Upshot: We seek to address several questions and statements made in the commentaries by elaborating on the four main aspects of the M-N-L framework. Before doing so, we discuss the issue of constructivist teaching in the context of schools. We conclude by hypothesizing on what would be lost in the M-N-L framework by taking constructivism out of the picture.

Context: Constructivist teachers who find themselves working within an educational system that adopts a realist epistemology, may find themselves at odds with their own beliefs when they catch themselves paying closer attention to the knowledge authorities intend them to teach rather than the knowledge being constructed by their learners. Method: In the preliminary analysis of the mathematical learning of six low-performing Year 7 boys in a Maltese secondary school, whom one of us taught during the scholastic year 2014-15, we constructed (...) a conceptual framework which would help us analyze the extent to which he managed to be sensitive to constructivism in a typical classroom setting. We describe the development of the framework M-N-L as a viable analytical tool to search for significant moments in the lessons in which the teacher appeared to engage in what we define as “constructivist teaching” during mathematics lessons. The development of M-N-L is part of a research program investigating the way low-performing students make mathematical sense of new notation with the help of the software Grid Algebra. Results: M-N-L was found to be an effective instrument which helped to determine the extent to which the teacher was sensitive to his own constructivist beliefs while trying to negotiate a balance between the mathematical concepts he was expected to teach and the conceptual constructions of his students. Implications: One major implication is that it is indeed possible for mathematics teachers to be sensitive to the individual constructions of their learners without losing sight of the concepts that society, represented by curriculum planners, deems necessary for students to learn. The other is that researchers in the field of education may find M-N-L a helpful tool to analyze CT during typical didactical situations established in classroom settings. (shrink)

Open peer commentary on the article “Building Bridges to Algebra through a Constructionist Learning Environment” by Eirini Geraniou & Manolis Mavrikis. Upshot: In their article, Geraniou and Mavrikis describe an environment to help children explore algebraic relationships through pattern building. They report on transfer of learning from the computer to paper, but also implicit is transfer from concrete to abstract contexts. I make the case that transfer from abstract to concrete contexts should complement such approaches.

On October 18, 2004, the Defendant Dover Area School Board of Directors passed by a 6-3 vote the following resolution: Students will be made aware of gaps/problems in Darwin’s theory and of other theories of evolution including, but not limited to, intelligent design. Note: Origins of Life is not taught.

Auditory verbal hallucinations (AVHs) are a highly complex and rich phenomena, and this has a number of important clinical, theoretical and methodological implications. However, until recently, this fact has not always been incorporated into the experimental designs and theoretical paradigms used by researchers within the cognitive sciences. In this paper, we will briefly outline two recent examples of phenomenologically informed approaches to the study of AVHs taken from a cognitive science perspective. In the first example, based on Larøi and Woodward (...) (Harv Rev Psychiatry 15:109–117, 2007 ), it is argued that reality monitoring studies examining the cognitive underpinnings of hallucinations have not reflected the phenomenological complexity of AVHs in their experimental designs and theoretical framework. The second example, based on Jones (Schizophr Bull, in press, 2010 ), involves a critical examination of the phenomenology of AVHs in the context of two other prominent cognitive models: inner speech and intrusions from memory. It will be shown that, for both examples, the integration of a phenomenological analysis provides important improvements both on a methodological, theoretical and clinical level. This will be followed by insights and critiques from philosophy and clinical psychiatry—both of which offer a phenomenological alternative to the empiricist–rationalist conceptualisation of AVHs inherent to the cognitive sciences approach. Finally, the paper will conclude with ideas as to how the cognitive sciences may integrate these latter perspectives into their methodological and theoretical programmes. (shrink)

