, all of which ultimately go back (...) to antiquity. Whereas some texts adopted a division of the inhabited portion of the earth into seven climes, others divided the earth into five zones of temperature, of which two were habitable and three were not owing to extreme temperatures. Some of these Jewish authors also pay attention to the question of how climatological or astrological conditions in a given region influence the mental constitution of its inhabitants. (shrink)

Jewish and Christian philosophy existed side by side in the Middle Ages. Both sought the same goal: the explanation of God and His universe. Both utilized the same sources; yet each attained different philosophical and theological systems. The Meditation of the Sad Soul illustrates this divergence between Christian and Jewish thought. Furthermore, since it stands midway between Neo-platonic and Aristotelian Judaism, it underlines the development of key philosophical concepts common to both Judaism and Christianity. Abraham Bar Hayya lived in (...) eleventh century Barcelona, an intellectual center for both Jews and Arabs. The major points of his philosophy blend rabbinical, Neo-platonic and Aristotelian ideas, yet maintain a unique independence of their own. For instance, Abraham cut through the rabbinical and Aristotelian proofs of God, demanding instead a primary positive faith in God's existence. Caught up in the theology of light, he rejected the Platonic idea that darkness was merely an absence of light. Rather, darkness had a force equal to light. Most important, darkness and light were opposites, as were good and evil. God created both. Abraham insists that each had an independent existence in the world. Abraham's thought shows a more "rational" strain which appears later in Christian and even Jewish "heresies." Since good and evil exist as positive forces, man can freely choose his path to salvation. Abraham never gets caught in the Augustinian dilemma of will, grace, and predestination. Further examples of Abraham's independent position crop up in his ideas of creation and time. Creation ex nihilo, of course, but creation in time. Time must have a beginning and, consequently, an end. But man does not have to await passively the Messiah's rectification of sin. Man must repent here on earth and actively lead a good life. He cannot repent after death. How influential was Abraham's tract? The editor calls it a "minor classic" yet does not indicate that it formed a basis for later Christian theology. Maimonides knew it and rejected some of its basic tenets. Still, the book is important since it indicates a striking combination of traditional philosophy subjected to a new critical rationalism, an it foreshadows some of the questions raised by deviant Christian and Jewish theologians.--J. K. B. (shrink)

In Abrahamic theism scripture is essential to belief-forming, yet scripture as an epistemic evidence source is plagued with difficulties. In the following article, I argue for a specific reductionist model of scriptural proposition justification utilising an account of scripture as testimony. I contend that for an individual to be justified in a belief sourced from a scriptural proposition, she must appeal to external evidence to “prop up her epistemic bar.” Accordingly, I consider some potential “epistemic bar-proppers.”.

We propose a modification of the exhaustivity operator from Fox Presupposition and implicature in compositional semantics, Palgrave Macmillan, London, pp 71–120, 2007. https://doi.org/10.1057/9780230210752_4) that on top of negating all the Innocently Excludable alternatives affirms all the ‘Innocently Includable’ ones. The main result of supplementing the notion of Innocent Exclusion with that of Innocent Inclusion is that it allows the exhaustivity operator to identify cells in the partition induced by the set of alternatives whenever possible. We argue for this property of (...) ‘cell identification’ based on the simplification of disjunctive antecedents and the effects on free choice that arise as the result of the introduction of universal quantifiers. We further argue for our proposal based on the interaction of only with free choice disjunction. (shrink)

a single life-span. Philosophers, then, do not see more or know more, and they do not see less or know less. They aim to see less detail and more of the abstract. Their details, if you like, are abstractions. Walking on God’s earth as a pedestrian, as a farmer working his fields or as a passer-by, one’s picture of one’s surroundings is every bit as intelligent as that of the pilot riding the sky. The views of the field are radically (...) different, however. One sees only a specific field and in all lively detail: the exact pattern of the land, or even the exact outline of a given leaf, grasshopper, grain of sand even. Acquaintance with minute detail is not without its price: details may stand in the way of conjuring the big picture. It may be difficult to compare whichever field one happens to be in with far off fields, with respect to their size or shape or any other quality. One may wish to inquire if far off fields were already planted, harvested, or even if they exist. A pedestrian may find it hard or even impossible to do so. The pedestrian view contains fine points that the pilot’s map never would, but it does not necessarily contain more information, for it lacks the general context. After all, there are only so many items that one can observe and account for at a single glance, a single map, a single book, a single life-span. (shrink)

