In lieu of an abstract, here is a brief excerpt of the content:Bonaventure's Reductio of the Nine Choirs of Angels:How Bonaventure Compressed Two Monumental Traditions into Nine Words and Nine Short PhrasesRandall B. Smith"There is probably no better illustration in medieval thought of how the genius of the symbolic imagination also involves deep speculative insight." So wrote Bernard McGinn of Bonaventure's Itinerarium mentis in deum in The Flowering of Mysticism: Men and Woman in the New Mysticism, 1200–1350.1 (...) There is no question that the Itinerarium is a book suffused with symbolic imagery; so much so, in fact, that it can sometimes seem to lapse into a confusing jumble.Certainly there are many sections of the Itinerarium that have baffled readers over the years, often because Bonaventure's use of imagery is so unique and creative and the truths he is attempting to enunciate are so far beyond our normal ways of thinking about God. But there is a short passage in chapter 4 of the Itinerarium that seems to defy interpretation precisely because of what one might describe as an almost austere terseness and brevity. The point Bonaventure wishes to make is one he communicates in little more than a list of nine words and nine short, parallel phrases.The passage I have in mind is this one in Itinerarium 4.4.When these things have been accomplished, and our spirit has been brought into conformity with the heavenly Jerusalem, it is ordered [End Page 583] hierarchically so that it can ascend upward. For no one enters into that city unless that city has first descended into the person's heart by means of grace, as John sees in his Apocalypse. It descends into the heart when our spirit has been made hierarchical by the reformation of the image, by means of the theological virtues, the enjoyment of the spiritual senses, and the ecstasy of rapture; for it has been purged, illumined and brought to perfection.In this way our spirit is adorned with nine orderly levels when within it the following are found in an appropriate order: announcing, dictating, leading, ordering, strengthening, commanding, receiving, revealing, and anointing. These correspond to the nine choirs of angels. The first three of the foregoing levels in the human mind relate to nature; the next three relate to work; and the final three relate to grace. When it has attained these, the soul, by entering into itself, enters into the heavenly Jerusalem where, as it considers the choirs of angels, it sees in them the God who dwells in them and who works in all their operations.Therefore, Bernard says to Pope Eugene that "God loves in the Seraphim as charity; knows in the Cherubim as truth; sits in the Thrones as justice; reigns in the Dominations as majesty; rules in the Principalities as a guiding principle; protects in the Powers as salvation; is at work in the Virtues as strength; reveals in the Archangels as light; assists in the Angels as kindness." From all this, God is seen as all in all when we contemplate God in our minds where God dwells through the gifts of the most generous charity.2Notice in the passage I have quoted above that Bonaventure says our spirit must be "brought into conformity with the heavenly Jerusalem," and that this requires it be "ordered hierarchically so that it can ascend upward." This serves as a transition into a rather odd pair of lists—one with nine words and the other with nine short, parallel phrases—that Bonaventure associates with the nine angelic choirs. These two lists of the nine choirs of angels do not, however, correspond exactly with one [End Page 584] another, for reasons I will explain below. And although these two lists of the nine ranks of angels in the angelic hierarchy take up just a few lines in Bonaventure's text, there is a lot of background information we will need to fill in to provide the necessary context to appreciate them. Indeed, as we will see, in this short passage, Bonaventure was able using the methods of the thirteenth-century sermo modernus style to reduce two monumental commentary traditions regarding the nine choirs of angels—one that... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Susanne Langer in Focus: The Symbolic MindMary J. ReichlingRobert E. Innis, Susanne Langer in Focus: The Symbolic Mind (Indiana University Press: Indianapolis, 2009)The very first sentence of this book establishes the author's goal: "to bring as clearly as possible the total range of Susanne Langer's work 'into focus'" (p. xi). Such an aim strains credulity when one is familiar with the depth, breadth, and complexity of Langer's philosophy (...) as it encompasses her complete works. Yet, Innis manages to trace the development of Langer's thought from its roots in her earliest work, The Practice of Philosophy, through the intervening books, and concluding with her theory of mind and the three volumes of Mind: An Essay on Human Feeling. Susanne Langer in Focus is the most comprehensive analysis of the progression of Langer's thought I have found to date. It is a project of Herculean proportion and one which Innis accomplishes quite well in a lucid and scholarly, though sometimes pedantic, manner despite some matters that I wish to pursue more fully.However it is important to note at the outset that Innis sharply limits his use of secondary sources and prefers to restrict involvement with "scholarly quarrels" thus choosing not to engage with Langer's detractors (p. xi). This was a disappointment for me because I share Innis's advocacy with respect to Langer's aesthetic theory and would appreciate a voice as knowledgeable and well grounded [End Page 213] as his taking on some of these arguments. Nevertheless, Langer has long been popular among musicians and music educators who will find here a sensitive and penetrating presentation of Langer's aesthetic theory and an analysis of music specifically as a paradigm for that theory.The text is divided into nine chapters preceded by an interesting biographical sketch of Langer. It appears to me that these chapters group nicely into three sections, my division, not Innis's. The first includes chapters one and two concerned with the origins of Langer's philosophy and symbol theory as found in The Practice of Philosophy, Introduction to Symbolic Logic, and to some extent, Philosophy in a New Key. The second embraces chapters three, four, and five giving primary consideration to her non-discursive or presentational symbolism, symbolic transformation, ritual, myth, and art as found in Philosophy in a New Key and Feeling and Form. The third section, chapter six, seven, and eight, is devoted to Langer's trilogy, the three volumes of Mind. A short ninth chapter concludes the book with Innes's perspective on the dimensions and position of Langer's philosophical undertaking in the broader context of philosophy in general.That said, I now wish to offer my take on some of the fruits of Innes's harvest examining each of the orchards (sections) in turn. At the outset, Innis stresses Langer's view of the position and purpose of philosophy stating that it embraces all the rational sciences in a systematic study of meaning. In fact for Langer, the logical analysis is to philosophy what observation is to science, a first step. This relation, as a kind of dialectical tension between philosophy and science, especially with respect to method, is one of Langer's major contributions as Innis points out much later in his concluding chapter. What I find quite helpful, though, is Innis's explanation of Langer's concept of a type of understanding that is non-discursive. This provides an epistemological basis for the nature of myth and art, so critical, in my opinion, to grasping Langer's theory of music as a symbol of feeling. (But I am ahead of Innis.)Innis shows that Langer's theory is grounded empirically in the psychology of perception and imagination because these allow the perceiver to abstract meaning from the form that embodies it. He continues illuminating and clarifying several terms such as abstraction, projection, semblance, virtual image, imagination, illusion, and more. His discussion of metaphor, primarily as it relates to Langer's theory of presentational symbolism, is extremely well done. His emphasis on metaphor as more than a mode of inquiry is particularly significant. Few, if any, writers about Langer... (shrink)

We consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.

In this paper, we give a thorough account of Brianchon and Poncelet’s joint memoir on equilateral hyperbolas subject to four given conditions, focusing on the most significant theorems expounded therein, and the determination of the “nine-point circle”. We also discuss about the origin of this very rare example of collaborative work for the time, and the general challenge of finding the nature of the loci described by the centres of the conic sections required to pass through m points and (...) to be tangent to n straight lines given in position, m + n = 4, which was posed at the end of their work. In the case m = 4, i.e. when the conic sections have to pass through the vertices of a quadrilateral, the locus of centres is another conic section passing through the intersection points of the opposite sides and the two diagonals of the quadrilateral, respectively, and, as Gergonne showed analytically shortly after, through other significant points connected with the quadrilateral; this curve was later given the name of the “nine-point conic”, being a natural generalization of the above mentioned circle. (shrink)

We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse and the theory of $\langle\mathbb{N}, +, R\rangle$ is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure $\langle\mathbb{Q},+, R\rangle$.

This paper investigates how specific notions of gender and ethnicity are integrated into diversity discourses presented on 241 top European company websites. Large European companies increasingly disclose equality and diversity policies in statements on websites. Such statements may be used to promote an ethical image of the company in terms of how well it manages diversity and guards against discrimination. In this paper, we argue that diversity statement discourses are important as they play a key part in socially constructing how (...) diversity should be regarded in the company by minority and majority groups, as well as indicating corporate values to external stakeholders. Sometimes, the notions of gender or ethnic diversity are positioned as a liability in need of protection, whilst in others, as a source of competitive advantage. We find evidence of use of discursive tools such as problematisation, rationalisation, fixation, reframing and naturalisation of the notions of gender and ethnic diversity, reinforced by use of symbols, such as statistics, photographs, membership badges and awards. Few statements directly associate gender and ethnic diversity with enhanced corporate performance. We found that diversity statements sometimes appear to reinforce existing business stereotypes of women and people from ethnic minorities, and in a few discourses, create new ones, particularly evident in photographs illustrating the diversity web pages. (shrink)

We construct a fibered dimension function in some topological differential fields.

We consider valued fields with a distinguished isometry or contractive derivation as valued modules over the Ore ring of difference operators. Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.

We consider separably closed fields of characteristic $p > 0$ and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the $p$-component functions.

The following strong form of density of definable types is introduced for theoriesTadmitting a fibered dimension functiond: given a modelMofTand a definable setX⊆Mn, there is a definable typepinX, definable over a code forXand of the samed-dimension asX. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

