Recent work on emergence in physics has focused on the presence of singular limit relations between basal and upper-level theories as a criterion for emergence. However, over-emphasis on the role of singular limit relations has somewhat obscured what it means to say that a property or behaviour is emergent. This paper argues that singular limits are not central to emergence and develops an alternative account of emergence in terms of the failure of basal explainability. As (...) a consequence, emergence and reduction, long held to be two sides of the same coin in the emergentist tradition, are largely decoupled. (shrink)

Recent work by Robert Batterman and Alexander Rueger has brought attention to cases in physics in which governing laws at the base level “break down” and singular limit relations obtain between base- and upper-level theories. As a result, they claim, these are cases with emergent upper-level properties. This paper contends that this inference—from singular limits to explanatory failure, novelty or irreducibility, and then to emergence—is mistaken. The van der Pol nonlinear oscillator is used to show that there (...) can be a full explanation of upper-level properties entirely in base-level terms even when singular limits are present. Whether upper-level properties are emergent depends not on the presence of a singular limit but rather on details of the ampliative approximation methods used. The paper suggests that focusing on explanatory deficiency at the base level is key to understanding emergence in physics. (shrink)

Assume \ is a singular limit of \ supercompact cardinals, where \ is a limit ordinal. We present two methods for arranging the tree property to hold at \ while making \ the successor of the limit of the first \ measurable cardinals. The first method is then used to get, from the same assumptions, the tree property at \ with the failure of SCH at \. This extends results of Neeman and Sinapova. The second method (...) is also used to get the tree property at the successor of an arbitrary singular cardinal, which extends some results of Magidor–Shelah, Neeman and Sinapova. (shrink)

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. We (...) then use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics. (shrink)

En este trabajo se analiza la propuesta en torno de los pensamientos singulares o “pensamientos de re” del filósofo contemporáneo John McDowell. Nuestra estrategia es abordar dicha reconstrucción a partir de la tesis de “la carencia de límites de lo conceptual” desarrollada en su producción más reciente. El contraste entre algunos aspectos de Mind and World (1994) y los artículos previos consagrados al pensamiento singular, asignan un valor explicativo concreto a la tesis de que lo conceptual no tiene límites.

Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 2013 Heft: 1 Seiten: 267-288.

Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216 89–117] and Steel [PFA implies AD L, J. Symbolic Logic70 1255–1296], we show that the failure of square principle at a singular strong limit cardinal implies that there is a nontame mouse. The proof presented is the first inductive step beyond L of the core model induction that is aimed at getting a model of ADℝ + "Θ is regular" from the failure of square at a (...) singular strong limit cardinal or PFA. (shrink)

What happens when machines become more intelligent than humans? One view is that this event will be followed by an explosion to ever-greater levels of intelligence, as each generation of machines creates more intelligent machines in turn. This intelligence explosion is now often known as the “singularity”. The basic argument here was set out by the statistician I.J. Good in his 1965 article “Speculations Concerning the First Ultraintelligent Machine”: Let an ultraintelligent machine be defined as a machine that can far (...) surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an “intelligence explosion”, and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make. The key idea is that a machine that is more intelligent than humans will be better than humans at designing machines. So it will be capable of designing a machine more intelligent than the most intelligent machine that humans can design. So if it is itself designed by humans, it will be capable of designing a machine more intelligent than itself. By similar reasoning, this next machine will also be capable of designing a machine more intelligent than itself. If every machine in turn does what it is capable of, we should expect a sequence of ever more intelligent machines. This intelligence explosion is sometimes combined with another idea, which we might call the “speed explosion”. The argument for a speed explosion starts from the familiar observation that computer processing speed doubles at regular intervals. Suppose that speed doubles every two years and will do so indefinitely. Now suppose that we have human-level artificial intelligence 1 designing new processors. Then faster processing will lead to faster designers and an ever-faster design cycle, leading to a limit point soon afterwards. The argument for a speed explosion was set out by the artificial intelligence researcher Ray Solomonoff in his 1985 article “The Time Scale of Artificial Intelligence”.1 Eliezer Yudkowsky gives a succinct version of the argument in his 1996 article “Staring at the Singularity”: “Computing speed doubles every two subjective years of work.. (shrink)

In “A Defense of Presentism ”, Ned Markosian addresses the problem of singular propositions about non-present objects. The proposed solution uses a paraphrasing strategy that differentiates between two kinds of meaning in declarative sentences, and also distinguishes between two truth-conditions for singular propositions. The solution, however, is unsatisfactory. I demonstrate that the both truth-conditions suffer from the same problems in spite of the examples used to support the claim that one is a proper treatment for singular propositions. (...) Part of the difficulty is in the limited expressivity of logical formalisms, a limitation not unique to the philosophy of time, but which calls for greater attention. (shrink)

