Provability logics with many modal operators for progressions of theories obtained by iterating their consistency statements are introduced. The corresponding arithmetical completeness theorem is proved.

We study the fragment of Peano arithmetic formalizing the induction principle for the class of decidable predicates, $I\Delta_1$ . We show that $I\Delta_1$ is independent from the set of all true arithmetical $\Pi_2-sentences$ . Moreover, we establish the connections between this theory and some classes of oracle computable functions with restrictions on the allowed number of queries. We also obtain some conservation and independence results for parameter free and inference rule forms of $\Delta_1-induction$ . An open problem formulated by J. (...) Paris is whether $I\Delta_1$ proves the corresponding least element principle for decidable predicates, $L\Delta_1$ (or, equivalently. the $\Sigma_1-collection$ principle $B\Sigma_1$ ). We reduce this question to a purely computation-theoretic one. (shrink)

Open peer commentary on the article “A Cybernetic Approach to Contextual Teaching and Learning” by Philip Baron. Upshot: The idea of personal, customized education has been around for a while, and few disagree that it would be superior to what we have now in most public education systems worldwide. So, the questions are: Why has it not been more broadly implemented? And what would it take to make it the dominant approach to education?

Open peer commentary on the article ““Black Box” Theatre: Second-Order Cybernetics and Naturalism in Rehearsal and Performance” by Tom Scholte. Upshot: Scholte proposes using the theatre as a laboratory for experimenting with ideas in second-order cybernetics, adding to the repertoire of approaches for advancing this way of thinking. Second-order cybernetics, as art, science and craft, raises questions about the forms of experimentation most useful in such a laboratory. Theatre provides an opportunity to “play” with the dynamics of human interactions and (...) relations and possibly demonstrate value in second-order cybernetic thinking. (shrink)

This work examines the claim to scienific status made by supporters and practitioners of neoclassical economics. The approach taken is that of the history and philosophy of science. Analysis points to the conclusion that theories of economic choice are necessarily normative, essentially because of the nature of human behavior.

Purpose: This paper intends to connect ideas from the radical constructivist approach to cognition and learning to ideas from the constraint-theoretic approach to social policy formulation. It then extends these ideas to a dialogic approach to social transformation and design. Method: After demonstrating a correspondence between von Glasersfeld's fit/match distinction and my constraint-oriented/goal-oriented distinction with respect to policy formulation, the paper evaluates the basic assumptions of radical constructivism and builds from them a framework for thinking and talking about a desirable (...) society and ways to participate in its realization. Findings: The ideas of von Glasersfeld's radical constructivism contribute significantly to the development of a conceptual base for applied research on social activism by raising new questions and stimulating new thinking. Practical implications: Social activism in everyday affairs can be a way of living in the "world." Conclusion: The work and thought of Ernst von Glasersfeld opens a path toward a rich array of concepts and ideas with the potential to inform efforts in a wide variety of human endeavors. (shrink)

Clocks and Rulers Play Tricks. 6. Work Changes Mass. 7. Summing Up. Index. Unabridged republication of the edition published by Basic Books, Inc.

Upshot: Conversational conferences are difficult to design in a way that avoids the consequences that arise when participants are not experienced with or fully value the conversational mode of interaction. So, the designers of such conferences must experiment with ways to build a culture, use a structure, and facilitate participation that might mitigate some of these consequences. The potential of the experimental conference designed in the light of second-order cybernetics lies, in part, in the prospect of identifying and acquiring the (...) conversational abilities and appreciations necessary to support a participative-dialogic society. (shrink)

Open peer commentary on the article “The Banathy Conversation Methodology” by Gordon Dyer, Jed Jones, Gordon Rowland & Silvia Zweifel. Upshot: The Banathy Conversation Methodology offers an approach to organizing and facilitating conversation groups among individuals self-identified as interested in a particular topic. As someone who would like to see more conversation integrated into academic conferences, I propose two extensions of BCM for consideration by the authors: one is an extension to the theoretical underpinnings, namely the conversation theory of Gordon (...) Pask, and the other is an extension to the tools and techniques, namely the group syntegration process developed by Stafford Beer. If the authors do not like the direction these extensions might take BCM, I would be interested in their assessment of the circumstances under which alternative approaches to conversation groups might be more or less useful. (shrink)

