How do people gather samples of evidence to learn about the world? Adults often prefer to sample evidence from diverse sources—for example, choosing to test a robin and a turkey to find out if something is true of birds in general. Children below age 9, however, often do not consider sample diversity, instead treating non‐diverse samples (e.g., two robins) and diverse samples as equivalently informative. The current study (N = 247) found that this discontinuity stems from developmental changes in standards (...) for evaluating evidence—younger children chose to learn from samples that best approximate idealized views of what category members are supposed to be like (e.g., the fastest cheetahs), with a gradual shift across age toward samples that cover more within‐category variation (e.g., cheetahs of varying speeds). These findings have implications for the relation between conceptual structure and inductive reasoning, and for the mechanisms underlying inductive reasoning more generally. (shrink)

This book's importance is derived from three sources: careful conceptualization of teacher induction from historical, methodological, and international perspectives; systematic reviews of research literature relevant to various aspects of teacher induction including its social, cultural, and political contexts, program components and forms, and the range of its effects; substantial empirical studies on the important issues of teacher induction with different kinds of methodologies that exemplify future directions and approaches to the research in teacher induction.

In "Logical consequence: A defense of Tarski" (Journal of Philosophical Logic, vol. 25, 1996, pp. 617-677), Greg Ray defends Tarski's account of logical consequence against the criticisms of John Etchemendy. While Ray's defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a (...) stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray's interpretation of Tarski's position on the modal status of the consequence relation is noted. (shrink)

This paper explores and criticizes Henry Sidgwick’s conception of the ethical societies he helped found at the end of the nineteenth century. I argue that the societies were not as involved in practical and political problems as one might have expected, and that the theoretical justification offered by Sidgwick -- that the primary obstacles to “right living” lie in our minds and hearts -- is not altogether satisfying. Sidgwick’s nearly exclusive emphasis on the problem of moral knowledge is then contrasted (...) with John Dewey’s attention to moral motivation; and Dewey’s more energetic involvement in current affairs and social issues is set in the context of his distinctive view of the relation between theory and practice. Finally, Sidgwick’s modest hopes for the ethical societies, and the reasons for that modesty, are compared with the confidence that permeated an earlier incarnation of the ethical society, Ben Franklin’s Junto club. (shrink)

Goodman’s account of the ‘grue’ paradox stands at a crossroads in the history of twentieth century epistemology. Published in 1954, Fact, Fiction, and Forecast is a reaction to the logical empiricist views that held sway in the first half of the last century and anticipates many of the conventionalist and/or relativist moves popular throughout the second half. Through his evaluation of Hume’s problem of induction, as well as his own novel reformulation of it, Goodman comes to reject a number of (...) the fundamental parts of logical empiricism. In particular, Goodman argues that the formal epistemic methods the logical empiricists wanted to rely upon are insufficient. This leads him to turn towards conventionalism, which is the basis of his rejection of the objective view of knowledge. In his conventionalism he is a precursor of writers such as Hanson, Kuhn and Feyerabend, who, seeing the inadequacy of formalism, sought to fill the gaps it left in epistemic methodology with scientific values, tacit knowledge and linguistic practices. Making use of Susan Haack’s distinction between three different kinds of foundationalism, we analyse Goodman’s position and its relation to the views of the logical empiricists. The two are reflections of each other in that, where the logical empiricists are foundationalists in their views on empirical evidence, methods used and objective criteria of justification, Goodman consistently opts for the corresponding coherentist options. As it turns out, this choice of options makes it impossible for Goodman to deal with the very objections he raises against the logical empiricists. In adding the new problem of induction to the old one, Goodman adds a problem which clearly can not be resolved by a purely syntactic solution. The charge Goodman raises is that logical empiricists cannot determine which predictions are sound and which are not. We argue that his method of identifying acceptable predictions based on the use of entrenchment is, in the end, arbitrary and only postpones the underlying problem. (shrink)

