This book presents fourteen new essays by international scholars about the intersections between pragmatism, education, and philosophy with children. Pragmatism from its beginnings has sought a revolution in learning, and is itself a special kind of philosophy of education. What can the applications of pragmatism to pedagogy around the world teach us today?

The article introduces the concept of ‘argumentational integrity’ as the basis for developing ethical criteria by which contributions to argumentative discussions can be evaluated; the focus is on the derivation, definition, and specification of the concept. The derivation of the concept starts out from a prescriptive use of ‘argumentation’, entailing in particular the goal of a rational as well as a cooperative solution. In order to make this goal attainable, contributions to argumentative discussions must meet certain conditions. It is assumed (...) that participants are not only intuitively aware of these conditions, but in fact expect of themselves and others that they will not consciously violate the conditions. This assumption leads to the most general definition of the norm of argumentational integrity: Speakers must not knowingly violate the argumentative conditions. On the basis of an empirical study drawing upon classifications of unethical strategies in popular rhetorical texts, the general norm is then specified in the form of 11 ‘standards of fair argumentation’. (shrink)

The Physikalische Gesellschaft zu Berlin , founded in 1845 as a local association, became a centre of interdisciplinarity. Until about 1880 the Physical Society contributed to the development of interdisciplinary sciences like bio(medical)physics, astrophysics and Physics of the earth (physical meteorology). In the same way the emergence of well-founded electrotechnics and scientific device construction was promoted by physics.

Nobelprizewinner Ferdinand Braun worked as a teacher for three years (1874–1977) at the Leipzig Thomas School. In this time, essential for him, he developed his most important discovery: the effect of semiconductivity. Furthermore he demonstrated his pedagogical talent as a teacher and wrote an approval, popularized book for young people. The experiences of that time had a influence upon his future work.

The Nielsen‐Schreier theorem asserts that subgroups of free groups are free. In the first section we show that this theorem does not follow from the Linear Ordering Principle, thus strengthening the fact that it implies the Axiom of Choice for families of finite sets. In the second section, we show that a stronger variant of the Nielsen‐Schreier theorem implies the Axiom of Choice.

RésuméNous introduisons la notion de structure algébrique dynamique, inspirée de l'évaluation dynamique et de la théorie des modèles. Nous montrons comment cette notion constructive permet une relecture de la théorie d'Artin-Schreier, avec la modification capitale que le résultat final est alors établi de manière constructive. Nous pensons que ce que nous avons réalisé ici sur un cas d'école peut être généralisé à des parties significatives de l'algèbre classique, et est donc une contribution à la réalisation du programme de Hilbert (...) pour l'algèbre classique.We introduce the notion of “Dynamic Algebraic Structure” inspired by Dynamic Evaluation and Model Theory. We show that this constructive notion allows a rereading of the Artin-Schreier-Robinson solution for the 17th Hilbert Problem. So, once we know how to reread the proofs, this kind of abstract theory contains an algorithm which computes the concrete result . Our method gives a constructive semantic for certain parts of abstract classical mathematics.The idea is the following: replace the classical algebraic structures “constructed” by Choice and Principle of Third Excluded Middle , by DAS and dynamic evaluations of these DAS. Then TEM is replaced by construction of branching in the trees of dynamic evaluation of the DAS. If Choice is used in the form of Godel completeness theorem, it is not really necessary to use it for obtaining concrete results: in DAS, Choice is simply replaced by … nothing!. This is because the classical proof is by contradiction: “if there were not a sum of squares then some formal theory would admit a pathological model”. The constructive reasoning is more direct: since the pathological theory proves 0 = 1 we know how to construct the sum of squares … and classical models have disappeared in the proof. They are replaced by dynamic evaluations of DAS. We think that we have given, for an academic example, a new method, realizing a kind of Hilbert Program for significant parts of classical algebra. (shrink)

We show that the Boolean Prime Ideal Theorem () does not imply the Nielsen‐Schreier Theorem () in, thus strengthening the result of Kleppmann from “Nielsen‐Schreier and the Axiom of Choice” that the (strictly weaker than ) Ordering Principle () does not imply in. We also show that is false in Mostowski's Linearly Ordered Model of. The above two results also settle the corresponding open problems from Howard and Rubin's “Consequences of the Axiom of Choice”.

According to Belegradek, a first order structure is weakly small if there are countably many $1$-types over any of its finite subset. We show the following results. A field extension of finite degree of an infinite weakly small field has no Artin-Schreier extension. A weakly small field of characteristic $2$ is finite or algebraically closed. A weakly small division ring of positive characteristic is locally finite dimensional over its centre. A weakly small division ring of characteristic $2$ is a (...) field. (shrink)

The Artin‐Schreier theorem says that every formally real field has orders. Friedman, Simpson and Smith showed in [6] that the Artin‐Schreier theorem is equivalent to over. We first prove that the generalization of the Artin‐Schreier theorem to noncommutative rings is equivalent to over. In the theory of orderings on rings, following an idea of Serre, we often show the existence of orders on formally real rings by extending pre‐orders to orders, where Zorn's lemma is used. We then (...) prove that “pre‐orders on rings not necessarily commutative extend to orders” is equivalent to. (shrink)

Jan Krajíček posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A is provable in length k for all n ϵ ω , then A is provable? It is argued that the answer to this question depends on the particular formulation of the “theory of real closed fields.” Four distinct formulations are investigated with respect to their generalization behavior. It is shown that there is a positive answer to (...) Krajíček's question for 1. the axiom system RCF of Artin-Schreier with Gentzen's LK as underlying logical calculus, 2. RCF with the variant LK B of LK allowing introduction of several quantifiers of the same type in one step, 3. LK B and the first-order schemata corresponding to Dedekind cuts and the supremum principle. A negative answer is given for 4. any system containing the schema of extensionality. (shrink)

We investigate some common points between stable structures and weakly small structures and define a structureMto befineif the Cantor-Bendixson rank of the topological space${S_\varphi }\left} \right)$is an ordinal for every finite subsetAofMand every formula$\varphi \left$wherexis of arity 1. By definition, a theory isfineif all its models are so. Stable theories and small theories are fine, and weakly minimal structures are fine. For any finite subsetAof a fine groupG, the traces on the algebraic closure$acl\left$ofAof definable subgroups ofGover$acl\left$which are boolean combinations of (...) instances of an arbitrary fixed formula can decrease only finitely many times. An infinite field with a fine theory has no additive nor multiplicative proper definable subgroups of finite index, nor Artin-Schreier extensions. (shrink)

What kind of reality is legal reality, how is it created, and what are its a priori foundations? These are the central questions asked by the early phenomenologists who took interest in social ontology and law. While Reinach represents the well-known “realist” approach to phenomenology of law, Felix Kaufmann and Fritz Schreier belonged to the “positivist” “Vienna School of Jurisprudence,” combining Hans Kelsen’s Pure Theory of Law with Edmund Husserl’s phenomenology—and thereby challenging Reinach’s views on how legal reality and (...) the legal a priori were to be conceived. This paper addresses the controversy between these positivist and realist approaches to phenomenology of law, with the goal of introducing the lesser known theories of Kaufmann and Schreier. The special focus on their critique of Reinach’s outline should give us an overview of their positions vis-à-vis the basic and a priori elements of which legal reality consists and the role that phenomenology plays in analyzing them. There is one general tendency to be noted: While the phenomenological legal positivists see the root of legal reality in an act of interpretation according to a “normative scheme of interpretation,” Reinach locates the roots of legal reality in social interaction and argues for the existence of entities independent of any interpretation. (shrink)