Located in Kleinbasel close to the Rhine, the Kaskadenkondensator is a place of mediation and experimental, research-and process-based art production with a focus on performance and performative expression. The gallery, founded in 1994, and located on the third floor of the former Sudhaus Warteck Brewery (hence cascade condenser), seeks to develop interactions between artists, theorists and audiences. Eight, maybe, nine or ten 40 litre bags of potting compost lie strewn about the floor of a high-ceilinged white washed hall. Dumped, (...) split open, the soil mixed with iridescent specks of green, blue and red glitter. On the walls hang large black and white photographic images—negative and positive prints barely clean, hardly sharp, scavenged from the world and presented half processed. On a third wall, hangs a framed golden and charcoal surface. Finally, a huge stain of black dye runs down a wall that descends into a sunken quarter of the Kaskadenkondensator gallery space. The results of a collaboration between Oliver Minder and Walter Derungs reflect on themes addressed in the recent Aesthetics in the 21st Century conference held by the department of English, University of Basel. In particular, the joint show questions how an aesthetic experience may be other than a human-world interaction, hinting at the withdrawal and veiling that objects perform, while demanding that different works engage with each other and play out this game under the non-supervisory eyes of a human audience. Things here are becoming—sometimes it’s a movement towards a more complete ontic whole in a projection of finality, other times it’s a dispersal, an atrophy to rather disarrayed entities. Yet, in the moment and place in which the objects are, we take them as here and now. Let’s get to the material of the stuff that Minder and Derungs have assembled. Oliver Minder employs organic materials—potting earth, cuttlefish ink secretion, rice, and insects; yet his works hardly seem natural in the sense of a harmonic relation between material and the form they are constrained into, the objects they are compelled to occupy. For the substrates on, through, or within which these natural materials are mediated are harshly inorganic substances—Plexiglas, safety glass, acrylic resin, boat varnish, spray paint. Minder, thus, generates a conflict within the materiality of his work between two polar opposites—from the human perspective—in the contiguity of materials engaging with each other in a thrown together formation that nonetheless appears to keep the materials and the objects they make in happy accidental relation to each other. Let me expand a little: on the one hand, the things Minder makes query our belief in substance as belonging in a particular domain, an environment suited to precisely that stuff. We are focused on thinking categorically where things belong, both in terms of natural place and natural relations they might extend to each other. Hence, we are driven to think of environment and order. On the other hand, while extracting things from their conventional place and arranging them within awkward constellations that we as observers feel isn’t quite right, Minder manages to persuade the viewer that the materials are nonetheless “doing alright.” So, simultaneous to our awareness of the appropriateness of the world according to our global notions of accord and uniformity, we are forced to accept the local discrepancies of disassociation, inappropriateness and misplacement. The tension between these two vectors generates a vacillation that intensifies Minder’s work. In the Kaskadenkondensator works, then, it is vital to first consider the material of Minder’s works: potting compost—what is it doing here in the first place?—seems to enjoy being “polluted” by sparkly glitter. Glitter has a long history, used in cosmetics by the Egyptians, and in cave paintings, too, earlier made of beetle shells and mica, nowadays glitter is made of plastic cut to minute sizes down to 50 microns. So what’s the point here? Well shiny bits of dust-like material are actually generated from ultra-thin plastic sheets and are normally cut into shapes that fit contiguously on a two-dimensional surface: squares, triangles, hexagons etc. What then appears to be totally random, chaotic decoration, is actually an array of extremely regular identifiable objects. 1 Of course scale has a role to play here. The minuteness of the dimensions means the regularity is beyond our recognition—all we see are the twinkling surfaces of the multi-coloured grains of plastic. In contrast, potting compost, which appears to be unary in its dull unresponsive lumpen disposition, is in fact an amalgam of a variety of organic and inorganic materials: peat, bark, mushroom compost, and sand and perlite, and should perhaps be more proactively exciting to the viewer because of this complexity. Yes; we can (if we care to) identify different textures, different sizes in the mixture of the medium, but I claim that we tend to treat this organic/inorganic assemblage as just a simple substance. Further and crucially important to our consideration here is that the medium is partially contained, but also partially spilling from the split plastic bags in which it is sold in garden centres. That the compost spills out gives it a movement suggesting life; that the bags are cast here and there in a random fashion by Oliver Minder, lying like discarded carcasses, hacked torsos, dismembered bodies, suggests a horrific murder scene, a Tatort. 2 The glitter flourishes in the medium, lies happy and decorative; that is simply what it does, how it is—always already broken, made-for-scattering, designed to be incomplete; the taken-to-be-natural compost, in contrast, cannot rest content but is forced to speak to us metaphorically in its abject overflowing of violence and rupture. While Oliver Minder’s elements in the installation direct our attention to material, Walter Derungs’ works raise questions around seeing and making in photography. There is a simultaneous flicker between the materials and their use in the production of a sense making representation, on the one hand, and on the other the very notion of what is worthy of picturing, framing, representing on the other. Derungs' images are of non-places. Ranging from archaic decaying monster buildings, buildings that have gone far beyond the ravages of a time that we can safely associate with the genteel preservation of a Bernd and Hill Belcher post-industrial decline, to the background “noise” of an urban world that is falling apart, and to which we most of the time seem to pay little attention, and habitually just pass by. In this respect, their non-ness differs somewhat from the conventional association of the term with Marc Augé 3 , where emphasis is on the specifics (if we do care to examine them for their non-placedness) of the spatial or place containment in which movement between multimodal coordinates occurs in supermodern late capitalist post-urban spaces. In other words, we might be in an Augéian non-place and (not) experience—be impervious to—that environment, or we might in Derungs’ manner look out from such a position at the “scenery” around us. I claim scenery, as this is what Derungs seems to do with his partial photography—construct a very purposefully