The works of Paul K. Feyerabend, Norwood Russell Hanson and Thomas S. Kuhn have come to occupy a central place in the annals of contemporary philosophy of science. Some of their contemporaries,, tend to regard them as the vanguard of a new “revolutionary” intellectual movement. Reacting against the views of their positivist predecessors, they embrace and propagate the idea that “pervasive presuppositions” are fundamental to scientific investigations. Thus, Feyerabend thinks that, “... scientific theories are ways of looking at the world; (...) and their adoption affects our general beliefs and expectations, and thereby also our experiences and our conception of reality”. This is in stark contrast to the positivist view that the aim of science is the systematization of experience that exists independently of any scientific theories. This new view of scientific theories also involves a “radical” conception of the nature of theoretical change. Rejecting the positivist notion of any constant element through such change, Kuhn regards a basic theoretical change as a conceptual revolution and “wants to say that after a revolution scientists are responding to a different world”. Hanson uses the phrase ‘theory-loaded’ to give expression to a view of the semantic content of observation statements that follows from this general position. (shrink)

Scientific anomalies are observations and facts that contradict current scientific theories and they are instrumental in scientific theory change. Philosophers of science have approached scientific theory change from different perspectives as Darden (Theory change in science: Strategies from Mendelian genetics, 1991) observes: Lakatos (In: Lakatos, Musgrave (eds) Criticism and the growth of knowledge, 1970) approaches it as a progressive “research programmes” consisting of incremental improvements (“monster barring” in Lakatos, Proofs and refutations: The logic of mathematical discovery, 1976), Kuhn (The structure (...) of scientific revolutions, 1996) observes that changes in “paradigms” are instigated by a crisis from some anomaly, and Hanson (In: Feigl, Maxwell (eds) Current issues in the philosophy of science, 1961) proposes that discovery does not begin with hypothesis but with some “problematic phenomena requiring explanation”. Even though anomalies are important in all of these approaches to scientific theory change, there have been only few investigations into the specific role anomalies play in scientific theory change. Furthermore, much of these approaches focus on the theories themselves and not on how the scientists and their experiments bring about scientific change (Gooding, Experiment and the making of meaning: Human agency in scientific observation and experiment, 1990). To address these issues, this paper approaches scientific anomaly resolution from a meaning construction point of view. Conceptual integration theory (Fauconnier and Turner, Cogn Sci 22:133–187, 1996; The way we think: Conceptual blending and mind’s hidden complexities, 2002) from cognitive linguistics describes how one constructs meaning from various stimuli, such as text and diagrams, through conceptual integration or blending. The conceptual integration networks that describe the conceptual integration process characterize cognition that occurs unconsciously during meaning construction. These same networks are used to describe some of the cognition while resolving an anomaly in molecular genetics called RNA interference (RNAi) in a case study. The RNAi case study is a cognitive-historical reconstruction (Nersessian, In: Giere (ed) Cognitive models of science, 1992) that reconstructs how the RNAi anomaly was resolved. This reconstruction traces four relevant molecular genetics publications in describing the cognition necessary in accounting for how RNAi was resolved through strategies (Darden 1991), abductive reasoning (Peirce, In: Hartshorne, Weiss (eds) Collected papers, 1958), and experimental reasoning (Gooding 1990). The results of the case study show that experiments play a crucial role in formulating an explanation of the RNAi anomaly and the integration networks describe the experiments’ role. Furthermore, these results suggest that RNAi anomaly resolution is embodied. It is embodied in a sense that cognition described in the cognitive-historical reconstruction is experientially based. (shrink)

A loose analogy relates the work of Laplace and Hilbert. These thinkers had roughly similar objectives. At a time when so much of our analytic effort goes to distinguishing mathematics and logic from physical theory, such an analogy can still be instructive, even though differences will always divide endeavors such as those of Laplace and Hilbert.

The Halpern–Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern–Läuchli theorem, and the same forcing from Harrington’s proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size (...) of the continuum. (shrink)

What is addiction? Why do some people become addicted while others do not? Is the addict rational? In this book, Craig Hanson attempts to answer these questions and more. Using insights from the beginnings of philosophy to contemporary behavioral economics, Hanson attempts to assess the variety of ways in which we can and cannot, understand addiction. Special consideration is given to a challenging (and controversial) proposal dubbed “hyperbolic discounting.” Hanson proposes some modifications to the hyperbolic discounting view that permit it (...) to explain not only addiction, but also a variety of psychological maladies, such as self-deception. (shrink)

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into (...) St. Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