My concern here is to motivate some theses in the philosophy of mind concerning the interpersonal character of intentions. I will do so by investigating aspects of shared agency. The main point will be that when acting together with others one must be able to act directly on the intention of another or others in a way that is relevantly similar to the manner in which an agent acts on his or her own intentions. What exactly this means will become (...) clearer once we understand what it is to act directly on one’s own intentions. But I take it to be a fundamental assumption of the prevailing individualism of the theory of action— one at the core of its conception of the separateness of individuals— that one person cannot act directly on another’s intention. I agree that there is an important way in which we are or can be separate and autonomous thinkers and agents. But the way the individualist tries to capture this separateness is misguided. (shrink)

I Introduction i Actions which otherwise would be arbitrary or capricious may be quite reasonable when they are in fact cases in which rights are being ...

I provide arguments in favor of an implicature approach to Homogeneity where the basic meaning of the kids laughed is some of the kids laughed, and its strengthened meaning is all of the kids laughed. The arguments come from asymmetries between positive and negatives sentences containing definite plurals with respect to children’s behavior, the availability of Non-maximal readings, and the robustness of neither-true-nor-false judgments :205–248, 2015). I propose to avoid some problems of Magri’s analysis by modeling the Implicature account of (...) Homogeneity after the Implicature account of Free Choice, based on a hitherto unnoticed analogy between the two phenomena. The approach that emerges has the advantages of Magri’s implicature account of Homogeneity, while at the same time bears a close resemblance to recent approaches to Non-maximality :1–58. https://doi.org/10.3765/sp.5.3, 2012; Križ and Spector in Interpreting plural predication: homogeneity and non-maximality, Ms., Institut Jean Nicod, 2017), which enables restating their account of Non-maximality as following from the context-sensitivity of implicature calculation. (shrink)

The relation between the notions of (medical) invasiveness and (actual or potential) harm has not been systematically discussed nor theoretically grounded, despite its importance to clinical-ethical practice. This paper aims to clarify the notion of invasiveness beyond the traditional notion of invasiveness as breaking skin or inserting mechanical objects into the body. The traditional notion of invasiveness is challenged by counterexamples. Three approaches to the notion of disorder applied here are: deviation from what is common; deviation from what is considered (...) ideal; and disruption of self-organization. Assuming that more extreme measures are related to more harm, all three approaches to the notion of disorder suggest that invasiveness is proportional if not identical to harm, and show no clear relation to the traditional notion of invasiveness. In conclusion, the notion of invasiveness may best be eliminated from medical terminology, replacing it with a detailed understanding of the notion of harm. (shrink)

Philosophical debates about the mental life of non-human animals provide an especially vivid illustration of how radically philosophers‘ intuitions concerning other minds can diverge. Do animals have mental states? Of what sort? Do any of the beasts have minds that overlap with ours? Is there any significant continuity between their minds and ours? Davidson is well known for arguing that, for conceptual reasons, at least when it comes to beliefs and other propositional attitudes, non-human animals differ from us in having (...) none. For example, he has argued that having beliefs requires having the concept of belief, which in turn requires language (Davidson (2001a), (2001b)). He has also argued that possession of any propositional attitude presupposes possession of belief, and that attributing any propositional attitude to a creature requires crediting them with the concepts that figure in the specification of the attitude‘s content (Davidson (2001a), (2001b) (2004)). Davidson‘s arguments are tantalizing, but also puzzling, and far from explicit; and they have been subjected to sharp scrutiny and powerful objections from a number of authors in recent years. (shrink)

This study examines the ends of medical intervention and argues that mainstream contemporary medicine assumes that appropriate ends may be discovered (i.e., naturalism), rather than created or decided upon (i.e., conventionalism). The essay then applies these considerations to the problem of the demarcation of the normal from the pathological. I argue that the common formulations of this dispute commit a fallacy, as they characterize the "normal" as a state of the organism and not as an ongoing process within it. Such (...) a process may be characterized as self-creation and self-repair. Such considerations support the conclusion that normality may be regarded as a regulative idea, rather than as an end-state, and as part of the ends of medical intervention, depending upon choice and context. (shrink)