articulated, symmetric, flat world of image. Mostly depopulated, his images construct a space in which the direction of time is uncertain: are these partial structures falling apart, or perhaps terminated in a never-to-be-completed state, or are they a few steps from final completion? Temporal and spatial dimensions figure large in Derungs’ image-making: his world, and perhaps this is in fact the only way for it to be registered photographically, is already image before it is photographed. A key combination of images in this show is a matrix of six black and white negative prints measuring 300 x 215 cm that form the image of a semi-derelict (or is it yet incomplete) church, and adjacent on a perpendicular wall, a single black and white positive print 150 x 250 cm of two bricked-up windows of a late-Victorian industrial building. What are we led to believe that we see here? In the negative print, the conditions of perception 4 are sufficiently reproduced for us to recognise the structure of the building, to distinguish ground and form, to relate some partial elements of narrative, and to recognize symbols such as the alter cross and figure of Christ, a looming crane, a traffic cone, and banks of tiered seating. We piece the image together both from the individual forms which we recognize despite the tonal reversal, and we piece the six prints together as a whole, the matrix of lines between them emphasizing our purview onto the world. While we recognise the forms at work in the image and might possibly relate the negative reversals to other figurations such as Vera Lutter’s camera obscura exposures, we cannot but avoid seeing the partialness of the image in the sponge marks of the developer that was spread by hand across the prints. 5 Derungs’ thus intervenes with our usual conception of photography as the mimetic realist vehicle sine qua non , by exposing the viewer to tonal reversal and incomplete or over developed areas of the print. We thus confront both the idiom of such image making and its raw (chemical) materiality at once in the simultaneity of the recognition of what the image pictures and the recognition that it is in the act of picturing. The church image, taken from the series “BW Negativs 2011,” thus orients us towards how we see things in the world via photographs. The single image of the bricked-up wall presents us with a completely different visuality that relates to a faciality 6 which we cannot easily escape from. We look, or rather try to look with no success, through the face of the windows, through the classic Albertian screen 7 which has already been given to us in the church matrix beside. Yet although we should be able to make more of these concealed windows because they are a positive print, because they are complete, because they approach us on a more realistic scale, reproduced at life size, we cannot. The objects pictured here withdraw from us; furthermore, they merely mock our blindness at not seeing how we look. Blocked up with quite a hint of paned glass behind, one window is blanked out with a white blind, the other simply blankly dark. The apertures look like eyes with teeth in them, or a Dogon mask, or even Man Ray’s Noire et Blanche (1926) if we want to get really perverse. The height of elegant modernist chauvinist beauty thrown against the vacuity of post-industrial decline. Derungs thus catapults us consciously into a world enfolded with and through images, but in such a way that the images themselves become objects that stand resistant to us, impervious to our gaze, indifferent. We—and indeed they—do not attempt to reach out to a real that is beyond, rather the images play in a world that is just theirs, and we can only enter that world if we too submit to their regime: tonal reversal, segmented, partial, inadequate, still, wrenched out of time. In contemplation, in the flood of the image “falling” off the wall, we too become image-object. Perhaps enough has now been said about the works, yet enough can never really be said, we know the image will always exceed the word—let’s accelerate the critique: Derungs’ work continues in a second space partially partitioned from this first room. Opposing three more “BW Negativs” which figure yet more quotidian aspects of the world is Minder’s gold spray paint and cuttlefish secretion mix: things that just shouldn’t work together do in the dialogue between stuff that Derungs and Minder have constructed. Minder makes things; Derungs makes images; together they make objects which inhabit their own world which we can approach and sensually engage with and come to grips with only on those objects’ own terms. This is best summarised by a final work made by Oliver Minder which on a third wall faces these two semi-partitioned spaces. A deep black stain about 100 X 200 cm with streak marks running down a further 2 metres hovers positioned to observe the whole work, and also to be part of this installation, too. This liminal flat suzerain lies in/out of the whole work. The stain of cuttlefish secretion resonates with Derungs’ sponge strokes on the church image; it mirrors the iris of an all-seeing eye; it combines material in situ with the situation itself. Where Minder’s other works have material and medium or substrate upon which the material is exercised, this single black hole is image which sucks everything up into itself. It draws the viewer, who must otherwise look away attentively at the floor work, and imagine horror, or smile at the ironic play of glitter. Look away at the image constructions that suggest how it is we too look to our world. See the play of thing and image in a third area. Or, finally return to the base of the pyramid that triangulates, to realise the stuff-image that unlocks it all for us. Black on white, organic on inorganic, material to substrate, that which in the falling out of one on the other, in its running down the wall simply gives form to both content and expression in one direction, and content and expression to form in another. NOTES In fact, glitter is used as associative forensic evidence: the 20,000 or so varieties are all uniquely identifiable. Joel Sternfeld, Tatorte: Bilder gegen das Vergessen (München: Schirmer/Mosel, 1996). Marc Augé, Non­places: Introduction to an Anthropology of Supermodernity trans. John Howe (London: Verso, 2006). An echo of the uneven paint strokes of light­sensitive chemicals in the paper preparations made by Henry Talbot some 170 years ago in the first sun drawings that also often pictured architectural forms. It was Talbot’s surprising discovery that where a weaker chemical solution was more thinly spread, greater light sensitivity was actualized, yet this virtual image had then to be chemically developed in a second step. Thus, Derungs unevenly finished spongings suggestively trace back to this originary technology (although his sweeps are the stains of uneven development and not those of the initial preparation of light–sensitive material). Umberto Eco, “Critique of the Image” in “Articulations of Cinematic Code” Cinematics 1, 1970. Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia trans. Brian Massumi (Minneapolis: University of Minnesota Press, 2007). Geoffrey Batchen, Burning With Desire: the Conception of Photography (Cambridge, Mass: MIT Press, 1999). (shrink)

