This chapter is offered as a contribution to the logic of down below. We attempt to demonstrate that the nature of human agency necessitates that there actually be such a logic. The ensuing sections develop the suggestion that cognition down below has a structure strikingly similar to the physical structure of quantum states. In its general form, this is not an idea that originates with the present authors. It is known that there exist mathematical models from the cognitive science of (...) cognition down below that have certain formal similarities to quantum mechanics. We want to take this idea seriously. We will propose that the subspaces of von Neumann-Birkhoff lattices are too crisp for modelling requisite cognitive aspects in relation to subsymbolic logic. Instead, we adopt an approach which relies on projections into nonorthogonal density states. The projection operator is motivated from cues which probe human memory. (shrink)

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, (...) 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision. (shrink)

The expressive power of logic is believed to be able to model most of the fundamental aspects of information retrieval. However, it is also understood that classical logic is ineffective for handling partiality and uncertainty in IR. Applying non-classical logics such as the AGM belief revision logic and the possibilistic logic to adaptive information retrieval is appealing since they provide a powerful and rigorous framework to model partiality and uncertainty inherent in any IR processes. The maxi-adjustment method, which is an (...) effective computational apparatus of the AGM paradigm, is applied to develop the learning components of the adaptive information agents. Essentially, maxi-adjustment allows the partial representation K of a user's information needs N to be refined gradually based on the user's relevance feedback t. Generally speaking, learning in adaptive information agents is characterised by the AGM belief revision Kt*. On the other hand, possibilistic logic supports a gradated assessment of the uncertainty arising from matching K with the imperfect characterisation d of an information object D. Information matching in adaptive information agents is underpinned by K ƕ d, where ƕ is the possibilistic inference relation. This paper illustrates how maxi-adjustment and possibilistic deduction can be applied to develop the adaptive information agents. Their impact on the agents learning autonomy and explanatory power is also discussed. (shrink)

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. (...) Additionally, the principle of semantic compositionality is underspecifi ed, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities. Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations. (shrink)

Diminishing awareness is a consequence of the information explosion: disciplines are becoming increasingly specialized; individuals and groups are becoming ever more insular. This paper considers how awareness can be enhanced via abductive knowledge discovery the goal of which is to produce suggestions which can span disparate islands of knowledge. Knowledge representation is motivated from a cognitive perspective. Words and concepts are represented as vectors in a high dimensional semantic space automatically derived from a text corpus. Information flow computation between vectors (...) is proposed as a means of suggesting potentially interesting implicit associations between concepts. Information flow is applied to computational scientific discovery by attempting to simulate Swanson's Raynaud-fish oil discovery in medical texts. Both automatic and semi-automatic attempts were studied and compared against suggestions computed via semantic association. Even though this work is preliminary and speculative in nature, there is some justification to believe that appropriate suggestions can be “abduced” from semantic space. (shrink)

Diminishing awareness is a consequence of the information explosion: disciplines are becoming increasingly specialized; individuals and groups are becoming ever more insular. This article considers how awareness can be enhanced via operational abductive systems. The goal is to generate and justify suggestions which can span disparate islands of knowledge. Knowledge representation is motivated from a cognitive perspective. Words and concepts are represented as vectors in a high dimensional semantic space automatically derived from a text corpus. Various mechanisms will be presented (...) for computing suggestions from semantic space: information flow, semantic similarity, pre-inductive generalization. The overall goal of this article is to introduce semantic space to the model-based reasoning and abduction community and to illustrate its potential for principled, operational abduction by semi-automatically replicating the Swanson Raynaud/fish oil discovery in medical text. (shrink)

Erwin Schrödinger holds a prominent place in the history of science primarily due to his crucial role in the development of quantum physics. What is perhaps lesser known are his insights into subject-object duality, consciousness and mind. He documented himself that these were influenced by the Upanishads, a collection of ancient Hindu spiritual texts. Central to his thoughts in this area is that Mind is only One and there is no separation between subject and object. This chapter aims to bridge (...) Schrödinger’s view on One Mind with the teachings of Dōgen, a twelfth century Zen master. This bridge is formed by addressing the question of how time relates to One Mind, and subject-object duality. Schrödinger describes the experience of One Mind to be like a timeless now, whereas subject-object duality involves a linear continuum of time. We show how these differing positions are unified in the notion of ‘absolute present’, which was put forward in the philosophy of Nishida Kitarō (1871–1945). In addition, we argue that it is in this notion of absolute present that the views of Schrödinger, Dōgen and Nishida meet. (shrink)

