Faculty in a large, urban school of engineering designed a longitudinal study to assess the critical thinking skills of undergraduate students as they progressed through the engineering program. The Paul-Elder critical thinking framework was used to design course assignments and develop a holistic assessment rubric. This paper presents the analysis of the freshman course artifacts (baseline and course critical thinking assignments) and associated faculty scoring sessions for all three cohorts. A total of 649 first semester freshman students at least 18 (...) years old agreed to participate in the study. The majority were white males with a mean high school grade point average of 3.73, ACT composite score of 28.33, and final freshman engineering course grade of 3.57. There was a statistically significant positive relationship between the freshman course artifacts and the faculty scores. Data from the study are being used to enhance the critical thinking experiences for undergraduate engineering students. (shrink)

In this paper, we study some new examples of ideals on $$\omega $$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order—known as the weak Rudin–Keisler order—and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177–214, 1991) on the Tukey order, we also show that there is an analytic P-ideal above all other analytic (...) P-ideals in the weak Rudin–Keisler order. (shrink)

Countable homogeneous relational structures have been studied by many people. One area of focus is the Ramsey theory of such structures. After a review of background material, a partition theorem of Laflamme, Sauer, and Vuksanovic for countable homogeneous binary relational structures is discussed with a focus on the size of the set of unavoidable colors.

Current textbooks in formal semantics are all versions of, or introductions to, the same paradigm in semantic theory: Montague Grammar. Knowledge of Meaning is based on different assumptions and a different history. It provides the only introduction to truth- theoretic semantics for natural languages, fully integrating semantic theory into the modern Chomskyan program in linguistic theory and connecting linguistic semantics to research elsewhere in cognitive psychology and philosophy. As such, it better fits into a modern graduate or undergraduate program in (...) linguistics, cognitive science, or philosophy. Furthermore, since the technical tools it employs are much simpler to teach and to master, Knowledge of Meaning can be taught by someone who is not primarily a semanticist. Linguistic semantics cannot be studied as a stand-alone subject but only as part of cognitive psychology, the authors assert. It is the study of a particular human cognitive competence governing the meanings of words and phrases. Larson and Segal argue that speakers have unconscious knowledge of the semantic rules of their language, and they present concrete, empirically motivated proposals about a formal theory of this competence based on the work of Alfred Tarski and Donald Davidson. The theory is extended to a wide range of constructions occurring in natural language, including predicates, proper nouns, pronouns and demonstratives, quantifiers, definite descriptions, anaphoric expressions, clausal complements, and adverbs. Knowledge of Meaning gives equal weight to philosophical, empirical, and formal discussions. It addresses not only the empirical issues of linguistic semantics but also its fundamental conceptual questions, including the relation of truth to meaning and the methodology of semantic theorizing. Numerous exercises are included in the book. (shrink)

The goal of this short note is to interest set theorists in the order type ω*ω1, and to encourage them to work on the question of whether or not the Continuum Hypothesis decides the partition relation τ→2, for τ=ω*ω1 and for τ=ω1ω+2.

Dive et al. argue to limit the scope, scale, and quantity of results in genomic screening programs at the population level. Their analysis offers two interrelated reasons for this recommendation: f...

This article deals with the relation between a theory of law and a theory of legal reasoning. Starting from a close reading of Chapter VII of H. L. A. Hart's The Concept of Law, it claims that a theory of law like Hart's requires a particular theory of legal reasoning, or at least a theory of legal reasoning with some particular characteristics. It then goes on to say that any theory of legal reasoning that satisfies those requirements is highly implausible, (...) and tries to show that this is the reason why not only Hart, but also writers like Neil MacCormick and Joseph Raz have failed to offer a theory of legal reasoning that is compatible with legal positivism as a theory of law. They have faced a choice between an explanation of legal reasoning that is incompatible with the core of legal positivism or else strangely sceptical, insofar as it severs the link between general rules and particular decisions that purport to apply them. (shrink)

Debates about moral judgments have raised questions about the roles of reasoning, culture, and conflict. In response, the cognitive prototype model explains that over time, through training, and as a result of cognitive development, people construct notions of blameworthy and praiseworthy behavior by abstracting out salient properties that lead to an ideal representation of each. These properties are the primary features of moral prototypes and include social context interpretation, intentionality, consent, and outcomes. According to this model, when the properties are (...) uniform and coherent, they depict a promoral or immoral prototype, relative to the orientations of the properties. A promoral prototype is represented by an action that is supported by the culture, intentionally benevolent or other-regarding, consensual, and resulting in positive outcomes. An immoral prototype is an action that is condemned by the culture, intentionally malevolent or self-serving, lacking consent, and resulting in negative outcomes. It is hypothesized that moral prototypes will result in a high level of agreement and require effortless processing. Alternatively, when properties conflict or the situation deviates from the prototype, a nonprototype will result. It is hypothesized that nonprototypical situations will act as a source of moral disagreement and may require more effortful processing. (shrink)

This collection of original essays on Yoga in honour of Professor Gerald James Larson provides fascinating new insights into the yoga traditions of India as a ...

