In a previous article an elementary semantic analysis showed that, logically, analogical terms and expressions must be treated as homonyms, though of a special type. The latter qualification is necessitated by the concomitant element of similarity that is found to be involved in all comparisons of the analogical type. Further, it was pointed out that the special types of similarity in question cannot be isolated through a purely semantic analysis. This is, in particular, a consequence of the fact that (...) analogy is itself an analogical notion and term. The kind of similarity involved may, therefore, vary in the different forms of analogy and it may prove impossible to abstract from these something like a common element, e.g., a particular type of resemblance. This implies that the full philosophical significance of a particular form of analogy can be gleaned only from a contextual examination of its rôle in relation to a particular problem. Nevertheless, some significant conclusions may emerge from a partial analysis of certain forms of resemblance which are usually associated with analogy. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides (...) the Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

Nelson Goodman has constructed two theories of simplicity: one of predicates; one of hypotheses. I offer a simpler theory by generalization and abstraction from his. Generalization comes by dropping special conditions Goodman imposes on which unexcluded extensions count as complicating and which excluded extensions count as simplifying. Abstraction is achieved by counting only nonisomorphic models and subinterpretations. The new theory takes into account all the hypotheses of a theory in assessing its complexity, whether they were projected prior to, or result (...) from, projection of a given hypothesis. It assigns simplicity post-projection priority over simplicity pre-projection. It better orders compound conditionals than does the theory of simplicity of hypotheses, and it does not inherit an anomaly of the theory of simplicity of predicates — its failure to order the ordering relations. Drop Goodman's special conditions, and the problems fall away with them. (shrink)

One of Kant’s famous questions about being human asks, “What may I hope?” This question places individual life within an encompassing horizon of human history and speculates on the possibility of perspectives beyond death. In our time mortality is generally repressed, though the development of personal consciousness is closely linked to realization of one’s finitude. This raises especially urgent questions for children, and they are left to deal with them alone. From the time awareness begins, knowledge that death can occur (...) at any moment is one of the a priori determinants of being alive; that is, life is structured in advance by its future pastness. . According to Max Scheler, death reveals itself as a necessary and manifest constituent of all possible inner experiences in the life process. The cultural and individual interpretations of death’s meaning and consequences derived from this insight opened up an ample space for imagined possibilities of “continued existence,” which affected approaches to life. In our research project “Inochi – The Concept of Life after Death in Children’s Construction of the World. A German-Japanese Comparison,” carried out with German and Japanese research support, we examine concepts developed within the community of inquiry concerning “the individual’s afterlife” as soul, angel, animal, star, etc. In this we want to examine whether a globalized media environment leads to a cultural convergence in children’s ideas, and whether there are differences between views of girls and boys. Relevance of ideas about death is seen in the example of Japanese children who, believing in reincarnation chose “killing oneself” with relative frequency as a problem-solving strategy. Our contribution will present children’s imaginings using the drawings they created within this framework, since these can be interpreted as expressions of “narrative philosophizing,” especially for the Japanese children. Here we follow Mark Johnson who says” Human beings are imaginative synthesizing animals” . These imaginations make up a large part of our understanding, not just our beliefs, but rather our socially constructed way of being in and inhabiting a world. (shrink)

We formalize the notion of isolated objects, and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless (...) elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects. (shrink)

This article studies perceptual differences of three social robots by elementary school children of ages 6–13 years at research fairs. The autonomous humanoid robot Pepper, an advanced social robot primarily designed as a personal assistant with movement and mobility, is compared to the teleoperated AV1 robot—designed to help elementary school children who cannot attend school to have a telepresence through the robot—and the flowerpot robot Tessa, used in the eWare system as an avatar for a home sensor system (...) and dedicated to people with dementia living alone. These three robots were shown at the Norwegian national research fair, held in every major Norwegian city annually, where children were able to interact with the robots. Our analysis is based on quantitative survey data of the school children concerning the robots and qualitative discussions with them. By comparing three different types of social robots, we found that presence can be differently understood and conceptualized with different robots, especially relating to their function and “aliveness.” Additionally, we found a strong difference when relating robots to personal relations to one’s own grandparents versus older adults in general. We found children’s perceptions of robots to be relatively positive, curious and exploratory and that they were quite reflective on their own grandparent having a robot. (shrink)

This article presents an analysis of one docent's discussion of Michigan history to a group of third-grade children as part of a week-long state-sponsored history program. By analyzing the docent's...