The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the (...) two. We prove from large cardinals that the tree property at κ+ is consistent with failure of the singular cardinal hypothesis at κ. (shrink)

We say that κ is μ-hypermeasurable for a cardinal μ≥κ+ if there is an embedding j:V→M with critical point κ such that HV is included in M and j>μ. Such a j is called a witnessing embedding.Building on the results in [7], we will show that if V satisfies GCH and F is an Easton function from the regular cardinals into cardinals satisfying some mild restrictions, then there exists a cardinal-preserving forcing extension V* where F is realised on all V-regular (...) cardinals and moreover, all F-hypermeasurable cardinals κ, where F>κ+, with a witnessing embedding j such that either j=κ+ or j≥F, are turned into singular strong limit cardinals with cofinality ω. This provides some partial information about the possible structure of a continuum function with respect to singular cardinals with countable cofinality.As a corollary, this shows that the continuum function on a singular strong limit cardinal κ of cofinality ω is virtually independent of the behaviour of the continuum function below κ, at least for continuum functions which are simple in that 2α{α+,α++} for every cardinal α below κ ≥F or j=κ+). (shrink)

In general, existential threats are those that may potentially result in the extinction of the entire human species, if not significantly endanger its living population. Among the said threats include, but not limited to, pandemics and the impacts of a technological singularity. As regards pandemics, significant work has already been done on how to mitigate, if not prevent, the aftereffects of this type of disaster. For one, certain problem areas on how to properly manage pandemic responses have already been identified, (...) like the following: (a) not being able to learn from previous experiences, (b) the inability to act on warning signals, and (c) the failure to reach a global consensus on a problem (i.e., in a timely manner). In terms of a singularity, however, it may be said that further research is still needed, specifically on how to aptly respond to its projected negative outcomes. In this paper, by treating the three problem areas noted above as preliminary assessment measures of a country’s capacity to coordinate a national response to large-scale disasters, we examine the readiness of the Philippines in preparing for an intelligence explosion. By citing certain instances of how the said country, specifically its national government, faced the coronavirus disease 2019 pandemic, it puts forward the idea that the likely Philippine disaster response towards a singularity needs to be worked on, appealing for a more comprehensive assessment of such for a more informed response plan. (shrink)

Philosophical thinking is interrupted by the finitude of what cannot be named, on the one hand, and that within which it is subsumed as one of multiple modes of sense-making, on the other. Sense and Singularity elaborates Jean-Luc Nancy’s philosophical project as an inquiry into the limits or finitude of philosophy itself, where it is interrupted, and as a practice of critical intervention where philosophy serves to interrupt otherwise unquestioned ways of thinking. Nancy’s interruption of philosophy, Van Den Abbeele argues, (...) reveals the limits of what philosophy is and what it can do, its apocalyptic end and its endless renewal, its Sisyphean interruption between the bounds of infinitely replicating sense and the conceptual vanishing point that is singularity. In examinations of Nancy’s foundational rereading of Descartes's cogito as iterative, his formal experimentations with the genres of philosophical writing, the account of “retreat” in understanding the political, and the interruptive play of sense and singularity in writings on the body, sexuality, and aesthetics, Van Den Abbeele offers a fresh account of one of our major thinkers as well as a provocative inquiry into what philosophy can do. (shrink)

This article considers the challenge posed by Gayatri Spivak to rethink world literature along postcolonial lines as an ethical encounter with alterity. Read in this way, Spivak participates in a reframing of world literature that retains the critical gains made by postcolonial theory and suggests that the work of world literary analysis ought not necessarily be de/prescriptive but might involve a contestation of the power relations that structure the world. In developing this argument, I draw on four further perspectives: Pascale (...) Casanova's problematic assertion of literary singularity in The World Republic of Letters; Fredric Jameson's theorization of “third world literature” as counterpoint to Casanova's limiting understanding of national literature; Gilles Deleuze, who offers a way to rethink world literature in a process of becoming; and Édouard Glissant, whose work proposes a “relational” vision of difference that, like that of Spivak, demands an ethical, imaginati.. (shrink)

I explore the limits of corporate responsibility standards – for example Social Accountability 8000 (SA 8000), the Global Reporting Initiative, the Fair Labor Association workplace code – by looking at these initiatives through Derrida's aporias of justice as set out in ‘Force of Law: The “Mystical Foundation of Authority”’. Based on a discussion of SA 8000, I uncover the unavoidable aporias that are associated with the use of this standard. I contribute to the literature on corporate responsibility standards in general (...) and SA 8000 in particular by showing (a) that attempts to standardise corporate responsibility can only be successful insofar as we recognise that compliance with SA 8000's rules requires a ‘fresh judgement’ every time they are applied, (b) that SA 8000 should not be pushed down the supply chain as such coercion does not require a truly responsible decision by suppliers and eventually leads to moral mediocrity and (c) that the necessarily time‐consuming reflections about the singular contexts within which SA 8000 is applied challenge the urgent need for implementing this standard. I discuss the implications of my analysis of SA 8000 for corporate responsibility standards in general. (shrink)

