The discourse marker use of the word like is considered by many to be superfluously sprinkled into talk, a bad habit best avoided. But a comparison of the use of like in successive tellings of stories demonstrates that like can be anticipated in advance and planned into stories. In this way, like is similar to other words and phrases tellers recycle during story telling. The anticipation of like contrasted with the uses of other discourse markers such as oh, you know, (...) and well, which almost never re-occurred in similar locations across tellings. Um and uh did sometimes re-occur; these uses are contrasted with like. Although discourse markers are generally used on the fly to handle various issues that come up in coordinating talk as it unfolds, like can be used as an integral part of the story -a marked contrast to the prevalent idea that likes are speech tics. (shrink)

Words like well, oh, and you know have long been observed and studied in spontaneous speech. With the proliferation of on-line dialogues, such as instant messaging between friends or back-and-forth postings at websites, there are increasing opportunities to observe them in spontaneous writing. In Experiment 1, the interpretation of discourse markers in on-line debates was compared to proposed functions of those markers identified in other settings. In Experiment 2, the use of discourse markers in spontaneous speech was compared to their (...) uses in spontaneous writing. Results support the conclusion that although they vary in frequency in spoken versus written domains, discourse markers are used similarly across domains, but with particular communicative functions that make them non-interchangeable. (shrink)

To generate empathy in the care of vulnerable older persons requires care providers to reflect critically on their care practices. Ethics education and training must provide them with tools to accomplish such critical reflection. It must also create a pedagogical context in which good care can be taught and cultivated. The care-ethics lab ‘sTimul’ originated in 2008 in Flanders with the stimulation of ethical reflection in care providers and care providers in training as its main goal. Also in 2008, sTimul (...) commenced the organization of empathy sessions as an attempt to achieve this goal by simulation. The empathy session is a practical and fairly straightforward way of working to provoke care providers and care providers in training to engage in ethical reflection. Characteristic of the empathy session in the care-ethics lab is the emphasis on experience as a basis for ethical reflection. (shrink)

This dissertation is a collection of three papers – “Knowing Oneself for Others,” “Stereotype Threat and the Value of Self-Knowledge,” and “Self-Knowledge, Epistemic Work, and Injustice” – in which I address the connections between self-knowledge production and social inequality. I explain, using a variety of contemporary political and cultural examples, that marginalized individuals are more likely to be required to know certain things about themselves than socially privileged individuals, especially about those aspects of their lives and identities which are essential (...) to their being marginalized. I argue that this should make us rethink our basic understanding of epistemic injustice, which is typically thought of as involving the prevention of marginalized individuals from producing knowledge. More specifically, in “Knowing Oneself for Others,” I introduce the notion of “compulsory self-disclosure,” a social phenomenon in which an individual is forced to reveal things about themselves, often in ways that further contribute to their oppression. “Stereotype Threat and the Value of Self-Knowledge” addresses how self-ignorance can actually be desirable for individuals facing stereotype threat, and I argue that treating stereotype threat as an epistemic injustice issue can actually harm rather than help individuals in certain cases. Finally, in “Self-Knowledge, Epistemic Work, and Injustice,” I assess the reasoning behind the assumption that marginalized people are self-ignorant; I argue that we need to appreciate the central role that epistemic work plays in self-knowledge production to understand why the standard assumption about marginalized self-ignorance is misguided. Ultimately, I would have us think of self-knowledge production as not just epistemic work but as work that is often emotionally difficult and even metaphysically transformative – coming to have self-knowledge in certain ways can quite literally change who you are. In light of this, the overarching aim of this work is to argue for there being an inextricable link between an individual’s knowledge of themselves and their social status, as well as to discourage readers from thinking of the production of self-knowledge as inherently desirable or as a wholly epistemic issue. (shrink)

