We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, which at the same time realize bosonic spin-1 and fermionic spin- $${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0em}\!\lower0.7ex\hbox{$2$}}$$ wave equations of relativistic field theory, showing some unexpected relations between various low-dimensional Lorentz representations. We include a geometrically and physically motivated introduction to Jordan triples and spin factors.

Usually the Lorentz transformations are derived from the conservation of the spacetime interval. We propose here a way of obtaining spacetime transformations between two inertial frames directly from symmetry, the isotropy of the space and principle of relativity. The transformation is uniquely defined except for a constant e, that depends only on the process of synchronization of clocks inside each system. Relativistic velocity addition is obtained, and it is shown that the set of velocities is a bounded symmetric domain. If (...) e=0, Galilean transformations are obtained. If e>0, the speed 1/√e and a spacetime interval are conserved. By assuming constancy of the speed of light, we get e=1/c 2 and the transformation between the frames becomes the Lorentz transformation. If e<0, a proper speed and a Hilbertian norm are conserved. (shrink)

Economists tend to view ignorance as ?rational,? neglecting the possibility that ignorance is unintentional. This oversight is reflected in economists? model of ?information search,? which can be fruitfully contrasted with ?information browsing.? Information searches are designed to discover unknown knowns, whose value is calculable ex ante, such that this value justifies the cost of the search. In this model of human information acquisition, there is no primal or ?radical? ignorance that might prevent people from knowing which information to look for, (...) lacking omniscience. Unlike ignorance that is rationally chosen on the basis of an accurate cost/benefit calculation, radical ignorance can explain human error. An account of error as grounded in radical ignorance bypasses the need to appeal to irrationality in order to explain economic (and other) mistakes. (shrink)

Virtually every infant in the United States (U.S.) undergoes a heel stick within the first week of life to test for a variety of metabolic, endocrine, and hematological conditions as part of state-run universal newborn screening (NBS) programs. In the U.S., NBS began in the 1960s for phenylketonuria (PKU), a metabolic condition that causes intellectual disability if left untreated. I review the history of how NBS came to be a mandatory public health program that did not require parental consent1 and (...) examine whether the policy was morally justifiable. I then examine how three changes to NBS programs are prompting a re-evaluation of the mandatory nature of NBS. The three changes are: (1) the implementation of .. (shrink)

Ketamine, a dissociative anesthetic commonly used by US physicians, has recently been shown to be a powerful anti-depressant and is also capable of eliciting transpersonal experiences that can be transformative. Although currently approved in the US only for use as an anesthetic, physicians there can legally prescribe it off-label to treat various psychological/ psychiatric problems and it has been used for these non-anesthetic purposes in Argentina, Iran, Mexico, Russia, and the UK, as well as in the US. The literature on (...) using ketamine psychotherapeutically is reviewed and two case studies using ketamine-enhanced psychotherapy for treating death anxiety in terminally-ill people are reported. The potential importance of beginning formal research on using KEP during end-of-life for those suffering death anxiety is emphasized. (shrink)

In August 2000, Arthur Matas and his colleagues de scribed a protocol in which their institution began to accept as potential donors, individuals who came to the University of Minnesota hospital offering to donate a kidney to any patient on the waiting list. Matas and his colleagues refer to these donors as nondirected donors by which is meant that the donors are altruistic and that they give their organs to an unspecified pool of recipients with whom they have no emotional (...) relationship. This paper represents an ethical and policy critique of the nondirected donation protocol that was implemented at the University of Minnesota in August 1999. Specifically, I address the ethical questions: Whether altruistic living solid organ donations by strangers should be permitted? And if so, What are appropriate ethical guidelines for such donations? (shrink)

In August 2000, Arthur Matas and his colleagues de scribed a protocol in which their institution began to accept as potential donors, individuals who came to the University of Minnesota hospital offering to donate a kidney to any patient on the waiting list. Matas and his colleagues refer to these donors as nondirected donors by which is meant that the donors are altruistic and that they give their organs to an unspecified pool of recipients with whom they have no emotional (...) relationship. This paper represents an ethical and policy critique of the nondirected donation protocol that was implemented at the University of Minnesota in August 1999. Specifically, I address the ethical questions: Whether altruistic living solid organ donations by strangers should be permitted? And if so, What are appropriate ethical guidelines for such donations? (shrink)

We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these definitions, under various complexity (...) measures. (shrink)

