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)

The renowned Israeli novelist and critic Abraham B. Yehoshua considers these crucial questions and illuminates his reading of nine texts -- from the story of ...

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)

Do the rich descriptions and narrative shapings of literature provide a valuable resource for readers, writers, philosophers, and everyday people to imagine and confront the ultimate questions of life? Do the human activities of storytelling and complex moral decision-making have a deep connection? What are the moral responsibilities of the artist, critic, and reader? What can religious perspectives—from Catholic to Protestant to Mormon—contribute to literary criticism? Thirty well known contributors reflect on these questions, including iterary theorists Marshall Gregory, James Phelan, (...) and Wayne Booth; philosophers Martha Nussbaum, Richard Hart, and Nina Rosenstand; and authors John Updike, Charles Johnson, Flannery O'Connor, and Bernard Malamud. Divided into four sections, with introductory matter and questions for discussion, this accessible anthology represents the most crucial work today exploring the interdisciplinary connections between literature, religion and philosophy. (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)

This article represents an analysis of the Jewish philosophy of the Modern and Contemporary as the holistic phenomenon. In contrast to antiquity and the Middle Ages, when philosophy was a rather marginal part of Jewish thought, in Modern Times Jewish philosophy is formed as a distinct part of the World philosophy. Despite the fact that representatives of Jewish philosophy wrote in different languages and actively participated in the different national schools of philosophy, their work has internal continuity and integrity. The (...) article formulates the following five criteria for belonging to Jewish philosophy: belonging to philosophy itself; reliance on Jewish sources; the addressee of Jewish philosophy is an educated European; intellectual continuity ; working with a set of specific topics, such as monism, ethics and ontology, the significance of behavior and practical life, politics, the problem of man, intelligence, language and hermeneutics of the text, Athens and Jerusalem, dialogism. The article provides a list of the main authors who satisfy these criteria. The central ones can be considered Baruch Spinoza, Moshe Mendelssohn, Shlomo Maimon, German Cohen, Franz Rosenzweig, Josef Dov Soloveichik, Leo Strauss, Abraham Yehoshua Heshel, Eliezer Berkovich, Emil Fackenheim, Mordechai Kaplan, Emmanuel Levinas. The main conclusion of the article is that by the end of the 20th century Jewish philosophy, continuing both the traditions of classical European philosophy and Judaism, has become an important integral part of Western thought. (shrink)

Including the first English edition of the Treatise of the Three Impostors since 1904, this book examines the treatise in its literary, political, and philosophical context.

The problem of the difficulties created by disjunctive concepts is shown to be a spurious one. It is due in part to a confusion between concept formation and concept identification, in part to unfortunate terminological moves, in part to confusions between logical and methodological matters. Behind this pseudo-problem there are a number of real problems: how to work efficiently with partially interpreted concepts? are there differences in comprehension of various logical connectives? how does this comprehension change with age and linguistic (...) exposure? (shrink)

[R]eflection is a system of thought no less closed than insanity, with this difference that it understands itself and the madman too, whereas the madman does not understand it.– Merleau-Ponty, Phen...

An innovative literary analysis of Freud's "Wolf Man.".

It is a matter of tacit consensus that rationalist adeptness in urban planning traces its foundations to the philosophy of the Renaissance thinker and mathematician Ren Descartes. This study suggests, in turn, that the planned urban environment of the Renaissance may have also led Descartes, and his intellectual peers, to tenets that became the foundations of modern philosophy and science. The geometric street pattern of the late middle ages and the Renaissance, the planned townscapes, street views and the formal garden (...) design, appeared as parables for the perfection of the universe and the supremacy of critical reason. It is within this urban metaphor that Descartes's philosophical narrative betrays perceptual and conceptual impact from the contrast between convoluted medieval townscapes and the emerging harmonious street patterns where defined vistas and predictable clarity of street views were paramount. The geometrically delineated street views of the Renaissance new town became the spark that lit the philosopher's sagacity in reflecting upon the concept of "clear and distinct ideas." Past suggestions that Descartes was led to his philosophical breakthroughs through his discovery of co-ordinate geometry reinforce further the stance that Renaissance planning predisposed rationalist thought. (shrink)

This paper seeks to explore the significance of a specific kind of religious experience for the rationality of religious belief. The context for this is a gap between what is often allowed as rational and what is embraced as certain in the life of faith. The claim to certainty at issue is related to the work and experience of the Holy Spirit; this experience has a structure which is explored phenomenologically. Thereafter various ways of cashing in the epistemic value of (...) the purported claim to certainty are examined. (shrink)

The theories of complexity comprise a system of great breadth. But what is included under this umbrella? Here we attempt a portrait of complexity theory, seen through the lens of complexity theory itself. That is, we portray the subject as an evolving complex dynamical system, or social network, with bifurcations, emergent properties, and so on. This is a capsule history covering the twentieth century. Extensive background data may be seen at www.visual-chaos.org/complexity.