Observing others in conversation is a common format for comprehending language, yet little work has been done to understand dialog comprehension. We tested whether overhearers use addressee backchannels as predictive cues for how to integrate information across speaker turns during comprehension of spontaneously produced collaborative narration. In Experiment 1, words that followed specific backchannels were recognized more slowly than words that followed either generic backchannels or pauses. In Experiment 2, we found that when the turn after the backchannel was a (...) continuation of the narrative, specific backchannels prompted the fastest verification of prior information. When the turn after was an elaboration, they prompted the slowest, indicating that overhearers took specific backchannels as cues to integrate preceding talk with subsequent talk. These findings demonstrate that overhearers capitalize on the predictive relationship between backchannels and the development of speakers’ talk, coordinating information across conversational roles. (shrink)

We explored the differential impact of auditory information and written contextual information on the recognition of verbal irony in spontaneous speech. Based on relevance theory, we predicted that speakers would provide acoustic disambiguation cues when speaking in situations that lack other sources of information, such as a visual channel. We further predicted that listeners would use this information, in addition to context, when interpreting the utterances. People were presented with spontaneously produced ironic and nonironic utterances from radio talk shows in (...) written or auditory form, with or without written contextual information. When the utterances were read without written contextual information, all utterances were rated as equally ironic. But when they were heard as opposed to read, or when they were presented in irony-biasing contexts, originally ironic utterances were rated as more sarcastic than originally nonironic utterances. This evidence suggests both acoustic and contextual information are used when inferring ironic intent in spontaneous speech, and validates previous manipulations of intonation in studies of irony understanding. (shrink)

The COVID-19 pandemic has presented a global threat to physical and mental health worldwide. Research has highlighted adverse impacts of COVID-19 on wellbeing but has yet to offer insights as to how wellbeing may be protected. Inspired by developments in wellbeing science and guided by our own theoretical framework, we examined the role of various potentially protective factors in a sample of 138 participants from the United Kingdom. Protective factors included physical activity, tragic optimism, gratitude, social support, and nature connectedness. (...) Initial analysis involved the application of one-sample t-tests, which confirmed that wellbeing in the current sample was significantly lower compared to previous samples. Protective factors were observed to account for up to 50% of variance in wellbeing in a hierarchical linear regression that controlled for a range of sociostructural factors including age, gender, and subjective social status, which impact on wellbeing but lie beyond individual control. Gratitude and tragic optimism emerged as significant contributors to the model. Our results identify key psychological attributes that may be harnessed through various positive psychology strategies to mitigate the adverse impacts of hardship and suffering, consistent with an existential positive psychology of suffering. (shrink)

This article discusses ways to operationalise the concept of culturally appropriate computer-mediated communication, utilising information systems (IS) development methodologies and adopting a postmodern and postcolonial perspective. By way of illustration, it describes progress on the participative development of the Ieramugadu Cultural Information System. This project is designed to develop and evaluate innovative procedures for elicitation, analysis, storage and communication of indigenous cultural heritage information. It is investigating culturally appropriate IS design techniques, multimedia approaches and ways to ensure protection of secret/sacred (...) information. Ethical issues are foregrounded. (shrink)

There has been little previous scholarship regarding the aims, options and impact of ethics education on residential care‐givers. This manuscript details findings from a pragmatic cluster trial evaluating the impact of three different approaches to ethics education. The focus of the article is on one of the interventions, an immersive simulation experience. The simulation experience required residential care‐givers to assume the profile of elderly care‐recipients for a 24‐hr period. The care‐givers were student nurses. The project was reviewed favourably by a (...) university ethics committee, and participants provided informed consent. Data from six postsimulation experience focus groups were analysed thematically and three themes were identified: the experience of vulnerability, dignity in care and the organisation of care. Findings suggest that the immersive simulation experience had a powerful immediate impact as participants described epiphanous insights relating to their care experiences. It is suggested that reflecting on and recording epiphanous events has the potential to sustain ethical care practices. Further research is required to evaluate the impact of different ethics education interventions in different cultural contexts. Exploration is also required regarding the meaning and significance of care epiphanies, those “most delicate and evanescent of moments,” for the sustainability of ethical care. (shrink)

