We study the Katětov order on Borel ideals. We prove two structural theorems, one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals.

We study the Mathias–Prikry and Laver–Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martinʼs number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias–Prikry forcing does not add a dominating real.

We study an extensive connection between quotient forcings of Borel subsets of Polish spaces modulo a σ-ideal and quotient forcings of subsets of countable sets modulo an ideal.

We investigate the pair-splitting number $\germ{s}_{pair}$ which is a variation of splitting number, pair-reaping number $\germ{r}_{pair}$ which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of F σ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Katětov-minimal among ideals not satisfying Fatou's lemma.

An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size.

We study the possible values of the cofinality invariant for various Borel ideals on the natural numbers. We introduce the notions of a fragmented and gradually fragmented ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.

The notion of strong measure zero is studied in the context of Polish groups and general separable metric spaces. An extension of a theorem of Galvin, Mycielski and Solovay is given, whereas the theorem is shown to fail for the Baer–Specker group Zω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{Z}^{\omega}}}$$\end{document}. The uniformity number of the ideal of strong measure zero subsets of a separable metric space is examined, providing solutions to several problems of Miller and Steprāns :52–59, 2006).

We investigate the following weak Ramsey property of a cardinal κ: If χ is coloring of nodes of the tree κ <ω by countably many colors, call a tree ${T \subseteq \kappa^{ < \omega}}$ χ-homogeneous if the number of colors on each level of T is finite. Write ${\kappa \rightsquigarrow (\lambda)^{ < \omega}_{\omega}}$ to denote that for any such coloring there is a χ-homogeneous λ-branching tree of height ω. We prove, e.g., that if ${\kappa < \mathfrak{p}}$ or ${\kappa > \mathfrak{d}}$ (...) is regular, then ${{\kappa \rightsquigarrow (\kappa)^{ < \omega}_{\omega}}}$ and that ${\mathfrak{b}}$ ${(\mathfrak{b})^{ < \omega}_{\omega}}$ and ${\mathfrak{d}}$ ${(\mathfrak{d})^{ < \omega}_{\omega}}$ . The arrow is applied to prove a generalization of a theorem of Hurewicz: A Čech-analytic space is σ-locally compact iff it does not contain a closed homeomorphic copy of irrationals. (shrink)

In this paper we show that it is consistent with ZFC that the cardinality of every maximal cofinitary group of Sym(ω) is strictly greater than the cardinal numbers o and a.

A metric space (X, d) is monotone if there is a linear order < on X and a constant c such that d(x, y) ≤ c d(x, z) for all x < y < z in X. We investigate cardinal invariants of the σ-ideal Mon generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are (...) also investigated. In particular, we show that non(Mon) ≥ ������ σ-linked , but non(Mon) < ������ σ-centered is consistent. Also cov(Mon) < c and cof(������) < cov(Mon) are consistent. (shrink)

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].

A question dating to Mardešić and Prasolov’s 1988 work [S. Mardešić and A. V. Prasolov, Strong homology is not additive, Trans. Amer. Math. Soc. 307(2) (1988) 725–744], and motivating a considerable amount of set theoretic work in the years since, is that of whether it is consistent with the ZFC axioms for the higher derived limits [Formula: see text] [Formula: see text] of a certain inverse system [Formula: see text] indexed by [Formula: see text] to simultaneously vanish. An equivalent formulation (...) of this question is that of whether it is consistent for all [Formula: see text]-coherent families of functions indexed by [Formula: see text] to be trivial. In this paper, we prove that, in any forcing extension given by adjoining [Formula: see text]-many Cohen reals, [Formula: see text] vanishes for all [Formula: see text]. Our proof involves a detailed combinatorial analysis of the forcing extension and repeated applications of higher-dimensional [Formula: see text]-system lemmas. This work removes all large cardinal hypotheses from the main result of [J. Bergfalk and C. Lambie-Hanson, Simultaneously vanishing higher derived limits, Forum Math. Pi 9 (2021) e4] and substantially reduces the least value of the continuum known to be compatible with the simultaneous vanishing of [Formula: see text] for all [Formula: see text]. (shrink)

We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we (...) show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets. (shrink)

