'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen (...) world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"--Provided by publisher. (shrink)

We show how to get canonical models from in which the nonstationary ideal on ω1 is ω1 dense and there is no P-point.

We show the Borel Conjecture is consistent with the continuum large.

We prove a strong boundedness theorem for dilators: if A ⊆ DIL is Σ 1 1 , then there is a recursive dilator D 0 such that ∀ D ∈ A.

Assume ZF + AD +V=L and letκ< Θ be an uncountable cardinal. We show thatκis Jónsson, and that if cof = ω thenκis Rowbottom. We also establish some other partition properties.

We consider the possible complexity of the set of reals belonging to an inner model M of set theory. We show that if this set is analytic then either 1M is countable or else all reals are in M. We also show that if an inner model contains a superperfect set of reals as a subset then it contains all reals. On the other hand, it is possible to have an inner model M whose reals are an uncountable Fσ set (...) and which does not have all reals. A similar construction shows that there can be an inner model M which computes correctly 1, contains a perfect set of reals as a subset and yet not all reals are in M. These results were motivated by questions of H. Friedman and K. Prikry. (shrink)

We extend work of H. Friedman, L. Harrington and P. Welch to the third level of the projective hierarchy. Our main theorems say that (under appropriate background assumptions) the possibility to select definable elements of non-empty sets of reals at the third level of the projective hierarchy is equivalent to the disjunction of determinacy of games at the second level of the projective hierarchy and the existence of a core model (corresponding to this fragment of determinacy) which must then contain (...) all real numbers. The proofs use Sacks forcing with perfect trees and core model techniques. (shrink)

L'A. soutient, contre Germain Grisez, Joseph Boyle, John Finnis et William May, que le contrôle naturel des naissances pratiqué avec une intention mauvaise n'est pas contraception. Il montre que les auteurs identifient de façon incorrecte la fin prochaine de la contraception comme choix qu'il n'y ait pas d'enfant, alors que la fin prochaine véritable est d'empêcher un enfant de venir au monde . Ainsi donc, puisque en NFP un couple ne cherche pas à empêcher la venue au monde d'un enfant, (...) NFP n'implique pas d'action contraceptive. L'A. soutient aussi qu'identifier la fin prochaine comme choix qu'il n'y ait pas d'enfant ne spécifie pas de façon adéquate une classe homogène d'actes objectifs, bien que cela spécifie une classe homogène d'actes moraux. (shrink)

Examines an important and controversial topic in lexical semantics: polysemy, the capacity of words to manifest a range of different meanings when employed in different contexts."--Publishers website.

For two hundred years, Americans have believed that they have an obligation to improve the lot of humanity, a belief that has consistently shaped U.S. foreign policy. Yet within this consensus, there are two competing schools of thought: the "exemplarist" school (Brands' term) which holds that what America chiefly owes the world is the benign example of a well-functioning democracy, and the "vindicationist" school which argues that force must sometimes supplement a good example. In this book, H.W. Brands traces the (...) evolution of these two schools as they emerged in the thinking and writing of the most important public thinkers of the past two centuries. (shrink)

David Hume was one of the most important British philosophers of the eighteenth century. The first part of his Treatise on Human Nature is a seminal work in philosophy. Hume on Knowledge introduces and assesses: * Humes life and the background of the Treatise * The ideas and text in the Treatise * Humes continuing importance to philosophy.

This article presents an analysis of "spirituality." Ryle said that a belief is not known to be truly held unless one bases crucial action on it; but the qualifications "truly" and "crucial" can be stripped away. Spirituality then becomes consistency of actual action with a belief; or in behavior analytic terms, spirituality is "rule-governed" behavior. Beliefs can function not only as "discriminative stimuli" but also as "reinforcing stimuli." A belief need not correspond to the world as experienced in order to (...) have these functions. Spirituality, thus far in the analysis, is only rule-governed behavior, regardless of the source of the rule and regardless of the content of the rule except that the rule must specify actually performable behavior so that consistency of the action with the belief can be assessed. The separation of action from belief is a form of alienation in a Marxian sense ; to paraphrase Kant, beliefs without actions are empty and actions without beliefs are blind. That is, a belief that is not acted upon is literally useless, and action that is not based on a belief is literally irrational. Alienation is resolved when action is based on "right" motives, which are motives based on a set of principles. Analogously, spirituality is a special kind of rule-governed behavior because the rules that govern this behavior are part of a coherent system that defines "rightness.". (shrink)

One area of language research that has received a great deal of attention, both theoretical and empirical, is the use of anaphoric expressions. Such expressions can be thought of as serving two functions: the primary function is to refer back to a referent from previous discourse, and the secondary, but no less important, function is to help provide discourse coherence and structure. Third person pronouns such as he or she are anaphoric expressions par excellence, but fuller anaphoric expressions, including demonstrative (...) and definite noun phrases (NPs) such as that woman and the woman are also used in natural discourse. In this chapter we shall focus primarily on issues concerning definite NP anaphor resolution, and in particular we shall examine the interaction of two factors that are related to the identification of antecedents: the focus status of the antecedent and the semantic relationship between the antecedent and the anaphor (including semantic overlap). After presenting these factors, we will discuss one particular approach to anaphor resolution, Almor's (1999) Informational Load Hypothesis (ILH), and present three experiments that examined the findings presented in Almor (1999). The results of these experiments will lead us to consider in more detail the secondary, discourse-structuring function of anaphoric expressions. (shrink)