We define rational Hermite interpolants to vector-valued functions and show that, in the context of Clifford algebras, the numerator and denominator polynomials belong to a complex extension of the Lipschitz group. We also discuss the problem of constructing an algebraic representation for the generalized inverse of a vector, which is at the heart of the usual development of vector rational approximation.

When, in Telos #55, we sought to evaluate the meaning and impact of French socialism in power, the verdict turned out to be peculiarly disappointing. The rhetorical question in the Introduction: “Beyond Reform or Revolution?” had already been effectively answered. As early as 1982 French socialism had revealed itself to be a “Gaullism with a Human Face” which did not have much to do either widi reform or revolution, and could provide nothing more -above and beyond the usual cliches—than a (...) continuation of the same berated but unsurpassed technocratic management of the given. Socialism had turned out to be a bad idea whose time had past. (shrink)

We respond to recent comments on our proposal to improve justice in ventilator triage, in which we used as an example New Jersey’s publicly available and legally binding Directive Number 2020-03. We agree with Bernard Lo and Doug White that equity implications of triage frameworks should be continually reassessed, which is why we offered six concrete options for improvement, and called for monitoring the consequences of adopted triage models. We disagree with their assessment that we mis-characterised their Model Guidance, as (...) included in the NJ Directive, in ways that undermine our conclusions. They suggest we erroneously described their model as a two-criterion allocation framework; that recognising other operant criterion reveals it ‘likely mitigate[s] rather than exacerbate[s] racial disparities during triage’, and allege that concerns about inequitable outcomes are ‘without evidence’. We highlight two major studies robustly demonstrating why concerns about disparate outcomes are justified. We also show that White and Lo seek to retrospectively—and counterfactually—correct the version of the Model Guideline included in the NJ Directive. However, as our facsimile reproductions show, neither the alleged four-criteria form, nor other key changes, such as dropping the Sequential Organ Failure Assessment score, are found in the Directive. These points matter because our conclusions hence stand, because the public version of the Model Guidance had not been updated to reduce the risk of inequitable outcomes until June 2021 and NJ’s Directive still does not reflect these revisions, and, hence, represents a less equitable version, as acknowledged by its authors. We comment on broader policy implications and call for ways of ensuring accurate, transparent and timely updates for users of high-stakes guidelines. (shrink)

This book demonstrates how the authors have experienced the power of phenomenology in their therapeutic work with patients, especially those struggling with horrific trauma; in their encounters with psychological and philosophical theories; and in their efforts to comprehend destructive ideologies and the collective traumas that give rise to them. The Power of Phenomenology presents the trajectory of this work. Each chapter begins with a contribution written by one or both authors, extending the power of phenomenological inquiry to one or more (...) of these diverse contexts. The contributions are followed, one or two at a time, by a dialogue between the authors, illustrating the dialectical process of their long collaboration. The unusual format seeks to bring the phenomenology of their collaborative efforts to life for the reader. (shrink)

We discuss the necessity of conscious thinking in the single-system propositional model of learning. Research from honeybees to humans suggests that associative learning can take place without the need for controlled reasoning or the development of beliefs of relationships between objects or events. We conclude that a single learning system is possible, but not if it depends on complex thinking.

Through case studies that highlight the type of information that is seldom reported in the news, Faces of Environmental Racism exposes the type and magnitude of environmental racism, both domestic and international. The essays explore the justice of current environmental practices, asking such questions as whether cost-benefit analysis is an appropriate analytic technique and whether there are alternate routes to sustainable development in the South.

Through case studies that highlight the type of information that is seldom reported in the news, Faces of Environmental Racism exposes the type and magnitude of environmental racism, both domestic and international. The essays explore the justice of current environmental practices, asking such questions as whether cost-benefit analysis is an appropriate analytic technique and whether there are alternate routes to sustainable development in the South.

We present an overview of the topics in the title and of some of the key results pertaining to them. These have historically been topics of interest in computability theory and continue to be a rich source of problems and ideas. In particular, we draw attention to the links and connections between these topics and explore their significance to modern research in the field.

Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (despite (...) some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)

In the present essay we explore a form of linguistic witchery (Wittgenstein) aimed at forging a sense of unity from incompatible visions of reality—namely, the formation of oxymoronic hybrids.

