Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: assuming ωV1 = ωL1, there is no real in V[d] which is eventually different from the reals in L[ d], where d is Hechler over V; adding one Hechler real makes the invariants on the left-hand side of Cichoń's diagram equal ω1 and those on the right-hand side equal 2ω (...) and produces a maximal almost disjoint family of subsets of ω of size ω1; there is no perfect set of random reals over V in V[ r][ d], where r is random over V and d Hechler over V[r], thus answering a question of the first and second authors. (shrink)

We investigate the set (ω) of partitions of the natural numbers ordered by ≤* where A ≤* B if by gluing finitely many blocks of A we can get a partition coarser than B. In particular, we determine the values of a number of cardinals which are naturally associated with the structure ((ω),≥*), in terms of classical cardinal invariants of the continuum.

Scientists and laypeople alike use the sense of understanding that an explanation conveys as a cue to good or correct explanation. Although the occurrence of this sense or feeling of understanding is neither necessary nor sufficient for good explanation, it does drive judgments of the plausibility and, ultimately, the acceptability, of an explanation. This paper presents evidence that the sense of understanding is in part the routine consequence of two well-documented biases in cognitive psychology: overconfidence and hindsight. In light of (...) the prevalence of counterfeit understanding in the history of science, I argue that many forms of cognitive achievement do not involve a sense of understanding, and that only the truth or accuracy of an explanation make the sense of understanding a valid cue to genuine understanding. (shrink)

Philosophical Analysis Its Development between the Two World Wars.

Ned Block argues that the higher-order (HO) approach to explaining consciousness is ‘defunct’ because a prominent objection (the ‘misrepresentation objection’) exposes the view as ‘incoherent’. What’s more, a response to this objection that I’ve offered elsewhere (Weisberg 2010) fails because it ‘amounts to abusing the notion of what-it’s-like-ness’ (xxx).1 In this response, I wish to plead guilty as charged. Indeed, I will continue herein to abuse Block’s notion of what-it’s-like-ness. After doing so, I will argue that the HO approach accounts (...) for the sense of what-it’s-like-ness that matters in a theory of consciousness. I will also argue that the only incoherence present in the HO theory is that generated by embracing Block’s controversial notion of what-it’s-like-ness, something no theorist of any stripe ought to do. Block is famous for (among other things) having introduced the notion of ‘phenomenal consciousness’ into contemporary philosophy of mind (Block 1995). This term is widely employed in the philosophical literature and it even appears in the empirical literature. But wide-speared usage has brought about divergent interpretations of the term. We can distinguish a ‘moderate’ and a ‘zealous’ reading of ‘phenomenal consciousness’. On the moderate reading, ‘phenomenal consciousness’ just means ‘experience’. Many people have embraced this sense of the term and use it to roughly pick out conscious experience involving sensory quality (states like conscious visual experiences or conscious pains, for example).2 On the zealous reading, however, phenomenal consciousness is held to be ‘distinct from any cognitive, intentional, or functional property’ (Block 1995: 234). That is, any explanation of phenomenal consciousness in exclusively cognitive, intentional, or functional terms will fail to capture, without remainder, what is really distinctive about phenomenal consciousness. Block, of course, is fully clear about embracing the zealous reading; indeed, his initial introduction of the notion is in those terms. The same ambiguity occurs with the much-used (and abused) idea of ‘what-it’s-like-ness’.. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Este volumen recoge las lecciones del X Curso de Cultura hispanojudía y sefardí de la Universidad de Castilla-La Mancha, organizado por la Asociación de Amigos del Museo Sefardí (Toledo, Septiembre 2000) y consagrado al Pensamiento y Mística hispanojudía y sefardí. Las quince conferencias aquí reunidas ofrecen una perspectiva amplia, representativa y completa de los momentos, autores y temas más significativos tratados por pensadores y místicos sefardíes desde la Edad Media hasta nuestros días. Se aprecia una continuidad en los problemas y (...) una búsqueda constante de nuevas soluciones, adaptadas a las circunstancias de cada época. Es la primera vez que aparece en lengua castellana una visión global de esta rica faceta de la cultura hispanohebrea, que permite al lector acercarse a la evolución del pensamiento de los judíos originarios de Sefarad antes y después de 1492, tanto en su faceta filosófica con en su faceta mística (cábala). (shrink)

Let κ < λ be regular uncountable cardinals. Using a finite support iteration (in fact a matrix iteration) of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.

We give characterizations for the sentences "Every $\Sigma^1_2$-set is measurable" and "Every $\Delta^1_2$-set is measurable" for various notions of measurability derived from well-known forcing partial orderings.