1. The theory of classes presented in this paper is a simplification of that presented by J. von Neumann in his paper Die Axiomatisierung der Mengenlehre. However, this paper is written so that it can be read independently of von Neumann's. The principal modifications of his system are the following.(1) The idea of ordered pair is defined in terms of the other primitive concepts of the system. (See Axiom 4.3 below.)(2) A much simpler proof of the well-ordering theorem, based (...) on von Neumann's equivalence axiom (Axiom 2.2 below) is given. (More exactly, the theory of ordinal numbers, on which the proof of the well-ordering theorem is based, is simplified—see §8.)(3) Functions are not assumed to be defined for all arguments. In place of “ = A” we have “is undefined.” This makes possible a constructive interpretation of the system. (See §2.)2. We wish first to give a rough picture of the system which we are trying to construct. Suppose that we have the idea “class,” but no material from which to construct classes. Nevertheless, we can construct the class 0 having no elements. And then the class 1 having 0 as its only element. And then the classes {1}, and {0, 1}, etc., using always the previously constructed classes as elements. To extend this method to infinite classes, we must give rules telling what elements are to be included. Since the nature of the rules which we can use is not altogether clear, we try to formalize the whole system; that is, to set up a system of axioms which seems to characterize this system of classes. Now in this set of axioms we find it necessary to use the idea of function (in the “Axiom of Replacement”). (shrink)

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ‘diagonal argument’ and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdos in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

In a number of areas, in particular in the Pacific region, it has been observed that languages have undergone simplification processes of their usually very elaborate grammatical structures, and that such elaborate grammatical features have decayed and in some cases entirely disappeared from some languages, hand in hand with the progressing decay, and falling into disuse, of the traditional cultures of the speakers of such languages. Such phenomena of simplification and decay of grammatical complexities are most readily observable (...) in Papuan languages of the New Guinea area and have also been found in Australian Aboriginal languages. Both these languages have very complex grammatical systems, the Papuan languages even more so than the Australian Aboriginal languages, and the multiplicity of grammatical features in them lend themselves more readily to simplification than may be the case with other languages in the Pacific area, such as Austronesian languages, also called Malayo-Polynesian languages, though such phenomena are by no means absent from them. (shrink)

Teaching is, to date, one of the most prone jobs to experiencing occupational stress and burnout. Owing to burnout’s negative personal, social, organizational and economic impacts, researchers, practitioners and education policy leaders are interested in developing practices and interventions aimed at preventing/reducing its prevalence. With teachers’ main professional demands to be of a social and emotional nature, interventions designed with a view to promote teachers’ social and emotional competence appears to be particularly promising, positively impacting teachers’ well-being and personal accomplishment (...) and contributing to a decrease in their psychological distress, namely emotional exhaustion. However, theoretical and empirically grounded interventions with ecological validity and specifically targeting teachers are still scarce. Thus, to bridge the previously identified gaps, the present study aimed to evaluate the efficacy and the quality of the intervention’s implementation of the A+, an online social and emotional learning intervention for elementary-school teachers. A quasi-experimental study was conducted with a total of 81 participants from three different school contexts. School clusters were similar in size, organizational structure and socioeconomic level, and as regards previous attendance at social and emotional learning interventions; however, they differed with regards to perceived organizational climate. Data on the efficacy of the A+ was collected across four waves using a set of self-report questionnaires that assessed proximal variables and distal variables, and analyzed through Robust Linear Mixed-Effects Models. Coefficient omegas suggested adequate reliability of the measures. Additionally, two trained observers completed an observation grid to evaluate the quality of the A+ implementation, with excellent inter-rater reliability. Results suggested that, over time, the A+ had positive impacts across proximal and distal variables favoring the experimental group. However, results differed across the school contexts. These findings were accompanied by good implementation quality indicators, namely high fidelity in the delivery of the A+ contents and high participants’ responsiveness. Despite its limitations, this study contributes to a growing body of research which reinforces the importance of investing in social and emotional learning interventions to prevent teachers’ burnout and improve their occupational health. Furthermore, it highlights the importance of implementation quality research as a component of program planning with a view to enhancing programs’ efficacy, as well as the need to adapt and consider context variables in research and practice. (shrink)

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ?diagonal argument? and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

A study of a group of elementary school students learning to control a computer‐implemented Newtonian object reveals a surprisingly uniform and detailed collection of strategies, at the core of which is a robust “Aristotelian” expectation that things should move in the direction they are last pushed. A protocol of an undergraduate dealing with the same situation shows a large overlap with the set of strategies used by the elementary school children and thus a marked lack of influence of (...) classroom physics training on this student's naive physics. The data from these two studies are pooled and elaborated into a “genetic task analysis” of how one might come to understand Newtonian dynamics as a more or less natural evolution from the naive state. (shrink)

