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.

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)

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)

The liberalism of flourishing : two versions -- Intellectualist-moralist liberalism of flourishing -- Comprehensive liberalism of flourishing -- The liberalism of flourishing and autonomy liberalism : some comparisons -- Flourishing, art, and the state -- Art and flourishing -- Art and the liberal state -- Liberalism, art, and religion -- Liberalism, religion, nationalism : liberalism in the domains of meaning.

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.

__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)

This is a survey paper giving a self-contained account of Shelah's theory of the pcf function pcf={cf:D is an ultrafilter on a}, where a is a set of regular cardinals such that a

Logic and Philosophy of Logic

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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.

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.

The constellation of pain, resentment, the body, and time – as they exist in the wake of the Enlightenment and in the dawn of a new barbarism - is found throughout the work of Jean Améry and Peter Sloterdijk. Both thinkers were especially influenced by Nietzsche’s readings of resentment, his challenge to the Enlightenment, and his turn to the body as the basis of a new kind of thinking which starts with pain, dwells in irreversible time, and ends with the (...) possibility of action and joy. While this new thinking is novel and appeals to all humankind, the most unexpected points of convergence between Améry and Sloterdijk can be found in their particular neo-Nietzschean articulations of Jewishness: using what Harold Bloom would call revision, they both propose a revision of Nietzsche’s reading of Judaism as resentment. Améry associates Jewishness with “revolt” while Sloterdijk asso ciates what he calls “kynicism” with Jewishness. 1 Intensely aware of the mortal blows that have been dealt to the Enlightenment, philosophy, and modernity as well as to the human body during the Holocaust, Améry and Sloterdijk both address – either directly or indirectly – the meaning of cynicism in relation to Jewishness, in particular, and the modern condition, in general. (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 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)

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 +.

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.

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)

French theorists have recently proposed a theory which describes all literature in terms of the probable, the vraisemblable.6 This poetics of the probable commences with a purely relativistic claim. What is probable not only changes in accordance with the audience’s concept of reality but also changes in accordance with the needs of the story and with the narrative possibilities open to various genres. It includes all of the norms and models making a given text understandable to the reader, however outlandish (...) and eccentric it may be. Various levels of the vraisemblable are distinguished from each other, and the vraisemblable based upon models of the world or the world view prevalent in a given culture is scrupulously separated from types of the vraisemblable that are based upon literary, generic models. However, as Tzvetan Todorov gladly admits, “the two notions tend to melt into each other.”7 He and other theorists see the literary genre itself as one of the models “probabilizing” a given text, at times in direct contradiction with “natural” models of the world. Still others see the world, or the prevalent world view, as the universal text which probabilizes other texts.[…]Rather than how this new concept of the vraisemblable, of probability, fares in relation to farce in films, theater, and literature, I prefer to ask how farce fares in relation to it. I think that it doesn’t do well. Farce shows that it is a mistake to unify the possibilities for understanding a text and the possibilities for understanding its fictional world within a single integrated concept. It is a further mistake to term such a concept “probability.” When dealing with the fantastic or the marvelous, for instance, probabilizing the text and probabilizing the work’s fictional world may legitimately be unified under a single principle or concept. If we agree to change or suspend a fundamental belief about the world, we will be able to perceive as logical and probable not only the texts but also the fictional worlds of such works. Coleridge’s “willing suspension of disbelief” excellently fits works that are written in these genres. Such works require that we temporarily forget a certain general belief about the world. After we’ve agreed, as a result of this suspension, to include certain elements in the world , we may then rebuild the fictional world while using the rest of our beliefs along with this new assumption. Farce’s incredibility creates a different situation. Before we have even begun to recover from an attack upon one probability principle, another is undermined. In farce the rules of probability are not neutralized in one specific realm of reality; their inversion operates constantly on all of reality’s realms. The image of a seemingly real world, reminding us of our own world and of our own set of probabilities, is all we need to be constantly astonished by farce’s persistently novel deviations from predictable probability. Here, in direct opposition to the marvelous, the new deviations must keep on coming from unexpected directions, because farce won’t allow its incredibilities to consolidate and become new rules of probability. The fictional world of overt farce lacks a specific factor, the one that would have probabilized all of the other factors of this world. Such an Archimedean center might seem to be located in the genre’s definition—this genre, however, does not probabilize the incredible. Farce’s definition does not make farce’s world more intelligible in any sense of that word. At the very most, farce allows us to forgo such intelligibility without transgressing the established boundaries of art.6. For an excellent presentation of their views, see Jonathan Culler, Structuralist Poetics: Structuralism, Linguistics, and the Study of Literature , pp. 131-60.7. Tzvetan Todorov, The Poetics of Prose, trans. Richard Howard , p. 83. See also his introduction to Communications 11 : 2. (shrink)

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.