This book reconstructs the concept and practice of dialectics as a means of grounding a critical theory of society. At the center of this project is the thesis of phronetic criticism or a form of reason that is able to synthesize human value with objective rationality. This book argues that defects in modern forms of social reason are the result of the powers of social structure and the norms and purposes they embody. Increasingly, modern societies are driven not by substantive (...) values concerning human good but by the technical imperatives of economic management leading to a cultural condition of nihilism that has eroded dialectical consciousness. The first half of the book demonstrates the various ways that social power erodes and undermines critical-rational forms of consciousness. The second part of the book constructs an alternative basis for critical reason by showing how it requires seeing human value as essentially ontological: that is, constituted by objective forms of sociality that either promote human freedom or pervert our capacities and drives toward pathological forms of life. The philosophical claim is that a critical theory of ethics must be rooted in these concrete forms of life and that this will serve as a critical vantage point for critical political judgment and transformational praxis. Descent of the Dialectic will be of interest to researchers working in philosophy, political theory, social theory, and critical theory. (shrink)

We show the consistency of ${\frak o} <{\frak d}$ where ${\frak o}$ is the size of the smallest off-branch family, and ${\frak d}$ is as usual the dominating number. We also prove the consistency of ${\frak b} < {\frak a}$ with large continuum. Here, ${\frak b}$ is the unbounding number, and ${\frak a}$ is the almost disjointness number.

Let A[ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions . We close with a detailed investigation of iterated Sacks indestructibility.

It is relatively consistent with ZFC that every countable $FU_{fin} $ space of weight N₁ is metrizable. This provides a partial answer to a question of G. Gruenhage and P. Szeptycki [GS1].

We investigate which filters onωcan contain towers, that is, a modulo finite descending sequence without any pseudointersection. We prove the following results:Many classical examples of nice tall filters contain no towers.It is consistent that tall analytic P-filters contain towers of arbitrary regular height.It is consistent that all towers generate nonmeager filters, in particular Borel filters do not contain towers.The statement “Every ultrafilter contains towers.” is independent of ZFC.Furthermore, we study many possible logical implications between the existence of towers in filters, (...) inequalities between cardinal invariants of filters $,${\rm{co}}{{\rm{f}}^{\rm{*}}}\left$,${\rm{no}}{{\rm{n}}^{\rm{*}}}\left$, and${\rm{co}}{{\rm{v}}^{\rm{*}}}\left$), and the existence of Luzin type families, that is, if${\cal F}$is a filter then${\cal X} \subseteq {[\omega ]^\omega }$is an${\cal F}$-Luzin family if$\left\{ {X \in {\cal X}:|X \setminus F| = \omega } \right\}$is countable for every$F \in {\cal F}$. (shrink)

We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, the splitting number, and the existence of certain kinds of splitting families.

“How can I, who am thinking about the entire, centerless universe, be anything so specific as this: this measly creature existing in a tiny morsel of space and time?” This metaphysically self-deprecating question, posed by Thomas Nagel, holds an insight into the nature of personhood and the ordinary ways we value it, in others and in ourselves. I articulate that insight and apply it to the phenomena of friendship, companionship, sexuality, solitude, and love. Although love comes in many forms, I (...) say, it always involves a sense of wonder at a finite creature thinking infinite thoughts. (shrink)

We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...) and it was proved that Σ21-Kσ-regularity implies Σ21-u-regularity. Here we show that these properties are in fact equivalent. Since the proof of analytic u-regularity uses a game argument it was clear that determinacy implies u-regularity of all sets. Here we show that an inaccessible cardinal is enough to construct a model for projective u-regularity, namely it holds in Solovay's model. Finally we show that forcing with uniform trees is equivalent to Laver forcing. (shrink)

Abstract:Qi has been both understood separately as substance and as field. This essay argues that qi in the Zhuangzi is both substance and field together. This qi field-substance is bidimensional where its vertical axis is that of substance and its horizontal axis that of field. This essay argues that the vertical dimension does not imply a substance dualism but a holism where qi differs in degrees of refinement; it argues that the horizontal dimension is composed of interrelated yinyang forces that (...) constitute an "empty" field. It also argues that at the center of this qi field-substance is the heart-mind and the body and, by drawing on rich resonances between the Zhuangzi and phenomenology, that human beings bring the fields of qi that they are situated in into certain coherences. (shrink)

We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster posets (where Fr is the Frechet ideal) via matrix iterations of <θ-ultrafilter-linked posets (restricted to some level of the (...) matrix). This is applied to prove consistency results about Cichoń's diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal invariants associated with it are pairwise different. At the end, we show that three strongly compact cardinals are enough to force that Cichoń's diagram can be separated into 10 different values. (shrink)

The existential analysis -- The death of dasein -- The timeliness of dasein -- The derivation of time -- The time of being.

Although the critical reconceptualization of Corporate Citizenship (CC) proposed by Néron and Norman appropriately focuses on connotations that enable us to distinguish between CC and the all-inclusive notion of Corporate Social Responsibility (CSR), I argue that they fail to properly account for the misguiding potential of the features of political citizenship they propose to develop further in CC theorizing. It is concluded that the notion of CC is better dispensed with altogether, and that a reorientation on concepts that can truly (...) transcend the boundaries of economic and political organization would benefit the field of business and society. (shrink)

We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to κ while the others are equal to λ, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when λ is singular. We also show that $\mathrm{cf}(\kappa_U(\mathscr{L})) < \kappa_A(\mathscr{M})$ is consistent with ZFC.

