Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is (...) coherent (in an informal sense) and places the problem of reliability within the province of the philosophy of mathematics. (shrink)

In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents genuine (...) meaning-dependent mathematical characteristics that cannot be captured by formal calculi. ‘…there is a conflict between mathematical practice and the formalist doctrine.’ [Kreisel, 1969, p. 39]. (shrink)

In this historical essay, we examine the reciprocal influences of philosophical doctrines and logic, their interrelations with language, and the place of mathematics in these developments.

The author's aim in this biography is to shed light on the contrasts and polarity—yet relationship—between the rational and the irrational in Gödel's work and personality. On the one hand there is the genius logician whose technical work can be said practically to have attained the limits of what rational thought can produce; on the other hand, one is struck, claims the author, by the irrationality in Gödel's personality and psychic structure, such as his belief in the existence of spirits, (...) demons, angels, the devil, and other evil-wishing forces that he thought had haunted and deprived him of a peaceful existence.As is well known from other biographies, Gödel was of a frail physical health and psychic balance, having suffered from his student days on from bouts of depression and ‘nervous’ breakdowns—generally attributed to being overworked—that required at times short hospitalization in a sanatorium and culminating toward the end of his life in a marked deterioration in his mental health that resulted in his starving himself to death out of fear of being poisoned. These events are only mentioned here in passing.The author, who teaches philosophy at the University of Lille, is naturally interested in Gödel's philosophical views as well as in his metaphysical reflections, such as his thoughts about life after death and the survival of an immaterial soul. From the 1940s Gödel kept a philosophical diary that contains 670 handwritten notes, written in the now defunct Gabelsberger shorthand. Having feared controversies whenever his metaphysical/philosophical views went against the spirit of the times, Gödel was never led to a comprehensive publication of these views, preferring to put these notes in the private format of notebooks that are now preserved in his Nachlassat Princeton University. 1 The author had several opportunities to study the two of these notebooks …. (shrink)

Among the aims of the author in this wide-ranging article is to draw attention to the numerous formal sciences which so far have received little scrutiny, if at all, on the part of philosophers of mathematics and of science in general. By the formal sciences the author understands such mathematical disciplines as operations research, control theory, signal processing, cluster analysis, game theory, and so on. First, the author presents a long list of such formal sciences with a detailed discussion of (...) their subject matter and with extensive references to the pertinent literature. Turning to the nature of the formal sciences, the author states that “the formal sciences, though they arose in most cases out of engineering requirements, are sciences and can be pursued without reference to applications”. It is argued, through a wealth of examples, that in a great number of cases the formal sciences permit the attainment of provable certainty about actual parts of the world. As Franklin puts it, “knowledge in the formal sciences, with its proofs about network flows, proofs of computer program correctness, and the like, gives every appearance of having achieved the philosophers’ stone; a method of transmuting opinion about the base and contingent beings of this world into the necessary knowledge of pure reason.” Franklin clearly distinguishes between certainty and necessity: “ g¤g¤g what the mathematician in offering is not, in the first instance, absolute certainty in principle, but necessity. This is how his assertion differs from one made by a physicist. A proof offers a necessary connection between premises and conclusion. One may extract practical certainty from this g¤g¤g but this is a separate step.” Though Franklin explicitly states that there is a gap between necessity and certainty as one passes from mathematical reasoning to applications, the main thrust of the article consists in arguing that the gap is considerably smaller than generally claimed.. (shrink)

This paper examines the claim that the two final articles of Rav Kook’s book Ikvei Hatzon were written as a response to a lecture given by Hermann Cohen. It first reviews Cohen’s lecture showing that, regarding the concept of God, Cohen argues for the compatibility of Judaism and Kantianism in denying the dogmatic-mythological preoccupation with the existence of God in favor of understanding God as the basis of morality. Second, it analyzes Kook’s articles, demonstrating that he accepts the compatibility of (...) Judaism and Kantianism together with the denial of the dogmatic relation to God as a substance. Nevertheless, Kook is not satisfied with the critical view that denies the dogmatic relation to the substance altogether, since it formulates a merely negative relationship with God. Instead, he develops his concept of the Divine Ideals, which synthesizes the dogmatic preoccupation with substantiality and the critical denial of it. The Divine Ideals are the moral progression of man, through which man gradually becomes identical to God. Within the Divine Ideals, dogmatism becomes an emotional striving to be identical with God as a substance, while criticism is the intellectual negation of the possibility of such identity, which ensures that the process will continue indefinitely. (shrink)

Kabbalistic reading in harav Yehuda L(acute}e on Ashk(acute}enazi (manitou)'s historiosophic teachings.