Context: A tension exists between the needs and desires of the institutions providing the funding for academics to attend conferences and the potential for transforming the knowledge and understanding of conference participants - than in advancing their own careers and celebrity. Approaches to the problem can recognize the importance of funding and career-building in the current society, while still experimenting in ways that could generate new ideas. Method: Ideas from second-order cybernetics are used to derive design principles that might alleviate (...) the tension and encourage deep conversations, idea generation and experimentation. The author draws on experiences with designing, organizing and participating in cybernetics conferences over a period of 34 years. Results: An academic conference designed to a set of broad, second-order cybernetic principles, where participants are informed of the design intent before they decide to attend, can open an opportunity for learning, understanding and the creation of new ideas in ways that would not otherwise be available. Although there are no guarantees, such designs can attenuate the tension, often experienced at traditionally designed conferences, between advancing individual careers/celebrity and building new knowledge together. Implications: The design principles derived, already exhibited in some conferences, could be useful to organizers wishing to foster incompatible and opposing ideas and facilitate dialogue among conference participants. These same principles have implications for the design of other social systems and point to the possibility of a new and more humane society. Constructivist content: A feature of second-order cybernetics is that knowledge is continually changing as our desires change, and we must take responsibility for the consequences of the ideas we construct and use to satisfy our desires. Key Words: Design by constraint, dynamics of interaction, asynchronicity, tyranny of the clock, times of truth, moments of art. (shrink)

A successful attempt to provide an accurate, non-technical introduction to philosophy which begins with the discussion of logic, moves to epistemology and metaphysics, then takes up political philosophy, ethics, and the philosophy of religion, and concludes with a special section on contemporary philosophy. There are references throughout to philosophers, such as Malebranche and Plotinus, who are frequently neglected in introductory texts. --D. Z. L.

Much of the mathematics with which Felix Klein and Sophus Lie are now associated (Klein’s Erlangen Program and Lie’s theory of transformation groups) is rooted in ideas they developed in their early work: the consideration of geometric objects or properties preserved by systems of transformations. As early as 1870, Lie studied particular examples of what he later called contact transformations, which preserve tangency and which came to play a crucial role in his systematic study of transformation groups and differential equations. (...) This note examines Klein’s efforts in the 1870s to interpret contact transformations in terms of connexes and traces that interpretation (which included a false assumption) over the decades that follow. The analysis passes from Klein’s letters to Lie through Lindemann’s edition of Clebsch’s lectures on geometry in 1876, Lie’s criticism of it in his treatise on transformation groups in 1893, and the careful development of that interpretation by Dohmen, a student of Engel, in his 1905 dissertation. The now-obscure notion of connexes and its relation to Lie’s line elements and surface elements are discussed here in some detail. (shrink)

Atualmente, biotecnologias são empregadas na forma de protocolos a fim de sincronizar o crescimento folicular e a ovulação, bem como permitir que vacas atuem como receptoras de embriões visando melhorar o potencial genético do rebanho. O objetivo desse estudo foi avaliar o efeito da utilização de implantes intravaginais de progesterona de 1º, 2º e 3º uso no protocolo de transferência de embriões em tempo fixo (TETF) sobre a taxa de prenhez em receptoras girolandas. O experimento ocorreu em uma fazenda localizada (...) no município de São Sebastião do Maranhão (MG). Foram utilizadas 74 vacas submetidas aos seguintes protocolos: No dia 0 (D0) administrou-se 2 ml de 17β-Estradiol e progesterona e foi colocado o implante intravaginal de progesterona. Estes implantes foram colocados de forma aleatória, sendo de 1° uso (grupo 1; n=15), 2° (grupo 2; n=24) ou 3° (grupo 3; n=35).No D8, os implantes foram retirados e administrou-se 2 ml PGF2α; 1,5 ml de eCG e 1 ml de 17β-Estradiol e progesterona. A inovulação dos embriões in vitroo correu no D (16) para todas as vacas que apresentaram um corpo lúteo. As variáveis qualitativas (prenhe ou não prenhe) foram comparadas em tabelas de contingência e analisadas pelo teste de qui-quadrado a 5% de probabilidade. Neste estudo não houve diferença estatística entre os grupos protocolados em relação ao aproveitamento como receptoras: 1º uso (53,3%), 2º (79,2%) e 3º (68,65). Ademais, observou-se uma taxa de prenhez entre os grupos de 37,5% para o 1º uso, 42,1% para o 2º e 33,3% para o 3º (P>0,05). Dentre as vantagens ao reaproveitamento dos implantes multiusos destaca-se a redução dos custos dos protocolos hormonais, já que a progesterona é o hormônio mais oneroso, desta forma, a maximização do uso reduz o valor final do protocolo sem prejuízos a taxa de prenhez. (shrink)

L. D. Harris; IV*—Solving the “Naval Battle”, Proceedings of the Aristotelian Society, Volume 78, Issue 1, 1 June 1978, Pages 45–62, https://doi.org/10.1093/ari.