Recognition that biological systems are stabilized far from equilibrium by self-organizing, informed, autocatalytic cycles and structures that dissipate unusable energy and matter has led to recent attempts to reformulate evolutionary theory. We hold that such insights are consistent with the broad development of the Darwinian Tradition and with the concept of natural selection. Biological systems are selected that re not only more efficient than competitors but also enhance the integrity of the web of energetic relations in which they are embedded. (...) But the expansion of the informational phase space, upon which selection acts, is also guaranteed by the properties of open informational-energetic systems. This provides a directionality and irreversibility to evolutionary processes that are not reflected in current theory.For this thermodynamically-based program to progress, we believe that biological information should not be treated in isolation from energy flows, and that the ecological perspective must be given descriptive and explanatory primacy. Levels of the ecological hierarchy are relational parts of ecological systems in which there are stable, informed patterns of energy flow and entropic dissipation. Isomorphies between developmental patterns and ecological succession are revealing because they suggest that much of the encoded metabolic information in biological systems is internalized ecological information. The geneological hierarchy, to the extent that its information content reflects internalized ecological information, can therefore be redescribed as an ecological hierarchy. (shrink)

A viable evolutionary cognitive psychology requires that specific cognitive capacities be (a) heritable and (b) ‘quasi-independent’ from other heritable traits. They must be heritable because there can be no selection for traits that are not. They must be quasi-independent from other heritable traits, since adaptive variations in a specific cognitive capacity could have no distinctive consequences for fitness if effecting those variations required widespread changes in other unrelated traits and capacities as well. These requirements would be satisfied by innate cognitive (...) modules, as the dominant paradigm in evolutionary cognitive psychology assumes. However, those requirements would also be satisfied by heritable learning biases, perhaps in the form of architec- tural or chronotopic constraints, that operated to increase the canalization of specific cognitive capacities in the ancestral environment (Cummins and Cummins 1999). As an organism develops, cognitive capacities that are highly canalized as the result of heritable learning biases might result in an organism that is behaviourally quite similar to an organism whose innate modules come on line as the result of various environ- mental triggers. Taking this possibility seriously is increasingly important as the case against innate cognitive modules becomes increasingly strong. (shrink)

For more than 20 years, both here and abroad, significant efforts have been undertaken to provide equal access to nutritional food for all citizens. Yet, the numbers of under-nourished continue to rise, as do those afflicted with non-communicable diseases (NCDs) such as obesity, diabetes, hypertension, and heart disease. Clearly, current efforts are not working. Relying on the psychological phenomena of learned helplessness and fundamental attribution error, it is argued that certain individuals may not be willing, or able, to take actions (...) that are currently prescribed regarding access to nutritious food. The water is muddied regarding potential solutions as the various actors involved (e.g., corporations, governments, individuals) cannot agree on a starting point and continue to point fingers regarding responsibility. It is posited that emphasis needs to shift from the current “one-size-fits-all” approach to one that is more tailored to the various actors, specifically the individuals. Within the group of individuals (consumers), based on Wenar’s Least Cost Theory, even further distinction must be made between those who see themselves as capable actors and those who do not. In this conceptual piece intended to refocus the discussion surrounding food access, we propose that future research should approach these issues from a unit of analysis perspective in an attempt to identify the solutions most likely to succeed at various participating levels. (shrink)

The notes that follow are concerned with certain mineralogical problems which could not be discussed at length in my edition of the De Lapidibus . For the most part, only the bare conclusions are stated there. In handling these problems I owe much to the discussions that I had during his lifetime with Dr. Stanley Smith, and to those that I have had more recently with Professor F. Coles Phillips and Mr. Robert H. S. Robertson.

This essay joins Wilhelm Dilthey’s conception of the metaphysical impulse as a flight from the tragedy of human finitude with Ludwig Wittgenstein’s understanding of how language bewitches intelligence. We contend that there are features of the phenomenology of language that play a constitutive and pervasive role in the formation of metaphysical illusion.

Division of labor and its associated phenomena have been viewed as prime examples of group-level adaptations. However, the adaptations are the result of the process of evolution by natural selection and thus require that groups of insects once existed and competed for reproduction, some of which had a heritable division of labor while others did not. We present models, based on those of Kauffman (1984) that demonstrate how division of labor may occur spontaneously among groups of mutually tolerant individuals. We (...) propose that division of labor itself is not a product of natural selection but instead is a "typical" outcome of self organization. (shrink)