This paper presents a case study carried out at Sofia University in Bulgaria, describing the relationship between two developments, firstly an expanding involvement with online learning and e-assessment, and secondly the development of institutional approaches to academic integrity. The two developments interact, the widening use of e-learning and e-assessment raising new issues for academic integrity, and the technology providing new tools to support academic integrity, with the involvement in technological developments acting as a catalyst for changes in approaches to academic (...) integrity. The aim of this study is to describe in what ways the integration of technologies for student authentication and authorship checking in this university has begun to influence teachers’ approach to academic integrity, and has also helped to identify specific issues that need to be resolved for the future of academic integrity in the university. Data collected during the implementation of pilots for the project TeSLA - An adaptive trust-based e-assessment system - enabled an examination of the perspectives of administrators, teachers and students on approaches to cheating and plagiarism, and on possible future directions. The data suggests that the piloting of the TeSLA system has triggered a deepening consideration of approaches to academic integrity, and has also helped to identify important issues for future developments. (shrink)

Student authentication and authorship checking systems are intended to help teachers address cheating and plagiarism. This study set out to investigate higher education teachers’ perceptions of the prevalence and types of cheating in their courses with a focus on the possible changes that might come about as a result of an increased use of e-assessment, ways of addressing cheating, and how the use of student authentication and authorship checking systems might impact on assessment practice. This study was carried out within (...) the context of the project TeSLA (an Adaptive Trust-based e-assessment System for Learning) which is developing a system intended for integration within an institution’s Virtual Learning Environment (VLE) offering a variety of instruments to assure student authentication and authorship checking. Data was collected at two universities that were trialling the TeSLA system, one in Turkey, where the main modes of teaching are face-to-face teaching and distance education, and one in Bulgaria, where the main modes of teaching are face-to-face teaching and blended learning. The study used questionnaires and interviews, building on existing TeSLA project evaluation activities and extending these to explore the specific areas we wished to examine in more depth.In three of the four contexts cheating was seen by teachers as a serious and growing problem, the exception was the distance education context where the teachers believed that the existing procedures were effective in controlling cheating. Most teachers in all four contexts expected cheating to become a greater problem with increased use of e-assessment. Student authentication was not seen as a major problem in any of the contexts, as this was felt to be well controlled through face-to-face proctored assessments, though the problem of assuring effective authentication was seen by many teachers as a barrier to increased use of e-assessment. Authorship checking was seen as a major issue in all contexts, as copying and pasting from the web, ghost writing and plagiarism were all reported as widely prevalent, and authorship checking was seen as becoming even more important with increased use of e-assessment. Teachers identified a third category of cheating behaviours, which was the accessing of information from other students, from written materials, and from the internet during assessments.Teachers identified a number of approaches to addressing the problem of cheating: education, technology, assessment design, sanctions, policy, and surveillance. Whilst technology was not seen as the most important approach to prevention, student authentication and authorship checking systems were seen as relevant in terms of reducing reliance on face-to-face proctored examinations, and in improving the quality of assessment through supporting the employment of a wider range of assessment methods. The development of authorship checking based on computational linguistic approaches was an area of particular interest. Student authentication and authorship checking systems were not seen as being able to address the third category of cheating behaviours that the study identified. (shrink)

The disruption -- Capital assembled -- Capital goes to work -- Capital goes to market -- Capital evolves -- The geography of it all -- Creative destruction on the land -- What is to be done? And who is going to do it?

In the Foundational Life, philosophy is commonly used as a method for choosing and analyzing fundamental concepts, and mathematics is commonly used for rigorous development. The mathematics informs the philosophy and the philosophy informs the mathematics.

We examine the writings of Adam Smith and Milton Friedman regarding their interpretation and use of the concept of self-interest.We argue that neither Smith nor Friedman considers self-interest to be synonymous with selfishness and thus devoid of ethicalconsiderations. Rather, for both writers self-interest embodies an other-regarding aspect that requires individuals to moderate theiractions when others are adversely affected. The overriding virtue for Smith in governing individual actions is justice; for Friedman it isnon-coercion.

