Entire libraries can be filled with volumes exploring the cultures, politics and geographies of the largely horizontal mobilities and transportation infrastructures that are intrinsic to urban modernity (highways, railways, subways, public transit and so on). And yet the recent ‘mobilities turn’ has almost completely neglected the cultural geographies and politics of vertical transportation within and between the buildings of vertically-structured cityscapes. Attempting to rectify this neglect, this article seeks, first, to bring elevator travel centrally into discussions about the cultural politics (...) of urban space and, second, to connect elevator urbanism to the even more neglected worlds of elevator-based descent in ultra-deep mining. The article addresses, in turn: the historical emergence of elevator urbanism; the cultural significance of the elevator as spectacle; the global ‘race’ in elevator speed; shifts towards the ‘splintering’ of elevator experiences; experiments with new mobility systems which blend elevators and automobiles; problems of vertical abandonment; and, finally, the neglected vertical politics of elevator-based ‘ultra-deep’ mining. (shrink)

This short note considers the migration of the skyscraper from New York and Chicago to Asia and its absence in the emerging megacities of the Global South. Following 9/11, many commentators assumed that the skyscraper was finished, but this was clearly not the case, with super-tall construction now accelerating. However, the distributions of contemporary skyscrapers show us that there are shifts in global power and also in urban form.

everyone loves superheroes. superheroes, of course, have incredible powers; they can leap tall buildings in a single bound, excel in combat, and have X-ray vision. But, in addition, superheroes have a kind of simplicity of motive and focus that makes them pure and comprehensible in the way in which the people we actually know rarely are. For Superman it is about Truth, Justice, and the American Way. For Batman it is all about fighting evil: defeating the Joker, the Riddler, (...) and other nefarious characters. For Spiderman it is an outsized sense of mission: “With great power comes great responsibility.” Superheroes are superhuman individuals, who have a simple philosophy of life that motivates their every action. Of.. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The (...) main feature of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

Ordinary people shudder at the thought that people in positions of power might do whatever they think they can get away with. But that is often the way it is in the real world, and the risks go even higher when opportunity is compounded with impatience. The ways of negotiation and diplomacy are not considered entirely outmoded. But more and more we are being duped by a dream of some ultimate technological fix: that one more fancy gadget is all it (...) will take to solve the vexing problems that less well-tooled folks have been stumbling over for centuries. Our success rate, this reasoning goes, has been limited so far only by the limits on our equipment. With the new super-missile, or the new super-plane, or the new superlaunching system in space, we will be able to leap tall buildings in a single bound-or, what is more to the point, just blow them away and walk across the crater. "Bombs can be clean." "Nuclearwar is winnable." The illusion of omnipotence that accompanies this megalomania is well nurtured by manufacturers who stand in line for contracts to help build some super-weapon. This should not be surprising. What at first glance is surprising is the almost total failure of our commercial media to call this myth into question. This criticism is meant to be sweeping, but I will here focus my remarks on film. (shrink)

I. Prelude -- About this Book -- II. School Mathematics and Its Consequences -- The Foundations of Mathematical Thinking -- Compression, Connection and Blending of Mathematical Ideas -- Set-befores, Met-befores and Long-term Learning -- Mathematics and the Emotions -- The Three Worlds of Mathematics -- Journeys through Embodiment and Symbolism -- Problem-Solving and Proof -- III. Interlude -- The Historical Evolution of Mathematics -- IV. University Mathematics and Beyond -- The Transition to Formal Knowledge -- Blending Knowledge Structures in the (...) Calculus -- Expert Thinking and Structure Theorems -- Contemplating the Infinitely Large and the Infinitely Small -- Expanding the Frontiers through Mathematical Research -- Reflections -- Appendix: Where the Ideas Came From. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large cardinals. We here dispense with them.

The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.

Aboitiz et al. describe a hypothesis on the origin of the isocortex. They propose the reptilian dorsal cortex to be the ancestral brain structure to the mammalian isocortex. But why did the dorsal cortex expand in mammals and not in reptiles? A change in development may have provided the mammalian cortex with the ability to organize and therefore the potential to expand.

The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.

Keywords: Elementary Submodel; Real Line; Order-Isomorphic.

We often encounter situations in which an undesirable outcome is brought about through a series or collection of seemingly inconsequen-tial actions. This phenomenon, referred to as the inefficacy paradox, oc-curs both intrapersonally and collectively. Paradoxically, while we have good reason to avoid such patterns of action, there appears to be no com-pelling reason to abstain from any of the individual actions constituting such a pattern given its trivial impact. This paper scrutinizes Chrisoula Andreou's prominent endeavor to resolve the inefficacy paradox (...) in both the intrapersonal and the collective context by utilizing their structural similarity. While her approach may prove successful in intrapersonal cases, the applicability of the proposed solution to collective cases is, I argue, ultimately limited. This is due to a fundamental dissimilarity be-tween these two kinds of cases, which I lay out in the paper. This insight may also shed light on the transferability of other proposed solutions to the inefficacy paradox from the intrapersonal to the collective context. (shrink)

Phillips & Silverstein argue that schizophrenia is a result of a deficit of the contextual coordination of neuronal responses. The authors propose that NMDA-receptors control these modulatory effects. However, hallucinations, which are among the principle symptoms of schizophrenia, imply a flaw in the interactions between neurons that is more fundamental than just a general weakness of contextual modulation.

By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

Given a space in an elementary submodel M of H, define XM to be X∩M with the topology generated by . It is established, using anti-large-cardinals assumptions, that if XM is compact and its regular open algebra is isomorphic to that of a continuous image of some power of the two-point discrete space, then X=XM. Assuming in addition, the result holds for any compact XM satisfying the countable chain condition.

A cardinal κ is tall if for every ordinal θ there is an embedding j: V → M with critical point κ such that j > θ and Mκ ⊆ M. Every strong cardinal is tall and every strongly compact cardinal is tall, but measurable cardinals are not necessarily tall. It is relatively consistent, however, that the least measurable cardinal is tall. Nevertheless, the existence of a tall cardinal is equiconsistent with the existence of (...) a strong cardinal. Any tall cardinal κ can be made indestructible by a variety of forcing notions, including forcing that pumps up the value of 2κ as high as desired. (shrink)

We construct two models containing exactly one supercompact cardinal in which all non-supercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the first of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness holds. Each universe has only one strongly compact cardinal and contains relatively few large cardinals.

In this paper, the properties of the super quantum measures are studied. Firstly, the products of Dirac measures are discussed; Secondly, based on the properties of Dirac measures, the structures of super quantum measures are characterized; At last, we prove that any super quantum measure can determine a unique diagonally positive strongly symmetric signed measure. This result verifies the conjecture which was proposed by Gudder.