The Dirac field and its quanta are obtained from the imposition of an infinite member of Dirac 2 nd class constraints on a system of complex scalar fields having an indefinite internal metric. The spin-1/2 character of the constrained system follows from constraint-induced coupling of the scalar system's independent internal and space-time symmetries, from constraint restrictions on allowed symmetries. The resulting spinor field quanta are seen to exist as a class of “elementary excitations” belonging to a dynamical algebra existing (...) naturally within the system of complex scalar fields. (shrink)

Sexual violence against women is an issue of urgency that arises in all cultures locally, nationally, globally and transnationally. This problem has broad dimensions in both the public and private domains, both cases that are reported or not reported to law enforcement. Factually, the trend of this problem has been identified as increasing every year in Maluku, Indonesia. Therefore, the church requires serious attention to prevention and systematic treatment to overcome it. This sensitivity and awareness are a manifestation of the (...) church’s sense of calling and responsibility for the restoration of human dignity. The pastoral sermon service model is the church’s strategic approach to handling this problem. This research aimed to develop a model of pastoral sermons for victims of sexual violence against women in Maluku. This research focused on identifying and exploring the tragic experiences and impacts of sexual violence against women. Furthermore, a cross-cultural pastoral model was created for victims of violence.Contribution: This article provided a new perspective from the post-modern homiletics to approach social issues. This new homiletical approach to dealing with the problem of women’s sexual violence is one of the main focuses of ‘Women’s Theological Studies’ in HTS. (shrink)

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

Anselm of Cantorbery wrote Proslogion, where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by absurd, (...) that “quod non posit cogitare non esse” by using the hypothesis: “to think in re” is taller than “to think in solo intelectu”. We discuss this relation and the difference between the meanings of the elementary predicates ‘to be in re’, ‘to be in intellectu’ and ‘to be in solo intellectu’. We propose a new logical approach of this ‘Unum argumentum’ of Anselm by using Curry’s Combinatory Logic. Indeed, Combinatory Logic is an abstract applicative formalism of operators applied to operands; in this formalism, the predicates, viewed as specific operators, can be composed and can be transformed, by an intrinsic way, into more complex predicates, by means of abstract operators, called “combinators”, studied by Combinatory Logic. We show that this formalism is a logical frame where it becomes possible to discuss and to formulate cognitive representations of the meanings of predicates used inside of the ‘Unum argumentum’ and to explain how the argument runs. (shrink)

Using a queer theory and disrupting heteronormativity framework, we applied a model lesson in the elementary methods course to understand preservice teachers’ experiences with LGBTQ individuals and families and their beliefs about utilizing children׳s literature portraying LGBTQ families in the elementary classroom. Participants reported a range of personal experiences with LGBTQ individuals and families and relatively positive responses to the family text set presented but wavered on LGBTQ themed books due to perceived conflict, religious beliefs, and ideas about (...) what is appropriate content for young learners. A discussion of the findings also includes preservice teachers’ intentions for future teaching related to LGBTQ topics. Implications for teacher education and social studies education are explored. (shrink)

The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...) paper then goes on to indicate the lines on which formal logic—and also the lambda calculus and set theory—needs to be restructured, to remove the difficulties. Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory in place of what it is a theory of, leading to a focus on mathematical manipulation, which ‘brackets off’ any natural language reading. (shrink)

Originally published in 1944, this book was originally intended as a continuation of the 1943 publication Nautical Mathematics, which is also reissued in this series. In it, the principles set out in Nautical Mathematics are given practical applications, and the text is supplied with exercises to test and clarify the lessons. This book will be of value to anyone with an interest in the history of education in the forces during WWII.

Our aim is to point out the role of scientific research in contemporary technological developments. Interactions between science and technology in the context of application-driven research projects of the 20th century are discussed. We define science and technology as two separate domains, and provide elementary models for their interaction by the means of applied and engineering sciences. These elementary models constitute linear and cascade models of science-technology interaction. We apply these elementary models for the purpose of further (...) methodological analysis of Soviet nuclear warfare project. The special role of organization and management in research and development activities is being emphasized. The new science-technology interaction model is devised in the course of nuclear project. This new interaction model is referred as non-linear or spiral. The model is seen as more collaborative and risk aware than linear and cascade interaction models present in twentieth century. The conclusion is the new model was of great impact to modern social forms in which research is carried out in the present. (shrink)

Pour soutenir les élèves du primaire dans leur apprentissage de la langue et des disciplines scolaires, tant en contexte de français langue d’enseignement que de français langue seconde, l’élaboration d’une liste de vocabulaire dit « transdisciplinaire » (Hiebert et Lubliner 2008) s’avère nécessaire. Il n’existe en effet pas de liste de référence pour l’enseignement ciblé des mots qui apparaissent fréquemment dans les matières scolaires au primaire en français et qui ont comme caractéristiques : soit d’être utilisés dans un même sens (...) quelle que soit la matière (souligner, examiner, répondre, expliquer, premièrement, enfin, etc.), soit de posséder des sens différents dans les différentes disciplines et dans la langue (nombre, base, somme, résultat, valeur, représenter, etc.). Dans cet article, nous rendons compte d’un projet de recherche ayant mené 1) à la constitution d’un corpus de plus de 4 millions de mots, à partir de manuels scolaires en usage au Québec pour tous les cycles du primaire, dans cinq disciplines (français, mathématiques, sciences, univers social, éthique et culture religieuse) et 2) à la sélection d’une liste de vocabulaire transdisciplinaire de plus de 2 000 vocables à des fins d’enseignement de la langue et des disciplines scolaires. (shrink)

We give a formal interpretation of Martin-Löf's Constructive Theory of Types in Elementary Topos Theory which is presented as a formalised theory with intensional equality of objects. Types are interpreted as arrows and variables as sections of their types. This is necessary to model correctly the working of the assumption x ∈ A. Then intensional equality interprets equality of types. The normal form theorem which asserts that the interpretation of a type is intensional equal to the pullback of its (...) “alignment” along some “base” arrow relates this interpretation to categorical semantic of types. (shrink)

Let T be Gödel's system of primitive recursive functionals of finite type in a combinatory logic formulation. Let $T^{\star}$ be the subsystem of T in which the iterator and recursor constants are permitted only when immediately applied to type 0 arguments. By a Howard-Schütte-style argument the $T^{\star}$ -derivation lengths are classified in terms of an iterated exponential function. As a consequence a constructive strong normalization proof for $T^{\star}$ is obtained. Another consequence is that every $T^{\star}$ -representable number-theoretic function is (...) class='Hi'>elementary recursive. Furthermore, it is shown that, conversely, every elementary recursive function is representable in $T^{\star}$ .The expressive weakness of $T^{\star}$ compared to the full system T can be explained as follows: In contrast to $T$ , computation steps in $T^{\star}$ never increase the nesting-depth of ${\mathcal I}_\rho$ and ${\mathcal R}_\rho$ at recursion positions. (shrink)

It seems very commonly agreed that Sappho's wedding-songs display none of the ritual obscenity so frequent in the genre. Thus D. L. Page wrote of fr. i ioa that ‘There is no trace here or elsewhere in Sappho of that ribaldry which was characteristic of the songs recited at this and other stages of Greek wedding-ceremonies’. Similarly Sir Maurice Bowra asserted of fr. 111 that it is ‘neither bawdy nor exalted, but playful. If the humour is a bit primitive, that (...) is due to tradition, which expected jokes at this level’. On the next page he writes of the songs sung outside the bridal chamber, as distinct from those sung in the procession thither, that ‘Here too Sappho seems to avoid bawdry but is not averse from rather elementary jokes’. (shrink)

It seems very commonly agreed that Sappho's wedding-songs display none of the ritual obscenity so frequent in the genre. Thus D. L. Page wrote of fr. i ioa that ‘There is no trace here or elsewhere in Sappho of that ribaldry which was characteristic of the songs recited at this and other stages of Greek wedding-ceremonies’. Similarly Sir Maurice Bowra asserted of fr. 111 that it is ‘neither bawdy nor exalted, but playful. If the humour is a bit primitive, that (...) is due to tradition, which expected jokes at this level’. On the next page he writes of the songs sung outside the bridal chamber, as distinct from those sung in the procession thither, that ‘Here too Sappho seems to avoid bawdry but is not averse from rather elementary jokes’. (shrink)

The article offers a reading of the famous tale by Kafka focused on the consequences triggered by the sudden transformation of Gregor Samsa into an insect. This event constitutes the starting point of a shift that involves phases and components of perception both of the self and of the world as well as the relations among the inner and the external world, the most elementary awareness and feelings and the most complex ones, which are affective, cognitive and related to (...) interactions, expressed with particular emphasis by the dynamics of the spatial dimension of the story. Two discursive paths intersect above all: on one side, the traveling salesman wakes up with the/in the body of cockroach while his soul is the same as always. He will have to try to become cockroach, that is to assume its perceptions and then, slowly, its tastes, its impressions and any other animal sentiment. At the same time, the becoming of Gregorio’s family will be antiphrastic to the one experienced by him: from inept, passive parasites of their akin, as they are depicted at the beginning of the story, his family members will gradually turn into active bourgeoisies full of projects, rejecting Gregory up to eliminate him: they are the ones dehumanizing themselves, while Gregory refines his sensitivity in suffering, even to the sacrifice. (shrink)