Concepts such as “symbolism” and “symbolic cognition” often remain unspecified in discussions the symbolic capacities of earlier hominins. In this paper, I use conceptual tools from phenomenology to reflect on the origins of early symbolic cognition. In particular, I discuss the possible early use of pointing gestures around the time of the earliest known stone tool industries. I argue that unlike more basic social acts such as expression, gaze following, and attention-getters, which are used by extant non-human great apes, communicative (...) pointing involves key elements that are characteristic of symbolic cognition. In particular, it involves “third order intentionality” as well as “shared practice horizons”: shared frameworks of understanding which are required for the interpretation of communicative acts whose meaning is not codified indexically or iconically in the signaling behavior. In the final part, I briefly review some indications for the use of pointing gestures around the time of the Lomekwian and Oldowan industries, as a way to sustain cooperation and possibly learning by instruction. It is suggested that pointing is more complex than is standardly acknowledged, and that it may have been an important communicative act for Early Stone Age hominins in transitioning to more fully symbolic speech capacities. (shrink)

The aim of our study is to highlight the obvious similarities that exist between the organizational structures of the biological world, particularly in terms of the number and distribution of the petals on flower and the geometric configurations used by the great masters of European painting, both in the East but also in the West, in order to elaborate the compositional framework of paintings and icons. Taking into consideration the symbolic connotations concerning the field of biology, we chose as a (...) case study the Russian icon from the 14th century entitled “The Triumphal Entry of Jesus into Jerusalem”, exhibited and venerated across the orthodox world on Palm Sunday. Starting with the circle of the aureole of Jesus, we have marked the harmonic series of concentric circles that are distributed across the nodal points of some regular polygons with seven and nine sides, which make reference to the ergonomic formulas of distribution of the petals on a flower and highlight the fact that the beauty of the natural world was and still is the main source of inspiration in the world of arts. (shrink)

Diving into the Gospel of John displays the rich and diverse arguments John presents for his thesis that Jesus is the Messiah, the Son of God, and that through believing, readers/listeners will find eternal life. John’s arguments are developed in four parts. The first two chapters develop the author’s literary techniques that are often based on ambiguity and his key symbols and concepts, the understanding of which are essential to fully appreciate the Gospel. Chapters three through six progressively portray the (...) author’s evidence for his thesis in the form of signs, testimony of those who encounter Jesus, Jesus’s self-identification, and Jesus’s relationships to others. Chapters seven and eight show how the author uses theatrically-patterned dialogues and triadic discourses to convey Jesus’s identity and mission. Finally, chapters nine through eleven provide important hints that the author gives for his thesis: Jesus’s appeals to time, the indirect use of seven as the number of completeness, and invocation of parentage in pointing to salvation. Through diving into the Gospel, readers will discover the richness of John’s argument, the Jesus he portrays, and the God Jesus reveals. The book aims to stimulate commitment, challenge mind and spirit, and encourage further study and conversation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Breathing Without a Head:Plant Respirations in John Gerrard's Smoke TreesOrchid Tierney (bio)About two hours from where I grew up in Invercargill, Aotearoa New Zealand, is a large finger lake called Lake Wakatipu. The lake is nested in the Southern Alps of the South Island and, at the extremes, its body measures three miles wide and fifty-two miles long. The surrounding mountains are haunting in the evenings when the coniferous (...) wildlife is silent, and for as long as I can remember, Wakatipu has been called the breathing lake. I must have read this moniker on a brochure or travel poster in a hotel or a restaurant—I used to visit the area around the lake regularly during the winter months as a child—but according to local legend, it is the beating heart of a taniwha—an ogre called Matau—that causes the lake's respirations. Matakauri, the hero of this particular myth, set alight the ogre whilst he slept in order to rescue his beloved Manata, the beautiful daughter of a local chief, whom the taniwha had kidnapped. As Matau burned, he left behind his heart, which continued to beat rhythmically in the years that followed Matakauri's daring rescue. The myth brilliantly invokes the scientific expertise of the local Indigenous people, for the lake really does rise and fall regularly throughout the day. Despite being landlocked, Wakatipu has an observable seiche, or standing wave, that occurs every 26.7 minutes and results in a tide that rises and falls almost eight inches. Of course, the seiche is the Western scientific explanation for the lake's regular aquatic behavior. The lake breathes because Matau's heart is still beating.Wakatipu's origin myth proposes a respiration that is both wonderfully metaphorical and scientific, but it also raises questions about the embodiments of breath itself. Namely, I'm curious here as to who is an agent of breath? Who and what breathes? Who can breathe easily in the Anthropocene? Who can breathe easily at all? And yet: what an unnecessarily [End Page 14] cruel question this is when so many people nowadays cannot breathe fluently or joyfully in a global pandemic. Over the course of the past two years, the ventilator has become a vexed symbol of the persistence of life, of political incompetence. Of medicalized racial injustice. The lungs that strain against the COVID-19 virus are sometimes the same lungs that have historically struggled against anthropogenic non-viral forms of air pollution. Industrial air pollutants are indicators of systemic racism, imperialism, colonialism, and the uneven urban distributions of risk. Indeed, in December 2020, a British coroner ruled, for the first time in legal history of the United Kingdom, that emissions of nitrogen dioxide and particulate matter on the South Circular Road of London were the cause of nine-year-old Ella Kissi-Debrah's acute respiratory failure in February 2013 (Laville). Toxic airborne pollution is vile matter that forcibly connects gentle lungs with racialized environments. As Timothy Choy notes, "Air muddies the distinction between subjects and environments, and between subjects. This thickness and porosity rendered by air is part of what makes the air and the airborne such deeply felt elements" (157). We, human animals, are too porous for the heavy industry and traffic routes that fill the air and the softness of our lungs. And so: we know the matter of the air by the smoothness of respiration; we feel the keen politics of the air when breathing is labored.I can point to numerous examples where respiration in the context of human life is fraught. Indeed, the act of breathing foregrounds the buoyancy of humanity and the formations of life. I want to acknowledge and hold those complexities because breathing in relation to human life, especially for populations of color, disabled people, and transgender communities, is not yet guaranteed. And I want to consider additionally, who and what has been excluded from the formulations of breathing more generally, and how breathing itself has been anthropomorphized at the expense of other forms of more-than-human life. As Jane Bennett suggests, "humans are always in composition with nonhumanity, never outside of a sticky... (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