Bilingualism has been identified as a potential cognitive factor linked to delayed onset of dementia as well as boosting executive functions in healthy individuals. However, more recently, this claim has been called into question following several failed replications. It remains unclear whether these contradictory findings reflect how bilingualism is defined between studies, or methodological limitations when measuring the bilingual effect. One key issue is that despite the claims that bilingualism yields general protection to cognitive processes, studies reporting putative bilingual differences (...) are often focused on domain specific experimental paradigms. This study chose a broader approach, by considering the consequences of bilingualism on a wide range of cognitive functions within individuals. We utilised 19 measures of different cognitive functions commonly associated with bilingual effects, to form a “cognitive profile” for 215 non-clinical participants. We recruited Welsh speakers, who as a group of bilinguals were highly homogeneous, as means of isolating the bilingualism criterion. We sought to determine if such analyses would independently classify bilingual/monolingual participant groups based on emergent patterns driven by collected cognitive profiles, such that population differences would emerge. Multiple predictive models were trained to independently recognise the cognitive profiles of bilinguals, older adults and higher education attainment. Despite managing to successfully classify cognitive profiles based on age and education, the model failed to differentiate between bilingual and monolingual cognitive ability at a rate greater than that of chance. Repeated modelling using alternative definitions of bilingualism, and just the older adults, yielded similar results. In all cases then, using our “bottom–up” analytical approach, there was no evidence that bilingualism as a variable indicated differential cognitive performance – as a consequence, we conclude that bilinguals are not cognitively different from their monolingual counterparts, even in older demographics. We suggest that studies that have reported a bilingual advantage could well have confounded other key variables that may be driving reported advantages. We recommend that future research refine the machine learning methods used in this study to further investigate the complex relationship between bilingualism and cognition. (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)

"Knowing how we know" is the subject of this book. Its authors present a new view of cognition that has important social and ethical implications, for, they assert, the only world we humans can have is the one we create together through the actions of our coexistence. Written for a general audience as well as for students, scholars, and scientists and abundantly illustrated with examples from biology, linguistics, and new social and cultural phenomena, this revised edition includes a new afterword (...) by Dr. Varela, in which he discusses the effect the book has had in the years since its first publication. (shrink)

The chapter talks about Shel Silverstein's The Giving Tree, which is a favorite of many children, adults, and teachers. The story of a relationship between a boy and a tree is charming for, despite the vicissitudes of the relationship, the two end up together at the end, with the boy — now an old man — sitting contentedly on the tree — itself reduced to a mere stump. The book raises an important issue in the field of environmental ethics. It (...) asks us to recognize that between childhood and old age, people operating within the Western tradition of ethics are not mindful of the value that the non‐human beings in their environment have for them as well as for future generations. Harkening to such warnings, environmental ethicists have attempted to raise important issues about our relationship with the other beings that make up our world. (shrink)

From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.

Brackets and tables, circles and maps, 1554-1872 -- Early botanical networks and trees, 1766-1815 -- The first evolutionary tree, 1786-1820 -- Diverse and unusual trees of the early nineteenth century, 1817-1834 -- The rule of five, 1819-1854 -- Pre-Darwinian branching diagrams, 1828-1858 -- Evolution and the trees of Charles Darwin, 1837-1868 -- The trees of Ernst Haeckel, 1866-1905 -- Post-Darwinian nonconformists, 1868-1896 -- More late-nineteenth-century trees, 1874-1897 -- Trees of the early twentieth century, 1901-1930 (...) -- The trees of Alfred Sherwood Romer, 1933-1966 -- Additional trees of the mid-twentieth century, 1931-1943 -- The trees of William King Gregory, 1938-1951 -- Hints of new approaches, 1954-1969 -- Phenograms and cladograms, 1958-1966 -- Early molecular trees, 1962-1987 -- Notable trees of the past four decades, 1970-2010 -- Primeval branches and universal trees of life, 1997-2010. (shrink)

Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.