Nelson Goodman’s work is universally regarded as pioneering and fundamental, and his attempts to clarify the nature of induction, symbol systems, art, theorizing and understanding have received and continue to receive great attention. Central to that work is a view Goodman describes as “radically relativist.” Goodman’s unusual brand of relativism, however, while basic to the entire Goodman corpus, has yet to be carefully delineated and studied. I hope in this paper to begin such a study. I will first briefly review (...) the development of Goodmanian relativism through his earlier books and articles. Then I will develop a more detailed and elaborate account of the relativist position Goodman develops in his most recent book, Ways of Worldmaking. Because Goodman’s relativism is significantly different from more traditional accounts of relativism, I will attempt to shed light on Goodmanian relativism by contrasting it with those more traditional accounts. Finally, I will argue that there is a crucial ambiguity in Goodman’s portrayal and defense of relativism, having to do with the role of “criteria of rightness” in Goodman’s system, and that this ambiguity licenses two quite distinct versions of Goodmanian relativism. I will argue that the weak version of relativism is defensible, and important, but that the strong, or “radical,” relativist position suffers from a fatal flaw. My hope is that the paper will serve to clarify not only Goodman’s position, but epistemological relativism more generally. (shrink)

This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, (...) this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students. Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual. (shrink)

Many years ago Wilamowitz desiderated a systematic collection of the texts which relate to the different types of poetry composed by the great lyric poets of Greece. He hoped that if we could only crystallize our admittedly scanty information about the characteristics of, say, the Paean or the Dirge, we might be able to reach a slightly better understanding than we have now of the formal structure and artistic design of the poems and fragments which have come down to us (...) under these titles. Indeed, this kind of knowledge is very important. (shrink)

The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).

Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.

Israel Scheffler is the pre-eminent philosopher of education in the English-speaking world today. This volume collects seventeen original, invited papers on Scheffler's philosophy of education by scholars from around the world. The papers address the wide range of topics that Scheffler's work in philosophy of education has addressed, including the aims of education, cognition and emotion, teaching, the language of education, science education, moral education, religious education, and human potential. Each paper is followed by a response from Scheffler himself. The (...) collection is essential reading for anyone concerned with contemporary scholarship in philosophy of education, or with the place of this singularly important author in it. (shrink)

The subtle, almost ineffable, and ineffable cardinals were introduced in an unpublished 1971 manuscript of R. Jensen and K. Kunen. The concepts were extended to that of k-subtle, k-almost ineffable, and k-ineffable cardinals in 1975 by J. Baumgartner. In this paper we give a self contained treatment of the basic facts about this level of the large cardinal hierarchy, which were established by J. Baumgartner. In particular, we give a proof that the k-subtle, k-almost ineffable, and k-ineffable cardinals define three (...) properly intertwined hierarchies with the same limit, lying strictly above “total indescribability” and strictly below “arrowing ω”. The innovation here is presented in Section 2, where we take a distinctly minimalist approach. Here the subtle cardinal hierarchy is characterized by very elementary properties that do not mention closed unbounded or stationary sets. This development culminates in a characterization of the hierarchy by means of a striking universal second-order property of linear orderings. (shrink)

One of the ways in which a poet may show his quality is by discrimination and originality in his choice of adjectives. Poetry likes to adorn the bare noun; a noun such as ‘the sky’ calls out for an attribute. But in practice the poet has to take care to avoid the cliche. He can seldom write ‘the blue sky’; even ‘the azure sky’ has become trite. He has to search for the epithet which will be both apt and original.

Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.

We now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.

In this article we examine the specific contributions Native American thought can make to the ongoing search for a Western ecological consciousness. We begin with a review of the influence of Native American beliefs on the different branches of the modem environmental movement and some initial comparisons of Western and Native American ways of seeing. We then review Native American thought on the natural world, highlighting beliefs in the need for reciprocity and balance, the world as a living being, and (...) relationships with animals. We conclude that Native American ideas are important, can prove inspirational in the search for a modem environmental consciousness, and affirm the arguments of both deep ecologists and ecofeminists. (shrink)

The kind of unknowability I will discuss concerns the count of certain natural finite sets of objects. Even the situation with regard to our present strong formal systems is rather unclear. One can just profitably focus on that, putting aside issues of general unknowability.

We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.

In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.

there are mathematical statements that cannot be proved or refuted using the usual axioms and rules of inference of mathematics.

We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [DSR 96,99,01,01X] involving coanalytic sets. The relevant proofs given there use substantial set theoretic methods, which were also shown to be necessary. We show that none of our Borel consequences can be proved without substantial set theoretic methods. The results are established for Baire space. We give equivalents of some of the main (...) results for the reals. (shrink)

We have been recently engaged in this search, and have announced a long series of successively simpler and more convincing examples. See [Fr09-10].

