The development of modern programmable pacemaker-systems has led to a series of questions which until now have apparently not existed in the treatment of cardiac rhythm disturbances. These questions touch especially on the problem of whether the relation which usually exists between a diagnostic step and its therapeutic consequence, namely its therapeutic relevance, is abolished or at least changed.

This volume takes on both issues and examines the relationship between organisms and artifacts from the perspective of functionality.

This paper develops a formal framework to model a process in which the formation of individual opinions is embedded in a deliberative exchange with others. The paper opts for a low-resolution modeling approach and abstracts away from most of the details of the social-epistemic process. Taking a bird's eye view allows us to analyze the chances for the truth to be found and broadly accepted under conditions of cognitive division of labour combined with a social exchange process. Cognitive division of (...) labour means that only some individuals are active truth seekers, possibly with different capacities. Both mathematical tools and computer simulations are used to investigate the model. As an analytical result, the Funnel Theorem states that under rather weak conditions on the social process, a consensus on the truth will be reached if all individuals possess an arbitrarily small capacity to go for the truth. The Leading the pack Theorem states that under certain conditions even a single truth seeker may lead all individuals to the truth. Systematic simulations analyze how close agents can get to the truth depending upon the frequency of truth seekers, their capacities as truth seekers, the position of the truth (more to the extreme or more in the centre of an opinion space), and the willingness to take into account the opinions of others when exchanging and updating opinions. (shrink)

A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel'sT as well as Kleene/Feferman's ) is applied to systems of intuitionistic and classical arithmetic (H andH c) in all finite types with full induction as well as to the corresponding systems with restricted inductionĤ↾ andĤ↾c.H and Ĥ↾ are closed under a generalized (...) fan-rule. For a restricted class of formulae this also holds forH c andĤ↾c.We give a new and very perspicuous proof that for each one can construct a functional such that $\tilde \Phi \alpha $ is a modulus of uniform continuity for Φ on {β1∣∧n(βn≦αn)}. Such a modulus can also be obtained by majorizing any modulus of pointwise continuity for Φ.The type structure ℳ of all pointwise majorizable set-theoretical functionals of finite type is used to give a short proof that quantifier-free “choice” with uniqueness (AC!)1,0-qf. is not provable within classical arithmetic in all finite types plus comprehension [given by the schema (C)ϱ:∨y 0ϱ∧x ϱ(yx=0⇔A(x)) for arbitraryA], dependent ω-choice and bounded choice. Furthermore ℳ separates several μ-operators. (shrink)

In this paper a new method, elimination of Skolem functions for monotone formulas, is developed which makes it possible to determine precisely the arithmetical strength of instances of various non-constructive function existence principles. This is achieved by reducing the use of such instances in a given proof to instances of certain arithmetical principles. Our framework are systems ${\cal T}^{\omega} :={\rm G}_n{\rm A}^{\omega} +{\rm AC}$ -qf $+\Delta$ , where (G $_n$ A $^{\omega})_{n \in {\Bbb N}}$ is a hierarchy of (weak) subsystems (...) of arithmetic in all finite types (introduced in [14]), AC-qf is the schema of quantifier-free choice in all types and $\Delta$ is a set of certain analytical principles which e.g. includes the binary König's lemma. We apply this method to show that the arithmetical closures of single instances of $\Pi^0_1$ -comprehension and -choice contribute to the growth of extractable bounds from proofs relative to ${\cal T}^\omega$ only by a primitive recursive functional in the sense of Kleene. In subsequent papers these results are widely generalized and the method is used to determine the arithmetical content of single sequences of instances of the Bolzano-Weierstraß principle for bounded sequences in ${\Bbb R}^d$ , the Ascoli-lemma and others. (shrink)

Volume 20, Issue 6, June 2020, Page 68-70.

