Kriesel and Wittgenstein

Georg Kreisel (15 September 1923 - 1 March 2015) was a formidable mathematical logician during a formative period when the subject was becoming a sophisticated field at the crossing of mathematics and logic. Both with his technical sophistication for his time and his dialectical engagement with mandates, aspirations and goals, he inspired wide-ranging investigation in the metamathematics of constructivity, proof theory and generalized recursion theory. Kreisel's mathematics and interactions with colleagues and students have been memorably described in Kreiseliana ([Odifreddi, 1996]). At a different level of interpersonal conceptual interaction, Kreisel during his life time had extended engagement with two celebrated logicians, the mathematical Kurt Gödel and the philosophical Ludwig Wittgenstein. About Gödel, with modern mathematical logic palpably emanating from his work, Kreisel has reflected and written over a wide mathematical landscape. About Wittgenstein on the other hand, with an early personal connection established Kreisel would return as if with an anxiety of influence to their ways of thinking about logic and mathematics, ever in a sort of dialectic interplay. In what follows we draw this out through his published essays—and one letter—both to elicit aspects of influence in his own terms and to set out a picture of Kreisel's evolving thinking about logic and mathematics in comparative relief.Accepted manuscrip

Kaleidoscope JEIRP on Learning Patterns for the Design and Deployment of Mathematical Games: Final Report

Project deliverable (D40.05.01-F)Over the last few years have witnessed a growing recognition of the educational potential of computer games. However, it is generally agreed that the process of designing and deploying TEL resources generally and games for mathematical learning specifically is a difficult task. The Kaleidoscope project, "Learning patterns for the design and deployment of mathematical games", aims to investigate this problem. We work from the premise that designing and deploying games for mathematical learning requires the assimilation and integration of deep knowledge from diverse domains of expertise including mathematics, games development, software engineering, learning and teaching. We promote the use of a design patterns approach to address this problem. This deliverable reports on the project by presenting both a connected account of the prior deliverables and also a detailed description of the methodology involved in producing those deliverables. In terms of conducting the future work which this report envisages, the setting out of our methodology is seen by us as very significant. The central deliverable includes reference to a large set of learning patterns for use by educators, researchers, practitioners, designers and software developers when designing and deploying TEL-based mathematical games. Our pattern language is suggested as an enabling tool for good practice, by facilitating pattern-specific communication and knowledge sharing between participants. We provide a set of trails as a "way-in" to using the learning pattern language. We report in this methodology how the project has enabled the synergistic collaboration of what started out as two distinct strands: design and deployment, even to the extent that it is now difficult to identify those strands within the processes and deliverables of the project. The tools and outcomes from the project can be found at: http://lp.noe-kaleidoscope.org

Three approaches in the research field of ethnomodeling: emic (local), etic (global), and dialogical (glocal)

The acquisition of both emic (local) and etic (global) knowledge is an alternative goal for the implementation of ethnomodeling research. Emic knowledge is essential for an intuitive and empathic understanding of mathematical ideas, procedures, and practices developed by the members of distinct cultural groups. It is essential for conducting effective ethnographic fieldwork. Furthermore, emic knowledge is a valuable source of inspiration for etic hypotheses. Etic knowledge is essential for cross-cultural comparisons, which are based on the components of ethnology. In this regard, such comparisons demand standard units and categories to facilitate communication. Dialogical (glocal) is a third approach for ethnomodeling research that makes use of both emic and etic knowledge traditions through processes of dialogue and interaction. Ethnomodeling is defined as the study of mathematical phenomena within a culture because it is a social construct and is culturally bound. Finally, the objective of this article is to show how we have come to use a combination of emic, etic and dialogical (glocal) approaches in our work in the area of ethnomodeling, which contributes to the acquisition of a more complete understanding of mathematical practices developed by the members of distinct cultural groups

Drawing Boundaries

In “On Drawing Lines on a Map” (1995), I suggested that the different ways we have of drawing lines on maps open up a new perspective on ontology, resting on a distinction between two sorts of boundaries: fiat and bona fide. “Fiat” means, roughly: human-demarcation-induced. “Bona fide” means, again roughly: a boundary constituted by some real physical discontinuity. I presented a general typology of boundaries based on this opposition and showed how it generates a corresponding typology of the different sorts of objects which boundaries determine or demarcate. In this paper, I describe how the theory of fiat boundaries has evolved since 1995, how it has been applied in areas such as property law and political geography, and how it is being used in contemporary work in formal and applied ontology, especially within the framework of Basic Formal Ontology

Macroevolutionary issues and approaches in evolutionary Biology

info:eu-repo/semantics/publishedVersio

Research Based Recommendation: Effective Parent Advocacy for Students who are Twice-Exceptional, Academically Gifted With Autism

This thesis’s purpose is twofold. The first purpose is to present both information about what twice-exceptionality is and to make recommendations based on the existing research as to how parents or guardians can become more effective advocates and advocate for effective programming and services for their children who are twice-exceptional. While this thesis focuses on a specific subset of twice-exceptional students, those who are both gifted and have autism, a good deal of the material presented will be applicable to children who are gifted with learning disabilities. Effective parent advocacy looks the same across exceptionalities: producing the best educational experience based on the child’s unique needs. Strengths-based programming has been demonstrated to benefit twice-exceptional students no matter the disability, however the areas of deficit will vary depending on the specific disability a child has and his/her unique learning profile. The resources for information on special education law and twice-exceptionality will be useful to parents regardless of the twice-exceptional child’s disability. The second, and I feel most important, purpose of the thesis is to provide those parents/guardians with a “Quick Start Guide to Advocacy” to help them get started on the path to becoming the most effective advocate they can be for their child(ren). While educators and school administrators are expected to have a solid understanding of the rights and responsibilities of all stakeholders, many times parents are thrust into the world of special and gifted education with no preexisting knowledge. The aim of this thesis is to help bridge this gap for parents and guardians of this unique subset of students

A Computable Economist’s Perspective on Computational Complexity

A computable economist.s view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of computational complexity theories from diverse traditions is emphasised. The unifications that emerged in the modern era was codified by means of the notions of efficiency of computations, non-deterministic computations, completeness, reducibility and verifiability - all three of the latter concepts had their origins on what may be called "Post's Program of Research for Higher Recursion Theory". Approximations, computations and constructions are also emphasised. The recent real model of computation as a basis for studying computational complexity in the domain of the reals is also presented and discussed, albeit critically. A brief sceptical section on algorithmic complexity theory is included in an appendix.