It is a matter of tacit consensus that rationalist adeptness in urban planning traces its foundations to the philosophy of the Renaissance thinker and mathematician René Descartes. This study suggests, in turn, that the planned urban environment of the Renaissance may have also led Descartes, and his intellectual peers, to tenets that became the foundations of modern philosophy and science. The geometric street pattern of the late middle ages and the Renaissance, the planned townscapes, street views and the formal garden (...) design, appeared as parables for the perfection of the universe and the supremacy of critical reason. It is within this urban metaphor that Descartes's philosophical narrative betrays perceptual and conceptual impact from the contrast between convoluted medieval townscapes and the emerging harmonious street patterns where defined vistas and predictable clarity of street views were paramount. The geometrically delineated street views of the Renaissance new town became the spark that lit the philosopher's sagacity in reflecting upon the concept of "clear and distinct ideas." Past suggestions that Descartes was led to his philosophical breakthroughs through his discovery of co-ordinate geometry reinforce further the stance that Renaissance planning predisposed rationalist thought. (shrink)

In the early twentieth century Walter Benjamin introduced the idea of epochal and ongoing progression in interaction between mind and the built environment. Since early antiquity, the present study suggests, Benjamin’s notion has been manifest in metaphors of gender in city-form, whereby edifices and urban voids have represented masculinity and femininity, respectively. At the onset of interaction between mind and the built environment are prehistoric myths related to the human body and to the sky. During antiquity gender projection can be (...) detected in western perceptions linking natural and built environments, commencing with Plato’s Atlantis and his Myth of Er, and later as a likely import of the Chinese yin-yang mythology. Culminating with the Age of Discovery, alongside advances in experiential awareness of the Earth’s sphericity, respective feminine and masculine earmarks can be detected in early modern perspicacity of the Earth’s southern and northern hemispheres. Our conceptions of natural and built environments inherently continue to contain gender traits. Yet urban voids, as the feminine face of city-form, have been severely understated in the built environment. Through design and configuration of urban voids, allegories of femininity in city-form ought to be celebrated, not discarded. (shrink)

Reuse of elements from existing ontologies in the construction of new ontologies is a foundational principle in ontological design. It offers the benefits, among others, of consistency and interoperability between such knowledge structures as well as sharing resources. Reuse is widely found within important collections of established ontologies, such as BioPortal and the OBO Foundry. However, reuse comes with its own potential problems involving ontological commitment, granularity, and ambiguity. Guidelines are proposed to aid ontology developers and curators in their prospective (...) reuse of content. These guidelines have been gleaned over years of practice in the ontology field. The guidelines are couched in experiential reports on designing and curating particular ontologies (e.g., EXACT and EXACT2) and using generally accepted approaches (e.g., MIREOT) in doing so. Various software tools to assist in ontology reuse are surveyed and discussed. (shrink)

This present study aims at exploring the meaning of the building of Santa Maria de Fatima Catholic Church (abbreviated as: SMFCC) or Toasebio Parish located in District Glodok, Jakarta, Indonesia. The author exposes in advance the meaning of the physical elements of the building SMFCC as understood by history writers and building experts. These meanings are not inseparable from the elements of human activities in the building. Through qualitative methods and literature review, the author describes in the Results section, how (...) those meanings can be further interpreted through the existing studies and expressions of the SMFCC Parish Head. It is found that these meanings are contested − from the direction of religious faith and of culture − but complete our understandings of the church which is well-known as an Indonesian cultural heritage and dominated by Chinese and pastors from Europe. (shrink)

Mutual feedback between human-made environments and facets of thought throughout history has yielded two myths: the Garden and the Citadel. Both myths correspond to Jung’s feminine and masculine collective subconscious, as well as to Nietzsche’s premise of Apollonian and Dionysian impulses in art. Nietzsche’s premise suggests, furthermore, that the feminine myth of the Garden is time-bound whereas the masculine myth of the Citadel, or the Ideal City, constitutes a spatial deportment. Throughout history the two myths have continually molded the built (...) environment and thought, but the myth of the Ideal City – from Plato to Descartes to modernity – came to dominate city-form and ensuing aspects of contemplation. This relationship seems to have shifted during the twentieth century. Intellectual dispositions have begun to be largely nurtured by an incongruous city-form emerging from the gap between the incessant promise for an automated, well-functioning city, on the one hand, and looming alienation, coupled with the factual, malfunctioning city, on the other hand. Urban decay, a persisting and time-bound urban event that is a byproduct of this configuration, suggests the ascent of the Garden myth in post-modern city-form. (shrink)

Philosophers have in the past had difficulty in determining how to define ethical terms. here they are defined as open-context terms with a loosely limited range of substitution instances, in conformity with actual language usage. ethical terms are in themselves meaningless. it is a misuse to say, "x is wrong in itself." ethical terms then reduce to empirical terms concerning wants, likes, knowledge of cause and effect and consequences, knowledge of how ethical terms themselves work. ethical commands reduce to if-then (...) statements. blame may possibly never make sense. (shrink)