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)

Knowledge: to know is to love -- Love: Abraham, Moses, and the meaning of circumcision -- Seasons: Hanukah and Purim reconfigured -- Women: marital and universal peace -- Holiness: commandments as intruments -- Asseverations: socila responsibility and sanctifying God's name -- Agriculture: sanctifying all human beings -- Temple service: the divinity of the comandments -- Offerings: the morality of the commandments -- Reitual purity: intellectual and moral purity -- Damages: who is a Jew? -- Acquision: slavery versus universal humkanity -- (...) Civil laws: God of Aristotle in the God of Abraham -- Judges: Messianic universalism -- Appendix: Maimonides' cosmic paradigm. (shrink)

heleḳ 1. Be-reshit, Shemot, va-Yikra -- heleḳ 2. ba-Midbar, Devarim.

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.

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)

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)

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.

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)

A self contained proof of Shelah's theorem is presented: If μ is a strong limit singular cardinal of uncountable cofinality and 2μ > μ+ then $\left( {\begin{array}{*{20}c} {\mu ^ + } \\ \mu \\ \end{array} } \right) \to \left( {\begin{array}{*{20}c} {\mu ^ + } \\ {\mu + 1} \\ \end{array} } \right)_{< cf\mu } $.

Starting from cardinals κ κ is measurable, we construct a model for the theory “ZF + n < ω[DCn] + ω + 1 is a measurable cardinal”. This is the maximum amount of dependent choice consistent with the measurability of ω + 1, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible.

Liḳuṭe amarim, Shaʻar ha-yiḥud ṿeha-emunah, Igeret ha-teshuvah, Igeret ha-ḳodesh (simanim 1-20).

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.

This article examines the role culture plays in contract law. It demonstrates that even in contract law, the branch of law most committed to the ideal of individual autonomy, law’s reliance on culture makes compulsion by the law an unavoidable outcome. The concept of culture is applied to contract law in two principal ways. First, it attempts to explain the rise of objectivism in late nineteenth-century contract law as a manifestation of some central experiences prevalent in modern culture. Second, it (...) analyzes the role played by culture within the context of some of the central doctrines of contract law, namely, the doctrines on the formation and interpretation of contracts. (shrink)

Over the last twenty years, liberal thinkers have invested a great deal of effort in adapting liberal political theory to the multicultural condition. The central question that has occupied these thinkers is how a liberal state ought to treat cultural practices of non-liberal groups living within it. One major group of thinkers insists that it is incumbent on the liberal state to make sure that autonomy, together with some other central liberal values, are made part of the lives of all (...) the citizens living in the state. Another major group holds that it is the function of the liberal state to serve as framework for the peaceful co-existence of people who have diverse conceptions of the good life. These thinkers therefore call for "restraint" on the part of the state in its relations with non-liberal groups. This Article wishes to go beyond these two approaches. It is motivated by the conviction that the only standards that a liberal state can invoke in its relations with non-liberal groups are universal standards, i.e., standards that can be viewed, to the utmost extent possible, as transcending any particular culture, and that can be applied not only to non-liberal cultures, but to the culture of the mainstream liberal society itself. The Article puts forth a series of considerations that must be taken into account when intervention on the part of a liberal state in cultural practices of non-liberal groups is considered. It also sets forth two proposals as to the standards that need to guide the liberal state in cases in which it considers intervention in cultural practices of groups living in it: the doctrine of human rights and the concept of humanness. (shrink)

A situation in which luck determines what happens in our lives is composed of two elements: the existence of a multiplicity of possible outcomes, and lack of control over the situation, namely that we have no way, or at least no meaningful way, to affect the outcome. Adjudication is a luck situation: law is indeterminate and in a decent society litigants are not supposed to have control over their judges. Can we minimize luck in adjudication? The primary way to do (...) this is to make every decision given in the system resemble as much as possible the decision that would have been reached by the majority of the judges active in the system had they all been given the opportunity to decide the case at hand as a group. Put differently, luck in judicial decisions can be lessened by increasing the number of judges in panels. Even though in a decent society the option of controlling the conduct of judges is out of the question, several means do exist for litigants to employ some control over the identity of the persons who are to resolve their disputes. (shrink)

Journal Name: The Law & Ethics of Human Rights Issue: Ahead of print.