Let κ be a cardinal which is measurable after generically adding ${\beth_{\kappa+\omega}}$ many Cohen subsets to κ and let ${\mathcal G= ( \kappa,E )}$ be the κ-Rado graph. We prove, for 2 ≤ m < ω, that there is a finite value ${r_m^+}$ such that the set [κ] m can be partitioned into classes ${\langle{C_i:i (...) G}$ in ${\mathcal G}$ such that ${[\mathcal{G} ^\ast ] ^m\cap C_i}$ is monochromatic. It follows that ${\mathcal{G}\rightarrow (\mathcal{G} ) ^m_{<\kappa/r_m^+}}$ , that is, for any coloring of ${[ \mathcal {G} ] ^m}$ with fewer than κ colors there is a copy ${\mathcal{G} ^{\prime}}$ of ${\mathcal{G}}$ such that ${[\mathcal{G} ^{\prime} ] ^{m}}$ has at most ${r_m^+}$ colors. On the other hand, we show that there are colorings of ${\mathcal{G}}$ such that if ${\mathcal{G} ^{\prime}}$ is any copy of ${\mathcal{G}}$ then ${C_i\cap [\mathcal{G} ^{\prime} ] ^m\not=\emptyset}$ for all ${i 2 we have ${r_m^+ > r_m}$ where r m is the corresponding number of types for the countable Rado graph. (shrink)

Extent health humanities readings of Gabriel García Márquez’s _Love in the Time of Cholera_ have focused on the doctor-patient relationship, the physician-scientist as a model for aspiring practitioners, and how individuals relate to the novel’s health themes of death, disease, and disability. However, such medicine-focused readings neglect the population-level public health concerns of the novel as they relate to contagion, community, and quarantine. This paper contributes to the growing field of public health humanities by using a close reading method to (...) explore how the competing endemic and epidemic public health issues shape the plot and metaphors of the novel. (shrink)

S. Ulam asked about the number of nonisomorphic projective algebras with k generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of nonisomorphic one-generated structures of finite dimension n, where n is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, cylindric set algebras, and cylindric algebras. The results of this paper extend earlier (...) results to the collection of cylindric set algebras and provide a uniform proof for all the results. Extensions of these results for dimension two are discussed where some modifications on the hypotheses are needed. Furthermore for α |geq 2, the number of isomorphism classes of regular locally finite cylindric set algebras of dimension α of the following two kinds are computed: ones of power κ for infinite $\kappa \geq|\alpha|$ , and ones with a single generator. (shrink)

Suppose that α = γ + δ where $\gamma \geq \delta > 0$ . Then there is a graph G = (ω ω α ,E) which has no independent set of order type ω ω α and has no pentagram (a pentagram is a set of five points with all pairs joined by edges). In the notation of Erdos and Rado, who generalized Ramsey's Theorem to this setting, $\omega^{\omega^\alpha} \nrightarrow (\omega^{\omega^\alpha},5)^2.$.

James Earl Baumgartner (March 23, 1943–December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied (...) his knowledge of set theory to a variety of areas in collaboration with other mathematicians, and he encouraged a community of mathematicians with engaging survey talks, enthusiastic discussions of open problems, and friendly mathematical conversations. (shrink)

Faculty in a large, urban school of engineering designed a longitudinal study to assess the critical thinking skills of undergraduate students as they progressed through the engineering program. The Paul-Elder critical thinking framework was used to design course assignments and develop a holistic assessment rubric. This paper presents the analysis of the freshman course artifacts (baseline and course critical thinking assignments) and associated faculty scoring sessions for all three cohorts. A total of 649 first semester freshman students at least 18 (...) years old agreed to participate in the study. The majority were white males with a mean high school grade point average of 3.73, ACT composite score of 28.33, and final freshman engineering course grade of 3.57. There was a statistically significant positive relationship between the freshman course artifacts and the faculty scores. Data from the study are being used to enhance the critical thinking experiences for undergraduate engineering students. (shrink)

This article deals with the relation between a theory of law and a theory of legal reasoning. Starting from a close reading of Chapter VII of H. L. A. Hart's The Concept of Law, it claims that a theory of law like Hart's requires a particular theory of legal reasoning, or at least a theory of legal reasoning with some particular characteristics. It then goes on to say that any theory of legal reasoning that satisfies those requirements is highly implausible, (...) and tries to show that this is the reason why not only Hart, but also writers like Neil MacCormick and Joseph Raz have failed to offer a theory of legal reasoning that is compatible with legal positivism as a theory of law. They have faced a choice between an explanation of legal reasoning that is incompatible with the core of legal positivism or else strangely sceptical, insofar as it severs the link between general rules and particular decisions that purport to apply them. (shrink)

