The class of stable posets is defined and investigated. We give a forcing construction of a universe of set theory which satisfies a weak form of Martin's Axiom and $2^{\aleph_0} > \aleph_1$ and yet some propositions which follow from CH hold in this universe.

ha-R. ha-ḳ. R. Elimelekh mi-Lizensḳ -- ha-R. ha-ḳ. R. Mosheh Leyb mi-Sasov -- ha-R. ha-ḳ. R. Menaḥem mi-Ḳasov -- ha-R. ha-ḳ. R. Yitsḥaḳ Ayziḳ mi-Ḳalov -- ha-R. ha-ḳ. R. Uri mi-Sṭrelisḳ -- ha-R. ha-ḳ. R. Naftali Tsevi me-Ropshits -- ha-R. ha-ḳ. R. Asher me-Ropshits -- ha-R. ha-ḳ. R. Tsevi Elimelekh mi-Dinov -- ha-R. ha-ḳ. R. Ḥ. Halbershṭam mi-Tsanz -- ha-R. ha-ḳ. R. Avraham mi-Sṭreṭin.

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

Śiḥot maran ha-Mashgiaḥ Mohari Leṿinshṭain, zatsal -- Ḥidushe torato ʻa. Mas. B.ḳ. ṿe-liḳuṭim -- Leḳeṭ mi-maʼamraṿ mi-moreshet Daṿid Heber ṿe-ʻinyene ha-shaʻah.

We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite language whose only recursively presentable model is saturated, gives the second non-trivial example of a spectrum produced in a finite language.

The current study aims to examine how the intense emotions experienced by different Israeli groups during the 2006 Second Lebanon War affected their perceptions of risk. Two weeks after the end of the war, a questionnaire was distributed among 205 people. Some were from the north and had been directly affected by the rocket attacks; others were from the center of Israel. The questionnaires, based on Lerner et al., measured emotions and perceived risk. The results show significant differences between those (...) living in the north and those in the center of Israel. As expected, people living in the north reported more emotional difficulties during the war, greater perceived risk, and more pessimism in comparison to the center group. Moreover, the results point to significant differences between Israeli Jews and Israeli Arabs regarding emotions and perceived risk. In addition, the study results show a positive relation between anger and perceived risk. (shrink)

We address the following questions in this paper: (1) Which set or number existence axioms are needed to prove the theorems of ‘ordinary’ mathematics? (2) How should Frege’s theory of numbers be adapted so that it works in a modal setting, so that the fact that equivalence classes of equinumerous properties vary from world to world won’t give rise to different numbers at different worlds? (3) Can one reconstruct Frege’s theory of numbers in a non-modal setting without mathematical primitives such (...) as “the number of Fs” ( $$\#F$$ ) or mathematical axioms such as Hume’s Principle? Our answer to question (1) is ‘None’. Our answer to question (2) begins by defining ‘x numbers G’ as: x encodes all and only the properties F such that being-actually-F is equinumerous to G with respect to discernible objects. We answer (3) by showing that the mere existence of discernible objects allows one to reconstruct Frege’s derivation of the Dedekind-Peano axioms in a non-modal setting. (shrink)

What is free will? Can it exist in a determined universe? How can we determine who, if anyone, possesses it? Philosophers have been debating these questions for millennia. In recent decades neuroscientists have joined the fray with questions of their own. Which neural mechanisms could enable conscious control of action? What are intentional actions? Do contemporary developments in neuroscience rule out free will or, instead, illuminate how it works? Over the past few years, neuroscientists and philosophers have increasingly come to (...) understand that both fields can make substantive contributions to the free-will debate, so working together is the best path forward to understanding whether, when, and how our choices might be free. We therefore asked leading philosophers and neuroscientists which questions related to free will they would most like the other field to answer. Those experts then voted on the 15 most important questions for each field to answer. This book is a collection of the answers to those questions along with follow-up questions from world experts in the neuroscience and philosophy of free will. These varied perspectives will fascinate, illuminate, and stimulate students from both fields along with anyone who wants to be brought up to date on these profound issues. (shrink)

We study the relative computational power of structures related to the ordered field of reals, specifically using the notion of generic Muchnik reducibility. We show that any expansion of the reals by a continuous function has no more computing power than the reals, answering a question of Igusa, Knight, and Schweber [7]. On the other hand, we show that there is a certain Borel expansion of the reals that is strictly more powerful than the reals and such that any Borel (...) quotient of the reals reduces to it. (shrink)