I explore the limits of corporate responsibility standards – for example Social Accountability 8000 (SA 8000), the Global Reporting Initiative, the Fair Labor Association workplace code – by looking at these initiatives through Derrida's aporias of justice as set out in 'Force of Law: The "Mystical Foundation of Authority"'. Based on a discussion of SA 8000, I uncover the unavoidable aporias that are associated with the use of this standard. I contribute to the literature on corporate responsibility standards in general (...) and SA 8000 in particular by showing (a) that attempts to standardise corporate responsibility can only be successful insofar as we recognise that compliance with SA 8000's rules requires a 'fresh judgement' every time they are applied, (b) that SA 8000 should not be pushed down the supply chain as such coercion does not require a truly responsible decision by suppliers and eventually leads to moral mediocrity and (c) that the necessarily time-consuming reflections about the singular contexts within which SA 8000 is applied challenge the urgent need for implementing this standard. I discuss the implications of my analysis of SA 8000 for corporate responsibility standards in general. (shrink)

Singularity is a future period during which the pace of technological change will be so rapid, its impact so deep, that human life will be irreversibly transformed. This chapter argues that within several decades information‐ based technologies will encompass all human knowledge and proficiency, ultimately including the pattern‐recognition powers, problem‐solving skills, and emotional and moral intelligence of the human brain itself. The Singularity will allow us to transcend these limitations of our biological bodies and brains. Most long‐range forecasts of what (...) is technically feasible in future time periods dramatically underestimate the power of future developments because they are based on the “intuitive linear” view of history rather than the “historical exponential” view. The history of evolution ‐ both biological and technological ‐ is conceptualized as occurring in six epochs. The Singularity begins with Epoch Five and will spread from Earth to the rest of the universe in Epoch Six. (shrink)

Assuming some large cardinals, a model of ZFC is obtained in which $\aleph_{\omega+1}$ carries no Aronszajn trees. It is also shown that if $\lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees.

It has become popular of late to identify the phenomenon of thinking a singular thought with that of thinking with a mental file. Proponents of the mental files conception of singular thought claim that one thinks a singular thought about an object o iff one employs a mental file to think about o. I argue that this is false by arguing that there are what I call descriptive mental files, so some file-based thought is not singular (...) thought. Descriptive mental files are mental files for which descriptive information plays four roles: determines which object the file is about, if any, it sets limits on possible mistakes that fall within the scope of successful reference for the file, it acts as a ‘gatekeeper’ for the file, and it determines persistence conditions for the file. Contrary to popular assumption, a description playing these roles is consistent with the file-theoretic framework. Recognising this allows us to distinguish the notion of singular thought from that of file-thinking and better understand the nature and role of both. (shrink)

The hypothetical approach to the supersensible developed by Kant in his three Critiques, exemplified by his analysis of the aesthetic and reflective judgment in his third Critique, with their principle fortuitous purposiveness, can be considered as the basis for a new foundation of metaphysics. According to Kant’s limitation of cognition to the realm of sense intuition, theoretical knowledge of God, the subject, things-in-themselves, transcendental ideas is impossible. This leads to a kind of “negative theology” of the highest principle and the (...) supersensible as a whole. The reasons are rooted in the character of propositional thought, which can only circumscribe a singular, supersensible reality by means of predicative sentences and discursive thought. Taking Kant’s lead, but in contrast to his terminology, I call really existent singularities, including the thinking, knowing, desiring, feeling unique individuals we know as human beings, spontaneities, in order to distinguish them from descriptive characteristics attributed to them by predicative thought. Kant’s “practico-dogmatic” account of the postulates of God and immortality of the soul, based on the “fact of freedom” and its connection to the moral imperative, ensure the possibility of the “highest good” as final aim of moral behaviour — but cannot satisfy our need for knowledge of the supersensible. To “lay the groundwork” for experience of our own self-conscious reality, the reality of others like ourselves, of things which transcend the boundaries of sense intuition, and of true reciprocity, a different method is needed, one which leads us “beyond being and thought” to the unconditional beginning of conditional reality. (shrink)

