Break philosophy through internally

This paper contrasts and illustrates two types of breakthroughs in philosophy; i.e., external and internal ones. Both are made possible through its application to a newfield. In the external breakthrough, a new field is discovered by such factors without philosophy as encounters with different traditions of thought and advance in technology. In the internal one, a new field is brought into attention by critical examination of one or another assumption within philosophy that has once dismissed the field as too trivial or insignificant to be its proper subject. Based on this distinction, a research guideline for philosophy is proposed that one must always seek the possibility of its internal breakthrough. It is also suggested that the philosophy of science and epistemology can be innovated internally when they are applied to a new field, that is, statistics. Finally the distinction between pure and applied philosophy is reinterpreted in the light of the internal breakthrough.     

Supporting the formal verification of mathematical texts

The formal verification of mathematical texts is one of the most interesting applications for computer systems. In fact, we argue that the expert language of mathematics is the natural choice for achieving efficient mathematician–machine interaction. Our empirical approach, the analysis of carefully authored textbook proofs, forces us to focus on the language and the reasoning pattern that mathematician use when presenting proofs to colleagues and students. Enabling a machine to understand and follow such language and argumentation is seen to be the key to usable and acceptable math assistant systems. In this paper, we first perform an analysis of three textbook proofs by hand; we then describe a computational framework that aims at mechanising such an analysis. The resulting proof-of-concept implementation is capable of processing simple textbook proofs and constitutes promising steps towards a natural mathematician–machine interface for proof development and verification.     

小学生数学应用题解题水平影响因素的研究——视空间能力、认知方式及表征方式的影响

研究采用3(年级)×2(场认知方式)×2(视空间能力水平)×3(问题表征方式)四因素混合实验设计,探讨了这四种因素对小学生数学应用题解题水平的影响。结果表明:年级、认知方式、空间能力以及问题表征方式均是影响小学生应用题解决水平的关键因素;问题表征方式、认知方式、空间能力以及年级四个因素对小学生解题水平存在交互作用,其中图形提示有利于场依存性学生解题水平的提高,低空间-场依存型的学生更适合图形提示;高空间-场依存型的学生随年级升高解题能力发展较快,而低空间-场依存型的学生解题水平提高较慢;随着年级的升高,图式表征对小学生问题解决的促进作用增强。     

Qualitative research in psychology: Attitudes of psychology students and academic staff

Qualitative research is experiencing a resurgence within the field of psychology. This study aimed to explore the range of attitudes towards qualitative research in psychology held by students and academics, using the model of attitudes by Eagly and Chaiken as a framework. Twenty‐one psychology students and academics were interviewed about their attitudes towards qualitative research. Interviews were transcribed and analysed using thematic analysis. While qualitative research was described as inherent to the psychology profession and useful for generating rich data, some participants felt that this approach was not well respected or considered as legitimate as quantitative methods. Reflecting common misperceptions about qualitative research, participants also expressed concerns that qualitative research was too subjective and had limited generalisability. Furthermore, some participants felt that they lacked the skills and confidence necessary to conduct qualitative research. Large investments in time and resources were identified as barriers to undertaking qualitative research. Identifying attitudes towards qualitative research provides a basis for future work in dispelling myths, promoting attitudinal change and increasing both the use and teaching of qualitative approaches in psychology.     

A model for residence time in concurrent variable interval performance

A component-functions model of choice behavior is proposed for performance on interdependent concurrent variable-interval (VI) variable-interval schedules based on the product of two component functions, one that enhances behavior and one that reduces behavior. The model is the solution to the symmetrical pair of differential equations describing behavioral changes with respect to two categories of reinforcers: enhancing and reducing, or excitatory and inhibitory. The model describes residence time in interdependent concurrent VI VI schedules constructed from arithmetic and exponential distributions. The model describes the data reported by Alsop and Elliffe (1988) and Elliffe and Alsop (1996) with a variance accounted for of 87% compared to 64% accounted for by the Davison and Hunter (1976) model and 42% by Herrnstein's (1970) hyperbola. The model can explain matching, undermatching, and overmatching in the same subject under different procedures and has the potential to be extended to performance on concurrent schedules with more than two alternatives, multiple schedules, and single schedules. Thus, it can be considered as an alternative to Herrnstein's quantitative law of effect.     

CONSTRUCTING AND DERIVING RECIPROCAL TRIGONOMETRIC RELATIONS: A FUNCTIONAL ANALYTIC APPROACH

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula‐to‐graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula‐to‐graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.     

情绪的数学公式

综合经验事实,提出对于同一个受试者和同一种呈现事件,近似描述情绪体验强度与客观呈现事件数量之间的一个数学公式.     

Recognition failure of recallable words: problems of mathematical constraint and dependence

The graph space of P ( RN | RL ) vs. P ( RN ), probabilities of recognition given recall and overall recognition, is the setting for the Tulving-Wiseman (TW) function of recognition failure research. According to Hintzman (1991, 1992), the moderate scatter of data points about the TW curve is an artefactual regularity caused by a mathematical constraint when P ( RN ) < P ( RL ). However, both constrained and unconstrained (when P ( RN ) ≥ P ( RL )) points conform equally well to the TW function, consistent with the unobserved fact that the location of both kinds of points is determined by the same mathematical rule. Hintzman's claim that there is no regularity in the data plot when P ( RN ) < P ( RL ) other than that produced by the constraint is not supported by this study. He based his claim on an incorrect use of the measure of dependence (association) called gamma. The graph space corresponding to gamma is that of P ( RN | RL ) vs. P ( RN | nRL ), as shown by using the Bayes function (Bayes' theorem). The margin-free measure gamma is a function of two thetas, theta being a margin-sensitive measure of dependence that is the parameter of the Bayes function. The variance of gamma reflects the fact that it is compounded of the theta variances, so a margin-free measure is obtained at the expense of greater variability.