The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from [Formula: see text] to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokobodzki independently showed that the Continuum Hypothesis implies the existence of medial limits. (...) We show that the Filter Dichotomy implies that there are no medial limits. (shrink)

The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.

We shall show the consistency of CH+ᄀ(+) and CH+(+)+ there are no club guessing sequences on ω₁. We shall also prove that ◊⁺ does not imply the existence of a strong club guessing sequence ω₁.

The canonical function game is a game of length ω1 introduced by W. Hugh Woodin which falls inside a class of games known as Neeman games. Using large cardinals, we show that it is possible to force that the game is not determined. We also discuss the relationship between this result and Σ22 absoluteness, cardinality spectra and Π2 maximality for H(ω2) relative to the Continuum Hypothesis.

We present Woodin's proof that if there exists a measurable Woodin cardinal δ, then there is a forcing extension satisfying all $\Sigma _{2}^{2}$ sentences ϕ such that CH + ϕ holds in a forcing extension of V by a partial order in V δ . We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary embedding (...) j: V → M with critical point $\omega _{1}^{V}$ such that M is countably closed in the forcing extension. (shrink)

In this paper, we study some new examples of ideals on $$\omega $$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order—known as the weak Rudin–Keisler order—and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177–214, 1991) on the Tukey order, we also show that there is an analytic P-ideal above all other analytic (...) P-ideals in the weak Rudin–Keisler order. (shrink)

In [P. Larson, Martin’s Maximum and the axiom , Ann. Pure App. Logic 106 135–149], we modified a coding device from [W.H. Woodin, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, Walter de Gruyter & Co, Berlin, 1999] and the consistency proof of Martin’s Maximum from [M. Foreman, M. Magidor, S. Shelah, Martin’s Maximum. saturated ideals, and non-regular ultrafilters. Part I, Annal. Math. 127 1–47] to show that from a supercompact limit of supercompact cardinals one could force (...) Martin’s Maximum to hold while the axiom fails. Here we modify that argument to prove a stronger fact, that Martin’s Maximum is consistent with the existence of a wellordering of the reals definable in H without parameters, from the same large cardinal hypothesis. In doing so we give a much simpler proof of the original result. (shrink)

In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω | . It was shown in [1] that (...) the Continuum Hypothesis does not imply (+) and that (+) does not imply the existence of a club guessing sequence on ω | . In this paper we give an alternate proof of the second of these results, using Woodin's P max technology, showing that a strengthening of (+) does not imply a weakening of club guessing known as the Interval Hitting Principle. The main technique in this paper, in addition to the standard P m a x machinery, is the use of condensation principles to build suitable iterations. (shrink)

The stationary set splitting game is a game of perfect information of length ω1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to Σ22 maximality with a predicate for the nonstationary ideal on ω1, and an example of a consistently (...) undetermined game of length ω1 with payoff de.nable in the second-order monadic logic of order. We also show that the determinacy of the game is consistent with Martin's Axiom but not Martin's Maximum. (shrink)

A function f from ω1 to the ordinals is called a canonical function for an ordinal α if f represents α in any generic ultrapower induced by forcing with math formula. We introduce here a method for coding sets of ordinals using canonical functions from ω1 to ω1. Combining this approach with arguments from, we show, assuming the Continuum Hypothesis, that for each cardinal κ there is a forcing construction preserving cardinalities and cofinalities forcing that every subset of κ is (...) an element of the inner model math formula. (shrink)

Argumentation as the public exchange of reasons is widely thought to enhance deliberative interactions that generate and justify reasonable public policies. Adopting an argumentation-theoretic perspective, we survey the norms that should govern public argumentation and address some of the complexities that scholarly treatments have identified. Our focus is on norms associated with the ideals of correctness and participation as sources of a politically legitimate deliberative outcome. In principle, both ideals are mutually coherent. If the information needed for a correct deliberative (...) outcome is distributed among agents, then maximising participation increases information diversity. But both ideals can also be in tension. If participants lack competence or are prone to biases, a correct deliberative outcome requires limiting participation. The central question for public argumentation, therefore, is how to strike a balance between both ideals. Rather than advocating a preferred normative framework, our main purpose is to illustrate the complexity of this theme. (shrink)

Psychologists' emerging interest in spirituality and religion as well as the relevance of each phenomenon to issues of psychological importance requires an understanding of the fundamental characteristics of each construct. On the basis of both historical considerations and a limited but growing empirical literature, we caution against viewing spirituality and religiousness as incompatible and suggest that the common tendency to polarize the terms simply as individual vs. institutional or ′good′ vs. ′bad′ is not fruitful for future research. Also cautioning against (...) the use of restrictive, narrow definitions or overly broad definitions that can rob either construct of its distinctive characteristics, we propose a set of criteria that recognizes the constructs' conceptual similarities and dissimilarities. Rather than trying to force new and likely unsuccessful definitions, we offer these criteria as benchmarks for judging the value of existing definitions. (shrink)

This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set (...) theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas. (shrink)

At the forefront of international concerns about global legislation and regulation, a host of noted environmentalists and business ethicists examine ethical issues in consumption from the points of view of environmental sustainability, economic development, and free enterprise.