In lieu of an abstract, here is a brief excerpt of the content:PrefaceScott Paeth and Kevin CarnahanThis issue of the Journal of the Society of Christian Ethics is organized around the theme of structural evil. Each of the essays deals with some dimension of the problem of how we can conceive of evil beyond the question of simple human volition, and understand it as embedded in the institutions and cultural assumptions that we often take for granted as societal givens.Cristina Traina's (...) presidential address, "This Is the Year," takes as its starting point the aftermath of the 2016 US presidential election, arguing that it exposes the way in which liberal narratives of progress have failed to address the deeply embedded structural evil within American society. She argues that this political moment provides an opportunity for liberals to engage in a critical self-examination with respect to their complicity in these structures by embracing a form of "utopian praxis."Ryan Darr's essay considers the intersection of structural evil and individual responsibility, arguing, on the one hand, for a distinction between sin and moral wrongdoing and, on the other, for an approach to both concepts that is social in form. Esther Reed's essay, meanwhile, offers an analysis of responsibility in light of the question of structural evil, using the theology of Dietrich Bonhoeffer to aid in understanding the connection between individual responsibility and distant harm.David Cloutier continues the examination of the tension between individual agency and structural evil in his critique of the "neo-Franciscan" and "Junian" approaches to issues of violence and racism, arguing that a "critical realist" approach to structural evil provides greater resources for Christian ethics.Elizabeth Sweeny Block offers a different approach to the question in her consideration of the role of conscience in grappling with crises on a global scale, such as climate change and the Zika virus. She contrasts the "reflexive conscience" predominant in Christian ethics with a model of "engaged conscience," which may provide a better approach to large-scale structural evil and its consequences.Stewart Clem uses Thomas Aquinas's conception of virtue to understand the problems inherent in striving for moral clarity in a "post-truth" context. In [End Page vii] light of Harry Frankfurt's philosophical analysis of the concept of "bullshit," he argues that Christian ethics needs to develop a way of speaking about truth as a virtue in order to respond to the structural problem of truth indifference in contemporary political discourse.Looking at the problem from a different perspective, Christopher Jones and Conor Kelly examine the sin of sloth from a structural point of view. Critiquing individualist conceptions of the idea, they make the case for retrieving the classical definition of sloth as a vice against charity and consider how sloth can be overcome through a reinvigoration of forms of civic virtue.Another dimension of structural evil is considered by Ryan Newson in his examination of the role that Confederate monuments play in the American South. For many, they stand as a symbol of the glorification of evil that should be removed, but Newson suggests that there may be reasons to keep at least some of these monuments as reminders of the failure of justice and the judgment of God.Wonchul Shin and Elizabeth Bounds consider these questions from the perspective of how "ordinary" experiences of moral harm need to be analyzed as dimensions of structural evil, and they call for an examination of structural responsibility and the ethics of repair as a means of addressing these questions.Finally, Willa Swenson-Lengyel looks at the connection between structural evil and environmental ethics, arguing that the "moral paralysis" often experienced in light of the ecological crisis exposes certain forms of privilege that need to be addressed from the perspective of Christian ethics. In many ways, she argues, privileged inaction can be a manifestation of "works righteousness" that can be addressed through a Lutheran conception of the doctrine of justification.________This year the JSCE is retiring the demographic survey that has been used since 2008 and adopting a new demographic survey. With the transition comes an apt time for reflection on what the data from the last nine years show.The first piece of data to... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Approaches to Teaching Spenser’s “Faerie Queene”Patricia B. PhillippyApproaches to Teaching Spenser’s “Faerie Queene,” edited by David Lee Miller and Alexander Dunlop; ix & 207 pp. New York: Modern Language Association of America, 1994, $37.50.In many respects, the teaching of Spenser’s Faerie Queene is an experience that most completely encapsulates both the challenges and the rewards of introducing students to the literature of the early modern period. As a (...) work whose length, complex narratives, substantial cast of characters, and polyvocal allegories are often daunting to undergraduates, Spenser’s epic can easily appear as a riddle to be solved rather than a work to be appreciated, let alone enjoyed. Too frequently the constraints of the syllabus and the resistance of students result in a one-dimensional rendering of the text, which permits students to feel that they have “learned something” about Spenser, and about literature generally, by seeing simple, point-by-point allegorizations (Archimago as the Pope, Duessa as Catholicism) as the work’s whole meaning. However, if these difficulties can be surmounted, few other works can equal the great opportunities available in The Faerie Queene to enrich students’ understanding of Elizabethan aesthetic, ethical, social, and political climates, and, perhaps more significantly, to impress upon them the fact that literature, as the most self-conscious of written works, seeks to elicit a multiplicity of meanings from its readers. Thus the task of critical reading appropriately moves toward expansiveness rather than inclusiveness, toward calling forth a plethora of meanings rather than eliminating all but the one “right” reading.Valuable help in overcoming the problems posed by Spenser’s work in the classroom is found in Approaches to Teaching Spenser’s “Faerie Queene.” The collection includes six essays that suggest various strategies for introducing the text to students, and nine essays devoted to more advanced study of the poem. The majority of essays in the former group concentrate on Book 1, and negotiate the practical difficulties of incorporating The Faerie Queene into undergraduate survey courses by suggesting methods to help students to bridge the gap between the work’s cultural context and their own, while also stressing the need to appreciate the text’s distinctiveness.The “special topics” essays treat individual books and themes within a variety of methodological frameworks and in light of cultural touchstones, such as the Renaissance association of painting and poetry (aided by the volume’s eight illustrations), Elizabethan colonial and imperial attitudes about Ireland, and early modern treatises and conduct books describing women’s character. A “Materials” section includes a descriptive bibliography of texts for classroom use and for students’ assigned readings, a wonderfully inclusive bibliography describing editions, reference works, background reading, and critical interpretations for the instructor’s use, and an outline of aids to teaching, such as portraits, films, and music. Even the experienced teacher of Spenser will find this a useful summary of the available materials. [End Page 278]While rooted in practical pedagogy, the essays in this collection also, for the most part, offer provocative comments on Spenser’s poem that are of scholarly interest beyond the classroom as well. Julia M. Walker’s discussion of Britomart alongside Elizabethan portraiture and Dorothy Stephens’ reading of the “feminine” in Book 4 are abridgments of longer articles from Modern Philology and ELH, respectively, and Theresa M. Krier’s provocative comments on the gendering of Spenserian symbol and allegory point toward her work in progress. Overall, the collection recommends numerous innovative techniques to energize and enliven one’s teaching of the poem and to enhance students’ experiences of it. While teachers’ awareness of the demographics and dynamics of their own students may preclude the adoption of specific approaches suggested in this volume, its essays dramatically illustrate the need to avoid reductive readings of The Faerie Queene and, at the same time, offer worthwhile guidance to prevent students from wandering endlessly through the woods of semiotic indeterminacy, error, and despair.Patricia B. PhillippyTexas A&M UniversityCopyright © 1996 The Johns Hopkins University Press... (shrink)

In this dissertation, a logical analysis of points of view is presented. It is based on the concept of determinable presented by Johnson in his book Logic. A point of view is a set of Determinables. Determinables generate a many-dimensional conceptual space. Concepts are subsets of this space, and their relations form a lattice. A logical system to present points of view is introduced and proved to be complete. Some applications of this logic are demonstrated (relative identity, scientific change, inductive (...) logic etc.). (shrink)

The purpose of this paper is to compare the notion of a Grzegorczyk point introduced in [19] (and thoroughly investigated in [3, 14, 16, 18]) to the standard notions of a filter in Boolean algebras and round filter in Boolean contact algebras. In particular, we compare Grzegorczyk points to filters and ultrafilters of atomic and atomless algebras. We also prove how a certain extra axiom influences topological spaces for Grzegorczyk contact algebras. Last but not least, we do not refrain from (...) a philosophical interpretation of the results from the paper. (shrink)

This open access book – as the title suggests – explores some of the historical roots and epistemological ramifications of perspectivism. Perspectivism has recently emerged in philosophy of science as an interesting new position in the debate between scientific realism and anti-realism. But there is a lot more to perspectivism than discussions in philosophy of science so far have suggested. Perspectivism is a much broader view that emphasizes how our knowledge is situated; it is always from a human vantage point. (...) This edited collection brings together a diverse team of established and early career scholars across a variety of fields. The resulting nine essays trace some of the seminal ideas of perspectivism back to Kant, Nietzsche, the American Pragmatists, and Putnam, while the second part of the book tackles issues concerning the relation between perspectivism, relativism, and standpoint theories, and the implications of perspectivism for epistemological debates about veritism, epistemic normativity and the foundations of human knowledge. (shrink)

We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second order logic, and we consider (...) questions related to the determinacy of games associated with alternating fixed points. (shrink)

When did we begin to exist? Barry Smith and Berit Brogaard argue that a new human organism comes into existence neither earlier nor later than the moment of gastrulation: 16 days after conception. Several critics have responded that the onset of the organism must happen earlier; closer to conception. This article makes a radically different claim: if we accept Smith and Brogaard’s ontological commitments, then human organisms start, on average, roughly nine months after conception. The main point of contention (...) is whether the fetus is or is not part of the maternal organism. Smith and Brogaard argue that it is not; I demonstrate that it is. This claim in combination with Smith and Brogaard’s own criteria commits to the view that human organisms begin, precisely, at birth. (shrink)

In this article the authors1 approach material and symbolic violence through transdisciplinary readings of theoretical debates, fiction and empirical narratives. They make use of the concept of turning points which disrupt dichotomous and static categorizations of victim and survivor, and their association with passivity and agency respectively. In situations of violence, turning points represent temporality instead of timelessness, dialogism instead of monologism, multilayering rather than any fixed identity. The authors draw on the theorists Bakhtin and Certeau, whose work highlights the (...) significance of meaning-making between self and other. They analyse empirical and fictional narratives to understand the creation of dialogic spaces, a space that both subordinates and subverts. Pointing to the procedural nature of turning points within the everyday, the authors argue that women, despite the pain and trauma, are neither just a victim nor just a survivor in a violent relationship. (shrink)

Excerpt from Nine Modern Moralists The greatness of the men whose insight and re ections are the subject of the following chapters is obviously a sufficient justification for this volume. The reader who simply wants to learn what was felt and thought and believed by some of the outstanding minds of the immediate past and of the present can, it is hoped, do so by reading the chapters of this book as expository essays. Here he will find their thought (...) anatomized; and, in relatively brief compass, it may be possible for him to become seriously engaged in thinking their thoughts after them. Certainly, no one can come to an understanding of the latest and best of contemporary ideas and ideals by going around these men; only by going through them can one gain a deeper understanding of himself and of our epoch. That is the first purpose of this book: to provide an introduction to nine selected modern moralists. The second purpose is constructive and critical. Exposition and ex planation by themselves are not the aim of these chapters. The highest tribute one can pay any thinker, or any body of writing, is to wrestle with it; and this may well be the best way to bring out the innermost and most vital meaning of what any man has said. I trust that in this wrestling I have nowhere simply commanded an issue to be gone, or have ignored the real meaning or the strength of an idea or point of view in rejecting or reformulating it. The procedure employed in criti cism is always an internal one. This is to say that it always seems best to go as far as one can with another man's thought, developing it up to the point where some criticism or objection or revision unfolds itself, as it were, from within the system or structure of thought under examina tion. In this way the most constructive results may be expected from criticism; and, in this way also, constructive and critical essays may fairly aim to be explanatory ones. As expository essays the chapters that follow may be taken one at a time and in any order, or one or more without the others. Their con structive and critical purpose, however, connects them all together. The author has been somewhat surprised at the extent to which this is true, when preparing for publication these papers which were written in some cases years apart. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.". (shrink)

We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

We define the notion of a weakly pointed tree, and characterize the amount of genericity necessary to prevent a uniformly branching tree being weakly pointed. We use these ideas to show there is no topological analogue of a measure-theoretic selection theorem of Graf and Mauldin.