Let ${\cal I}$ be an ideal on ω. By cov${}_{}^{\rm{*}}$ we denote the least size of a family ${\cal B} \subseteq {\cal I}$ such that for every infinite $X \in {\cal I}$ there is $B \in {\cal B}$ for which $B\mathop \cap \nolimits X$ is infinite. We say that an AD family ${\cal A} \subseteq {\cal I}$ is a MAD family restricted to${\cal I}$ if for every infinite $X \in {\cal I}$ there is $A \in {\cal A}$ such that $|X\mathop (...) \cap \nolimits A| = \omega$. Let a$\left$ be the least size of an infinite MAD family restricted to ${\cal I}$. We prove that If $max${a,cov${}_{}^{\rm{*}}\}$ then a$\left = {\omega _1}$, and consequently, if ${\cal I}$ is tall and $\le {\omega _2}$ then a$\left = max$ {a,cov${}_{}^{\rm{*}}\}$. We use these results to prove that if c$\le {\omega _2}$ then o$= \overline o$ and that as$= max${a,non$\}$. We also analyze the problem whether it is consistent with the negation of CH that every AD family of size ω1 can be extended to a MAD family of size ω1. (shrink)

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.

If $\mathcal{F}$ is a filter on $\omega$, we say that $\mathcal{F}$ is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is $F_{\sigma}$, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a $\mathsf{MAD}$ family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the “classical” (...) models of $\mathsf{ZFC}$ there are $\mathsf{MAD}$ families whose Mathias forcing does not add a dominating real. We also study ideals generated by branches, and we uncover a close relation between Canjar ideals and the selection principle $S_{\mathrm{fin}}$ on subsets of the Cantor space. (shrink)

In this paper I outline the PAIR account of joint attention as a perceptual-practical, affectively charged intentional relation. I argue that to explain joint attention we need to leave the received understanding of propositions and propositional attitudes and the picture of content connected to it behind and embrace the notions of subject mode and position mode content. I also explore the relation between joint attention and communication.

The American Journal of Bioethics, Volume 12, Issue 7, Page 27-30, July 2012.

We study the intersection number of families of tall ideals. We show that the intersection number of the class of analytic P-ideals is equal to the bounding number ${\mathfrak{b}}$ , the intersection number of the class of all meager ideals is equal to ${\mathfrak{h}}$ and the intersection number of the class of all F σ ideals is between ${\mathfrak{h}}$ and ${\mathfrak{b}}$ , consistently different from both.

It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In this note (...) we construct, in ZFC, ${2^{\mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces. (shrink)

In this article we, given a free ultrafilter p on ω, consider the following classes of ultrafilters:(1) T(p) - the set of ultrafilters Rudin-Keisler equivalent to p,(2) S(p)={q ∈ ω*:∃ f ∈ ω ω , strictly increasing, such that q=f β (p)},(3) I(p) - the set of strong Rudin-Blass predecessors of p,(4) R(p) - the set of ultrafilters equivalent to p in the strong Rudin-Blass order,(5) P RB (p) - the set of Rudin-Blass predecessors of p, and(6) P RK (p) (...) - the set of Rudin-Keisler predecessors of p,and analyze relationships between them. We introduce the semi-P-points as those ultrafilters p ∈ ω* for which P RB (p)=P RK (p), and investigate their relations with P-points, weak-P-points and Q-points. In particular, we prove that for every semi-P-point p its α-th left power α p is a semi-P-point, and we prove that non-semi-P-points exist in ZFC. Further, we define an order ⊴ in T(p) by r⊴q if and only if r ∈ S(q). We prove that (S(p),⊴) is always downwards directed, (R(p),⊴) is always downwards and upwards directed, and (T(p),⊴) is linear if and only if p is selective.We also characterize rapid ultrafilters as those ultrafilters p ∈ ω* for which R(p)∖S(p) is a dense subset of ω*.A space X is M-pseudocompact (for ) if for every sequence (U n ) n < ω of disjoint open subsets of X, there are q ∈ M and x ∈ X such that x=q-lim (U n ); that is, for every neighborhood V of x. The P RK (p)-pseudocompact spaces were studied in [ST].In this article we analyze M-pseudocompactness when M is one of the classes S(p), R(p), T(p), I(p), P RB (p) and P RK (p). We prove that every Frolik space is S(p)-pseudocompact for every p ∈ ω*, and determine when a subspace with is M-pseudocompact. (shrink)