It has sometimes been suggested that people represent the structure of action in terms of an action tree. A question now arises about the relationship between this action tree representation and people’s moral judgments. A natural hypothesis would be that people first construct a representation of the action tree and then go on to use this representation in making moral judgments. The present paper argues for a more complex view. Specifically, the paper reports a series of experimental studies that appear (...) to show that people’s moral judgments can actually impact their representations of the action tree itself. (shrink)

Previous examinations of the scope of moral concern have focused on aggregate attributions of moral worth. However, because trade‐offs exist in valuing different kinds of entities, tabulating total amounts of moral expansiveness may conceal significant individual differences in the relative proportions of moral valuation ascribed to various entities. We hypothesized that some individuals (“tree‐huggers”) would ascribe greater moral worth to animals and ecosystems than to humans from marginalized or stigmatized groups, while others (“human‐lovers”) would ascribe greater moral worth to outgroup (...) members than to the natural world. Additionally, because moral valuation is often treated as being zero‐sum, we hypothesized that there would be no difference in aggregate levels of moral concern between tree‐huggers and human‐lovers. Finally, because attributions of mental capacities substantially contribute to moral valuation, we predicted that tree‐huggers and human‐lovers would show different patterns of mind attribution for animals versus humans. Three studies (N = 985) yielded evidence in support of our hypotheses. First, over one‐third of participants valued nature over outgroups. Second, extending moral value to animals and nature was not indicative of more expansive moral concern overall; instead, tree‐huggers and human‐lovers were identical in their aggregate ascriptions of moral worth. Third, tree‐huggers had relatively amplified tendencies to attribute mental capacities to animals and relatively reduced tendencies to attribute mental capacities to outgroup members—thus having elevated rates of both anthropomorphism and dehumanization. These findings necessitate a reconceptualization of both the extension of moral worth and the attribution of minds. (shrink)

We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.

Originally published in 1972, Should Trees Have Standing? was a rallying point for the then burgeoning environmental movement, launching a worldwide debate on the basic nature of legal rights that reached the U.S. Supreme Court. Now, in the 35th anniversary edition of this remarkably influential book, Christopher D. Stone updates his original thesis and explores the impact his ideas have had on the courts, the academy, and society as a whole. At the heart of the book is an eminently (...) sensible, legally sound, and compelling argument that the environment should be granted legal rights. For the new edition, Stone explores a variety of recent cases and current events--and related topics such as climate change and protecting the oceans--providing a thoughtful survey of the past and an insightful glimpse at the future of the environmental movement. This enduring work continues to serve as the definitive statement as to why trees, oceans, animals, and the environment as a whole should be bestowed with legal rights, so that the voiceless elements in nature are protected for future generations. (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.

We show that strongly compact cardinals and MM are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding ‘regressive' $\lambda$-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.

This study explored local controls relating to trees and spacesof the local environment in Nyamaropa Communal Lands in theNyanga District of eastern Zimbabwe. Controls were consideredin a broad and inclusive framework encompassing codified rules,taboos, and, regulatory norms and emotions. Special emphasis waslaid on people‘s emotional and ethical investment in the abovecomponents of the environment – trees and spaces. The studyemployed intensive informal and group interviews. Results showthat there is tremendous emotional and ethical investment intrees and spaces of the (...) environment in Nyamaropa. Emotions comein a variety of forms: fear, shunning, love, reverence, andconfidence and security enhancement. The emotional and ethicalnorms are designed to govern behavior and the context of resourceutilization. These norms have implications on the organization ofspaces of the local environment and regimes of resource utilizationoccurring in them. Location of resources in spaces of the environmenthas implications on the management of resources within them. Thedomains of human habitation – home bases and home fields – werefound to be the most emotionally laden spaces with trees in thembeing actively planted, nurtured, conserved, eliminated, or destroyedon the basis of certain emotions and norms. The findings of the studyhave implications within the framework of decentralization and ofdemocratization of natural resource management. (shrink)

An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$-ITP holds for all $\lambda\geq \kappa$. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where for every $n\geq 2$ and $\mu\geq \aleph_n$, we have $(\aleph_n, \mu)$-ITP.

