By B2 we denote the σ-ideal of all subsets A of the Cantor set {0,1}ω such that for every infinite subset T of ω the restriction A∣{0,1}T is a proper subset of {0,1}T. In this paper we investigate set theoretical properties of this and similar ideals.

By $\mathfrak{B}_2$ we denote the $\sigma$-ideal of all subsets $A$ of the Cantor set $\{0,1\}^\omega$ such that for every infinite subset $T$ of $\omega$ the restriction $A\mid\{0,1\}^T$ is a proper subset of $\{0,1\}^T$. In this paper we investigate set theoretical properties of this and similar ideals.

We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

Using matrix iterations of ccc posets, we prove the consistency with ZFC of some cases where the cardinals on the right hand side of Cichon’s diagram take two or three arbitrary values (two regular values, the third one with uncountable cofinality). Also, mixing this with the techniques in J Symb Log 56(3):795–810, 1991, we can prove that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s diagram.

We make a more systematic study of the van Douwen diagram for cardinal coefficients related to combinatorial properties of partitions of natural numbers.

The termination of rewrite systems for parameter recursion, simple nested recursion and unnested multiple recursion is shown by using monotone interpretations both on the ordinals below the first primitive recursively closed ordinal and on the natural numbers. We show that the resulting derivation lengths are primitive recursive. As a corollary we obtain transparent and illuminating proofs of the facts that the schemata of parameter recursion, simple nested recursion and unnested multiple recursion lead from primitive recursive functions to primitive recursive functions.

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable.

Let F be a signature and R a strictly orthogonal rewrite system on ground terms of F . We give an effective proof of a bounding condition for R , based on a detailed analysis of how terms are transformed during the rewrite process, which allows us to give recursive bounds on the derivation lengths of terms. We give a syntactic characterisation of the Grzegorczyk hierarchy and a rewriting schema for calculating its functions. As a consequence of this, using results (...) of Elias Tahhan–Bittar, it can be shown that, for n⩾3 , the derivation length functions for functions in Grzegorczyk class E n belong to Grzegorczyk class E n+1 . We also give recursive bounds for the derivation lengths of functions defined by parameter recursion. (shrink)

Recent studies indicate that mammalian chromosomes contain discretecis‐acting loci that control replication timing, mitotic condensation, and stability of entire chromosomes. Disruption of the large non‐coding RNA gene ASAR6 results in late replication, an under‐condensed appearance during mitosis, and structural instability of human chromosome 6. Similarly, disruption of the mouse Xist gene in adult somatic cells results in a late replication and instability phenotype on the X chromosome. ASAR6 shares many characteristics with Xist, including random mono‐allelic expression and asynchronous replication timing. (...) Additional “chromosome engineering” studies indicate that certain chromosome rearrangements affecting many different chromosomes display this abnormal replication and instability phenotype. These observations suggest that all mammalian chromosomes contain “inactivation/stability centers” that control proper replication, condensation, and stability of individual chromosomes. Therefore, mammalian chromosomes contain four types ofcis‐acting elements, origins, telomeres, centromeres, and “inactivation/stability centers”, all functioning to ensure proper replication, condensation, segregation, and stability of individual chromosomes. (shrink)

In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one.

Vaesen infers unique properties of mind from the appearance of specific cultural innovation – a correlation without causal direction. Shifts in habitat, population density, and group dynamics are the only independently verifiable incentives for changes in cultural practices. The transition from Acheulean to Late Stone Age technologies requires that we consider how population and social dynamics affect cultural innovation and mental function.

The first English translation of Fichte’s second set of 1804 lectures on the Wissenschaftslehre.

Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.

This new edition of Law and Medical Ethics continues to chart the ever-widening field that the topics cover. The interplay between the health caring professions and the public during the period intervening since the last edition has, perhaps, been mainly dominated by wide-ranging changes in the administration of the National Health Service and of the professions themselves but these have been paralleled by important developments in medical jurisprudence.

The purpose of this text is to draw attention to eight forgotten heroes: William C. Bagley, Charles DeGarmo, David Felmley, William Torrey Harris, Isaac L. Kandel, Charles McMurry, William C. Ruediger, and Edward Austin Sheldon. They have been marginalized from our profession, and drawing upon their legacy is the best hope for restoring the profession of teaching today. This work also includes a chapter at the end of the book entitled "John Dewey's Forgotten Essays." The audience for this book includes: (...) 1) classroom teachers, 2) school administrators, 3) teacher educators, 4) deans and other university administrators, 5) college and university presidents, 6) legislators, 7) historians of education, 8) curriculum specialists, 9) specialists in teacher training, and 10) the general public. (shrink)