We present two forms of “sentential reflection”, which are shown to be mutually interpretable with Z2 and ZFC, respectively.

A lot of the well known impact of the Gödel phenomena is in the form of painful messages telling us that certain major mathematical programs cannot be completed as intended. This aspect of Gödel – the delivery of bad news –is not welcomed, and defensive measures are now in place.

It turns out, time and time again, in order to make serious progress in f.o.m., we need to take actual reasoning and actual development into account at precisely the proper level. If we take these into account too much, then we are faced with information that is just too difficult to create an exact science around - at least at a given state of development of f.o.m. And if we take these into account too little, our findings will not have (...) the relevance to mathematical practice that could be achieved. (shrink)

We begin by presenting the language L(N,℘N,℘℘N). This is the standard language for presenting third order sentences, using its intended interpretation.

1. Transfer principles from N to On. A. Mahlo cardinals. B. Weakly compact cardinals. C. Ineffable cardinals. D. Ramsey cardinals. E. Ineffably Ramsey cardinals. F. Subtle cardinals. G. From N to (...) 4. Decidability of statements on N. 5. Decidability of statements on shrink)

Russell’s way out of his paradox via the impredicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.

This is widely accepted, inside and outside philosophy, but one can spend an entire career clarifying, justifying, and amplifying on this statement. Certainly a graduate student career.

This topic has been discussed earlier on the FOM email list in various guises. The common theme is: big numbers and long sequences associated with mathematical objects. See..

The equation P = NP concerns algorithms for deciding membership in sets. The consensus is that P ≠ NP, although some prominent experts guess otherwise.

NOTE: This is an expanded version of my lecture at the special session on reverse mathematics, delivered at the Special Session on Reverse Mathematics held at the Atlanta AMS meeting, on January 6, 2005.

This distinction between logic and mathematics is subject to various criticisms and can be given various defenses. Nevertheless, the division seems natural enough and is commonly adopted in presentations of the standard foundations for mathematics.

We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hilbert's Tenth Problem. The limited number of facts used from recursion theory are isolated at the beginning.

C. To what extent, and in what sense, is the natural hierarchy of logical strengths rep resented by familiar systems ranging from exponential function arithmetic to ZF + j:V Æ V robust?

This article examines the relative efficacy of Abraham Kuyper and Herman Dooyeweerd’s sphere sovereignty for holistic transformation in Asia. It examines interest in China and Malaysia in Neo-Calvinism, Civil Society, and sphere sovereignty and its social, cultural, and political implications. It considers the strengths and weaknesses of sphere sovereignty in a secular age particularly in light of the sharp antithesis Kuyper and Dooyeweerd posited between the epistemological and ethical frameworks of secular modernist versus Christian approaches to understanding and social, cultural, (...) and political engagement. The article concludes that although this antithesis marginalizes Christian perspectives in a secular age, Herman Bavink’s softening of Neo-Calvinist emphasis on antithesis offers a fresh way to consider transformational engagement. (shrink)

To prove this, we fix P(x) to be any polynomial of degree ≥ 1 with a positive and negative value. We define a critical interval to be any nonempty open interval on which P is strictly monotone and where P is not strictly monotone on any larger open interval. Here an open interval may not have endpoints in F, and may be infinite on the left or right or both sides. Obviously, the critical intervals are pairwise disjoint.

AT the conclusion of his recently published paper on Corinna1 Professor Page leaves open the question whether the poetess was a contemporary of Pindar or of Moschus-whether she belongs to the middle of the fifth century or the end of the third. He gives excellent reasons for believing that these two dates exhaust the possibilities: they are far more probable than a date either outside or between them; but there seems to be no sure criterion by which we can decide (...) between the two, and Professor Page has to end his researches with a suspension of judgement. (shrink)

If someone reports that he had been thinking that he would very much like to seduce his sister, an appropriate comment might be: “Shame on you for having such a nasty idea.” But if one reports that he dreamt he seduced his sister the situation appears quite different, for while we might be repulsed by the dream shaming seems, to say the least, far less appropriate.We do not ordinarily, if ever, say things like, “It was bad of you to dream (...) that.” A child may be sent to bed without supper for saying that he hates his father, but not for reporting a dream which clearly expresses hate for his father. (shrink)

This paper was referred to in the Introduction in our paper [Fr97a], “The Axiomatization of Set Theory by Separation, Reducibility, and Comprehension.” In [Fr97a], all systems considered used the axiom of Extensionality. This is appropriate in a set theoretic context.