The question of justice in Western philosophy finds its humble beginnings in the interplay of life and death. I am referring here to Plato’s Apology. The Apology is not only a text tracing the fate of the great philosopher Socrates by recounting his final speech before the judges of Athens, but it is also a text that, on a more subtle level, announces the advent of a promising justice that is birthed from death, or, to be more precise, from a (...) specific kind of death. Socrates, here, develops a justice that does not surge from the defence of one’s determination as a singular accused, or from the reconciliation of the criminal singularity into the ethical social body through pardon or punishment, but which rather derives from a negation, a radical annihilation of the category of pure singularity. Socrates does not defend himself as an accused who is determinately and definitively singular, but rather affirms the fact that, in some sense, there is no such singular to be defended, that he is not even one (οὐδείς), less than one, nothing. It is, precisely, in this affirmation of a negative, in this opening of a chasm, that a radically other conception of justice and its relation to the singular is subtly proposed. By pushing the singular to the margins of its possibility, by challenging, bending, pushing the question of the singular and its defence to its outmost limit, Socrates redeploys justice not as a remedying balance, but as the abysmal economy of the bottomless question, a fall into the void, in which life, death, the singular and justice co-incide to burst all definitive determination, substantial opposition and the possibility of establishing a firm ground for any such categories to hold as such. In gradually shedding off the substantial presuppositions of his singularity (knowledge, self-relation and relation to others), he unleashes a modality of the singular which deploys a kind of justice, a wholly other justice, which has shaken the tradition ever since, and, as this article will seek to show, reverberates again in what Jacques Derrida called deconstruction. (shrink)

"The idea that human history is approaching a singularity - that ordinary humans will someday be overtaken by artificially intelligent machines or cognitively enhanced biological intelligence, or both - has moved from the realm of science fiction to serious debate. Some singularity theorists predict that if the field of artificial intelligence continues to develop at its current dizzying rate, the singularity could come about in the middle of the present century. Murray Shanahan offers an introduction to the idea of the (...) singularity and considers the ramifications of such a potentially seismic event. Shanahan's aim is not to make predictions but rather to investigate a range of scenarios. Whether we believe that singularity is near or far, likely or impossible, apocalypse or utopia, the very idea raises crucial philosophical and pragmatic questions, forcing us to think seriously about what we want as a species. Shanahan describes technological advances in AI, both biologically inspired and engineered from scratch. Once human-level AI - theoretically possible, but difficult to accomplish - has been achieved, he explains, the transition to superintelligent AI could be very rapid. Shanahan considers what the existence of superintelligent machines could mean for such matters as personhood, responsibility, rights, and identity. Some superhuman AI agents might be created to benefit humankind; some might go rogue. The singularity presents both an existential threat to humanity and an existential opportunity for humanity to transcend its limitations. Shanahan makes it clear that we need to imagine both possibilities if we want to bring about the better outcome. (shrink)

According to the singularity hypothesis, rapid and accelerating technological progress will in due course lead to the creation of a human-level artificial intelligence capable of designing a successor artificial intelligence of significantly greater cognitive prowess, and this will inaugurate a series of increasingly super-intelligent machines. But how much sense can we make of the idea of a being whose cognitive architecture is qualitatively superior to our own? This article argues that one fundamental limitation of human cognitive architecture is an inbuilt (...) commitment to a metaphysical division between subject and object, a commitment that could be overcome in an artificial intelligence lacking our biological heritage. (shrink)

Let κ be a singular cardinal. Karp's notion of a chain model of size κ is defined to be an ordinary model of size κ along with a decomposition of it into an increasing union of length cf. With a notion of satisfaction and -isomorphism such models give an infinitary logic largely mimicking first order logic. In this paper we associate to this logic a notion of a dynamic EF-game which gauges when two chain models are chain-isomorphic. To this (...) game is associated a tree which is a tree of size κ with no κ-branches -branches). The measure of how non-isomorphic the models are is reflected by a certain order on these trees, called reduction. We study the collection of trees of size κ with no κ-branches under this notion and prove that when cf = ω this collection is rather regular; in particular it has universality number exactly κ+. Such trees are then used to develop a descriptive set theory of the space cf κ. The main result of the paper gives in the case of κ strong limit singular an exact connection between the descriptive set-theoretic complexity of the chain isomorphism orbit of a model, the reduction order on the trees and winning strategies in the corresponding dynamic EF games. In particular we obtain a neat analog of the notion of Scott watershed from the Scott analysis of countable models. (shrink)