ABSTRACT An intellectually charitable understanding of populism might begin by recognizing that, since populist citizens tend to be politically uninformed and lacking in higher education, populist ideas are likely to be inarticulate reproductions of the tacit assumptions undergirding non-populist or “mainstream” culture rather than stemming from explicit theoretical constructs, such as an apotheosis of the unity or the will of “the people.” What features of our ambient culture, then, could explain the simplistic and combative approach that populists seem to take (...) to politics and policy, their impatience with political debate and deliberation, their willingness to set aside democratic legal forms and political norms, their nationalism, their personalization of politics, their inclination toward conspiracy theorizing, their fondness for fringe sources of information, and their suspicion of political, scientific, and media elites? Using focus group and survey data, we can understand these populist traits as reflections of the culture of “democratic technocracy”: a regime in which we, the people, are assumed capable of rendering sound judgments about how to solve our social and economic problems. Whether or not this assumption is warranted, its cultural dominance seems likely to generate the ideas that populist citizens apparently take for granted. (shrink)

In this paper we review the most common forms of reflection and introduce a new form which we call sharp‐generated reflection. We argue that sharp‐generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp‐maximality with the corresponding hypothesis. The statement is an analogue of the (Inner Model Hypothesis, introduced in ) which is compatible with the existence of large cardinals.

The debate over Green and Shapiro's Pathologies of Rational Choice Theory sustains their contention that rational choice theory has not produced novel, empirically sustainable findings about politics?if one accepts their definition of empirically sustainable findings. Green and Shapiro show that rational choice research often resembles the empirically vacuous practices in which economists engage under the aegis of instrumentalism. Yet Green and Shapiro's insistence that theoretical constructs should produce accurate predictions may inadvertently lead to instrumentalism. Some of Green and Shapiro's critics (...) hint at a better approach, which would eschew predictive testing in favor of testing the applicability of the theory to particular cases. (shrink)

There is a direct relationship between epistemology and one's attitude toward those with whom one disagrees. Those who think that the truth is difficult to ascertain can be expected, other things equal, to tend to tolerate (in the sense of sympathizing with) those with whom they disagree, as the blameless victims of an opaque reality. Those who think that the truth is easy to ascertain can be expected, other things equal, to tend to be intolerant (in the sense of being (...) unsympathetic) toward those with whom they disagree, who perversely refuse to acknowledge what should be clear to any well-intentioned inquirer. However, these tendencies toward tolerant or intolerant attitudes can be offset by other factors; and they do not, in any case, necessarily dictate whether one will favor tolerant or intolerant policies regarding those toward whom one feels tolerant or intolerant. The complex relationship between epistemology, tolerant or intolerant attitudes, and tolerant or intolerant policies is evident in the thought of prominent early-modern Protestant theologians who, under the pressure of rampant and violent religious disagreement, theorized tolerance. (shrink)

ABSTRACT This essay considers the relationship between history of science and philosophy of science from Thomas Kuhn to the present. This relationship, of course, has often been troubled, but there is now new hope for an ongoing productive interaction—due to an increasing awareness, among other things, of the mutual entanglement between the development of modern science and the development of modern philosophy on the part of both professional (historically minded) philosophers and professional historians of science. This idea is illustrated with (...) several examples, including the entanglement of Einstein's theory of relativity with logical empiricism and its precursors and the entanglement of the analytic tradition in philosophy first with mathematical logic and then (through mathematical logic) with the cognitive sciences. Against this background, finally, the essay considers the emergence of contemporary social and cultural history of science from the Kantian and neo‐Kantian philosophical traditions. (shrink)

More than 24,000 patients await organ transplants and the number is increasing yearly. Living donors are an important source of transplant organs. In this paper, I argue that we can morally justify allowing children to serve as donors. Yet, I also argue that their participation must be restricted in order to prevent their exploitation.The paper is divided into six sections. In the first section, I show why the traditional principles of personal autonomy and beneficence are not adequate morally to justify (...) the participation of children in the nontherapeutic role of organ donor. Next, I argue that the moral justification of the child’s participation must be based on the intimate family relationship which permits activities that would be unacceptable in the public domain. In the third section, I argue that family autonomy ought to be limited by the principle of respect for persons. In the fourth section, I propose five principles to guide the participation of children as organ donors. In section five, I discuss the role of the child in the decision-making process. In section six, I critically examine the criteria for equity in donor selection. (shrink)

The “best interest standard” is the guidance principle for pediatric healthcare in the United States (US) and the United Kingdom (UK). In the UK, the best interest standard may also be used as an intervention principle when parents make good but non-ideal decisions whereas intervention in the US requires a determination of abuse or neglect. I examine whether and how the different uses of the best interest standard influence predictive genetic testing of children.

Hoerl & McCormack suggest that saving tools does not require temporal reasoning. However, we identify a class of objects that are only possessed in anticipation of future needs. We propose that investigating these future-oriented objects may help identify temporal reasoning in populations where this ability is uncertain.