We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of the (...) four classes of trees mentioned above. (shrink)

The canonical view of a 3‐domain (3D) tree of life was recently challenged by the discovery of Asgardarchaeota encoding eukaryote signature proteins (ESPs), which were treated as missing links of a 2‐domain (2D) tree. Here we revisit the debate. We discuss methodological limitations of building trees with alignment‐dependent approaches, which often fail to satisfactorily address the problem of ‘‘gaps.’’ In addition, most phylogenies are reconstructed unrooted, neglecting the power of direct rooting methods. Alignment‐free methodologies lift most difficulties but require (...) employing realistic evolutionary models. We argue that the discoveries of Asgards and ESPs, by themselves, do not rule out the 3D tree, which is strongly supported by comparative and evolutionary genomic analyses and vast genomic and biochemical superkingdom distinctions. Given uncertainties of retrodiction and interpretation difficulties, we conclude that the 3D view has not been falsified but instead has been strengthened by genomic analyses. In turn, the objections to the 2D model have not been lifted. The debate remains open. Also see the video abstract here: https://youtu.be/-6TBN0bubI8. (shrink)

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the (...) game tree representation and solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks. (shrink)

Our aim here is to lay the groundwork for formal tree-ring analysis combining data from dendrochronology with formal techniques from semantics. We will present the basic syntax of, and basic compositional semantics of tree-ring structures.

Locke claimed that God superadded various powers to matter, including motion, the perfections of peach trees and elephants, gravity, and that he could superadd thought. Various interpreters have discussed the question whether Locke's claims about superaddition are in tension with his commitment to mechanistic explanation. This literature assumes that for Locke mechanistic explanation involves deducibility. We argue that this is an inaccurate interpretation and that mechanistic explanation involves a different type of intelligibility for Locke.

Given a regular cardinal λ and λ many supercompact cardinals, we describe a type of forcing such that in the generic extension there is a cardinal κ with cofinality λ, the Singular Cardinal Hypothesis at κ fails, and the tree property holds at κ+.

"The Natural System" is the name given to the underlying arrangement present in the diversity of life. Unlike a classification, which is made up of classes and members, a system or arrangement is an integrated whole made up of connected parts. In the pre-evolutionary period a variety of forms were proposed for the Natural System, including maps, circles, stars, and abstract multidimensional objects. The trees sketched by Darwin in the 1830s should probably be considered the first genuine evolutionary diagrams (...) of the Natural System—the first genuine evolutionary trees. Darwin refined his image of the Natural System in the well-known evolutionary tree published in the Origin of Species, where he also carefully distinguished between arrangements and classifications. Following the publication of the Origin, there was a great burst of evolutionary tree building, but interest in trees declined substantially after 1900, only to be revived in recent years with the development of cladistic analysis. ¶ While evolutionary trees are modern diagrams of the Natural System, they are at the same time instances of another broad class of diagrams that may be called "trees of history": branching diagrams of genealogical descent and change. During the same years that Darwin was sketching his first evolutionary trees, the earliest examples of two other trees of history also appeared: the first trees of language evolution and of manuscript genealogy. Though these were apparently independent of evolutionary trees in their origin, the similarities among all these trees of history, and among the historical processes that underlie them, were soon recognized. Darwin compared biological evolution and language evolution several times in the Origin of Species, and both Ernst Haeckel and the linguist August Schleicher made similar comparisons. Both linguists and stemmaticists (students of manuscript descent) understood the principle of apomorphy—the principle that only shared innovations provide evidence of common ancestry—more clearly than did systematists, and if there had been more cross-fertilization among these fields the cladistic revolution in systematics might well have taken place in the nineteenth century. ¶ Although historical linguists and stemmaticists have in some respects had sounder theory than have systematists, at least until recently, they have also had the practical problem of very large amounts of data, a problem not often faced by systematists until the advent of molecular sequencing. The opportunity now exists for systematists to contribute to the theory and practice of linguistics and stemmatics, their sister disciplines in historical reconstruction, through application of our commonly used computer programs for tree estimation. Preliminary results from the application of numerical cladistic analysis to a large stemmatic data set have been very encouraging, and have already generated much discussion in the stemmatics community. (shrink)