The so-called weak König's lemma WKL asserts the existence of an infinite path b in any infinite binary tree . Based on this principle one can formulate subsystems of higher-order arithmetic which allow to carry out very substantial parts of classical mathematics but are Π 2 0 -conservative over primitive recursive arithmetic PRA . In Kohlenbach 1239–1273) we established such conservation results relative to finite type extensions PRA ω of PRA . In this setting one can consider also a uniform (...) version UWKL of WKL which asserts the existence of a functional Φ which selects uniformly in a given infinite binary tree f an infinite path Φf of that tree. This uniform version of WKL is of interest in the context of explicit mathematics as developed by S. Feferman. The elimination process in Kohlenbach [10] actually can be used to eliminate even this uniform weak König's lemma provided that PRA ω only has a quantifier-free rule of extensionality QF-ER instead of the full axioms of extensionality for all finite types. In this paper we show that in the presence of , UWKL is much stronger than WKL: whereas WKL remains to be Π 2 0 -conservative over PRA, PRA ω ++ UWKL contains full Peano arithmetic PA. We also investigate the proof–theoretic as well as the computational strength of UWKL relative to the intuitionistic variant of PRA ω both with and without the Markov principle. (shrink)

In this note we show that the so-called weakly extensional arithmetic in all finite types, which is based on a quantifier-free rule of extensionality due to C. Spector and which is of significance in the context of Gödel"s functional interpretation, does not satisfy the deduction theorem for additional axioms. This holds already for Π0 1-axioms. Previously, only the failure of the stronger deduction theorem for deductions from (possibly open) assumptions (with parameters kept fixed) was known.

LetA H be the Herbrand normal form ofA andA H,D a Herbrand realization ofA H. We showThere is an example of an (open) theory ℐ+ with function parameters such that for someA not containing function parameters Similar for first order theories ℐ+ if the index functions used in definingA H are permitted to occur in instances of non-logical axiom schemata of ℐ, i.e. for suitable ℐ,A In fact, in (1) we can take for ℐ+ the fragment (Σ 1 0 -IA)+ (...) of second order arithmetic with induction restricted toΣ 1 0 -formulas, and in (2) we can take for ℐ the fragment (Σ 1 0,b -IA) of first order arithmetic with induction restricted to formulas VxA(x) whereA contains only bounded quantifiers.On the other hand, $$PA^2 \vdash A^H \Rightarrow PA \vdash A,$$ wherePA 2 is the extension of first order arithmeticPA obtained by adding quantifiers for functions andA∈ℒ(PA). This generalizes to extensional arithmetic in the language of all finite types but not to sentencesA with positively occurring existential quantifiers for functions. (shrink)

Few bioethicists are educated with a view into nursing. Thus, much of the conceptual and empirical research on ethical issues in nursing practice has been conducted by nurse ethicists themselves and, to a lesser degree, by individuals with a strong interest in nursing ethics. Although this work has internally shaped nursing practice, education, and policy, the broader field of bioethics has seldom examined and acknowledged the everyday ethical concerns of practicing nurses and their important contributions to bioethics discourse. In this (...) special report of the Hastings Center Report —the first to focus on nursing—Christine Grady, Ann Hamric, and I, along with consulting editor Nancy Berlinger, strive to give voice to the contributions of nurses in addressing some of our obstinate everyday ethics and health policy challenges. (shrink)

Existe uma tendência evidente de computadorizar cada vez mais atividades do dia-a-dia. Ferramentas de IA, de tomada de decisão e aprendizado de máquina são algumas destas tecnologias. Neste artigo analisamos como a modelagem de aplicações de bancos de dados deve evoluir para atender a estes requisitos. Coisas estruturais e ocorrêncais adequadas são consideradas e, para cada conceito, têm que ser definidas regras que garantem a integridade do sistema como um todo. Caracteristicas específicas de sistemas complexos ativos e/ou reativos, questões de (...) autonomia, aspectos espaciais e temporais, assim como informações imprecisas, devem ser levados em consideração. (shrink)

Our understanding of epithelial development in Drosophila has been greatly improved in recent years. Two key regulators of epithelial polarity, Crumbs and DE‐cadherin, have been studied at the genetic and molecular levels and a number of additional genes are being analyzed that contribute to the differentiation of epithelial cell structure. Epithelial architecture has a profound influence on morphogenetic movements, patterning and cell‐type determination. The combination of embryological and genetic/molecular tools in Drosophila will help us to elucidate the complex events that (...) determine epithelial cell structure and how they relate to morphogenesis and other developmental processes. (shrink)

For the first time in his Doctrine of Right, Kant employs an expanded, three dimensional concept of public law. In addition to constitutional law, it also includes international law and cosmopolitan law. Each of these concepts of law is assigned its own principle of reason: constitutional law declares that a republic is the only rightful constitution for an individual state; international law requires at least an association of states with higher level instruments of coercion; and cosmopolitan law primarily defines the (...) basic rights of stateless peoples or individuals with respect to existing states. For the principles of reason for constitutional and international law, Kant formulates permissive laws, which allow for imperfections in an effort to promote the optima which the legal principles of reason dictate. Kant justifies these less perfect solutions not only with pragmatic considerations but also with reasons relating to the theory of the sovereignty of nations. Kants Rechtslehre verwendet erstmals einen erweiterten, dreidimensionalen Begriff des öffentlichen Rechts, der neben dem Staatsrecht nun auch das Völkerrecht und das Weltbürgerrecht umfaßt. Jeder dieser Begriffssphären wird ein eigenes vernunftrechtliches Prinzip zugeordnet: das Staatsrecht erklärt die Republik zur einzig rechtmäßigen Verfassung, während das Völkerrecht mindestens eine Staatenassoziation mit höherstufiger Zwangsgewalt erfordert und das Weltbürgerrecht in der Hauptsache die elementaren Rechte von staatslosen Völkern oder Einzelpersonen gegenüber Staaten definiert. Für das staatsrechtliche und das völkerrechtliche Prinzip formuliert Kant Erlaubnisgesetze, die zur Beförderung der vernunftrechtlichen Optima Minderformen zulassen, zu deren Rechtfertigung Kant nicht allein pragmatische, sondern ebenso volkssouveränitätstheoretische Gründe anführt. (shrink)

Recently, Coquand and Palmgren considered systems of intuitionistic arithmetic in a finite types together with various forms of the axiom of choice and a numerical omniscience schema which implies classical logic for arithmetical formulas. Feferman subsequently observed that the proof theoretic strength of such systems can be determined by functional interpretation based on a non-constructive μ-operator and his well-known results on the strength of this operator from the 70's. In this note we consider a weaker form LNOS of NOS which (...) suffices to derive the strong form of binary König's lemma studied by Coquand/Palmgren and gives rise to a new and mathematically strong semi-classical system which, nevertheless, can proof theoretically be reduced to primitive recursive arithmetic PRA. The proof of this fact relies on functional interpretation and a majorization technique developed in a previous paper. (shrink)

Part of the scientific enterprise is to measure the material world and to explain its dynamics by means of models. However, not only is measurability of the world limited, analyzability of models is so, too. Most often, computer simulations offer a way out of this epistemic bottleneck. They instantiate the model and may help to analyze it. In relation to the material world a simulation may be regarded as a kind of a “non-material scale model”. Like any other scale model, (...) it does not per se give any scientific explanation but is first in itself an object of scientific enquiry, a world. Since this world is numerical, it is a priori measurable. Its role in scientific explanation will be discussed. (shrink)

Among philosophers in the period of change between the late 18th and early 19th centuries it was a widespread conviction that, because the status of a demonstrative theory made up of axioms and proofs was neither available nor desirable for philosophy, philosophical critique would also not be external to the business of philosophy. Rather it was to belong to the essence of philosophy itself. Against this background Hegel occupied himself almost from the beginning of his philosophical thinking with the question (...) of how a critique that is also able to convince an adherent of a theory differing from one’s own should proceed. Initially it must provide him with a description of his standpoint that he himself can accept. Moreover, the critique must tie up with a method of examination that is part of this standpoint itself, because its adherent would not otherwise have to agree to the procedure. Hegel is interested in this matter not only as a description of the hermeneutic situation in which the adherents of two particular, opposing positions find themselves. Rather, he asks himself whether an idea for the procedure of philosophical critique that commits itself to such considerations can also be generalized. This would require giving a minimalist description of the starting point in a way that allows as large a spectrum as possible of positions that are to be the object of the critique to recognize themselves within it. And the procedure of the critique must be able to be developed from this description itself. (shrink)

This book publishes for the first time notes from two notebooks of Gödel which formed the basis of a course on intuitionism Gödel delivered at Princeton in the.

It is no secret that there are problems within hospitals and other healthcare settings across the United States that have been simmering for some time. With the emergence of the deadly SARs-CoV-2 v...