The Kuzari: In Defense of the Despised Faith is the first new translation into English of The Kuzari since 1905, annotated and explained based on the classic commentaries. Written by Rabbi Yehuda HaLevi of Spain over a period of twenty years and completed in 1140, The Kuzari has enthralled generations of Jews and non-Jews alike with its clear-cut presentation on Judaism, and its polemics against Greek philosophy, Christianity, Islam, and Karaism.

Introduction -- The idea of the university -- The aims of the university, or Humboldt then and Humboldt now -- Principles for undergraduate curricula -- Rhetoric, arguments, episteme metis and phronesis -- Some thoughts for curricula in the natural, social and human sciences and the establishment of new disciplines -- Research, teaching, publications, admission, assessment -- Democracy, higher education and the philosophy of education -- Doctoral education -- The university at the dawn of the digital age: realizing technology's transformative potential.

Introduction -- Fraud in research : frequency patterns -- An organizational approach to research fraud -- Fraud, lies, deceptions, fabrications, and falsifications -- Deviance in scientific research : norms, hot spots, control -- Concluding discussion.

How faith in God maintains the link between the physical realm and the spiritual realm. Discusses free will, resurrection, God's immanence and transcendence, and similar topics.

Following participation in Dr. Yair Caspi’s “Psychology in Judaism” workshop, the writers contemplate whether the teaching of Caspi’s model in academic settings could become simultaneously a fresh addition to interdisciplinary approaches to the teaching of Judaism in Israeli Academic life, and an academic addition to the contemporary trend to Jewish renewal in Israeli society. The model is based on weekly facilitated workshops in which participants both reflect on and discuss their lives and also explore unique interpretations of Jewish texts and (...) ideas, constantly seeking the borderline where their lives inform the text and vice versa. The process leads to the re-enchantment of ancient Jewish concepts, the reinvention of the Jewish religious experience in a contemporary paradigm and idiom, and the possibility of deep transformative insight. (shrink)

Fichte claims in Section 5 of the Grundlage der gesamten Wissenschaftslehre (GWL) that the absolute I contains a difference between two directions. In this paper, I argue that this specific claim complements, rather than contradicts, his general position in Section 1, according to which the absolute I is a simple identity or a point. I first show that we can identify a version of what I call Fichte’s Two-Directions Theory in texts written both before and after the GWL. I term (...) this version his Two-Series Theory. Drawing on this reading, I demonstrate, in contrast to previous research, that Fichte consistently formulates the absolute I in a twofold manner: as a pure act that precedes any difference and as a proposition that contains a relation. I further argue that Fichte’s treatment of the absolute I as a simple unity and as a unity of two directions maps onto two stages within his philosophical investigation. On my account, Fichte seeks to comprehend the absolute I by considering the I’s activity both as it is in itself and as it presents itself to thought. (shrink)

Book of Jewish philosophy including such topics as reconciling science and religion, Divine providence, God's infinitude and omniscience, reincarnation, how faith has the power to alter nature, God's immutability, how to reconcile spirituality with the physical universe, and resurrection.

This study introduces the concept of deviant behavior in a moderated-mediation framework of incentives and organizational justice perception. The proposed relationships in the theoretical framework were tested with a sample of 311 academics, using simple random sampling, via causal models and structural equation modeling. The findings suggest that incentives might boost the apparent performance, but not necessarily the intended performance. The results confirm that employees’ affection for incentives has direct, indirect, and conditional indirect effects on their deviant behavior likelihood. The (...) relationship between employee deviant behavior likelihood and affection for incentives was moderated by organizational justice perception and partially mediated by reward expectancy, thus having significant contributions toward the extant literature of deviant behavior and incentives. The findings have important implications for managers, academicians, and policy makers for mitigating adverse behavior in professional employees through proper use of incentives. (shrink)

Fichte claims in Section 5 of the Grundlage der gesamten Wissenschaftslehre that the absolute I contains a difference between two directions. In this paper, I argue that this specific claim complements, rather than contradicts, his general position in Section 1, according to which the absolute I is a simple identity or a point. I first show that we can identify a version of what I call Fichte’s Two-Directions Theory in texts written both before and after the GWL. I term this (...) version his Two-Series Theory. Drawing on this reading, I demonstrate, in contrast to previous research, that Fichte consistently formulates the absolute I in a twofold manner: as a pure act that precedes any difference and as a proposition that contains a relation. I further argue that Fichte’s treatment of the absolute I as a simple unity and as a unity of two directions maps onto two stages within his philosophical investigation. On my account, Fichte seeks to comprehend the absolute I by considering the I’s activity both as it is in itself and as it presents itself to thought. (shrink)

We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.

