The Rudin-Keisler ordering of ultrafilters is extended to complete Boolean algebras and characterised in terms of elementary embeddings of Boolean ultrapowers. The result is applied to show that the Rudin-Keisler poset of some atomless complete Boolean algebras is nontrivial.

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...) of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)

Open peer commentary on the article “Modeling Subjects’ Experience While Modeling the Experimental Design: A Mild-Neurophenomenology-Inspired Approach in the Piloting Phase” by Constanza Baquedano & Catalina Fabar. Upshot: Baquedano and Fabar’s provoking article highlights several difficulties of neurophenomenology, and brings into light the necessity of further clarification of its basic concepts such as human experience, first-person perspective, phenomenological validation, explanation, adequate measurement and so on. Particularly, it becomes more and more clear that the “explanatory gap” cannot be liquidated by means (...) of explanation procedures alone, for the unavoidable variety of modes and forms of human understanding cannot be exhaustively reduced to just any one of these modes. (shrink)

Open peer commentary on the article “Consciousness as Self-Description in Differences” by Diana Gasparyan. Upshot: The aim of my commentary is to support some of Gasparyan’s ideas and to reformulate them in a more constructive way in terms of both formalized hermeneutical procedures and networks and in the light of game-theory approaches.

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments (Pinus sylvestris (...) L.) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, ‘dimension-like’ exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches. (shrink)

We attempt to defend the species-as-individuals hypothesis by examining the logical role played by the binomials (e.g., "Homo sapiens," "Pinus ponderosa") in biological discourse about species. Those who contend that the binomials can be properly understood as functioning in biological theory as singular terms opt for an objectual account of species and view species as individuals. Those who contend that the binomials can in principle be eliminated from biological theory in favor of predicate expressions opt for a predicative account (...) of species and view species as kinds. We contend that biologists' talk about species is talk about species as individuals, and we conclude that the most plausible account of species is an objectual account. (shrink)

This study on the cambium of Pinus sylvestris L. examines the intrusive growth of fusiform cambial initials and its possible contribution to the tangential and radial expansions of the cambial cylinder. The location and extent of intrusive growth of the fusiform initials were determined by microscopic observations and by mathematical modeling. In order to meet the required circumferential expansion of the cambial cylinder, the fusiform initials grow in groups by means of a symplastic rather than intrusive growth, leaving no (...) room for the assumption that intrusive growth of the initials takes place between radial walls and has a direct role in the increase of the cambial circumference. Therefore, it is postulated that the fusiform initials grow intrusively between the tangential walls of the neighboring initials and their immediate derivatives and not between the radial walls of the adjacent initials as per common belief. (shrink)

Open peer commentary on the article “What Can the Global Observer Know?” by Diana Gasparyan. Upshot: My comments are aimed at certain difficulties and ambivalent statements in Gasparyan’s paper that are necessary to clarify before any productive discussion can start. Particularly, the underlying problem of her research should be made more explicit and internal differentiation of various research contexts should be more precise.

The Problem of Perception offers two arguments against direct realism--one concerning illusion, and one concerning hallucination--that no current theory of ...

In this paper I examine Grace A. de Laguna’s theory of universals in its historical context and in relation to contemporary debates in analytic metaphysics. I explain the central features of her theory, arguing that her theory should be classified as a form of immanent realism and as a powers ontology. I then show in what ways her theory affords a theory of modality in terms of potentialities and discuss some of its consequences along the way.