Abstract: Biology continues to use the Tree of Life image to show the temporal continuity and discontinuity of the living beings. Moreover, the development of genetic, molecular biology and paleontology has originated phylogenetics. This discipline studies evolutionary relatedness among various groups of organisms through molecular sequencing data and morphological data matrices. The Tree offers interesting points for semiotic perspectives and for theological approaches too. The symbolic reading of the Tree of Life, on the one hand, and the analogies with the (...) Biblical genealogies and some Christian images, on the other hand, will be explored. -/- . (shrink)

As a way forward in assessing how the Old Testament wisdom tradition might speak to decisions in a modern medical context, in this paper, I propose exploring the iconographic function of the “tree of life” in the Old Testament, which is consistently associated with both wisdom as well as life and health, in order to tease out two-related issues that can help in providing a Christian theological framework for thinking about the problem of the medicalization of risk: first, how should (...) the natural and good human desire for health and long life be framed in terms of the pursuit of wisdom? And, second, how might a sapientially formed character approach risk and uncertainty in making medical decisions? The answers to these questions help establish a framework in which more specific questions related to the medicalization of risk can be assessed. As such, this paper is deliberately programmatic and perspectival rather than prescriptive. (shrink)

An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with two supercompact cardinals, then there is a model of ZFC where simultaneously \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\aleph_2, \mu)}$$\end{document} -ITP and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\aleph_3, \mu')}$$\end{document} -ITP hold, for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu\geq \aleph_2}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu'\geq \aleph_3}$$\end{document}. (shrink)

We introduce insertion domains that support the placement of new, higher, vertices into finite trees. We prove that every nonincreasing insertion domain has an element with simple structural properties in the style of classical Ramsey theory. This result is proved using standard large cardinal axioms that go well beyond the usual axioms for mathematics. We also establish that this result cannot be proved without these large cardinal axioms. We also introduce insertion rules that specify the placement of new, higher, (...) vertices into finite trees. We prove that every insertion rule greedily generates a tree with these same structural properties; and every decreasing insertion rule generates (or admits) a tree with these same structural properties. It is also necessary and sufficient to use the same large cardinals (in the precise sense of Corollary D.25). The results suggest new areas of research in discrete mathematics called "Ramsey tree theory" and "greedy Ramsey theory" which demonstrably require more than the usual axioms for mathematics. (shrink)

We show that it is not possible to extend the ranking of one-stage lotteries based on their weak-expectation to a reflexive and transitive relation on the collection of one- and two-stage lotteries that satisfies two basic axioms, the minimal value axiom and the reduction axiom. We propose an extension that satisfies only the first axiom. This ranking takes payoffs, their probabilities, and the tree structure into account.

In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.

This paper delves into the intricate connections between the Abrahamic religions and the ancient mystery cults, reaching as far back as to Neolithic shamanism. They all unite in a shared pursuit: the quest for divine knowledge. Long before the Tree of Knowledge of Good and Evil in the biblical Genesis took on its profound symbolic meaning, shamanic initiation held a distinctly different view of botany. Indeed, It regarded plants primarily for their psychedelic properties, as a medium to perceive “reality” with (...) heightened intensity. However, the sacred Tree has a uniquely numinous character, and their consumption is sternly prohibited by God, in both, the Bible and the Quran. Therefore, this effectively positions all monotheistic religions in an unequivocal distance from their prehistoric origins. More precisely, we can argue that these mythologies are in fact constructed as counternarratives, advocating, primarily for a social ethic (based on the holy writings of the Bible), and evoking secondly a fundamental gnostic quest. (shrink)

Elementary first-order theories of trees allowing at most, exactly $\mathrm{m}$, and any finite number of immediate descendants are introduced and proved mutually interpretable among themselves and with Robinson arithmetic, Adjunctive Set Theory with Extensionality and other well-known weak theories of numbers, sets, and strings.