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

The guiding inspiration of this book is the attraction and distance that mark the relation between anthropology and philosophy. This theme is explored through encounters between individual anthropologists and particular regions of philosophy. Several of the most basic concepts of the discipline—including notions of ethics, politics, temporality, self and other, and the nature of human life—are products of a dialogue, both implicit and explicit, between anthropology and philosophy. These philosophical undercurrents in anthropology also speak to the question of what it (...) is to experience our being in a world marked by radical difference and otherness. In The Ground Between, twelve leading anthropologists offer intimate reflections on the influence of particular philosophers on their way of seeing the world, and on what ethnography has taught them about philosophy. Ethnographies of the mundane and the everyday raise fundamental issues that the contributors grapple with in both their lives and their thinking. With directness and honesty, they relate particular philosophers to matters such as how to respond to the suffering of the other, how concepts arise in the give and take of everyday life, and how to be attuned to the world through the senses. Their essays challenge the idea that philosophy is solely the province of professional philosophers, and suggest that certain modalities of being in the world might be construed as ways of doing philosophy. Contributors. João Biehl, Steven C. Caton, Vincent Crapanzano, Veena Das, Didier Fassin, Michael M. J. Fischer, Ghassan Hage, Clara Han, Michael Jackson, Arthur Kleinman, Michael Puett, Bhrigupati Singh. (shrink)

Eldred offers a remedy to the consequences of ancient Greek misconceptions of time that are also entrenched in today’s mathematized physics. Here time is spatialized as the one-dimensionally linear ‘arrow of time’ for the sake of predicting and controlling movement. But such spatialized time distorts the phenomenon of time itself. An alternative, hermeneutic-phenomenological path begins with a pre-spatial concept of time that is genuinely three-dimensional. This paves the way for recasting who we are as humans in belonging, first of all, (...) to the free openness of 3D-temporality. This belonging enables temporally 3D-vision of the psyche that empowers us to see movement at all and reconcile its inherent contradictoriness. We are then also able to conceive ourselves no longer merely as internally cogitating, self-conscious subjects, but as engaged existentially in temporally 3D-interplay, mutually estimating and esteeming who we are. This unpredictable interplay is constrained, however, by being played out in the sociating medium of thingified value, the accumulative movement of thingified value having gained the upper hand in dictating our life-movements as well as our interplay with the earth. (shrink)

Der private, sehr gefahrdete Bucherbestand Friedrich Nietzsches gilt als ein besonders interessantes Beispiel einer Schriftstellerbibliothek des 19. Jahrhunderts.

Virtually all philosophers agree that for a belief to be epistemically justified, it must satisfy certain conditions. Perhaps it must be supported by evidence. Or perhaps it must be reliably formed. Or perhaps there are some other "good-making" features it must have. But does a belief's justification also require some sort of awareness of its good-making features? The answer to this question has been hotly contested in contemporary epistemology, creating a deep divide among its practitioners. Internalists, who tend to focus (...) on scientific or theoretical beliefs as the ideal, insist that such awareness is required for justification. Externalists, who think children's ordinary beliefs in obvious facts are paradigm cases of justified belief, say it isn't required. Michael Bergmann's book offers a decisive refutation of internalism and a sustained defense of externalism. (shrink)

This is a revision of game theory which takes account of agents' own descriptions of their situations, and which allows people to reason as members of groups.

In this book, Michael Arbib, a researcher in artificial intelligence and brain theory, joins forces with Mary Hesse, a philosopher of science, to present an integrated account of how humans 'construct' reality through interaction with the social and physical world around them. The book is a major expansion of the Gifford Lectures delivered by the authors at the University of Edinburgh in the autumn of 1983. The authors reconcile a theory of the individual's construction of reality as a network (...) of schemas 'in the head' with an account of the social construction of language, science, ideology and religion to provide an integrated schema-theoretic view of human knowledge. The authors still find scope for lively debate, particularly in their discussion of free will and of the reality of God. The book integrates an accessible exposition of background information with a cumulative marshalling of evidence to address fundamental questions concerning human action in the world and the nature of ultimate reality. (shrink)

A liberal society seeks not to impose a single way of life, but to leave its citizens as free as possible to choose their own values and ends. It therefore must govern by principles of justice that do not presuppose any particular vision of the good life. But can any such principles be found? And if not, what are the consequences for justice as a moral and political ideal? These are the questions Michael Sandel takes up in this penetrating (...) critique of contemporary liberalism. Sandel locates modern liberalism in the tradition of Kant, and focuses on its most influential recent expression in the work of John Rawls. In the most important challenge yet to Rawls' theory of justice, Sandel traces the limits of liberalism to the conception of the person that underlies it, and argues for a deeper understanding of community than liberalism allows. (shrink)