This article extends the combinatorial approach to support the determination of contextuality amidst causal influences. Contextuality is an active field of study in Quantum Cognition, in systems relating to mental phenomena, such as concepts in human memory. In the cognitive field of study, a contemporary challenge facing the determination of whether a phenomenon is contextual has been the identification and management of disturbances. Whether or not said disturbances are identified through the modeling approach, constitute causal influences, or are disregardableas as (...) noise is important, as contextuality cannot be adequately determined in the presence of causal influences. To address this challenge, we first provide a formalization of necessary elements of the combinatorial approach within the language of canonical causal models. Through this formalization, we extend the combinatorial approach to support a measurement and treatment of disturbance, and offer techniques to separately distinguish noise and causal influences. Thereafter, we develop a protocol through which these elements may be represented within a cognitive experiment. As human cognition seems rife with causal influences, cognitive modelers may apply the extended combinatorial approach to practically determine the contextuality of cognitive phenomena. (shrink)

The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful (...) as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon. (shrink)

Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.

A decade ago, we reviewed the field of clinical ethics; assessed its progress in research, education, and ethics committees and consultation; and made predictions about the future of the field. In this article, we revisit clinical ethics to examine our earlier observations, highlight key developments, and discuss remaining challenges for clinical ethics, including the need to develop a global perspective on clinical ethics problems.

In this paper, we suggest some of the dimensions of the problematic concept of Alzheimer Disease as a natural disease discerned by increasingly sophisticated medical scientific progress. Taking a page from Max Weber concerning unique events, we show some of the conceptual building blocks and social processes that have coalesced into the perception of certain phenomena as abnormalities that are seen as implicated in the development of a degenerative disease distinct from the process of normal, but variable, brain aging. We (...) note some of the decisions and social forces pushing for particular conceptualizations, interpretations, and reifications of brain alterations. In so doing, we suggest that the mystery of the "there" may not be much different from, and probably is, the mystery of the "everywhere". (shrink)

Motile bacteria respond to environmental cues to move to more favorable locations. The components of the chemotaxis signal transduction systems that mediate these responses are highly conserved among prokaryotes including both eubacterial and archael species. The best‐studied system is that found in Escherichia coli. Attractant and repellant chemicals are sensed through their interactions with transmembrane chemoreceptor proteins that are localized in multimeric assemblies at one or both cell poles together with a histidine protein kinase, CheA, an SH3‐like adaptor protein, CheW, (...) and a phosphoprotein phosphatase, CheZ. These multimeric protein assemblies act to control the level of phosphorylation of a response regulator, CheY, which dictates flagellar motion. Bacterial chemotaxis is one of the most‐understood signal transduction systems, and many biochemical and structural details of this system have been elucidated. This is an exciting field of study because the depth of knowledge now allows the detailed molecular mechanisms of transmembrane signaling and signal processing to be investigated. BioEssays 28:9–22, 2006. © 2005 Wiley Periodicals, Inc. (shrink)

Building on an illustrative case of a systemic environmental threat and its multi‐stakeholder response, this paper draws attention to the changing political impacts of corporations in the digital age. Political Corporate Social Responsibility (PCSR) theory suggests an expanded sense of politics and corporations, including impacts that may range from voluntary initiatives to overcome governance gaps, to avoiding state regulation via corporate political activity. Considering digitalization as a stimulus, we explore potential responsibilities of corporations toward public goods in contexts with functioning (...) governments. We show that digitalization—in the form of transparency, surveillance, and data‐sharing—offers corporations’ scope for deliberative public participation. The starry sky beetle infestation endangering public and private goods is thereby used to illustrate the possibility of expanding the political role of corporations in the digital sphere. We offer a contribution by conceptualizing data‐deliberation as a Habermasian variation of PCSR, defined as the (a) voluntary disclosure of corporate data and its transparent, open sharing with the public sector (b) along with the cooperation with governmental institutions on data analytics methods for examining large‐scale datasets (c) thereby complying with existing national and international regulations on data protection, in particular with respect to privacy and personal data. (shrink)

We address concerns raised by Maul (2012) regarding the validity of the Mayer-Salovey-Caruso Emotional Intelligence Test (MSCEIT). We respond to requests for clarifications of our model, and explain why the MSCEIT’s scoring methods stand up to scrutiny and why many reported reliabilities of the MSCEIT may be underestimates, using reanalyses of the test’s standardization sample of N = 5,000 to illustrate our point. We also organize findings from four recent articles that provide evidence for the MSCEIT’s validity based on its (...) relations with other tests. (shrink)