How can the sacred be artistically expressed? The answer to this question depends greatly on the precise relation of the aesthetic to the religious experience. F. David Martin considers them both to be participative experiences which reveal the ontological beyond the ontic. Yet while the aesthetic experience and its artistic expression only implicitly attain Being as transcendent, religious art conveys an explicit awareness of transcendence. Religious expressiveness is achieved by a strong embodiment of the iconic element present in all art. (...) Still without the addition of conventional symbols iconic symbols can never become explicitly religious. The presence of conventional religious symbols alone, however, is not sufficient to sacralize art. A painting may remain secular even if it represents a Madonna. To function religiously it also needs what the author terms an "iconic foundation." Thus the religious dimension of art appears on three levels: 1) in the artistic expression as such which, even though it may not articulate religious feelings, is implicitly religious by letting Being shine forth; 2) in the evocation of Being-as-transcendent by means of iconic symbols, which remains still religiously ambiguous; 3) in the clear assertion of transcendent Being by iconic and conventional symbols, which is explicitly religious. The thesis is developed successively for music, painting, literature, and architecture. Each chapter is illustrated with appropriate examples testifying to the author’s unusual aesthetic sensitivity. (shrink)

Cicero's De finibus, written in 45 BC, consists of three separate dialogues, dealing respectively with the ethical systems of Epicureanism, Stoicism, and the `Old Academy' of Antiochus of Ascalon. This critical edition of the text, based on a fresh study and collation of the manuscripts, is the first to appear for many years and the first to reflect a clear understanding of the whole manuscript tradition. It will be the second in a series of editions of Cicero's philosophical works; the (...) first volume, the De officiis, edited by Michael Winterbottom, appeared in 1994. (shrink)

A general equation is derived describing the concentration of all possible complexes of a central molecule with a set of ligands bound to the central molecule. This deduction allows the reaction rate constants for the binding of a given molecule to the central molecule to depend on the species of molecules already bound and the location of the molecules already bound. The model thus allows for structural alteration of the central molecule by binding. Functions describing the concentration dependence of any (...) effect whatever depending on the distribution of complexes are deduced. Possible applications and methods of application are indicated.II est dérivé une équation qui décrit la concentration des toutes les complexes d'une molécule centrale avec une collection de ligands connectés à la molécule centrale. La déduction montre comme les coefficients de la rapidité de reaction entre la molécule centrale et les molécules de la collection dépend de l'espèce et de la location des molécules déjà connectées.La modèle dérivée de l'équation montre les changements structurelles par la connection. Les functions qui décrivent la dependence de chaque effet à la concentration, sont dérivés. Ces effects dépendent aussi à la distribution des complexes. Des applications et des méthodes sont indiqués.Eine allgemeine Vergleichung hat man bekommen welche die Konzentration aller möglichen Komplexen eines zentralen Moleküles mit einer Reihe von „Ligands” verbunden mit dem zentralen Molekül beschreibt. Diese Folgerung gestattet dass die Reaktiongeschwindigkeit Konstanten für die Bindung eines gegebenen Moleküles mit dem zentralen Molekül abhÄngt von den Arten schon gegebenen Molekülen und die Ortsbestimmung der schon gebundenen Molekülen. Das Model zeigt die strukturelle Änderungen des zentralen Moleküls durch Bindung. Funktionen, die die Konzentrationband jedes Effektes beschreiben dass abhÄngt von der Distribution der Komplexen, sind abgeleitet.Mögliche Anwendungen und Methoden von Anwendung sind dargelegt. (shrink)

By a result of L.D. Beklemishev, the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over any $$\Pi _2$$ -axiomatizable base theory extending Elementary Arithmetic collapses to its first level. We prove that this result cannot in general be extended to base theories of arbitrary quantifier complexity. In fact, given any recursively enumerable set of true $$\Pi _2$$ -sentences, S, we construct a sound $$(\Sigma _2 \! \vee \! \Pi _2)$$ -axiomatized theory T extending S such that (...) the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over T is proper. Our construction uses some results on subrecursive degree theory obtained by L. Kristiansen. (shrink)