Parental perceptions of mathematical talent

Parents often become frustrated when their perception of their child’s talent in mathematics differs from that held by the school. Yet for the young child, research suggests parents have a much deeper insight into the interests and talents of their child. Failure to recognize talent can result in lost opportunities for the child as well as a loss to society. This article evaluates the development of an instrument designed to assess parent perceptions of mathematical talent. Parental perceptions and family demographics were collected for third grade students participating in Project M³: Mentoring Mathematical Minds, a research program conducted collaboratively by the University of Connecticut, Northern Kentucky University and Boston University, and for second grade students under consideration for the program. The data were correlated with other identification tools used for the identification of talented second graders for Project M³ to explore a research-based means of parent identification of mathematical talent.

The reception of western philosophy in the Lithuanian philosophy of religion

The article examines the reception of Western philosophy in Lithuanian philosophy of religion. The purpose is to show how the discourse of philosophy of religion came about in Lithuania. This branch of philosophy has been not only culturally and socially important in Lithuania, it has been significant as well for the formation and maintenance of national identity. By the same token, it also was the most developed and controversial theoretically. The first part of the article lays out the genesis of the autonomous Lithuanian philosophy of religion, though strongly influenced by the transformations in the broader context of European philosophy. For that reason it will be useful to present the ideas of the most prominent Lithuanian thinkers in the field who have successfully adopted and adapted vital trends in Western philosophy into the Lithuanian cultural and intellectual context. The second part of the article is less historical and more problematic as it deals with specific issues concerning faith, God, anthropological problems as reflected in the works of contemporary Lithuanian philosophers of religion. Only after having explored certain affiliations of Lithuanian philosophy of religion with Western thought can we state that, although the latter was the necessary precondition of the former, Lithuanian philosophy of religion does substantiate its sovereign status while correlating in an original way major cultural transformations with the changes in theoretical context, according to the specific concerns of Lithuanian society. In addition, this historical and philosophical examination aims to look at the formation of Lithuanian identity, mentality, values, their roots in the Christian tradition as well as the capacity to respond at critical historical moments.

走向整合的智力研究 ——Demetriou的经验结构式认知发展理论述评

基于经验结构式认知发展理论的智力结构包含环境指向系统、超认知系统和加工系统三个层次。环境指向系统用于表征和加工不同领域的信息,加工系统是个体加工信息的操作平台,超认知系统负责监控和调节其他两个系统的认识活动。三个层次的发展既具有各自的特点又相互影响。因此,该理论指出智力结构的发展是一个动态平衡过程,存在三种发展变化模式：自下而上、自上而下和平行变化。智力结构层次内和层次间的发展都要遵循四种变化的机制。该理论作为整合型智力理论有自己的优势,但在概念使用、超认知概念的提出以及执行功能在结构中定位等问题有待商榷     

What is to be done in the history of philosophy

Because the History of Philosophy is a branch of both History and Philosophy, it faces tasks which are Historical, tasks which are Philosophical, and tasks which overlap both. As Philosophy typically flourishes by incorporating and assimilating ideas and bodies of text which have either not previously been part of its stock in trade or have been forgotten, the main task facing the History of Philosophy today is that of developing serious scholarship in areas that have been largely neglected, such as Philosophy in Arabic and Persian as well as in Sanskrit and Chinese.     

The extended cognition thesis: Its significance for the philosophy of (cognitive) science

While the extended cognition (EC) thesis has gained more followers in cognitive science and in the philosophy of mind and knowledge, our main goal is to discuss a different area of significance of the EC thesis: its relation to philosophy of science. In this introduction, we outline two major areas: (I) The role of the thesis for issues in the philosophy of cognitive science, such as: How do notions of EC figure in theories or research programs in cognitive science? Which versions of the EC thesis appear, and with which arguments to support them? (II) The potentials and limits of the EC thesis for topics in general philosophy of science, such as: Can naturalism perhaps be further advanced by means of the more recent EC thesis? Can we understand “big science” or laboratory research better by invoking some version of EC? And can the EC thesis help in overcoming the notorious cognitive/social divide in science studies?     

Myths, models, and metaphors: Religion as model and the philosophy of science

Clifford Geertz's widely-used paper ‘Religion as a Cultural System’, makes the claim that ‘the importance of religion lies in its capacity to serve … as a source of general, yet distinctive conceptions of the world, the self and the relations between them …—its model of aspect—and of rooted, no less distinctive “mental” dispositions—its model for aspect’. However, apart from a highly critical article by Nancy Frankenberry and Hans Penner (1999) little attempt has been made to investigate this understanding of religion as model. This paper briefly considers the validity of Frankenberry and Penner's criticism and investigates possible applications of the elaborate analysis of models and metaphors in the philosophy of science since the time of Mary Hesse to the analysis of religious phenomena.     