Samkhya is one of the oldest, if not the oldest, system of classical Indian philosophy. This book traces its history from the third or fourth century B. C. up through the twentieth century. The Encyclopedia as a whole will present the substance of the various Indian systems of thought to philosophers unable to read the Sanskrit and having difficulty in finding their way about in the translations (where such exist). This volume includes a lengthy introduction by Gerald James Larson, (...) which discusses the history of Samkhya and its philosophical contours overall. The remainder of the book includes summaries in English of all extant Sanskrit texts of the system. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Thought and its subject-matter, by J. Dewey.--Thought and its subject-matter: the antecedents of thought, by J. Dewey.--Thought and its subject-matter: the datum of thinking, by J. Dewey.--Thought and its subject-matter: the content and object of thought, by J. Dewey.-- Bosanquet's theory of judgment, by H. B. Thompson.--Typical stages in the development of judgement, by S. F. McLennan.--The nature of hypothesis, by M. L. Ashley.--Image and idea in logic, by W. C. Gore.--The logic of the pre-Socratic philosophy, (...) by W.A. Heidel.--Valuation as a logical process, by H. W. Strart.--Some logical aspects of purpose, by A. W. Moore. (shrink)

The need for a recovery of philosophy, by J. Dewey.--Reformation of logic, by A. W. Moore.--Intelligence and mathematics, by H. C. Brown.--Scientific method and individual thinker, by G. H. Mead.--Consciousness and psychology, by B. H. Bode.--The phases of the economic interest, by H. W. Stuart.--The moral life and the construction of values and standards, by J. H. Tufts.--Value and existence in philosophy, art, and religion, by H. M. Kallen.

The Pragmatism Reader is the essential anthology of this important philosophical movement. Each selection featured here is a key writing by a leading pragmatist thinker, and represents a distinctively pragmatist approach to a core philosophical problem. The collection includes work by pragmatism's founders, Charles Peirce, William James, and John Dewey, as well as seminal writings by mid-twentieth-century pragmatists such as Sidney Hook, C. I. Lewis, Nelson Goodman, Rudolf Carnap, Wilfrid Sellars, and W.V.O. Quine. This reader also includes the most (...) important work in contemporary pragmatism by philosophers like Susan Haack, Cornel West, Hilary Putnam, Richard Rorty, Cheryl Misak, and Robert Brandom. Each selection is a stand-alone piece--not an excerpt or book chapter--and each is presented fully unabridged. The Pragmatism Reader challenges the notion that pragmatism fell into a midcentury decline and was dormant until the advent of "neopragmatism" in the 1980s. This comprehensive anthology reveals a rich and highly influential tradition running unbroken through twentieth-century philosophy and continuing today. It shows how American pragmatist philosophers have contributed to leading philosophical debates about truth, meaning, knowledge, experience, belief, existence, justification, and freedom. Covers pragmatist philosophy from its origins to today Features key writings by the leading pragmatist thinkers Demonstrates the continuity and enduring influence of pragmatism Challenges prevailing notions about pragmatism Includes only stand-alone pieces, completely unabridged Reflects the full range of pragmatist themes, arguments, concerns, and commitments. (shrink)

Racism and Its Presuppositions: Towards a Pragmatic Ethics of Social Change Racism has been described as a litmus test or a barium meal which reveals other disorders and injustices within the body politic. It presupposes the legitimacy of racial classifications and the metaphysical reality of races and therefore provides a vital area of scrutiny for philosophical traditions. This paper examines racism and its anti-social effects both on the individual and the society at large. It argues that racism is generally driven (...) by fear and hatred hence all forms of racism are dangerous, socially harmful and morally wrong in practice. The paper recommends ways of overcoming the evil of racism by emphasizing social intelligence and self-realization as moral ideals drawing on John Dewey's pragmatism in ethics. It concludes by stressing Dewey's moral pragmatism as a potent instrument of social change. (shrink)