Practical medical decisions are closely integrated with ethical and religious beliefs in the Philippines. This is shown in a survey of Filipino physicians' attitudes towards severely compromised neonates. This is also the reason why the ethical analysis of critical care practices must be situated within the context of local culture. Kagandahang loob and kusang loob are indigenous Filipino ethical concepts that provide a framework for the analysis of several critical care practices. The practice of taking-from-the-rich-to-give-to-the-poor in public hospitals is not (...) compatible with these concepts. The legislated definition of death and other aspects of the Philippine Law on Organ Transplants also fail to be compatible with these concepts. Many ethical issues that arise in a critical care setting have their roots outside the seemingly isolated clinical setting. Critical care need not apply only to individuals in a serious clinical condition. Vulnerable populations require critical attention because potent threats to their lives exist in the water that they drink and the air that they breathe. We cannot ignore these threa ts even as we move inevitably towards a technologically dependent, highly commercialized approach to health management. (shrink)

Scientific realists claim we can justifiably believe that science is getting at the truth. But they have long faced historical challenges: various episodes across history appear to demonstrate that even strongly supported scientific theories can be overturned and left behind. In response, realists have developed new positions and arguments. As a result of specific challenges from the history of science, and realist responses, we find ourselves with an ever increasing data-set bearing on the (possible) relationship between science and truth. The (...) present volume introduces new historical cases impacting the debate, and advances the discussion of cases that have only very recently been introduced. At the same time, shifts in philosophical positions affect the very kind of case study that is relevant. Thus the historical work must proceed hand in hand with philosophical analysis of the different positions and arguments in play. It is with this in mind that the volume is divided into two sections, entitled “Historical cases for the debate,” and “Contemporary scientific realism”. All sides agree that historical cases are informative with regard to how, or whether, science connects with truth. Defying proclamations as early as the 1980s announcing the death knell of the scientific realism debate, here is that rare thing: a philosophical debate making steady and definite progress. Moreover, the progress it is making concerns one of humanity’s most profound and important questions: the relationship between science and truth, or, put more boldly, the epistemic relation between humankind and the reality in which we find ourselves. (shrink)

COVID-19 has revealed that science needs to learn how to better deal with the irreducible uncertainty that comes with global systemic risks as well as with the social responsibility of science towards the public good. Further developing the epistemological principles of new theories and experimental practices, alternative investigative pathways and communication, and diverse voices can be an important contribution of history and philosophy of science and of science studies to ongoing transformations of the scientific enterprise.

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

Infinitism is an ancient view in epistemology about the structure of knowledge and epistemic justification, according to which there are no foundational reasons for belief. The view has never been popular, and is often associated with skepticism, but after languishing for centuries it has recently begun a resurgence. Ad Infinitum presents new work on the topic by leading epistemologists. They shed new light on infinitism's distinctive strengths and weaknesses, and address questions, new and old, about its account of justification, reasoning, (...) epistemic responsibility, disagreement, and trust, among other important issues. The volume clarifies the relationship between infinitism and other epistemological views, such as skepticism, coherentism, foundationalism and contextualism, and it offers novel perspectives on the metaphysics, epistemology, and ethics of regresses and reasons. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

The Protein Ontology provides terms for and supports annotation of species-specific protein complexes in an ontology framework that relates them both to their components and to species-independent families of complexes. Comprehensive curation of experimentally known forms and annotations thereof is expected to expose discrepancies, differences, and gaps in our knowledge. We have annotated the early events of innate immune signaling mediated by Toll-Like Receptor 3 and 4 complexes in human, mouse, and chicken. The resulting ontology and annotation data set has (...) allowed us to identify species-specific gaps in experimental data and possible functional differences between species, and to employ inferred structural and functional relationships to suggest plausible resolutions of these discrepancies and gaps. (shrink)

Mit der Digitalisierung geht ein fundamentaler, herausfordernder Wandel einher. Durch eine Begriffsbestimmung und Operationalisierung wird in diesem Beitrag der digitale Wandel aus wirtschaftsphilosophischer Sicht vorgestellt. Zunächst werden wirtschaftsphilosophische Grundlagen der Digitalisierung wie die Informationsethik erläutert, gefolgt von einer Diskussion der digitalen Wertschöpfung, die auf Überwachung aufbaut und von einer Überwachungskultur gespeist wird. Schließlich werden Zukunftsperspektiven zum Internet der Dinge, Pricing, Privatheit und der Digitalen Demokratie skizziert.

