Introduction to special issue on contributions of mathematical psychology to clinical science and assessment

Evolution of clinical mathematical psychology, exemplifying integrative, translational psychological science, is considered in light of target, idealized scientific systems. It is observed that mutual benefits to psychological clinical science, and quantitative theory, potentiated through their interlacing as exemplified in this special issue, stand to parallel the historical symbiosis between older disciplines and mathematics. Enumerated are the range of psychological processes and clinical groups addressed, forms of modeling implemented, and clinical issues engaged, the latter ranging from intervention, to elucidation of deviant basic processes. A denouement comprising cogent quotations from historical figures in science concludes this Introduction.     

Working memory resources in young children with mathematical difficulties

Kyttälä, M., Aunio, P. & Hautamäki, J. (2010). Working memory resources in young children with mathematical difficulties. Scandinavian Journal of Psychology, 51 , 1–15.
Working memory (WM) ( Baddeley, 1986, 1997 ) is argued to be one of the most important cognitive resources underlying mathematical competence ( Geary, 2004 ). Research has established close links between WM deficits and mathematical difficulties. This study investigated the possible deficits in WM, language and fluid intelligence that seem to characterize 4- to 6-year-old children with poor early mathematical skills before formal mathematics education. Children with early mathematical difficulties showed poor performance in both verbal and visuospatial WM tasks as well as on language tests and a fluid intelligence test indicating a thoroughly lower cognitive base. Poor WM performance was not moderated by fluid intelligence, but the extent of WM deficits was related to language skills. The educational implications are discussed.     

THE DYNAMICS OF THE LAW OF EFFECT: A COMPARISON OF MODELS

Dynamical models based on three steady‐state equations for the law of effect were constructed under the assumption that behavior changes in proportion to the difference between current behavior and the equilibrium implied by current reinforcer rates. A comparison of dynamical models showed that a model based on Navakatikyan's (2007) two‐component functions law‐of‐effect equations performed better than models based on Herrnstein's (1970) and Davison and Hunter's (1976) equations. Navakatikyan's model successfully described the behavioral dynamics in schedules with negative‐slope feedback functions, concurrent variable‐ratio schedules, Vaughan's (1981) melioration experiment, and experiments that arranged equal, and constant‐ratio unequal, local reinforcer rates.     

论牟宗三易学思想的演变

牟宗三的易学是其原创性哲学的重要内容,体现着时代精神。他的早期著作《从周易方面研究中国之元学及道德哲学》,以罗素哲学、数理逻辑、新实在论解读《周易》,阐述了自然哲学和自然主义道德论,对缺乏科学与逻辑并高度意识形态化而成为人性之桎梏的中国传统文化补缺救失;在中后期,面对物质主义和唯科学主义在世界的泛滥,寻求人类的终极关怀,创立道德形上学,其易学即为这一体系的构成部分。牟氏易学的发展既反映了时代的变化,也显示出其视野由中国到世界的逐步开阔化。     

THE DISPOSITIONALIST DEITY: HOW GOD CREATES LAWS AND WHY THEISTS SHOULD CARE

How does God govern the world? For many theists “laws of nature” play a vital role. But what are these laws, metaphysically speaking? I shall argue that laws of nature are not external to the objects they govern, but instead should be thought of as reducible to internal features of properties. Recent work in metaphysics and philosophy of science has revived a dispositionalist conception of nature, according to which nature is not passive, but active and dynamic. Disposition theorists see particulars as being internally powerful rather than being governed by external laws of nature, making external laws in effect ontologically otiose. I will argue that theists should prefer a dispositionalist ontology, since it leads them toward the theory of concurrentism in divine conservation, rather than occasionalism, and revives the distinction between internal and external teleology. God on this view does not govern the world through external laws of nature, but rather through internal aspects of powerful properties.     

