Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students (...) in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library. (shrink)

Michael T. Ferejohn presents a new analysis of Aristotle's theory of explanation and scientific knowledge, in the context of its Socratic roots. Ferejohn shows how Aristotle resolves the tension between his commitment to the formal-case model of explanation and his recognition of the role of efficient causes in explaining natural phenomena.

_This sweeping discussion of the philosophy of evolutionary biology is based on the revolutionary idea that species are not kinds of organisms but wholes composed of organisms._.

A coherent treatment of the flow of ideas throughout Darwin's works, this volume presents a unified theoretical system that explains Darwin's investigations, evaluating the literature from a historical, scientific, and philosophical perspective.

Classifying is a fundamental operation in the acquisition of knowledge. Taxonomic theory can help students of cognition, evolutionary psychology, ethology, anatomy, and sociobiology to avoid serious mistakes, both practical and theoretical. More positively, it helps in generating hypotheses useful to a wide range of disciplines. Composite wholes, such as species and societies, are “individuals” in the logical sense, and should not be treated as if they were classes. A group of analogous features is a natural kind, but a group of (...) homologous features is not. Imposing hypotheses justified only on the basis of nominalist, realist, phenomenalist, or conceptualist metaphysics upon the neurophysiology of organisms or upon the causes of behavior exemplifies the “psychologist's fallacy” of William James. Levels should be distinguished from their members and from classes of levels, and the ontological status of entities ranked at levels should be made clear. It is important not to confuse such categories as substance and process with one another. Several genetical terms, such as “gene” and chromosome,” are even more equivocal than has been realized. Discussions about units of selection, behavior, and thinking suffer from the ambiguity of a “unit of” an entity. An important source of misunderstanding about natural selection is the habit of treating it as an “agent”: in an important sense, natural selection does not “act” at all. (shrink)

Atran's treatment of classification suggests a need to recognize the difference between ontological categories and less metaphysically fundamental distinctions. The shift that scientists have made from classes to individuals may not be as pervasive as he proposes, and the same may be said for the abandonment of essences. It is also possible that the sort of causality that is of concern to scientists plays a role in folk classification.

Traditionally, species have been treated as classes. In fact they may be considered individuals. The logical term “individual” has been confused with a biological synonym for “organism.” If species are individuals, then: 1) their names are proper, 2) there cannot be instances of them, 3) they do not have defining properties, 4) their constituent organisms are parts, not members. “ Species " may be defined as the most extensive units in the natural economy such that reproductive competition occurs among their (...) parts. Species are to evolutionary theory as firms are to economic theory: this analogy resolves many issues, such as the problems of “reality” and the ontological status of nomenclatorial types. (shrink)

"Adaptation" has several meanings which have often been confused, including relations, processes, states, and intrinsic properties. It is used in comparative and historical contexts. "Adaptation" and "environment" may designate probabilistic concepts. Recognition of these points refutes arguments for the notions that: 1) all organisms are perfectly adapted; 2) organisms cannot be ill-adapted and survive or well-adapted and die; 3) adaptation is necessarily relative to the environment; 4) change in environment is necessary for evolution; 5) preadaptation implies teleology. Such notions are (...) associated with metaphysical ideas, and may affect the thinking of biologists. (shrink)

Donne used Plato’s Lambda numbers to construct “A Litany.” Specifically, each number in the Lambda sequence ties not only to the concept of world-creation as outlined in Timaeus, but also to its notion of the circular nature of the world, of man returning to the monad.

Within Luis Buñuel's classic surrealist film The Exterminating Angel is a philosophical motif which expresses, demonstrates, and develops two of Ludwig Wittgenstein's central concepts: language lays traps for the unwary that can lead to illogical thought and mind-bending quests; and any picture of the world is formed through cultural habits that cannot be rationally expressed but can be changed. This article argues that what we find in Buñuel's Angel is a “picture” that is at one level rational and habitual and (...) at another entirely absurd. These apparently rational preconceptions – the insular habits of privilege and the language that maintains it – produce a certain “aspect” which, when clung to, can entrap us. In this effort we thread a series of chance meetings into a web of encounters: of people at a dinner party, of a philosopher and a filmmaker, and perhaps most significantly, of games that form a totality of gamesmanship – a chance meeting of the game... (shrink)

Many state that they have a friend in Jesus, but close analysis reveals that this claim is difficult to defend. Furthermore, only once does Jesus claim that humans can be friends with him. This essay explores whether humans can be friends with Jesus. In arguing that this is possible, attention is given to what kind of friendship is possible in Aristotle’s taxonomy of utility, pleasure, and character-friendships. None of these describes the kind of friendship possible between humans and Jesus, but (...) holy-friendship (developed from character-friendship) suffices to demonstrate how such friendship is possible. (shrink)

Excerpt from Cultures and Institutions of Natural History: Essays in the History and Philosophy of Science This volume consists mainly of papers delivered at two meetings cosponsored by the Museo Civico di Storia Naturale in Milan and the California Academy of Sciences in San Francisco. The first, on the Culture of Natural History, was held in Milan, November l4-l 6, I996. The second, on Institutions of Natural History, was held in San Francisco, October 5 - 7, 1998. They followed two (...) earlier conferences on Biology as History (pinna and Ghiselin I996; Ghiselin and Pinna I996) likewise held in Milan and San Francisco. We intend to continue the series of meetings and have publications based on them in commemoration of the Academy's sesquicentennial in 2003. The emphasis here is mainly upon natural history museums and the kind of science that goes on in them. Although the essays were originally written to stand by themselves, when arranged in chronological order they suggest a common theme. To paraphrase Darwin, the culture and institutions of natural history have been, and are being, evolved. They have adapted to local circumstances, diversified, and sometimes even progressed. We may hope that the future holds more than just retrogression and extinction in store. Read as case studies the essays provide valuable insights into not just how, but why, the institutions have come into being and subsequently been transformed. Previous generations had quite different ideas than we do about how a collection of naturalia is supposed to function and how it should be organized. And there were con icting goals and serious disputes about policy, much as there are today. Often, though not always, the institutions turn out to be very different from what had been envisioned by their founders. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.". (shrink)

Can an ugly experiment be a good experiment? Philosophers have identified many beautiful experiments and explored ways in which their beauty might be connected to their epistemic value. In contrast, the present chapter seeks out (and celebrates) ugly experiments. Among the ugliest are those being designed by AI algorithms. Interestingly, in the contexts where such experiments tend to be deployed, low aesthetic value correlates with high epistemic value. In other words, ugly experiments can be good. Given this, we should conclude (...) that beauty is not generally necessary or sufficient for epistemic value, and increasing beauty will not generally tend to increase epistemic value. (shrink)

Imagination is important for many things in science: solving problems, interpreting data, designing studies, etc. Philosophers of imagination typically account for the productive role played by imagination in science by focusing on how imagination is constrained, e.g., by using self-imposed rules to infer logically, or model events accurately. But the constraints offered by these philosophers either constrain too much, or not enough, and they can never account for uses of imagination that are needed to break today’s constraints in order to (...) make progress tomorrow. Thus, epistemology of imagination needs to make room for an element of epistemological anarchy. (shrink)

Table of Contents: Chapter 1: The Need for Philosophy of Nature Chapter 2: Analogy and the Search for Truth Chapter 3: Doing What Comes Naturally Chapter 4: Dawkins or Aristotle? Chapter 5: The Mystery of Motion Chapter 6: Is Time Real? Chapter 7: Place, Space and Science Fiction Chapter 8: What is a Human Being? Chapter 9: The Powers of the Human Person Chapter 10: Are Humans Really Free? Chapter 11: Human Action Chapter 12: The Place of Law in Human (...) Life Chapter 13: St. Thomas Aquinas and Catholic Social Teaching> Chapter 14: The Just Price Chapter 15: Charging for the Loan of Money Chapter 16: What Happens after Death? Chapter 17: Is That All There Is? Chapter 18: What Can We Say about Fido? Chapter 19: Important Nicknames Chapter 20: Causality and God Chapter 21: The Existence of God (1) Chapter 22: The Existence of God (2) Chapter 23: The unchanging God Chapter 24: "It's God's will!" Chapter 25: Creation. (shrink)

Joshua Greene has argued that the empirical findings of cognitive science have implications for ethics. In particular, he has argued (1) that people’s deontological judgments in response to trolley problems are strongly influenced by at least one morally irrelevant factor, personal force, and are therefore at least somewhat unreliable, and (2) that we ought to trust our consequentialist judgments more than our deontological judgments when making decisions about unfamiliar moral problems. While many cognitive scientists have rejected Greene’s dual-process theory of (...) moral judgment on empirical grounds, philosophers have mostly taken issue with his normative assertions. For the most part, these two discussions have occurred separately. The current analysis aims to remedy this situation by philosophically analyzing the implications of moral dilemma research using the CNI model of moral decision-making – a formalized, mathematical model that decomposes three distinct aspects of moral-dilemma judgments. In particular, we show how research guided by the CNI model reveals significant conceptual, empirical, and theoretical problems with Greene’s dual-process theory, thereby questioning the foundations of his normative conclusions. (shrink)

Criminalizing arson is both easy and hard. On the substantive merits, the conduct of damaging property by fire uncontroversially warrants criminal sanction. Indeed, punishment for such conduct is overdetermined, as the conduct threatens multiple harms of concern to the criminal law: both damage to property and injury to people. Yet the same multiplicity of harms or threats that makes it easy to criminalize arson (in the sense of deciding to proscribe the underlying behavior) also makes it hard to criminalize arson (...) (in the sense of formulating the offense(s) that will address that behavior). This article asks whether adopting one or more arson offenses is the best way for criminal law to address the conduct in question, or whether that conduct is more properly conceptualized, criminalized, and punished as multiple distinct offenses. (shrink)

In Darwinian terminology, “sexual selection” refers to purely reproductive competition and is conceptually distinct from natural selection as it affects reproduction generally. As natural selection may favor the evolution of sexual dimorphism by virtue of the division of labor between males and females, this possibility needs to be taken very seriously.