Argumentation as the public exchange of reasons is widely thought to enhance deliberative interactions that generate and justify reasonable public policies. Adopting an argumentation-theoretic perspective, we survey the norms that should govern public argumentation and address some of the complexities that scholarly treatments have identified. Our focus is on norms associated with the ideals of correctness and participation as sources of a politically legitimate deliberative outcome. In principle, both ideals are mutually coherent. If the information needed for a correct deliberative (...) outcome is distributed among agents, then maximising participation increases information diversity. But both ideals can also be in tension. If participants lack competence or are prone to biases, a correct deliberative outcome requires limiting participation. The central question for public argumentation, therefore, is how to strike a balance between both ideals. Rather than advocating a preferred normative framework, our main purpose is to illustrate the complexity of this theme. (shrink)

This article discusses the concept of constituent power and its application to the situation in Chile after the 18th October 2019. In particular, it discusses the relation between constituted and constituent powers, with a view to understanding the significance of the 15 November Agreement that opened the way for the ongoing constituent process.

This paper studies the formality of law and legal reasoning. It argues that, though the law (and its application) is indeed formal in that it does not take into account a significant number of considerations that should in principle be relevant for an all–things–considered decision, this is not to be explained on the basis of some ontology of rules (i.e., rules as exclusionary reasons), but upon the nature of legal discourse when viewed as a social practice. How the law is (...) applied to particular cases, when substantive considerations not referred to by the rules are important enough to defeat their application to the case and questions of this kind are not answered by the legal material (which includes or might include rules, principles etc.), but by beliefs that underlie legal practice, beliefs about the world and its relation to human beings and society. Insofar as these beliefs have impact upon practices we recognise as legal they are termed “images of law.” Legal reasoning cannot be understood without paying due attention to the nature and evolution of images of law. (shrink)

Mentoring Away the Glass Ceiling in Academia: A Cultured Critique describes how women of diverse backgrounds perceive their mentoring experiences or the lack of mentoring experiences in the academy. This book provides a space for envisioning strategies and practices to improve mentoring practices and the collegiate environment.

Assuming the existence of a supercompact limit of supercompact cardinals, we modify the original consistency proof of Martin's Maximum to obtain a model in which MM holds but the axiom fails.

The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from [Formula: see text] to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokobodzki independently showed that the Continuum Hypothesis implies the existence of medial limits. (...) We show that the Filter Dichotomy implies that there are no medial limits. (shrink)

The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.

In any attempt to present an overview of the conceptions of reality and divinity in classical Indian (Hindu) civilization, it is helpful, first of all, to highlight some of the basic cultural and intellectual presuppositions that appear to be operative in classical Indian thought (which, for the purposes of this article, will be taken as consisting of the so‐called six classical schools of Sāṃkhya, Yoga, Nyāya, Vaiśeṣika, Mīmāṃsā, and Advaita Vedānta during the classical period, from the first centuries of the (...) Common Era up to the coming of Islamic traditions in the eleventh century). This can be accomplished in various ways, but perhaps the simplest way is to articulate some basic questions to which classical Indian thought provides some interesting, albeit unusual, answers. The questions can be framed as follows: (1) What truly is? (2) How does one know what truly is? (3) Who knows what truly is? (4) With whom does one know what truly is? And, finally: (5) What does God have to do with what truly is? The questions have to do, respectively, with (1) ontology, (2) epistemology, (3) psychology, (4) social anthropology, and (5) theology. Classical Indian thought, of course, provides a variety of answers to all of these questions, and there was much vigorous debate and polemic through the centuries about precisely how to form satisfactory answers. Generally speaking, however, it appears to be the case that the classical Indian philosophical schools tended to deal with these basic questions in a manner quite different from the way these questions have been dealt with in traditional or modern Western thought, and it is important to understand some of these differences if one wishes to appreciate the unique conceptual frameworks in classical Indian thought. (shrink)

To the best of my knowledge, no one in recent decades has written a book of this magnitude about the semantics of natural language. Certainly, nothing available today matches this volume in depth, precision, and coherence. The authors present classical and recent results of linguistic semantics within the framework of interpretative T-theories and defend the philosophical foundations of their approach by showing how it fits into the larger enterprise of cognitive linguistics. The book also includes an array of excellent exercises (...) and a good list of references. (shrink)

At the forefront of international concerns about global legislation and regulation, a host of noted environmentalists and business ethicists examine ethical issues in consumption from the points of view of environmental sustainability, economic development, and free enterprise.