In August 2001, the Maryland Court of Appeals harshly criticized the Kennedy Krieger Institute of Johns Hopkins University for knowingly exposing poor children to lead-based paint. The court’s decision made national news, and is worth examining because it raises several very important issues for research ethics.The research conducted by the Institute was an attempt to understand how successful different lead abatement programs were in reducing continued lead exposure to children. Previously, Julian Chisolm and Mark Farfel, of John Hopkins University, had (...) disclosed the dangers of traditional dust-generating deleading practices. In the current study, Dr. Farfel and colleagues sought to document the longevity of various lead-based paint abatement strategies. (shrink)

This overview describes the breadth of topicscovered in this volume devoted to children inresearch. It summarizes how these articles areinterrelated and how they all respond to thechallenge proposed by the Children's Health Actof 2000: to consider what modifications, ifany, are necessary to current regulations ``toensure the adequate and appropriate protectionof children participating in research.''.

Montague [7] translates English into a tensed intensional logic, an extension of the typed -calculus. We prove that each translation reduces to a formula without -applications, unique to within change of bound variable. The proof has two main steps. We first prove that translations of English phrases have the special property that arguments to functions are modally closed. We then show that formulas in which arguments are modally closed have a unique fully reduced -normal form. As a corollary, translations of (...) English phrases are contained in a simply defined proper subclass of the formulas of the intensional logic. (shrink)

We show that if M is a countable transitive model of $\text {ZF}$ and if $a,b$ are reals not in M, then there is a G generic over M such that $b \in L[a,G]$. We then present several applications such as the following: if J is any countable transitive model of $\text {ZFC}$ and $M \not \subseteq J$ is another countable transitive model of $\text {ZFC}$ of the same ordinal height $\alpha $, then there is a forcing extension N of (...) J such that $M \cup N$ is not included in any transitive model of $\text {ZFC}$ of height $\alpha $. Also, assuming $0^{\#}$ exists, letting S be the set of reals generic over L, although S is disjoint from the Turing cone above $0^{\#}$, we have that for any non-constructible real a, $\{ a \oplus s : s \in S \}$ is cofinal in the Turing degrees. (shrink)

This chapter contains section titled: Care Ethics Applied Ethics Autonomy Communicative Ethics Feminist Ethical Strategies Notes Further Reading.

In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of 2κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^\kappa $$\end{document}, κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document} inaccessible, and study its associated ideal of null sets and notion of measurability. This issue was addressed by Shelah ), arXiv:0904.0817, Problem 0.5) and concerns the definition of a forcing which is κκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa ^\kappa $$\end{document}-bounding, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,>\,$$\end{document}cov_λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\_\lambda $$\end{document}), arXiv:0904.0817, Problem 0.5), and in this paper we independently reprove this result by using a different type of construction. This also contributes to a line of research adressed in the survey paper :439–456, 2016). (shrink)

The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).

As is well known, it was only in 1926 that a comprehensive mathematical theory of braids was published—that of Emil Artin. That said, braids had been researched mathematically before Artin’s treatment: Alexandre Theophile Vandermonde, Carl Friedrich Gauß and Peter Guthrie Tait had all attempted to introduce notations for braids. Nevertheless, it was only Artin’s approach that proved to be successful. Though the historical reasons for the success of Artin’s approach are known, a question arises as to whether other approaches to (...) deal with braids existed, approaches that were developed after Artin’s article and were essentially different from his approach. The answer, as will be shown, is positive: Modesto Dedò developed in 1950 another notation for braids, though one, which was afterward forgotten or ignored. This raises a more general question: what was the role of Artin’s notation, or, respectively, Dedò’s, that enabled either the acceptance or the neglect of their theories? More philosophically, can notation be an epistemic technique, prompting new discoveries, or rather, can it also operate an as obstacle? The paper will analyze the method introduced by Dedò to notate braids, and also its history and implications. It aims to show that Dedò, in contrast to Artin, focused on factorizations of braids and the algebraic relations between the operations done on these factorizations. Dedò’s research was done against the background of Oscar Chisini’s research of algebraic curves on the one hand and of Artin’s successful notation of braids on the other hand. Taking this into account, the paper will in addition look into the epistemic role of notation, comparing Dedò’s work with Artin’s, as both presented different notations of braids and their deformations. (shrink)

The main result in this paper is a method for obtaining derivation trees from sentences of certain formal grammars. No parsing algorithm was previously known to exist for these grammars.Applied to Montague's PTQ the method produces all parses that could correspond to different meanings. The technique directly addresses scope and reference and provides a framework for examining these phenomena. The solution for PTQ is implemented in an efficient and useful computer program.

We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’11-CA0 over..