Auditory verbal hallucinations (AVHs) are a highly complex and rich phenomena, and this has a number of important clinical, theoretical and methodological implications. However, until recently, this fact has not always been incorporated into the experimental designs and theoretical paradigms used by researchers within the cognitive sciences. In this paper, we will briefly outline two recent examples of phenomenologically informed approaches to the study of AVHs taken from a cognitive science perspective. In the first example, based on Larøi and Woodward (...) (Harv Rev Psychiatry 15:109–117, 2007), it is argued that reality monitoring studies examining the cognitive underpinnings of hallucinations have not reflected the phenomenological complexity of AVHs in their experimental designs and theoretical framework. The second example, based on Jones (Schizophr Bull, in press, 2010), involves a critical examination of the phenomenology of AVHs in the context of two other prominent cognitive models: inner speech and intrusions from memory. It will be shown that, for both examples, the integration of a phenomenological analysis provides important improvements both on a methodological, theoretical and clinical level. This will be followed by insights and critiques from philosophy and clinical psychiatry—both of which offer a phenomenological alternative to the empiricist–rationalist conceptualisation of AVHs inherent to the cognitive sciences approach. Finally, the paper will conclude with ideas as to how the cognitive sciences may integrate these latter perspectives into their methodological and theoretical programmes. (shrink)

The phenomenology of auditory verbal hallucinations occurring in hypnagogic and hypnopompic states has received little attention. In a sample of healthy participants, 108 participants reported H&H AVHs and answered subsequent questions on their phenomenology. AVHs in the H&H state were found to be more likely to only feature the occasional clear word than to be clear, to be more likely to be one-off voices than to be recurrent voices, to be more likely to be voices of people known to the (...) individual than unknown persons, to be more likely to talk directly to the person rather than not, and to only rarely give commands, ask questions, or to result in an interactive conversation. Their phenomenology was similar to normative AVHs in wakefulness in that the voice-hearer was usually the target of the voice, and the voice was more likely to be of a recognized person. However, H&H AVHs differed from AVHs in wakefulness in that commands and questions were rare, and there was typically no dialogical engagement with the voice. We conclude by proposing that two distinct types of H&H AVHs may exist, based on an analysis of the phenomenology of the experience, and suggest avenues for future research. (shrink)

Abstract.The paper outlines the approach to the analysis of deontic conditionals taken in earlier work by Jones and Pörn, compares it very briefly with two main trends within dyadic deontic logic, and then discusses problems associated with the augmentation principle and the factual detachment principle. The author then modifies Jones and Pörn's previous system, using a classical but not normal (in the sense of Chellas) deontic modality to provide the basis for an alternative analysis of deontic conditionals. This new analysis (...) validates neither the factual detachment nor the augmentation principles. However, influenced by the approach of James Delgrande to default reasoning, the author tries to show how a restricted form of factual detachment may be accommodated within the revised system. (shrink)

. The current literature in the Artificial Intelligence and Law field reveals uncertainty concerning the potential role of deontic logic in legal knowledge representation. For instance, the Logic Programming Group at Imperial College has shown that a good deal can be achieved in this area in the absence of explicit representation of the deontic notions. This paper argues that some rather ordinary parts of the law contain structures which, if they are to be represented in logic, will call for use (...) of a reasonably sophisticated deontic logic. (shrink)

The paper discusses the potential value of a deontic approach to database specification. More specifically, some different types of integrity constraints are considered and a distinction is drawn between necessary (hard) and deontic (soft) constraints.Databases are compared with other normative systems. A deontic logic for database specification is proposed and the problems of how to react to, and of how to correct, or repair, a situation which arises through norm violation are discussed in the context of this logic. The limitations (...) of the proposed logic and possible modifications and extensions of it are analysed. (shrink)

Chagas disease or American trypanosomiasis is an important health problem in Latin America. Due to the mobility of Latin American population around the world, countries without vector presence started to report disease cases. We developed a deterministic compartmental model in order to gain insights into the disease dynamics in a scenario without vector presence, considering congenital transmission and transmission by blood transfusion. The model was used to evaluate the epidemiological effect of control measures. It was applied to demographic data from (...) Spain and sensitivity analysis was performed on model parameters associated with control strategies. (shrink)

