For many, the two key thinkers about science in the twentieth century are Thomas Kuhn and Karl Popper, and one of the key questions in contemplating science is how to make sense of theory change. In Creatively Undecided, philosopher Menachem Fisch defends a new way to make sense of the rationality of scientific revolutions. He argues, loosely following Kuhn, for a strong notion of the framework dependency of all scientific practice, while at the same time he shows how such (...) frameworks can be deemed the possible outcomes of keen rational deliberation along Popperian lines. Fisch's innovation is to call attention to the importance of ambiguity and indecision in scientific change and advancement. Specifically, he backs the problem up, looking not at how we might communicate rationally across an already existing divide but at the rational incentive to create an alternative framework in the first place. Creatively Undecided will be essential reading for philosophers of science, and its vivid case study in Victorian mathematics will draw in historians. (shrink)

__The View from Within_ _examines the character of reason and the ability of an individual to effectively distance himself from the normative framework in which he functions in order to be self-critical and innovative. To accomplish this task, Menachem Fisch and Yitzhak Benbaji critically employ or reject the recent writings of Brandom, Friedman, Frankfurt, Walzer, Davidson, Williams, Habermas, Rorty, and McDowell to offer a fundamental analysis of the character of reason and the problem of relativism. This ambitious book forcefully (...) raises the problem of rational normative change and makes the unique and insightful claim that although we cannot be _convinced _by normative criticism to modify or replace our norms, we can be rationally _motivated_ to do so by the effect of exposure to trusted critics. Its unprecedented analysis, with its solution to the problem of normative self-criticism that has baffled philosophers for the past sixty years, will be welcomed by both students and scholars of philosophy. “__The View from Within_ _is a thorough evaluation of the arguments made by contemporary philosophers about the normative character of reason and the derivative problem of relativism. Fisch and Benbaji have admirably compared and contrasted competing positions, and with a balanced critique, they have made a sustained effort to ‘save’ rationality and provide new guideposts for its philosophical evaluation. A timely and important contribution.” —_Alfred I. Tauber, Boston University_. (shrink)

Assuming some large cardinals, a model of ZFC is obtained in which $\aleph_{\omega+1}$ carries no Aronszajn trees. It is also shown that if $\lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees.

We prove that the statement "For every pair A, B, stationary subsets of ω 2 , composed of points of cofinality ω, there exists an ordinal α such that both A ∩ α and $B \bigcap \alpha$ are stationary subsets of α" is equiconsistent with the existence of weakly compact cardinal. (This completes results of Baumgartner and Harrington and Shelah.) We also prove, assuming the existence of infinitely many supercompact cardinals, the statement "Every stationary subset of ω ω + 1 (...) has a stationary initial segment.". (shrink)

The paper attempts to elucidate and evaluate William Whewell's notion of a "consilience of inductions." In section I Whewellian consilience is defined and shown to differ considerably from what latter-day writers talk about when they use the term. In section II a primary analysis of consilience is shown to yield two types of consilient processes, one in which one of the lower-level laws undergoes a conceptual change (the case aptly discussed in Butts [1977]), and one in which the explanatory theory (...) undergoes conceptual "stretching." In section III both consilient cases are compared to the non-consilient case in reference to L. J. Cohen's method of relevant variables. In section IV we examine the test procedures of the theory in all three cases, and it is shown that in the event of genuine consilience (consilience of the second type) a theory acquires extraordinarily high support. In the final section something is said of the short-comings of standard Bayesian confirmation theories that are highlighted by Whewellian consilience. (shrink)

William Whewell was a giant of Victorian intellectual culture. His influence, whether recognized or forgotten, is palpable in areas as diverse as moral philosophy, mineralogy, architecture, the politics of education, physics, engineering, and theology. Recent studies of the place of the sciences in nineteenth-century Britain have repeatedly indicated the significance of Whewell's sweeping and critical proposals for a reformed account of scientific knowledge and moral values. However, until now there has been no detailed study of the context and impact of (...) his project. This collection of essays by recognized authorities in the fields of history, history of science, and philosophy thus represents the first attempt to do justice to a magisterial nineteenth-century intellectual. More generally, it makes an important contribution to our understanding of Victorian intellectual life and its aftermath. (shrink)

A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

Our theme is that not every interesting question in set theory is independent of ZFC. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZFC a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove--again in ZFC--that for a large class of cardinals there is no universal linear order (e.g. in every regular $\aleph_1 < (...) \lambda < 2^{\aleph_0}$). In fact, what we show is that if there is a universal linear order at a regular λ and its existence is not a result of a trivial cardinal arithmetical reason, then λ "resembles" ℵ1--a cardinal for which the consistency of having a universal order is known. As for singular cardinals, we show that for many singular cardinals, if they are not strong limits then they have no universal linear order. As a result of the nonexistence of a universal linear order, we show the nonexistence of universal models for all theories possessing the strict order property (for example, ordered fields and groups, Boolean algebras, p-adic rings and fields, partial orders, models of PA and so on). (shrink)

Robert Brandom's "The Pragmatist Enlightenment" describes the advent of American pragmatism as signaling a sea-change in our understanding of human reason away from the top-down Euclidian models of reasoning, warrant and knowledge inspired by the physical sciences, toward the far more bottom-up, narrative, inherently fallible and dialogical forms of reasoning of the life and human sciences. It is against this backdrop that Talmudic Judaism emerges not only as an early anticipation of the pragmatist enlightenment, but as going a substantial and (...) radical step beyond it, that in the context of religious commitment and reasoning, is unprecedented. (shrink)

We show that, assuming the consistency of a supercompact cardinal, the first inaccessible cardinal can satisfy a strong form of a Löwenheim–Skolem–Tarski theorem for the equicardinality logic L, a logic introduced in [5] strictly between first order logic and second order logic. On the other hand we show that in the light of present day inner model technology, nothing short of a supercompact cardinal suffices for this result. In particular, we show that the Löwenheim–Skolem–Tarski theorem for the equicardinality logic at (...) κ implies the Singular Cardinals Hypothesis above κ as well as Projective Determinacy. (shrink)

The paper describes a form a non-Socratic dialogue which aims at exposing oneself to the normative critique of interlocutors with different commitments. It further argues that such exposure is the only way in which one can achieve critical distance from one's own commitments. It goes on to explore the epistemic and political virtues of this form of dialogue.

The paper charts the main points of my ongoing dispute with Heiko Schulz by teasing out the differences between my account of self and rationality, and Schulz’s Kierkegaardian alternative.

Kojman, M. and S. Shelah, The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic 58 57–72. It is shown that if T is stable unsuperstable, and 1 [brvbar]T[brvbar], T stable and κ<κ then there is a universal tree of height κ + 1 in cardinality λ.

Menachem Lorberbaum; Learning from Mistakes: Resources of Tolerance in the Jewish Tradition, Journal of Philosophy of Education, Volume 29, Issue 2, 30 May 2006.

With the widening schism between Orthodox and non-Orthodox and secular Jews, Kellner (Jewish religious thought, U. of Haifa) addresses the timely issue of the future of Judaism in the context of the classical faith. Appends notes on Maimonides, other Jewish thinkers, and prayers (Yigdal,Ani ma'amin). Distributed in the US by ISBS. Annotation copyrighted by Book News, Inc., Portland, OR.

This study charts the development of creed formulation in Judaism from its inception with Moses Maimonides (1135-1204) to the beginning of the 16th century, when systematic attention to the problem disappeared from the agenda of Jewish intellectuals. Kellner describes, analyzes, and compares the dogmatic systems of Maimonides, Duran, Crescas, Albo, Bibago, Abravanel, and many others, and provides English translations of several previously unexamined or untranslated texts.

More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by (...) Leibniz with a powerful and comprehensive notation’, wrote the young John Herschel and Charles Babbage of the calculus in 1813, ‘as if the soil of this country [was] unfavourable to its cultivation, it soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us’. (shrink)

We prove thatµ=µ <µ , 2 µ =µ + and “there is a non-reflecting stationary subset ofµ + composed of ordinals of cofinality <μ” imply that there is a μ-complete Souslin tree onµ +.

Providence and the rabbinic tradition -- Mosaic prophecy: Maimonides and Gersonides -- Eschatology and miracles -- Creation, miracles, revelation -- Song of Songs and Gersonides' world -- Maimonides and Gersonides on astronomy and metaphysics -- Gersonides on the Song of Songs and the nature of science -- Politics and perfection: Gersonides vs. Maimonides -- The role of the active intellect in human cognition -- Imitatio dei and the dissemination of scientific knowledge -- Moses ibn Tibbon and Gersonides on Song of (...) Songs -- Misogyny: Gersonides vs. Maimonides -- Gersonides and his cultured despisers: Arama and Abravanel. (shrink)

This book explores the emergence of the fundamental political concepts of medieval Jewish thought, arguing that alongside the well known theocratic elements of the Bible there exists a vital tradition that conceives of politics as a necessary and legitimate domain of worldly activity that preceded religious law in the ordering of society. Since the Enlightenment, the separation of religion and state has been a central theme in Western political history and thought, a separation that upholds the freedom of conscience of (...) the individual. In medieval political thought, however, the doctrine of the separation of religion and state played a much different role. On the one hand, it served to maintain the integrity of religious law versus the monarch, whether canon law, Islamic law, or Jewish law. On the other hand, it upheld the autonomy of the monarch and the autonomy of human political agency against theocratic claims of divine sovereignty and clerical authority. Postulating the realm of secular politics leads the author to construct a theory of the precedence of politics over religious law in the organization of social life. He argues that the attempts of medieval philosophers to understand religion and the polity provide new perspectives on the viability of an accommodation between revelation and legislation, the holy and the profane, the divine and the temporal. The book shows that in spite of the long exile of the Jewish people, there is, unquestionably, a tradition of Jewish political discourse based on the canonical sources of Jewish law. In addition to providing a fresh analysis of Maimonides, it analyzes works of Nahmanides, Solomon ibn Adret, and Nissim Gerondi that are largely unknown to the English-speaking reader. Finally, it suggests that the historical corpus of Jewish political writing remains vital today, with much to contribute to the ongoing debates over church-state relations and theocratic societies. (shrink)

Israel’s conduct in the Occupied Territories in recent decades has been profoundly affected by three theologies: the messianic-kabalistic theology of Rabbi Abraham Yitzhak Ha-Cohen Kook and his son Rabbi Zvi Yehuda Ha-Cohen Kook; the messianic-Hasidic-kabalistic-racist theology of Rabbi Yitzhak Ginsburg; the violent, racist theology of Rabbi Meir Kahane. In the spirit of the three theologies, Israeli politics of the past four and a half decades has set the continuous possession of Judea and Samaria, and the deepening and expansion of the (...) settlement project therein, as the supreme goal of Zionism, Jewish nationalism. Moreover, the three theologies dictated much of the settlement policies of the government. Additionally, the three theologies have dictated much of the daily practices to which the Palestinian residents of the Territories have been subjected. All of this means that soldiers who are required to serve in the Occupied Territories, to die in them, and to kill Palestinians in the course of their military service therein, have been subjected to a politics motivated, to a substantial extent, by a religious culture premised on religious theologies. If such soldiers wish to refuse to abide by the orders given them to serve in the Occupied Territories, they can resort to the two traditional doctrines recgnized by liberal jurisprudence: the doctrine of civil disobedience and the doctrine of conscientous objection (Often there is an overlapp between the two defences). I argue that in addition to these two traditional doctrines, secular soldiers who are asked to serve in the Occupied Territories may resort to a doctrine I call “culture-based refusal.”. (shrink)

We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra contains a complete subalgebra which is isomorphic to the collapse algebra CompCol. Consequently, adding a generic filter to the quotient algebra collapses μ0 to 1. Another corollary is that the Baire number of the space U of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory.

The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem gives a necessary and sufficient condition for the existence of an exact upper bound ƒ for a ¦A¦+ is regular: an eub ƒ with lim infI cf ƒ = μ exists if and only if for every regular κ ε the set of flat points in tf of cofinality κ is stationary. Two applications of the main Theorem to set theory (...) are presented. A theorem of Magidor's on covering between models of ZFC is proved using the main theorem : If V-W are transitive models of set theory with ω-covering and GCH holds in V, then κ-covering holds between V and W for all cardinals κ. A new proof of a Theorem by Cummings on collapsing successors of singulars is also given . The appendix to the paper contains a short proof of Shelah's trichotomy theorem, for the reader's convenience. (shrink)

. The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite $\kappa$ modulo some ideal I. If a $<_I$ -increasing sequence of ordinal functions has regular length which is larger than $\kappa^+$ , then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length $\kappa^+$ . It is shown that this is not the case.