John Wilkins and Malte Ebach respond to the dismissal of classification as something we need not concern ourselves with because it is, as Ernest Rutherford suggested, mere ‘‘stamp collecting.’’ They contend that classification is neither derivative of explanation or of hypothesis-making but is necessarily prior and prerequisite to it. Classification comes first and causal explanations are dependent upon it. As such it is an important (but neglected) area of philosophical study. Wilkins and Ebach reject Norwood Russell Hanson’s thesis that (...) classification relies on observation that is theory-laden and deny the need for aetiological assumptions and historical reconstruction to justify its arrangement. What they offer instead is a significant (albeit controversial) contribution to the philosophical literature on classification, a pre-theoretic natural classification based on the observation of patterns in data of ready-made phenomena. Their notion of ready-made phenomena rests on a conception of tacit knowledge or know-how. This is evident in their distinction between strong Theory-dependence and na ̈ıve theory-dependence. Their small t-theory-dependence permits patterns of observation that facilitate know-how but does not rely on a domain-specific explanatory theory of their aetiology. Wilkins and Ebach suggest classification differs from theory building in that it is passive (whereas theory building is active). Classification is possible just because it does not require the sieve of theory to capture classes that are ‘‘handed to you by your cognitive dispositions and the data that you observe’’ (p. 18). Finding regularities sans-theory is just something we do and can do without any prior theory about the underlying causes or origins of the resultant regularities. Luke Howard’s classification of clouds serves as an exemplar of a passive, theory-free classification system and the periodic table and the DSM help to illustrate this type of non-aetiological patterning. A recurrent theme is the nature of naturalness. For Wilkins and Ebach, the conception of naturalness is not one that is based on the generation or discovery of natural kind categories popular in both the traditional metaphysics of Mill and Wittgenstein as well as updated notions within philosophy of biology such as Boyd’s Homeostatic Property Cluster kinds. Instead, Wilkins and Ebach define the naturalness of classification as the falling into hierarchical patterns, aligning the search for natural arrangement with the aim of systematics, and as something that is grounded in a cognitive task or activity. However, they leave the question of realism v. antirealism open. ‘‘In natural classification...we must have real relations no matter how we might interpret ‘real’’’ (p. 70). There is tension with regard to their ontological commitments as they vacillate between constructive, operationalist, and realist approaches. Wilkins and Ebach initially define real as that which is causal and important (pp. 70–71), and later as that which ‘‘depends in no way upon a mind or observer’’ (p. 122). This makes their claim that there was ‘‘no real theory involved [in the pre-Darwinian classifications of Jussieu and Adanson]’’ (p. 64) difficult to interpret. Cont’d……. (shrink)

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The (...) first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples. (shrink)

Despite recurring efforts, a gap exists across a variety of contexts between the protection of patients' safety in theory and in practice. This timely Research Handbook highlights these critical issues and suggests both legal and policy changes are necessary to better protect patients' safety. Multidisciplinary in nature, this Research Handbook features contributions from eminent academics, policy makers and medical practitioners from the Global North and South, discussing the essential facets concerning patient safety and the law. It highlights how the role (...) of legislation and case law has the potential to influence, both positively and negatively, medical practice and the quality of care. Chapters explore patient safety and the global health agenda; physiotherapy; 'non-therapeutic' clinical research with children; patient safety awareness in healthcare education; and the increasing use of robotics and artificial intelligence in healthcare. Outlining a wide range of international perspectives on patient safety and the law, this Research Handbook will appeal to academics and researchers specialising in health and medical law, human rights and healthcare regulation. It will also serve as a valuable resource for legal and medical practitioners alike, as well as clinicians and professionals working in healthcare governance. (shrink)

Generic language (e.g., “tigers have stripes”) leads children to assume that the referenced category (e.g., tigers) is inductively informative and provides a causal explanation for the behavior of individual members. In two preregistered studies with 4- to 7-year-old children (N = 497), we considered the mechanisms underlying these effects by testing how correcting generics might affect the development of these beliefs about novel social and animal kinds (Study 1) and about gender (Study 2). Correcting generics by narrowing their scope to (...) a single individual limited beliefs that the referenced categories could explain what their members would be like while broadening the scope to a superordinate category (Study 2) uniquely limited endorsement of gender norms. Across both studies, correcting generics did not alter beliefs about feature heritability and had mixed effects on inductive inferences, suggesting that additional mechanisms (e.g., causal reasoning about shared features) contribute to the development of full-blown essentialist beliefs. These results help illuminate the mechanisms by which generics lead children to view categories as having rich inductive and causal potential; in particular, they suggest that children interpret generics as signals that speakers in their community view the referenced categories as meaningful kinds that support generalization. The findings also point the way to concrete suggestions for how adults can effectively correct problematic generics (e.g., gender stereotypes) that children may hear in daily life. (shrink)

We have been discussing some of the fundamental features of the classical calculus of probability. The equiprobability of rival events was seen to be a major assumption of the calculus. Moreover, it is an assumption which the pure mathematician need not bother to justify. He need only present his formal system as follows.