Recent developments in global business gave rise to innovative forms of digital-exchange, facilitated by a new big data-based infrastructure – the sharing economy platform. SEPs are rapidly expanding, challenging the political-economic order and the classical division of work in society. Against the background of the current sustainability crisis, we discuss the increasingly momentous role of SEPs as a potential driver toward a more sustainable economy and society. Drawing on the theoretical lens of political CSR theory, we first outline how SEPs (...) are applying institutional strategies to gain a competitive advantage, thereby shaping contexts in their favor and triggering an erosion of foundations of social sustainability. However, SEPs also strive for legitimacy by taking over novel social responsibilities via profound digital capacities. Thus SEPs carry the potential to contribute to a more sustainable future economy. Our chapter considers future pathways of platform CSR regimes and a democratization of SEPs building on political CSR theory. (shrink)

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this (...) article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified. (shrink)

In recent years, scholars have begun to lay the groundwork to justify a distinct application of ethics to the field of public health. They have highlighted important features that differentiate public health ethics from bioethics, especially public health’s emphasis on population health rather than issues of individual health. Articulations of public health ethics also tend to emphasize the role of social justice compared to the predominance of autonomy in the bioethical literature. Now that the field of public health ethics is (...) developing a unique focus and a language of its own, including a code of ethics disseminated by the American Public Health Association, the future of public health ethics may well be global health ethics, focusing on issues of global justice. As public health ethics evolves from its nascent stage of reflection to a place of action and application in the national and global arenas, two interrelated developments will need to occur: public health professionals, including practitioners, policymakers, and scholars, will need a richer understanding of the ethical challenges practitioners face on a daily basis and scholars will need to develop useful tools that practitioners may employ for identifying and tackling these ethical challenges. (shrink)

Ethical challenges in public health can have a significant impact on the health of communities if they impede efficiencies and best practices. Competing needs for resources and a plurality of values can challenge public health policymakers and practitioners to make fair and effective decisions for their communities. In this paper, the authors offer an analytic framework designed to assist policymakers and practitioners in managing the ethical tensions they face in daily practice. Their framework is built upon the following set of (...) six considerations: determining population-level utility of the proposed action; demonstrating evidence of need and effectiveness of actions; establishing fairness of goals and proposed implementation strategies; ensuring accountability; and, assessing expected efficiencies and costs associated with the proposed action. Together, these considerations create a structured guide to assist decision-makers in identifying potential ethical challenges and in assessing the moral considerations that underlie public health practice - and possibly even, if the conditions are met, reduce the creation of ethical tension. Although the authors’empirical experiences provide the basis for the framework advanced here, their approach remains to be tested and evaluated by public health practitioners. (shrink)

Representing species-specific proteins and protein complexes in ontologies that are both human and machine-readable facilitates the retrieval, analysis, and interpretation of genome-scale data sets. Although existing protin-centric informatics resources provide the biomedical research community with well-curated compendia of protein sequence and structure, these resources lack formal ontological representations of the relationships among the proteins themselves. The Protein Ontology (PRO) Consortium is filling this informatics resource gap by developing ontological representations and relationships among proteins and their variants and modified forms. Because (...) proteins are often functional only as members of stable protein complexes, the PRO Consortium, in collaboration with existing protein and pathway databases, has launched a new initiative to implement logical and consistent representation of protein complexes. We describe here how the PRO Consortium is meeting the challenge of representing species-specific protein complexes, how protein complex representation in PRO supports annotation of protein complexes and comparative biology, and how PRO is being integrated into existing community bioinformatics resources. The PRO resource is accessible at http://pir.georgetown.edu/pro/. (shrink)

The Protein Ontology (PRO) web resource provides an integrative framework for protein-centric exploration and enables specific and precise annotation of proteins and protein complexes based on PRO. Functionalities include: browsing, searching and retrieving, terms, displaying selected terms in OBO or OWL format, and supporting URIs. In addition, the PRO website offers multiple ways for the user to request, submit, or modify terms and/or annotation. We will demonstrate the use of these tools for protein research and annotation.

The Protein Ontology (PRO) provides a formal, logically-based classification of specific protein classes including structured representations of protein isoforms, variants and modified forms. Initially focused on proteins found in human, mouse and Escherichia coli, PRO now includes representations of protein complexes. The PRO Consortium works in concert with the developers of other biomedical ontologies and protein knowledge bases to provide the ability to formally organize and integrate representations of precise protein forms so as to enhance accessibility to results of protein (...) research. PRO (http://pir.georgetown.edu/pro) is part of the Open Biomedical Ontologies (OBO) Foundry. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

Identity, Morality, and Threat offers a critical examination of the social psychological processes that generate outgroup devaluation and ingroup glorification as the source of conflict. Daniel Rothbart and Karyna Korostelina bring together essays analyzing the causal relationship between escalating violence and opposing images of the Self and Other.

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this (...) article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified. (shrink)