The Viewpoint article expressed the feelings of unease often encountered at the display of human corpses in museums, whether relating to prehistoric or recent times. The reasons frequently stem from what is seen as a lack of respect for the remains of another human being. In this instance, the underlying concerns are that the corpses are displayed naked, along with lack of consent from anyone with an interest in them. While these are legitimate queries, ethical interests extend further afield to (...) include whether the corpses are identifiable, are prehistoric or recent, and the existence of living descendants. Additional interests include the uses to which corpses are put, namely, research, teaching and/or public displays.In recent years, it has become commonplace to hear of human remains that had been held for many years by universities or museums being repatriated to indigenous people groups in America, Australia and New Zealand for subsequent reburial.1 ,2 However, the debate regarding the ethical uses to which dead bodies may be put has taken a surprising turn in recent years with the extremely popular, highly publicised, public displays of dissected and plastinated whole body cadavers.3Over the years, most people have had few misgivings looking at the remains of prehistoric individuals, or Egyptian mummies.i Attitudes towards viewing mummies have been shaped by the perception that prehistoric remains are located outside our immediate social relationships, and so, have often been considered as anatomical objects rather than the remains of people-now-dead. In other words, their anonymity appears to protect both the corpses …. (shrink)

This paper is a preliminary investigation into the application of the formal-logical theory of normative positions to the characterisation of normative-informational positions, pertaining to rules that are meant to regulate the supply of information. First, we present the proposed framework. Next, we identify the kinds of nuances and distinctions that can be articulated in such a logical framework. Finally, we show how such nuances can arise in specific regulations. Reference is made to Data Protection Law and Contract Law, among others. (...) The proposed approach is articulated around two essential steps. The first involves identifying the set of possible interpretations that can be given to a particular norm. This is done by using formal methods. The second involves picking out one of these interpretations as the most likely one. This second step can be resolved only by using further information (e.g., the context or other parts of the regulation). (shrink)

This chapter contains sections titled: An Approach to the Logic of Action Normative Act Positions.

There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of a methodology for its use in (...) the analysis and representation of law.The essential point for which we argue is that deontic logic — in some form or other —needs to be taken seriously whenever it is necessary to make explicit, and then reason about, the distinction between what ought to be the case and what is the case, or as we also say, between the ideal and the actual. We take the library regulations at Imperial College as the main illustration, and small examples from genuinely legal domains to introduce specific points. In conclusion, we touch on the role of deontic logic in the development of the theory of normative positions. (shrink)

Call a bit of scientific discourse a description of a missing system when (i) it has the surface appearance of an accurate description of an actual, concrete system (or kind of system) from the domain of inquiry, but (ii) there are no actual, concrete systems in the world around us fitting the description it contains, and (iii) that fact is recognised from the outset by competent practitioners of the scientific discipline in question. Scientific textbooks, classroom lectures, and journal articles abound (...) with such passages; and there is a widespread practice of talking and thinking as though there are systems which fit the descriptions they contain perfectly, despite the recognition that no actual, concrete systems do so—call this the face value practice. There are, furthermore, many instances in which philosophers engage in the face value practice whilst offering answers to epistemological and methodological questions about the sciences. Three questions, then: (1) How should we interpret descriptions of missing systems? (2) How should we make sense of the face value practice? (3) Is there a set of plausible answers to (1) and (2) which legitimates reliance on the face value practice in our philosophical work, and can support the weight of the accounts which are entangled with that practice? In this paper I address these questions by considering three answers to the first: that descriptions of missing systems are straightforward descriptions of abstract objects, that they are indirect descriptions of “property-containing” abstracta, and that they are (in a different way) indirect descriptions of mathematical structures. All three proposals are present in the literature, but I find them wanting. The result is to highlight the importance of developing a satisfactory understanding of descriptions of missing systems and the face value practice, to put pressure on philosophical accounts which rely on the practice, and to help us assess the viability of certain approaches to thinking about models, theory structure, and scientific representation. (shrink)

I begin by distinguishing two notions of model, the notion of a truth-making structure and the notion of a mathematical model (in one specific sense). I then argue that although the models of the semantic view have often been taken to be both truth-making structures and mathematical models, this is in part due to a failure to distinguish between two ways of truth-making; in fact, the talk of truth-making is best excised from the view altogether. The result is a version (...) of the semantic view which is better supported by the direct evidence offered for it, better equipped to achieve its avowed aims, and, I think, closer to the intentions of the original proponents of the view in many ways, despite some of their own declarations to the contrary. (shrink)