Zionism: the idea of a territorial concentration of the Jewish people in an autonomous entity as a solution to the Jewish Question. This definition (and the essay that follows) refers to Zionism as conceived by its first leaders and theoreticians — Leo Pinsker, Theodor Herzl, and Israel Zangwill, that is, to what is generally called “political” Zionism (as opposed to the nationalistic-religious trends that now dominate the so-called official “Zionist ideology in Israel). Detective fiction: one narrative in search of another, (...) the first arising from the discovery (or anticipation) of a crime, the second providing the identity of the criminal, his motivations and the modalities of his act. (shrink)

The “Assyrian Century,” the period of Assyrian rule in the Levant, is usually regarded as an era of prosperity and economic progress. As far as the southern Levant is concerned, this reconstruction more or less reflects the reality on the southern edge of the region—in the areas of Philistia, Judah, and Edom. But what was the situation in the northern part of the country, in the territories of the former kingdom of Israel and adjacent territories, regions that had become Assyrian (...) provinces? It is the aim of this paper to scrutinize the archaeological data from these regions in order to shed light on the settlement and demographic reality in those provinces, and furthermore to reassess Assyrian policy in the west. After summarizing previous research, the article will present the available archaeological data, which will then be compared with that from the southern part of the country in order to enable a reexamination of the Assyrian empire’s policy in the west. (shrink)

The lambda model of Feldman & Levin for intentional hand movement is compared with a hemispheric motor model (IIMM). Both models imply similar conclusions independently. This increases the validity of both models.

Name der Zeitschrift: Naharaim Jahrgang: 8 Heft: 2 Seiten: 210-226.

The article examines the relation between two kinds of ontological relations that hold together the building blocks of Spinoza’s metaphysics: “being in” and “affection of.” It argues that in order to speak of existence in a single sense, Spinoza equivocates on the notion of affection. On the one hand, substance is in itself in the same sense that every other existing thing is in substance. On the other hand, substance is not the affections of itself, affections of substance are not (...) related to substance in the same sense that affections of modes are related to modes, and affections of modes, which are affections of affections of substance, cannot, at least in some cases, be regarded as affections of substance. Thus, although “God is without passions,” the passions themselves exist in the same sense that God, human beings, and other modes exist, that is, in the sense that they are all in nature; but while the meaning of “being” remains the same, the meaning of “being affected,” or “feeling,” necessarily changes as the Ethics unfolds. (shrink)

Este artículo analiza las numerosas versiones de un Apocalipsis islámico que predice la aparición de 12 soberanos entre los musulmanes. Mantiene que las primeras versiones de este apocalipsis fueron puestas en circulación durante el período omeya, alrededor del año 100 H, cuando el número de califas se acercaba al duodécimo. La coincidencia entre los dos números simbólicos, 12 y 100, alimentó una atmósfera apocalíptica que favoreció la circulación de las primeras versiones del apocalipsis. Estas versiones hacen uso del modelo bíblico (...) de los doce príncipes de Israel que se han identificado con los doce soberanos musulmanes. El artículo continúa examinando varias versiones de este apocalipsis básico, versiones que reflejan circunstancias políticas posteriores, surgidas durante el final del período omeya y el comienzo del ‛abbāsī En estas versiones revisadas, el modelo bíblico ha sido reemplazado por el coránico y por un modelo árabe. El artículo examina también la función de este apocalipsis en el šī‛īsmo Duodecimano. (shrink)

According to Alix Cohen, Kant defines emotions as ‘feelings’. Although I find her account of Kantian feelings compelling, I provide three reasons to doubt that it is an account of emotions: (1) it is unclear why Cohen identifies emotions with Kantian feelings; (2) some Kantian feelings are not emotions; (3) some Kantian desires may be emotions. I propose, however, that with some qualifications Cohen’s account may be upheld, provided its extra-textual assumptions about emotions are explicated. Against her claim that Kantian (...) feelings have a derived intentionality, I argue that the text is compatible with their being intrinsically intentional. (shrink)

This paper connects the debate regarding perceptual representation of high-level properties and the debate regarding non-conceptual perceptual representation. I present and defend a distinction between representationally-complex properties and properties that are simpler to represent and offer ways of assessing whether a property is representationally complex. I address conditions under which such a property might be non-conceptually represented and conclude that most representationally-complex properties are simply too complex to be non-conceptually represented. Thus, most mental states that represent representationally-complex properties must be (...) conceptual. This conclusion is relevant for a variety of philosophical theories (perception, ethics, emotions, pain) and is especially dramatic with respect to accounts according to which a mental state can non-conceptually represent such properties. As a test case for applying my argument I consider a group of such accounts: non-conceptual perceptual views of emotions, which my argument entails are false. I end by considering the implications my argument has for different theories. -/- . (shrink)

How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first—debunking arguments—aims to put pressure on realism by emphasising the (...) seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy—indispensability arguments—aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics, and vice versa, the papers collected here break new ground in both areas. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area. (shrink)