In lieu of an abstract, here is a brief excerpt of the content:A Bridge From Analysis to Action:Psychodynamic Analyses of Religion and Michael S. Hogue's American ImmanenceAJ Turner (bio)I. IntroductionThe purpose of this essay is to work constructively with Michael S. Hogue's groundbreaking American Immanence: Democracy for an Uncertain World to demonstrate how psychodynamic analyses of religion are essential theoretical allies in the fight for resilient democracy. The "revolution in mind"1 that psychodynamic approaches contribute, especially in their analyses of religion, (...) both complements and complicates socio-political theory as a whole. In the improvisational spirit of "yes-and," the goal here is not to identify and decry the failures and shortcomings of Hogue's theopolitical vision but rather to inspire the recovery of a sibling discourse—a kind of "rebirth of a forgotten alternative"2—that also draws deeply from the American immanental tradition in order to add psychodynamic depth to Hogue's timely and important analysis. Psychodynamic theories of religion shed light on how symbolic identifications, including and especially ultimate concerns, structure personal and collective experience. By engaging religion and theology sympathetically, constructively, and creatively, theorists such as Rollo May, Gordon Allport, Karen Horney, Erich Fromm, and Ernest Becker departed from the skepticism, reductionism, and dismissal that characterized psychoanalytic analyses of religion in the wake of Freud.3 Each of these figures, and especially Becker whose work will be a focus in this essay, are noteworthy interlocutors for extending Hogue's theopolitical theorizing of resilient democracy, particularly in how they drew unique inspiration from the American immanental tradition [End Page 44] in their social analyses. In this respect, they provide a more robust theorization of the psychosocial conditions of the associational ethos needed to connect Hogue's conception of resilient democracy with forms of agonistic organization and democratic activism. Briefly stated, psychodynamic approaches are a helpful bridge for connecting these proposals to strategies of organization, their impediments, and collective action.In this way, both psychodynamic analyses of religion and Hogue's theopolitical innovation insist that no revolutionary political change is possible, and certainly not of the kind or scale needed to counter our wickedly entangled global crises, without a deep engagement with theological imaginaries. They differ, however, in their theoretical aims. Whereas Hogue compellingly argues for the political upshot of a theology deriving from the American immanental tradition, psychodynamic analysts of religion focus on the function of ultimate concerns in individual and collective life. In other words, American Immanence rests on a methodology of analyzing the philosophical and theological assumptions that have contributed to our climate crises and then presenting clear and compelling articulation of an alternative paradigm meant to open up new ways of being. In contrast psychodynamic analyses leverage conceptual clarity of psychic reality for the fundamentally therapeutic aim of transformation. At their best, both approaches share what could be called an etiological orientation to ontological questions in order to provide liberative alternatives through rational understanding and clarification, but the terrain, and thus the problems they hope to mitigate in their analyses are focused differently. Extending the visual metaphor, they are different lenses highlighting different areas of the same landscape. Furthermore, it must be said that neither are sufficient in themselves, but the psychodynamic theorists of religion to be highlighted in this essay share deeply with Hogue's heading in American Immanence.II. A Problematic AssumptionIn emphasizing and attempting to explain4 the role of non-rational processes in the both individual and social processes of perception and organization of experience, psychodynamic theories confound a widely held and problematic assumption that the triumph of rational analysis is the hallmark for building the society to which we should aspire. Political theory in general, [End Page 45] especially as it has taken its cues from a rationalist legacy about the inherently liberating force of Reason, has been weighted toward an assumption that its task of exposing the mystifications of power would suffice in inspiring more "rational" and therefore necessarily equitable social organization. This speaks to the longstanding socio-political interest in "consciousness raising" tactics, which are often meant to dispel "false consciousness." It even comes across in the emphases of Deweyan pragmatists on education. Psychologists of all stripes point out that this approach... (shrink)

We explore the connection between combinatorial principles on uncountable cardinals, like stick and club, on the one hand, and the combinatorics of sets of reals and, in particular, cardinal invariants of the continuum, on the other hand. For example, we prove that additivity of measure implies that Martin’s axiom holds for any Cohen algebra. We construct a model in which club holds, yet the covering number of the null ideal is large. We show that for uncountable cardinals κ≤λ and , (...) if all subsets of λ either contain, or are disjoint from, a member of , then has size at least etc. As an application, we solve the Gross space problem under by showing that there is such a space over any countable field. In two appendices, we solve problems of Fuchino, Shelah and Soukup, and of Kraszewski, respectively. (shrink)

Telling a patient that the outcome of his illness is not good, or even hopeless, requires sensitivity and the ability to communicate with him in the setting of a hospital which is an unnatural environment divorced from family and friends. It is a task which must be taught and learned by doctors and nurses.

We consider several game versions of the cardinal invariants \, \ and \. We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually shows that their game counterparts are small. On the other hand we show that \ and \ are both relatively consistent with ZFC, where \ and \ are the principal game versions of \ and \, respectively. The corresponding question for \ remains open.

We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to $\kappa$ while the others are equal to $\lambda$, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when $\lambda$ is singular. We also show that $\mathrm{cf}) < \kappa_A$ is consistent with ZFC.