Knowledge, like other things of value, can be faked. According to Hawley (2011), know-how is harder to fake than knowledge-that, given that merely apparent propositional knowledge is in general more resilient to our attempts at successful detection than are corresponding attempts to fake know-how. While Hawley’s reasoning for a kind of detection resilience asymmetry between know-how and know-that looks initially plausible, it should ultimately be resisted. In showing why, we outline different ways in which know-how can be faked even when (...) a given performance is successful; and in doing so, we distinguish how know-how can be faked (no less than know-that) via upstream and downstream indicators of its presence, and within each of these categories, we’ll distinguish (in connection with detection resilience) both faking symptoms and (various kinds of) criteria. The unappreciated resilience of faked knowledge-how to successful detection highlights a largely overlooked dimension of social-epistemic risk – risk we face not just in our capacity as recipients of testimony, but in our capacity as both (would-be) apprentices and clients of knowledge-how. (shrink)

In management research, theory testing confronts a paradox described by Meehl in which designing studies with greater methodological rigor puts theories at less risk of falsification. This paradox exists because most management theories make predictions that are merely directional, such as stating that two variables will be positively or negatively related. As methodological rigor increases, the probability that an estimated effect will differ from zero likewise increases, and the likelihood of finding support for a directional prediction boils down to a (...) coin toss. This paradox can be resolved by developing theories with greater precision, such that their propositions predict something more meaningful than deviations from zero. This article evaluates the precision of theories in management research, offers guidelines for making theories more precise, and discusses ways to overcome barriers to the pursuit of theoretical precision. (shrink)

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

The philosophical literature on sport and games has had little to say about boredom beyond presuming that sports and games can be important ways of overcoming or preventing it. But boredom is an interesting and often misunderstood phenomenon with overlooked implications in this context. Boredom has significant human value and motivates play in ways that contribute to well-being and culture, often through encouraging engaged agency and exploration of novelty. Understanding boredom can also help to clarify problems and tendencies in sports (...) and games that qualify them as havens from boredom. (shrink)

In this era of increased polarization of opinion and contentious disagreement, CRITICAL REASONING presents a cooperative approach to critical thinking and formation of beliefs. CRITICAL REASONING emphasizes the importance of developing and applying analytical skills in real life contexts. This book is unique in providing multiple, diverse examples of everyday arguments, both textual and visual, including hard to find long argument passages from real-life sources. The book provides clear, step-by-step procedures to help you decide for yourself what to believe--to be (...) a consumer of information in our contemporary "world of experts.". (shrink)

Human brain organoids (HBOs) are novel entities that may exhibit unique forms of cognitive potential. What moral status, if any, do they have? Several authors propose that consciousness may hold the answer to this question. Others identify various _kinds of_ consciousness as crucially important for moral consideration, while leaving open the challenge of determining whether HBOs have them. This paper aims to make progress on these questions in two ways. First, it proposes a framework for thinking about the moral status (...) of entities other than paradigmatic persons. This framework identifies four qualities that ground moral status: evaluative stance, self-directedness, agency, and other-directedness. Second, we speculate on ways in which these qualities are relevant to dimensions of conscious experience that have been, or could be, identified in nonhuman animals. We further explore how these approaches could be adapted for use in HBOs, and argue that such studies, or something similar to them, will have to be performed if we wish to have empirical indications that HBOs have consciousness of a morally significant kind. We end by proposing that in our current scientific and epistemic situation, it is too soon to attribute any moral status to HBOs, but that this might change in the future. (shrink)

Epistemic relativists often appeal to an epistemic incommensurability thesis. One notable example is the position advanced by Wittgenstein in On certainty (1969). However, Ian Hacking’s radical denial of the possibility of objective epistemic reasons for belief poses, we suggest, an even more forceful challenge to mainstream meta-epistemology. Our central objective will be to develop a novel strategy for defusing Hacking’s line of argument. Specifically, we show that the epistemic incommensurability thesis can be resisted even if we grant the very insights (...) that lead Hacking to claim that epistemic reasons are always relative to a style of reasoning. Surprisingly, the key to defusing the argument is to be found in recent mainstream work on the epistemic state of objectual understanding. (shrink)

New Tenth Anniversary edition of this classic text with a new preface by the author, compares myths about meat-eating with myths about manliness, and seeks to ...

The phenomenon of ambivalence is an important one for any philosophy of action. Despite this importance, there is a lack of a fully satisfactory analysis of the phenomenon. Although many contemporary philosophers recognize the phenomenon, and address topics related to it, only Harry Frankfurt has given the phenomenon full treatment in the context of action theory - providing an analysis of how it relates to the structure and freedom of the will. In this paper, I develop objections to Frankfurt's account, (...) all revolving around the charge that his account contains a serious ambiguity between willing and identifying. With such objections in place, I then develop an analysis that avoids the difficulties and ambiguities that Frankfurt's analysis is prey to. I briefly distinguish ambivalence from other types of internal conflict. This paper aims to offer conceptual clarification on the phenomenon of ambivalence, which will then allow for discussions about the normative merits and demerits of ambivalence, the effects of ambivalence on autonomous action, and methods of resolution of ambivalence. (shrink)