Essay review of Y. Gingras, Science and Religion: An Impossible Dialogue, Polity Press, 2017.

This article introduces the confrontational theology of the rabbinic literature of late antiquity by means of a well-known, yet ill-understood legend. It goes on to argue that Talmudic confrontationalism comes coupled with an insistent dialogism that, unlike any other major human undertaking, displays a profound awareness of the indispensable role of external normative critique in the process of changing one’s mind.

The problems divulged, analyzed and allegedly solved in Science, Order & Creativity are not scientific problems. They attest to a fundamental failure of science but not to scientific failure per se. Bohm and Peat's meta-scientific undertaking cannot afford, therefore, to remain negative. However, neither science itself nor current professional philosophy are capable of the radical positive rethinking required, in their view, in order to restore and ensure scientific creativity.

Science studies the world, but does not include itself in it. The task of systematically studying science falls to the humanities. The problem is that philosophers who take recent developments in philosophy seriously are forced to deny any credence to the self-image of science as a steadily progressive, self-critical enterprise, while philosophers who take what scientists do and feel more seriously, are forced to ignore some of the most profound latter-day findings of philosophy. What makes this issue highly relevant in (...) the present context, is that at its heart it is a dispute about language. This paper explores the possibility not of adjudicating this dispute, but of somehow bridging it. What it asks and proposes to answer positively is whether it is possible to remain committed to both horns of the dilemma: to salvage a philosophically viable account of science as a self-critical enterprise, without having to breach the latter-day philosophical framework that would seem to deem this impossible. (shrink)

Babbage wrote two relatively detailed, yet significantly incongruous, autobiographical accounts of his pre-Cambridge and Cambridge days. He published one in 1864 and in it advertised the existence of the other, which he carefully retained in manuscript form. The aim of this paper is to chart in some detail for the first time the discrepancies between the two accounts, to compare and assess their relative credibility, and to explain their author's possible reasons for knowingly fabricating the less credible of the two.

An interesting question arises in the context of the typically medieval description of the universe presented at the beginning of Maimonides' (1138–1204) great law code, theMishneh Torah. What was Maimonides' own attitude towards that account? Was it meant only as a statement of the best description of nature available at the time (and thus radically distinct from thehalakhic(i.e. Jewish legal) matters which make up the bulk of theMishneh Torah) or was it meant to be a description of the true nature (...) of the universe as it really is, not subject to revision in the light of new paradigms or new models (and thus essentially similar to thehalakhicmatters in the text)? Answering this question will lead us to a better understanding of Maimonides' understanding of the nature of science and of what I shall call, for lack of a better term, scientific progress. Maimonides will be shown to hold that while sublunar science can reach perfection and completion such is not possible for superlunar science and that to the extent that the scientific matters in theMishneh Torahdeal with the latter they could not have been presented as the final description of the universe as it truly is. (shrink)

We characterize the ordinals α of uncountable cofinality such that α is the standard part of a nonstandard model of ZFC (or equivalently KP).

Toldot ha-meḥaber - Petaḥ davar -- Psikhonoyroʼimunologyah, yaḥase gomlin nefesh guf -- Hakarat ha-ṭov la-tseṿet ha-metapel -- Peʻilut hatsalah ha-ʻalulah le-hasev nezaḳim -- ha-Ḥoleh ha-sofani ha-noṭeh la-mut -- ʻAl saf gesher ha-ḥayim -- Ḳedushat ha-ḥayim -- Ḥoleh dimenṭi, ḥasar deʻah, Altshaimer -- Ḥolim ḳashim ʻim ekhut ḥayim yerudah u-mugbaluyot -- Refuʼat nashim (geniḳologyah), ʻubarim, yiludim ṿi-yeladim -- Bediḳot seḳer -- Amirat emet la-ḥoleh.