THE ARTIFICIALIZATION OF MIND AND WORLD

The rapid advancement of artificial intelligence (AI) has led to renewed ambitions of developing artificial general intelligence. Alongside this has been a resurgence in the development of virtual and augmented reality (V/AR) technologies, which are viewed as “disruptive” technologies and the computing platforms of the future. V/AR effectively bring the digital world of machines, robots, and artificial agents to our senses while entailing the transposition of human activity and presence into the digital world of artificial agents and machine forms of intelligence. The intersection of humans and machines in this shared space brings humans and machines into ontological continuity as informational entities in a totalizing informational environment, which subsumes both cyber and physical space in an artificially constructed virtual world. The reconstruction of mind (through AI) and world (through V/AR) thus has significant epistemological, ontological, and anthropological implications, which constitute the underlying features in the artificialization of mind and world.     

Before and beyond dialogicality: Transformative trialectics of human dialogues

I first revisit Bakhtin's discourse-driven account of dialogue to situate the concept in its broad sociohistorical, political, and philosophical (i.e., epistemology-ontology-ethics-aesthetics-praxis) meaning context. Not only is the concept of dialogicality highly relevant for the psychology of difference but it also poses many strong meta/theoretical challenges. Second, therefore, I rapidly evaluate psychology's disciplinary developmental status and transformative potentials of Bakhtinian dialogicalism in/for psychological discourses. I pay particular attention to the (im)possibilities of a potential dialogue between psycho-logic/-logy and dia-logic/-logue in reference to our biosociocultural (real-symbolic-imaginary) human be(com)ings. Thus, while triangulating, reframing and refracting with/in my seemingly more radically pluralist and dynamic perspective, using some core notions from its conceptual matrix for(potentially) self-reflective transformative-transformations, such as triopus and transformational trialectics, it is hoped that the fascination with pragmatics of dialogicality would not overshadow the concept's hermeneutically transformative utility which asks for serious dialogical confrontations, insights, bold philosophical commitments and consistent knowledge-practices in/towards all areas of our human(e) worlds.     

A Note on Prototypes,Convexity and Fuzzy Sets

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy.     

Mathematical psychology: Prospects for the 21st century: A guest editorial

The twenty-first century is certainly in progress by now, but hardly well underway. Therefore, I will take that modest elasticity in concept as a frame for this essay. This frame will serve as background for some of my hopes and gripes about contemporary psychology and mathematical psychology’s place therein. It will also act as platform for earnest, if wistful thoughts about what might have (and perhaps can still) aid us in forwarding our agenda and what I see as some of the promising avenues for the future. I loosely structure the essay into a section about mathematical psychology in the context of psychology at large and then a section devoted to prospects within mathematical psychology proper. The essay can perhaps be considered as in a similar spirit, although differing in content, to previous editorial-like reviews of general or specific aspects of mathematical psychology such as [Estes, W. K. (1975). Some targets for mathematical psychology. Journal of Mathematical Psychology, 12, 263-282; Falmagne, J. C. (2005). Mathematical psychology: A perspective. Journal of Mathematical Psychology, 49, 436-439; Luce, R. D. (1997). Several unresolved conceptual problems of mathematical psychology. Journal of Mathematical Psychology, 41, 79-87] that have appeared in this journal.     

Subjectivity and essential individuality: A dialogue with Peter Van Inwagen and Lynne Baker

Each person is perceived by others and by herself as an individual in a very strong sense, namely as a unique individual. Moreover, this supposed uniqueness is commonly thought of as linked with another character that we tend to attribute to persons (as opposed to stones or chairs and even non-human animals): a kind of depth, hidden to sensory perception, yet in some measure accessible to other means of knowledge. I propose a theory of strong or essential individuality. This theory is introduced by way of a critical discussion of Van Inwagen’s and Baker’s ontologies of persons. Composition Theory and Constitution Theory are shown to be complementary, in their opposite strong and weak points. I argue that both theories have unsatisfactory consequences concerning personal identity, a problem which the proposed theory seems to solve more faithfully both to folk intuitions and the phenomenology of personal life.