This essay situates “singularity” at the heart of the power dynamics operative in contemporary pedagogy and the system supporting it. More than merely academic learning, indeed, “school” here denotes not only the range of disciplinary authorities at work within the classroom and the educational system at large but also discursive obedience to knowledge. Supported by close readings of Arendt and Derrida, this paper thus argues that nothing less than the formation of identity is at stake in “school.” What are the (...) boundaries, limits, and conditions of possibility for a student’s invention of his or her own singularity within an institution and curriculum that, at the same time, demands obedience to authority? This paradoxical formation of identity within the constrictive demands of authority constitutes the primary task of thinking the “invention of singularity” at the heart of schooling in conjunction with democracy, language, vocation, and ideology. (shrink)

Keisler in [7] proved that for a strong limit cardinal κ and a singular cardinal λ, the transfer relation κ → λ holds. We analyze the λ -like models produced in the proof of Keisler's transfer theorem when κ is further assumed to be regular. Our main result shows that with this extra assumption, Keisler's proof can be modified to produce a λ -like model M with built-in Skolem functions that satisfies the following two properties: M is generated (...) by a subset C of order-type λ. M can be written as union of an elementary end extension chain 〈Ni: i < δ 〉 such that for each i < δ, there is an initial segment Ci of C with Ci ⊆ Ni, and Ni ∩ = ∅. (shrink)

We deal here with colorings of the pair , when μ is a strong limit and singular cardinal. We show that there exists a coloring c with no refinement. It follows that the properties of colorings of when μ is singular differ in an essential way from the case of regular μ.

The book explores the way in which apophatic discourse of negative theology has illuminated contemporary critical theory. It demonstrates the significance of apophasis both in Jacques Derrida’s search for a «new language», responsive to singularity and alterity, and in the analyses of the experience of transgression developed by Maurice Blanchot, George Bataille and Michel Foucault. Following Derrida’s understanding of negative theology as a transgressive concept that transcends the linguistic, historical and religious contexts from which it arises, the book proves that (...) apophasis is not merely a discourse on language restricted to one theological tradition, but should be viewed as a mode of dialogue and openness, essential to all responsible thinking. (shrink)

I argue that there are no physical singularities in space–time. Singular space–time models do not belong to the ontology of the world, because of a simple reason: they are concepts, defective solutions of Einstein’s field equations. I discuss the actual implication of the so-called singularity theorems. In remarking the confusion and fog that emerge from the reification of singularities I hope to contribute to a better understanding of the possibilities and limits of the theory of general relativity.

O artigo pretende discutir a possiblidade da percepção interna, delimitando-a do compreender da pessoa, que pode ser tanto compreensão do próximo como autocompreensão. Do mesmo modo, a percepção interna poder ser a percepção de si mesmo como percepção do outro. Parte-se, portanto, de uma indicação recorrente na fenomenologia de Scheler, de acordo com a qual a percepção interna não pode ser reduzida à autopercepção, entendida, sobretudo, no sentido de autoconsciência. Nesta direção, primeiramente, tenta-se uma definição fenomenológica do ato em questão, (...) visando, sobretudo, libertá-lo das determinações idealistas enquanto autoconsciência e das compreensões subjetivistas, tais como a auto-observação e meio de autoconhecimento. Para tanto, demonstra-se que a percepção interna é uma direção de um único ato perceptivo e que o seu objeto não é uma forma lógica pura e vazia, mas sim a apreensão do eu material, concreto e singular. A intuição imediata e direta deste eu, então, aparecerá como a base sobre a qual se rompe com as duas interpretações supracitadas. Por fim, discute-se os elementos internos que contribuem para estes limites, em especial a fisiologia do sentido interno e os interesses do corpo-próprio, o que permite entender positivamente os limites e descrever os seus primeiros significados. A partir deste ganho fenomenológico, a investigação detém-se nos fatores externos, responsáveis por transformar a percepção interna em mero instrumento do autoconhecimento e por subjugá-la às metas e interpretações da cosmovisão natural, analisando brevemente as fontes da idolatria do autoconhecimento. Conclui-se que, na delimitação de sua possibilidade essencial, a desconsideração do papel psicofisiológico do sentido interno, a transladação das leis e relações espaço-temporais próprias da esfera física para a psíquica e, consequentemente, a superposição da percepção externa sobre a interna em consonância com a interpretação sensualista da última são as principais fontes da ilusão denominada idolatria do autoconhecimento. (shrink)

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But (...) there is no need to take a limit when moving from a crystal lattice based description to the phonon description. Not only does this demonstrate that we can have emergence without limits, but also provides a way of understanding cases that do involve limits. (shrink)

Economic growth is determined by the supply and demand of investment capital; technology determines the demand for capital; while human nature determines the supply. The supply curve has two distinct parts; giving the world economy two distinct modes. In the familiar slow growth mode; rates of return are limited by human discount rates. In the fast growth mode; investment is limited by the world's wealth. Historical trends suggest that we may transition to the fast mode in roughly another century and (...) a half. Can some new technology switch us to the fast mode more quickly than this? Perhaps; but such a technology must greatly raise the rate of return for the world's expected worst investment project. It must thus be very broadly applicable; improving almost all forms of capital and investment. Furthermore; investment externalities must remain within certain limits. (shrink)

REF is the statement that every stationary subset of a cardinal reflects, unless it fails to do so for a trivial reason. The main theorem, presented in Sect. 0, is that under suitable assumptions it is consistent that REF and there is a κ which is κ+n -supercompact. The main concepts defined in Sect. 1 are PT, which is a certain statement about the existence of transversals, and the “bad” stationary set. It is shown that supercompactness (and even the failure (...) of PT) implies the existence of non-reflecting stationary sets. E.g., if REF then for manyλ ⌝ PT(λ, ℵ1). In Sect. 2 it is shown that Easton-support iteration of suitable Levy collapses yield a universe with REF if for every singular λ which is a limit of supercompacts the bad stationary set concentrates on the “right” cofinalities. In Sect. 3 the use of oracle c.c. (and oracle proper—see [Sh-b, Chap. IV] and [Sh 100, Sect. 4]) is adapted to replacing the diamond by the Laver diamond. Using this, a universe as needed in Sect. 2 is forced, where one starts, and ends, with a universe with a proper class of supercompacts. In Sect. 4 bad sets are handled in ZFC. For a regular λ {δ<+ : cfδ<λ} is good. It is proved in ZFC that ifλ=cfλ>ℵ1 then {α<+ : cfα<λ} is the union of λ sets on which there are squares. (shrink)

This paper addresses a relatively common scientific (as opposed to philosophical) conception of intertheoretic reduction between physical theories. This is the sense of reduction in which one (typically newer and more refined) theory is said to reduce to another (typically older and coarser) theory in the limit as some small parameter tends to zero. Three examples of such reductions are discussed: First, the reduction of Special Relativity (SR) to Newtonian Mechanics (NM) as (v/c)20; second, the reduction of wave optics (...) to geometrical optics as 0; and third, the reduction of Quantum Mechanics (QM) to Classical Mechanics (CM) as0. I argue for the following two claims. First, the case of SR reducing to NM is an instance of a genuine reductive relationship while the latter two cases are not. The reason for this concerns the nature of the limiting relationships between the theory pairs. In the SR/NM case, it is possible to consider SR as a regular perturbation of NM; whereas in the cases of wave and geometrical optics and QM/CM, the perturbation problem is singular. The second claim I wish to support is that as a result of the singular nature of the limits between these theory pairs, it is reasonable to maintain that third theories exist describing the asymptotic limiting domains. In the optics case, such a theory has been called catastrophe optics. In the QM/CM case, it is semiclassical mechanics. Aspects of both theories are discussed in some detail. (shrink)

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal (...) in κ for each n ε ω.We also prove several results which extend or are related to this result, notably Theorem. If 2ω ω1 then there is a sharp for a model with a strong cardinal.In order to prove these theorems we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders. (shrink)

In this chapter, Kelly Oliver argues that while risk-benefit analysis may be necessary in a crisis situation such as the Covid-19 pandemic, that does not make it ethical. To the contrary, risk-benefit analysis is antithetical to ethics defined as responsibility to the singularity of each living being. Triage medicine, developed for the battlefield during wartime, relies on risk-benefit calculations. For example, calculations about which patient has the best chance for survival, or which patient has the best chance of quality of (...) life or continued longevity. In the current pandemic, these calculations were based on population categories of health such as diabetes, coronary disease, obesity, and age, along with assessments of the individual patient’s condition. While such assessments may meet practical policy demands, ultimately, they are not ethical. In the end, she argues for what she calls “response ethics” as an alternative to utilitarian risk-benefit analysis. (shrink)

Este artigo analisa diversos textos da obra de Tomás de Aquino relativos aos temas do conhecimento divino e das ideias divinas com o intuito de mostrar como duas interpretações sustentadas por comentadores recentes da obra tomásica não se mantêm diante da análise rigorosa dos textos. Uma primeira e menos radical interpretação sustenta haver ideias práticas distintas de cada coisa particular, enquanto que, de acordo com uma interpretação ainda mais forte, ideias em sentido estrito pertencem primordialmente a coisas singulares. O objetivo (...) deste artigo é mostrar que, embora Tomás sustente que Deus conhece todas as coisas, inclusive os particulares, a doutrina das ideias, tal como Tomás a concebe, tem limites muito estreitos, não permitindo o pleno desenvolvimento de suas convicções de cunho aristotélico concernentes à cognoscibilidade dos particulares. (shrink)

We show that the tree property, stationary reflection and the failure of approachability at \ are consistent with \= \kappa ^+ < 2^\kappa \), where \ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if \ is a regular cardinal, then stationary reflection at \ is indestructible under all \-cc forcings.

Essences play a central role in Spinoza’s philosophy, not only in his metaphysics, but also in his philosophy of mind, his theory of affects, and his political philosophy. Despite their importance, however, it is surprisingly difficult to determine what exactly essences are for Spinoza. On a widespread reading, the essence of X is nothing but the concept of X. This paper argues against this identification of essences and concepts. Spinozistic concepts are maximally inclusive: the concept of X contains everything that (...) is needed to make X conceivable. The essence of X, in contrast, is more limited in scope and does not include everything that is needed to make X conceivable. Thus, Spinoza avoids the ‘overloading’ of essences and the problems that would ensue. The account developed in this paper has a surprising implication, namely that the essences of non-divine, singular things do not suffice to render these things fully conceivable on Spinoza’s view. Thus, Spinoza breaks with a tradition according to which the essence of a thing states ‘what the thing is.’ As a result, his conception of essence is much further removed from traditional Aristotelian accounts, and from other seventeenth-century accounts, than usually acknowledged. (shrink)

After situating Andreas Reckwitz’s The Society of Singularities within the broader context of the tradition of social theory, we discuss in detail the obvious strengths of this book, notably its impressive range and originality. Subsequently, we elaborate on two limitations of Reckwitz’s argument. Firstly, we argue that Reckwitz’s use of categories such as ‘singularity’ and ‘universality’ is too all-embracing, lacking the clarity and focus needed to sustain a productive line of inquiry. Secondly, and related to the previous point, we contend (...) that Reckwitz’s claims about the recent trend towards increasing singularity are so broad that they are difficult to refute empirically. Further, we discuss briefly contemporary political developments to demonstrate why the core societal issues at stake cannot be explained through all-inclusive categories such as singularity. Finally, we maintain that existence theory can provide an alternative fruitful perspective on some of the phenomena discussed in this book. (shrink)

Suicidality, a significant problem in New Zealand for the past decade or so, has invited a substantial body of research into causes and prevention. However, given the effort, the prevention results do not appear to be sufficiently convincing when coroners’ views are considered. This paper focuses on two mainstream therapeutic approaches towards persons with borderline personality disorder, in which suicidal behaviour is a prominent feature demanding understanding and active attention. It is argued that dialectical behaviour therapy and psychoanalytically informed therapies (...) are lacking on two accounts. Firstly, the philosophical and methodological underpinnings of both approaches perpetuate what Heidegger refers to as the compound misunderstanding of ourselves as human beings. Secondly, what this translates into is a practice which forgets the human order and misunderstands the experience of the singular human present in despair. As an alternative approach towards dealing with suicide in practice, the author presents concepts central to Heidegger’s phenomenology of human existence and discusses how these may inform and enhance the treatment of suicidal patients. Indo-Pacific Journal of Phenomenology , Volume 7, Edition 2 September 2007. (shrink)

We extend the core model induction technique to a choiceless context, and we exploit it to show that each one of the following two hypotheses individually implies that , the Axiom of Determinacy, holds in the of a generic extension of : every uncountable cardinal is singular, and every infinite successor cardinal is weakly compact and every uncountable limit cardinal is singular.

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality ℵ0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are $\mu^{++}$ graphs on μ+ that taken jointly are universal for the graphs on μ+, while $2^{\mu^+} \gg \mu^{++}$ . The paper also addresses the general problem of obtaining a framework for consistency results (...) at the successor of a singular strong limit starting from the assumption that a supercompact cardinal κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method. (shrink)

Many writers who have discussed the Singularity have treated it not only as the inevitable outcome of advancements in cybernetic technology, but also as natural consequence of broader patterns in the development of human knowledge, or of human history itself. In this paper I examine these claims in light of Karl Popper’s famous philosophical critique of historicism. I argue that, because the Singularity is regarded as both a product of human ingenuity and a reflection of the permanent limitations of our (...) rational capacities, speculation about its likelihood occupies an interesting border zone between what Popper referred to as “technological prediction” and what he lambasted as “prophecy.” I go on to examine representations of a post-singularity world in the novels of Iain M. Banks, as well as in Bruce Sterling’s short story “The Beautiful and the Sublime.” These narratives demonstrate how trying to imagine what human life might be like in the presence of intellectually superior AIs requires a more aggressively skeptical attitude toward the human capacity to understand our own history than even Popper was prepared to allow for. (shrink)

Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle’s state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0–1/4. This prevents the oscillations (...) form growing without limit giving a lower bound to the energy spectrum and forcing the Hamiltonian of the system to be self-adjoint. Technically, this translates into a regularization scheme whereby the inverse square potential is replaced near the origin by another that has the same singularity but with a weak coupling strength. Here, we take the Eckart as the regularizing potential and obtain the corresponding solutions (discrete bound states and continuum scattering states). (shrink)

Educational philosophy has not discussed Foucault’s publications on the Iranian Revolution and the related controversy. Foucauldian concepts are applied to education, though his only writings which ‘sidetracked’ him from exploring power within the state, namely, his journalistic accounts of his visits to Iran, remain unexplored in our field. Against moralist accusations of Foucault’s views on Iran as ‘singularly uncritical’, and beyond standard postcolonial charges of Foucault with exoticism and orientalism, I examine how the writings in question reveal ambivalences and limits (...) of Foucauldian philosophy and complicate the glorification of limit-experience in educational theory. (shrink)

Vincent Ardourel discusses the eliminability of infinite limits in the explanations of phase transitions—an important point in the debate on the reducibility of thermodynamics to statistical mechanics. To this end, he examines alternative physical theories that deal with phase transitions in finite systems.

This essay considers the ‘limit’ in Derrida's work from the early consideration of linearisation in ‘Ousia and Grammē’ to the conception of limit as aporia in Aporias. Developing Derrida's tripartite definition of the limit via a reading of Being and Time as closure, border and demarcation, the essay then considers the earlier presentation of limit in Heidegger as temporal primordiality. Developing the metaphysics of line as presentation of presence in terms of Aristotle's aporetics of time as (...) line, the circle is then considered as representing the closed field of presence and its definition via the negation of being's other. This leads to Derrida's early, foundational definition of the law of metaphysics as submission-subtraction, and his proposal of the trace as an alternate way of thinking spatially about being, nonbeing and difference. The second half of the essay then proposes a series of alternative ways of thinking geometrically to those of the traditional metaphysics of point-line-circle topography. Thus topology is proposed as an alternate means of thinking field enclosure, similarity and difference. The figures of the double torus and mathematical limit are proposed as a potential alternative geometry for Western thought. Finally the essay concludes on the apotropaic logic of the problem which echoes that of the trace and is developed in contradistinction to the aporia. Proposing the edge as an interim state between the metaphysics of the line and the deconstructive impossibilities of the aporia, it suggests that the limits of metaphysics are to be found not merely in the apotropaic law of submission-subtraction, but also across alternate geometries which facilitate the bringing together of the two central elements of the totality of Derrida's thinking the limit: différance and singularity. (shrink)

Suppose $\lambda$ is a singular cardinal of uncountable cofinality $\kappa$. For a model $\mathscr{M}$ of cardinality $\lambda$, let No ($\mathscr{M}$) denote the number of isomorphism types of models $\mathscr{N}$ of cardinality $\lambda$ which are L$_{\infty\lambda}$- equivalent to $\mathscr{M}$. In [7] Shelah considered inverse $\kappa$- systems $\mathscr{A}$ of abelian groups and their certain kind of quotient limits Gr($\mathscr{A}$)/ Fact($\mathscr{A}$). In particular Shelah proved in [7, Fact 3.10] that for every cardinal $\mu$ there exists an inverse $\kappa$-system $\mathscr{A}$ such that $\mathscr{A}$ (...) consists of abelian groups having cardinality at most $\mu^\kappa$ and card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse $\kappa$-systems and possible values of No (under the assumption that $\theta^\kappa < \lambda$ for every $\theta < \lambda$): if $\mathscr{A}$ is an inverse $\kappa$- system of abelian groups having cardinality < $\lambda$, then there is a model $\mathscr{M}$ such that card $(\mathscr{M}) = \lambda$ and No($\mathscr{M}$) = card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)). The following was an immediate consequence (when $\theta^\kappa < \lambda$ for every $\theta < \lambda$): for every nonzero $\mu < \lambda$ or $\mu = \lambda^\kappa$ there is a model $\mathscr{M}_\mu$ of cardinality $\lambda$ with No$(\mathscr{M}_\mu) = \mu$. In this paper we show: for every nonzero $\mu \leq \lambda^\kappa$ there is an inverse $\kappa$-system $\mathscr{A}$ of abelian groups having cardinality < $\lambda$ such that card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$ (under the assumptions $2^\kappa < \lambda$ and $\theta^{<\kappa} < \lambda$ for all $\theta < \lambda$ when $\mu > \lambda$), with the obvious new consequence concerning the possible value of No. Specifically, the case No($\mathscr{M}$) = $\lambda$ is possible when $\theta^\kappa < \lambda$ for every $\theta < \lambda$. (shrink)