Distributing mathematical practice of third and seventh graders: Applicability of the spacing effect in the classroom

We examined the effect of distributed practice on the mathematical performance of third and seventh graders (N = 213) in school. Students first received an introduction to a mathematical topic, derived from their curriculum. Thereafter, they practiced in one of two conditions. In the massed condition, they worked on three practice sets in 1 day. In the distributed condition, they worked on one practice set per day for 3 consecutive days. Bayesian analyses of the performance in two follow‐up tests 1 and 6 weeks after the last practice set revealed a positive effect of distributed practice as compared with massed practice in Grade 7. In Grade 3, a positive effect of distributed practice was supported by the data only in the test 1 week after the last practice set. The results suggest that distributed practice is a powerful learning tool for both elementary and secondary school students in the classroom.     

Ideas and processes in mathematics: A course on history and philosophy of mathematics

This paper describes an attempt to develop a program for teaching history and philosophy of mathematics to inservice mathematics teachers. I argue briefly for the view that philosophical positions and epistemological accounts related to mathematics have a significant influence and a powerful impact on the way mathematics is taught. But since philosophy of mathematics without history of mathematics does not exist, both philosophy and history of mathematics are necessary components of programs for the training of preservice as well as inservice mathematics teachers.     

Structuralism as a form of scientific realism

Structural realism has recently re‐entered mainstream discussions in the philosophy of science. The central notion of structure, however, is contested by both advocates and critics. This paper briefly reviews currently prominent structuralist accounts en route to proposing a metaphysics of structure that is capable of supporting the epistemic aspirations of realists, and that is immune to the charge most commonly levelled against structuralism. This account provides an alternative to the existing epistemic and ontic forms of the position, incorporating elements of both. Structures are here identified with relations between first order, causal properties: properties that confer specific dispositions for relations. This form of structuralism constitutes an explicit proposal for what seem implicit structuralist tendencies in sophisticated but more traditional characterizations of realism. An outline of the proposal's response to the anti‐realist's pessimistic induction on the history of scientific theories is considered.     

Hilbert,logicism, and mathematical existence

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom).     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

"不可或缺性论证"与反实在论数学哲学

The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2006, (8): 74–83     

论马克思实践哲学的政治意蕴

In order to deepen the studies on the philosophy of practice, it is essential to explore the political significance of Marx's philosophy of practice. Marx's philosophy of practice is rooted in the problem of modernity and the separation between “individual subjectivity” and “societal community” in the modern context is the basic background of Marx's practical philosophy. It is the basic interest of Marx's philosophy of practice to find a way to end this separation via critique of civil society. Therefore, Marx's philosophy of practice has a clear significance, which manifests in the following aspects: one is “liberation politics,” and the other, “the regulatory mode of the socio-political institution.” Translated by Zhang Lin from Zhexue Yanjiu 哲学研究 (Philosophical Research), 2007, (1): 3–10     

Why philosophy and history matter: A conversation with Ann Taves

The article picks up some ideas that Ann Taves presents in her book Religious Experience Reconsidered, and looks at possible conversations that are not fleshed out in detail in Taves' book. In particular, it is argued that the disciplinary confrontation with philosophy and with historiography is of crucial importance if the disciplines of cognitive science and psychology of religion want to become in the future what they pretend to be nowda serious alternative and complement to the study of religion as we know it from other contexts, such as cultural studies and historiography     

Why philosophy and history matter: A conversation with Ann Taves

The article picks up some ideas that Ann Taves presents in her book Religious Experience Reconsidered, and looks at possible conversations that are not fleshed out in detail in Taves’ book. In particular, it is argued that the disciplinary confrontation with philosophy and with historiography is of crucial importance if the disciplines of cognitive science and psychology of religion want to become in the future what they pretend to be now—a serious alternative and complement to the study of religion as we know it from other contexts, such as cultural studies and historiography.     

An application of Carnapian inductive logic to an argument in the philosophy of statistics

I claim that an argument from the philosophy of statistics can be improved by using Carnapian inductive logic. Gelman and Shalizi [9] criticise a philosophical account of how statisticians ought to choose statistical models which they call ‘the received view of Bayesian inference’ and propose a different account inspired by falsificationist philosophy of science. I introduce another philosophical account inspired by Carnapian inductive logic and argue that it is even better than Gelman and Shalizi's falsificationist account.     

<Emphasis Type="Italic">Wissenschaftslogik</Emphasis>: The role of logic in the philosophy of science

Carl Hempel introduced what he called “Craig’s theorem” into the philosophy of science in a famous discussion of the “problem of theoretical terms.” Beginning with Hempel’s use of ‘Craig’s theorem,” I shall bring out some of the key differences between Hempel’s treatment of the “problem of theoretical terms” and Carnap’s in order to illuminate the peculiar function of Wissenschaftslogik in Carnap’s mature philosophy. Carnap’s treatment, in particular, is fundamentally anti-metaphysical—he aims to use the tools of mathematical logic to dissolve rather solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine.