Emile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.

Reliabilist philosophy of science considers scientific misconduct a transgression against the principles of good cognitive practice. Good practice in research is characterised by the reliability, efficiency and fertility of the cognitive processes involved. The reliabilist approach is closely connected to the idea of mutual cognitive dependency of the research community. Trust in the testimony of others is not an inevitable but a favouring factor of scientific progress — and misconduct damages the testimonial chain, respectively the principle of trustworthiness. Within the (...) reliabilist framework, the main focus on questionable research is not on whether or not there are fraudulent intentions , but on recognisable consequences for the research community. Criticising the constructivist modeling of questionable research, we reconstruct certain contributions by Emil Abderhalden, Richard Goldschmidt, Franz Moewus, and Ernst Waldschmitz-Leitz as serious misconducts respectively frauds. We also show that specific social factors — often regarded as “apologising” conditions — decisively interfere with the principle of trustworthiness in the scientific community. (shrink)

INTRODUCTION In ita original form the present paper was presented to the American Mathematical Society, April 2k,, as a companion piece to the writer's ...

Ulrich Meyer defends a novel theory about the nature of time, and argues against the consensus view that time and space are fundamentally alike. He presents the first comprehensive defense of a 'modal' account, which emphasizes the similarities between times and possible worlds in modal logic, and is easily reconciled with the theory of relativity.

We show that IPC, K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.

We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most (...) nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal. (shrink)

La Déclaration commune sur la Doctrine de la Justification proposée par l'Institut pour la Recherche oecuménique de Strasbourg affirme que nous avons atteint un tel consensus concernant la question de la justification que les condamnations du XVIe siècle n'existent plus. Cet article montre d'abord que cette déclaration est le résultat d'un long dialogue au sein des théologies catholique et protestante, puis des comités officiels, au cours des quarante dernières années. Puis il en indique la signification et les limites. Il expose (...) ensuite comment elle a été reçue dans les Eglises luthériennes et la réponse officielle de la Fédération Mondiale Luthérienne, et celle de l'Eglise catholique. Il indique pour finir les tâches du dialogue oecuménique dans le futur. (shrink)

Short description: One of the major works of the great German theologian Emil Brunner, The Divine Imperative deals with one the many uncertainties in which we ...

We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...) of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)

By a well-known result of Cook and Reckhow [S.A. Cook, R.A. Reckhow, The relative efficiency of propositional proof systems, Journal of Symbolic Logic 44 36–50; R.A. Reckhow, On the lengths of proofs in the propositional calculus, Ph.D. Thesis, Department of Computer Science, University of Toronto, 1976], all Frege systems for the classical propositional calculus are polynomially equivalent. Mints and Kojevnikov [G. Mints, A. Kojevnikov, Intuitionistic Frege systems are polynomially equivalent, Zapiski Nauchnyh Seminarov POMI 316 129–146] have recently shown p-equivalence of (...) Frege systems for the intuitionistic propositional calculus in the standard language, building on a description of admissible rules of IPC by Iemhoff [R. Iemhoff, On the admissible rules of intuitionistic propositional logic, Journal of Symbolic Logic 66 281–294]. We prove a similar result for an infinite family of normal modal logics, including K4, GL, S4, and. (shrink)

This is a reproduction of a book published before 1923. This book may have occasional imperfectionssuch as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed worksworldwide. We appreciate your understanding of the imperfections in the (...) preservation process, and hope you enjoy this valuable book.++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Naturwissenschaftliche Plaudereien 3 Emil Arnold Budde. (shrink)

The elementary arithmetic operations +,·,≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${+,\cdot,\le}$$\end{document} on integers are well-known to be computable in the weak complexity class TC0, and it is a basic question what properties of these operations can be proved using only TC0-computable objects, i.e., in a theory of bounded arithmetic corresponding to TC0. We will show that the theory VTC0 extended with an axiom postulating the totality of iterated multiplication proves induction for quantifier-free formulas in the language ⟨+,·,≤⟩\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle{+,\cdot,\le}\rangle}$$\end{document}, and more generally, minimization for Σ0b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma_{0}^{b}}$$\end{document} formulas in the language of Buss’s S2. (shrink)

Der Beitrag der Mathematik zur Naturwissenschaft besteht darin, Erkenntnisse a priori von den (empirischen) Gegenständen der letzteren zu gewinnen und — unter der Voraussetzung, daß es überhaupt Empirisches g i b t -, die Existenz solcher Gegenstände a priori zu sichern. Die Aufgabe der Metaphysik ist es, besondere Begriffe ( in bezug auf die körperliche Natur) zu bilden und die Prinzipien für deren mathematische Konstruktion zu entwickeln. Die so "metaphysischkonstruierten" Begriffe werden dann durch Angabe empirischer Modelle physikalisch interpretiert.

We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the level of the substructural hierarchy.

Istarted my nursing career as a pediatric nurse working with children and their families at the Children's Hospital National Medical Center in Washington, DC. My first position was a staff nurse on a busy surgical floor called 4 Blue. To some degree, and as I reflect on that time, one is never truly prepared as a newly minted nurse or physician for the realities of becoming a clinician. So it was for me. I initially worked a rotational schedule of two (...) weeks of days and two weeks of nights where textbook pediatric cases became everyday experiences. Caring for the most complex of childhood illnesses included patients with osteosarcoma, Wilms tumor, neuroblastoma, short gut syndrome, biliary... (shrink)

Starting from the presupposition that European democracy is necessary to the survival and development of the European Union, the author deals with the process which may entail a European constitution, and discusses the elements of the present legal structure of the EU which are conducive to a European Democracy. In particular, the author focuses on the incomplete, polycentric, and dynamic character of a possible EC/EU constitution, and on the duality of its legitimating principle. This claim is that these characteristics necessitate (...) some institutional modifications of democratic principles if compared with national democracy, and that Euro‐democracy is possible if we do not simply apply the standards of democracy valid for Member States, but succeed in developing criteria which are adequate to the institutional qualities of the EC/EU. Finally, the author maintains the legal character of the regulatory power of the Community, and invokes the mutual legal bonds linking the Member States and their peoples as the source of the Community. (shrink)

Platónov Sókratés v záverečnom príhovore pred hlasovaním o svojej vine či nevine sudcom pripomína, že má rodinu, ktorá zahŕňa dospievajúceho syna a dvoch malých chlapcov. Pritom odkazuje na verše z Homérovej Odyssey, aby poukázal na skutočnosť, že sa nenarodil „ani z duba ani zo skaly“ (34d). Cieľom článku bude analyzovať a interpretovať zmysel uvedenej citácie v rámci Sókratovej argumentácie. V prvej časti sa autor sústredí na komparáciu Homérovho verša s jeho podobou v Platónovej Apológii. V druhej časti bude skúmať, akú (...) stratégiu Sókratés sledoval tým, keď sa odvolal na uvedený verš. V záverečnej časti sa zameria na otázku, z akého dôvodu Platónov Sókratés cituje Homéra napriek svojmu predchádzajúcemu vyhláseniu, že básnici nedisponujú múdrosťou. (shrink)

We show that the universally axiomatized, induction-free theory equation image is a sequential theory in the sense of Pudlák's 5, in contrast to the closely related Robinson's arithmetic.

We show that $$ VTC ^0$$, the basic theory of bounded arithmetic corresponding to the complexity class $$\mathrm {TC}^0$$, proves the $$ IMUL $$ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the $$\mathrm {TC}^0$$ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, $$ VTC ^0$$ can also prove the integer division axiom, and (by our previous results) the $$ RSUV $$ -translation of induction and minimization for sharply (...) bounded formulas. Similar consequences hold for the related theories $$\Delta ^b_1\text{- } CR $$ and $$C^0_2$$. As a side result, we also prove that there is a well-behaved $$\Delta _0$$ definition of modular powering in $$I\Delta _0+ WPHP (\Delta _0)$$. (shrink)

" -- Franklin H. Littell In To Mend the World Emil L. Fackenheim points the way to Judaism's renewal in a world and an age in which all of our notions -- about ...