The current studies (N = 255, children ages 4–5 and adults) explore patterns of age‐related continuity and change in conceptual representations of social role categories (e.g., “scientist”). In Study 1, young children's judgments of category membership were shaped by both category labels and category‐normative traits, and the two were dissociable, indicating that even young children's conceptual representations for some social categories have a “dual character.” In Study 2, when labels and traits were contrasted, adults and children based their category‐based induction (...) decisions on category‐normative traits rather than labels. Study 3 confirmed that children reason based on category‐normative traits because they view them as an obligatory part of category membership. In contrast, adults in this study viewed the category‐normative traits as informative on their own (not only as a cue to obligations). Implications for continuity and change in representations of social role categories will be discussed. (shrink)

Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of ZFC and independence results about the C-sequence number and its relationship with large cardinals, stationary reflection, and square principles. We then introduce and study the more general C-sequence spectrum and uncover some tight connections between the C-sequence spectrum and the strong (...) coloring principle U(. . .), introduced in Part I of this series. (shrink)

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of introduced by Brodsky and Rinot for the purpose of constructing κ‐Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, implies the existence of a special ‐tree with a cf(μ)‐ascent path, thus answering a question of Lücke.

The Sickness unto Death is commonly regarded as one of Kierkegaard's most important works – but also as one of his most difficult texts to understand. It is a meditation on Christian existentialist themes including sin, despair, religious faith and its redemptive power, and the relation and difference between physical and spiritual death. This volume of new essays guides readers through the philosophical and theological significance of the work, while clarifying the complicated ideas that Kierkegaard develops. Some of the essays (...) focus closely on particular themes, others attempt to elucidate the text as a whole, and yet others examine it in relation to other philosophical views. Bringing together these diverse approaches, the volume offers a comprehensive understanding of this pivotal work. It will be of interest to those studying Kierkegaard as well as existentialism, religious philosophy, and moral psychology. (shrink)

With all the research on mind/brain connections these days -- Your brain in lust or love! While gambling or feeling envious! While meditating, praying, or having an out-of-body experience! -- it’s natural to wonder about ’big questions’ about the relationships among the mind, the brain, and God. For instance, some people have taken the findings that some spiritual experiences have neural correlates to mean that the hand of God is at work in the brain. Others have interpreted the same research (...) to mean that spiritual experiences are "just" neural, and thus evidence against the existence of God or other supernatural forces. These debates are updated versions of longstanding philosophical and religious wrestlings with how God and nature might or might not intertwine. What’s your own gut view, right now, as a kind of snapshot: Do you think that God is involved in some way in your thoughts and feelings? In your most intimate sense of being? In this essay, we’ll explore what mind, brain, and. (shrink)

Viale introduced covering matrices in his proof that SCH follows from PFA. In the course of the proof and subsequent work with Sharon, he isolated two reflection principles, CP and S, which, under certain circumstances, are satisfied by all covering matrices of a certain shape. Using square sequences, we construct covering matrices for which CP and S fail. This leads naturally to an investigation of square principles intermediate between □κ and □ for a regular cardinal κ. We provide a detailed (...) picture of the implications between these square principles. (shrink)

We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa $, the existence of a strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is a theorem of $\textsf{ZFC}$. Adding the requirement of subadditivity to a strongly unbounded coloring is a significant strengthening, though, and here we see that in many cases the existence of a subadditive strongly unbounded coloring (...) $c:[\kappa ]^2 \rightarrow \theta $ is independent of $\textsf{ZFC}$. We connect the existence of subadditive strongly unbounded colorings with a number of other infinitary combinatorial principles, including the narrow system property, the existence of $\kappa $ -Aronszajn trees with ascent paths, and square principles. In particular, we show that the existence of a closed, subadditive, strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is equivalent to a certain weak indexed square principle $\boxminus ^{\operatorname {\mathrm {ind}}}(\kappa, \theta )$. We conclude the paper with an application to the failure of the infinite productivity of $\kappa $ -stationarily layered posets, answering a question of Cox. (shrink)