Bishop and Trout here present a unique and provocative new approach to epistemology. Their approach aims to liberate epistemology from the scholastic debates of standard analytic epistemology, and treat it as a branch of the philosophy of science. The approach is novel in its use of cost-benefit analysis to guide people facing real reasoning problems and in its framework for resolving normative disputes in psychology. Based on empirical data, Bishop and Trout show how people can improve their reasoning by relying (...) on Statistical Prediction Rules. They then develop and articulate the positive core of the book. Their view, Strategic Reliabilism, claims that epistemic excellence consists in the efficient allocation of cognitive resources to reliable reasoning strategies, applied to significant problems. The last third of the book develops the implications of this view for standard analytic epistemology; for resolving normative disputes in psychology; and for offering practical, concrete advice on how this theory can improve real people's reasoning. This is a truly distinctive and controversial work that spans many disciplines and will speak to an unusually diverse group, including people in epistemology, philosophy of science, decision theory, cognitive and clinical psychology, and ethics and public policy. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

A major contribution to the social scientific understanding of how people make sense of their lives, Ideological Dilemmas presents an illuminating new approach to the study of everyday thinking. Contradictory strands abound within both ideology and common sense. In contrast to many modern theorists, the authors see these dilemmas of ideology as enabling, rather than inhibiting: thinking about them helps people to think meaningfully about themselves and the world. The dilemmas within ideology and their effects on thinking are explored through (...) the analysis of what people say in specific key situations: education, medical care, race and gender. The authors identify common ideological themes running through the common-sense discourses they analyse. They highlight the tensions between themes of equality and authority, freedom and necessity, individuality and collectivity. Time and again, the contradictions between these ideological themes crop up as respondents argue and puzzle over their social worlds. Written with refreshing clarity, the discussion cuts across the boundary which often separates sociology from social psychology. Sociologists are reminded that the reproduction of ideology involves individual processes of thinking; social psychologists are urged to recognize the ideological nature of thought. (shrink)

John Locke is the greatest English philosopher. _An Essay Concerning Human Understanding_, one of the most influential books in the history of thought, is his greatest work. In this study the historical meaning and philosophical significance of Locke's _Essay_ are investigated more comprehensively than ever before. _Locke_ was originally published in two volumes, _Epistemology_ and _Ontology_. This paperback edition has within its covers the full text of both volumes.

Michael Davis, a leading figure in the study of professional ethics, offers here both a compelling exploration of engineering ethics and a philosophical analysis of engineering as a profession. After putting engineering in historical perspective, Davis turns to the Challenger space shuttle disaster to consider the complex relationship between engineering ideals and contemporary engineering practice. Here, Davis examines how social organization and technical requirements define how engineers should (and presumably do) think. Later chapters test his analysis of engineering judgement (...) and autonomy empirically, engaging a range of social science research including a study of how engineers and managers work together in ten different companies. (shrink)

Science and philosophy study well-being with different but complementary methods. Marry these methods and a new picture emerges: To have well-being is to be "stuck" in a positive cycle of emotions, attitudes, traits and success. This book unites the scientific and philosophical worldviews into a powerful new theory of well-being.

The concept that peope have of themselves as a 'person' is one of the most intimate notions that they hold. Yet the way in which the category of the person is conceived varies over time and space. In this volume, anthropologists, philosophers, and historians examine the notion of the person in different cultures, past and present. Taking as their starting point a lecture on the person as a category of the human mind, given by Marcel Mauss in 1938, the contributors (...) critically assess Mauss's speculation that ntions of the person, rather than being primarily philosophical or psychological, have a complex social and ideological origin. Discussing societies ranging from ancient Greece, India, and China to modern Africa and Papua New Guinea, they provide fascinating descriptions of how these different cultures define the person. But they also raise deeper theoretical issues: What is universally constant and what is culturally variable in people's thinking about the person? How can these variations be explained? Has there been a general progressive development toward the modern Western view of the person? What is distinctive about this? How do one's notions of the person inform one's ability to comprehend alternative formulations? These questions are of compelling interest for a wide range of anthropologists, philosophers, historians, psychologists, sociologists, orientalists, and classicists. The book will appeal to any reader concerned with understanding one of the most fundamental aspects of human existence. (shrink)