A. H. Louie's More Than Life Itself is an exploratory journey in relational biology, a study of life in terms of the organization of entailment relations in living systems. This book represents a synergy of the mathematical theories of categories, lattices, and modelling, and the result is a synthetic biology that provides a characterization of life. Biology extends physics. Life is not a specialization of mechanism, but an expansive generalization of it. Organisms and machines share some common features, but organisms (...) are not machines. Life is defined by a relational closure that places it beyond the reach of physicochemical and mechanistic dogma, outside the reductionistic universe, and into the realm of impredicativity. Function dictates structure. Complexity brings forth living beings. (shrink)

This book argues for the use of nonideal theory in social ontology. The central claim is that a paradigm shift is underway in contemporary social ontology, from ideal to nonideal, and that this shift should be fully followed through. To develop and defend this central claim, the first step is to show that the key questions and central dividing lines within contemporary social ontology can be fruitfully reconstructed as a clash between two worlds, referred to as ideal and nonideal social (...) ontology. Ideal social ontology is characterized by consensus and cooperation, while nonideal social ontology is characterized by conflict and contestation. The second step is to show that, when taken together, objections to the standard model of ideal social ontology (the dominant version of ideal social ontology) imply that this model needs to be given up in favor of nonideal social ontology. In other words, we should look to nonideal rather than ideal social ontology for core concepts. The third step is to offer a positive account, called the power view, of nonideal social ontology. This account places the concept of social power at the core of a general theory of the social world and replaces the flat and narrow conception of power in ideal social ontology with a richer and more extensive conception. In addition, it rectifies a shortcoming in nonideal social ontology by attending to class, which has been notably and oddly overlooked in the literature. (shrink)

This companion is a cutting-edge primer to critical forms of the posthumanities and the feminist posthumanities, aimed at students and researchers who want to catch up with the recent theoretical developments in various fields in the humanities, such as new media studies, gender studies, cultural studies, science and technology studies, human animal studies, postcolonial critique, philosophy and environmental humanities. It contains a collection of nineteen new and original short chapters introducing influential concepts, ideas and approaches that have shaped and developed (...) new materialism, inhuman theory, critical posthumanism, feminist materialism, and posthuman philosophy. A resource for students and teachers, this comprehensive volume brings together established international scholars and emerging theorists, for timely and astute definitions of a moving target – posthuman humanities and feminist posthumanities. (shrink)

I. Ókor -- II. A középkor és a reneszánsz -- III. Az újkor.

La admirable riqueza cultural y artística del Renacimiento esconde una desoladora miseria y aquella "edad de la abundancia" contrasta con una inmensa pobreza. Lejos de ser una broma o una pesadilla, la celebrada Utopía de Tomás Moro fue antes que nada un desafío insoslayable, pues proponía que ninguna sociedad merece tal nombre si tolera la miseria de un solo pobre. Rico y pobre explora la cuestión en ese libro de 1516 y en otros del escritor londinense para concluir con un (...) esbozo de su vida a la luz de la pobreza como virtud indispensable y libertadora. He aquí un hombre afortunado que no fue indiferente ante el infortunio de tantos y que vio en la humanitas la virtud por excelencia que lleva a una constante atención y cuidado del prójimo. Inspirado por un cambio de actitud en su época, así como por su fe cristiana y la mejor tradición estoica, mostró una robusta preocupación sobre el tema subrayando el valor social que debe tener toda riqueza, tanto a nivel estatal como individual, destacando la grave obligación cívica de los ricos y la necesidad que tienen todos, ricos y pobres, de empeñarse en la práctica de cierto desprendimiento y generosidad si no quieren mermar su propia humanidad y fallecer en su avaricia. La percepción de la miseria había cambiado de tal manera que su remedio ya no podía estar en una u otra limosna en plazas e iglesias, sino en la acción bien pensada y perentoria de todo gobierno que se tenga por justo. Sir Tomás Moro, privilegiado desde la cuna y seguro en su trabajo profesional, vio la pobreza de tantos como un desastre social, pero uno que, al mismo tiempo, debería llevar a todo ser humano a ver en el desprendimiento y generosidad una excelencia o virtud que alumbra la "otra" libertad, y tan íntima y valiosa que en su caso brilló aun en la prisión y ante el horror de una muerte injusta y atroz." -- Page 4 of cover. (shrink)

Articles on the life and works of Āraja Ālī Mātubbara, 1901-1986, Muslim philosopher and author from Bangladesh.

Commentary on the Brahmasūtra of Bādarāyaṇa, aphoristic work on Vedanta philosophy.