Given a weakly o-minimal structure${\cal M}$and its o-minimal completion$\bar{{\cal M}}$, we first associate to$\bar{{\cal M}}$a canonical language and then prove thatTh$\left$determines$Th\left$. We then investigate the theory of the pair$\left$in the spirit of the theory of dense pairs of o-minimal structures, and prove, among other results, that it is near model complete, and every definable open subset of${\bar{M}^n}$is already definable in$\bar{{\cal M}}$.We give an example of a weakly o-minimal structure interpreting$\bar{{\cal M}}$and show that it is not elementarily equivalent to any reduct (...) of an o-minimal trace. (shrink)

We introduce a first order extension of GL, called ML 3 , and develop its proof theory via a proxy cut-free sequent calculus GLTS. We prove the highly nontrivial result that cut is a derived rule in GLTS, a result that is unavailable in other known first-order extensions of GL. This leads to proofs of weak reflection and the related conservation result for ML 3 , as well as proofs for Craig’s interpolation theorem for GLTS. Turning to semantics we prove (...) that ML 3 is sound with respect to arithmetical interpretations and that it is also sound and complete with respect to converse well-founded and transitive finite Kripke models. This leads us to expect that a Solovay-like proof of arithmetical completeness of ML 3 is possible. (shrink)

The purpose of our lives is to grow step by step toward a fundamental transformation. Instead of always seeking some form of gratification, we can learn to give to others with no self-interest at all. The is the essential teaching of the Kabbalah portrayed in these essays by Baal Hasulam – the greatest modern explicator of Kabbalah. Rabbi Gottlieb provides an illuminating commentary as a living Chassidic rebbe devoted to the practice and teaching of Baal Hasulam’s spiritual path.

PREFACE This volume is a sequel to yet independent of our Paranoia: A Study in Diagnosis, Reidel, Dordrecht and Boston, 1976. Whereas our first book centered on diagnosis, this centers on treatment. In our first volume, all discussions of nosology (theory of illness) and of treatment was ancillary to our discussion of diagnosis; similarly all discussion of this volume dealing with nosology - there is very little on diagnosis here - is ancillary to our discussion of psychotherapy. It is still (...) our profoundest conviction that to speak of treatment without diagnosis is meaningless, if not irresponsible, since otherwise one does not know what one is talking about. Hence, our present study, though it centers on theories of treatment, links psychotherapy with psychopathology. It is the rationale of psychotherapy which is of importance, and the rationale dwells in this link. We wish our present study to be self-contained and understood by readers who are not familiar with our first book - or with any specific literature. Our discussion of medicine in general, meaning the rationale of therapy in general, helps the uninitiated reader, as well as the initiated, we hope: it certainly has helped us. We did not see how else can we study a branch of medicine; we felt the need for some idea of how medicine is supposed to work. (shrink)

William Alston has identified what he calls a “Christian Mystical Practice” as one of the many doxastic practices in which humans engage. He defends CMP as being as rational as other doxastic practices, including the sense perceptual practice, having its own input and output rules, and its own background overrider system. I argue that there seems to be a serious problem with Alston’s characterization of the overrider system for CMP. The presence of this problem threatens to damage Alston’s argument for (...) the rationality of engaging in the Christian Mystical Practice. (shrink)

The Zohar, the Cabbalistic ‘Bible’, has a special theory concerning magic. Magic, which for the Zohar is the essence of idolatry, is depicted there as identical in its form with Cabbalistic mystical theurgy, but directed not towards God but towards evil demons. This theory has been labeled in research Hermetic and Neo-Platonic, but only in general terms. This article makes a further step and finds a parallelism between a paragraph in the Zohar and a paragraph in On the Mysteries of (...) Iamblichus, the Neo-Platonic philosopher. The two paragraphs expound the above theory in similar terms, and also cite as their source a similar authority, namely eastern sages or Chaldaean prophets. This parallelism may establish a literary connection between the Zohar and Iamblichus, who may be related also in other respects. (shrink)

Permitting social researchers access to employees can raise ethical issues for management and researchers which are here identified and examined. Dr Baruch is Research Fellow in Human Resources at City University Business School, London. He wishes to thank Professor Roger Jowell from the Social & Community Planning Research and Mr Steve Birault from the Centre for Social Development for their helpful comments on an early draft of this article.

Dyuḳan inṭeleḳṭuʼali shel manhig ruḥani be-ʻidan mahapkhani. Yehuda leʼon Ashkenazi (Meniṭo) 1922-1996 hogeh, mekhanekh ṿe-ish maʻaśhe.