The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal almost (...) disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : oguzman@matmor.unam.mxURL : https://arxiv.org/abs/1810.09680. (shrink)

Drawing on convergent work in a broad range of disciplines, this article uses the tipping point paradigm to frame a new account of how early human ancestors may have first broken free from, as Bickerton calls it, the “prison of animal communication.” Under building pressure for an enhanced signaling system capable of supporting joint attentional-intentional activities, a cultural tradition of disambiguated indexical pointing (a finger point disambiguated by a facial expression, vocalization, or other gesture), combined with increasingly sophisticated mindreading circuitry (...) and prosocial tendencies, may have sparked the first in the series of biocultural explosions that led from a simple protolanguage to fully modern human language. This account successfully integrates at least ten other competing hypotheses, and is shown to pass nine important tests that have been proposed for language origin scenarios of its type. (shrink)

While it seems unlikely that any method of guaranteeing human-friendliness on the part of advanced Artificial General Intelligence systems will be possible, this doesn’t mean the only alternatives are throttling AGI development to safeguard humanity, or plunging recklessly into the complete unknown. Without denying the presence of a certain irreducible uncertainty in such matters, it is still sensible to explore ways of biasing the odds in a favorable way, such that newly created AI systems are significantly more likely than not (...) to be Friendly. Several potential methods of effecting such biasing are explored here, with a particular but non-exclusive focus on those that are relevant to open-source AGI projects, and with illustrative examples drawn from the OpenCog open-source AGI project. Issues regarding the relative safety of open versus closed approaches to AGI are discussed and then nine techniques for biasing AGIs in favor of Friendliness are presented: 1. Engineer the capability to acquire integrated ethical knowledge.2. Provide rich ethical interaction and instruction, respecting developmental stages.3. Develop stable, hierarchical goal systems.4. Ensure that the early stages of recursive self-improvement occur relatively slowly and with rich human involvement.5. Tightly link AGI with the Global Brain.6. Foster deep, consensus-building interactions between divergent viewpoints.7. Create a mutually supportive community of AGIs.8. Encourage measured co-advancement of AGI software and AGI ethics theory.9. Develop advanced AGI sooner not later. In conclusion, and related to the final point, we advise the serious co-evolution of functional AGI systems and AGI-related ethical theory as soon as possible, before we have so much technical infrastructure that parties relatively unconcerned with ethics are able to rush ahead with brute force approaches to AGI development. (shrink)

We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence (...) of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)

What is the difference between the discriminations made by a home appliance able to distinguish salt from sugar, and my sensations of salty and sweet? It is never taken into consideration that, in contrast to the appliance, I can have offline sensations, i.e., phenomenal experiences in the absence of direct environmental stimuli, mainly evoked by words occurring into thought, conversation, reading, etc. If we put this detachment stimuli/sensations in relation with the correlative detachment signs/referents inaugurated by the cognitive revolution of (...) symbolic language , we might rethink the role played by language in our phenomenal experience as a whole. Qualia can be defined as forms of relationship between organisms and environment, given that human environment is extended to the linguistic dimension, and that the latter has ignited a coevolutionary process with human cognition. The very same properties we attribute to qualia, even when conceiving of them as pre-linguistic phenomenal traits, rely on the cognitive resources that language has made available. The substantialist notion of qualia, I argue, is formed by an online sensation on which the focus shifts from the perceived object to the sensory quality by virtue of linguistic modes of thinking, which are systematically neglected. (shrink)

Minimal predicates P satisfying a given first-order description φ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order ‘PIA conditions’ φ(P) which guarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of ‘predicate intersection’. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal (...) in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)

China has undergone unprecedented changes since the Reform and Opening-up policy in 1978. Policy experimentation (PE) has been key in generating and catalysing reforms in the process. This study proposes a conceptual framework to describe the different pathways of PE-enabled reforms. Comparing two empirically informed case studies, this study demonstrates the functions of this policy tool plays within China’s higher education policy-making and development: generative, rhetorical and regulatory. The paper argues that PE can be a genuinely productive mechanism for producing, (...) identifying and negotiating new policy options while allowing the government to supervise and regulate institutional reform behaviours. However, under certain conditions, it assumes more of a symbolic role allowing the government to acquire or consolidate reform legitimacy without engaging substantial innovation. By highlighting those key roles of PE, this paper provides a distinctive perspective for understanding the policy-making and reform process in China’s higher education development. (shrink)

Reading noir and Lacan together can establish a structural corollary between the function of the signifier 'noir' in film criticism and the retroactive function of the point de capiton in Lacan's theory of language. Furthermore, at a narrative level, the function of the point de capiton can also be found in the retroactive constructions of film noir flashbacks. It is therefore possible to say that a retroactive 'noir temporality' is also the temporality of the Symbolic order. This article explores the (...) way in which the signifier 'noir' enables the analysis of a certain type of 1940s Hollywood film, and how a noir film such as Double Indemnity (Billy Wilder, 1944) is concerned with the retroactive production of knowledge through narrative structure. (shrink)