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 extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove that (...) dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (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)

Timothy Michael Fowler has argued that, as a consequence of their commitment to neutrality in regard to comprehensive doctrines, political liberals face a dilemma. In essence, the dilemma for political liberals is that either they have to give up their commitment to neutrality (which is an indispensible part of their view), or they have to allow harm to children. Fowler’s case for this dilemma depends on ascribing to political liberals a view which grants parents a great degree of freedom in (...) deciding on the education of their children. I show that ascribing this view to political liberals rests upon a misinterpretation of political liberalism. Since political liberals have access to reasons based upon the interests of children, they need not yield to parent’s wishes about the education of their children. A correct understanding of political liberalism thus shows that political liberals do not face the dilemma envisaged by Fowler. (shrink)

We formalize the construction of Paterson’s variant of the Ajtai–Komlós–Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory , under the assumption of the existence of suitable expander graphs. We derive a conditional p-simulation of the propositional sequent calculus in the monotone sequent calculus.

Excerpt from Die Lehre vom Urteil Windelband hat in seinen "präludien und in dem Aufsatz der Festschrift für Zeller "beiträge zur Lehre vom nega tiven Urteil gerade vermittelst der Urteilslehre den ent scheidenden Schritt zu tun vermocht, der Logik wieder ihre sachliche Heimat im Ganzen der Philos0phie zu bestimmen. Rickerts "gegenstand der Erkenntnis ist sodann das Grund buch für alle logischen Untersuchungen der Werttheorie geworden und geblieben. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. (...) Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

1. Fichtes idealismus und die geschichte. Rechtsphilosophie. Hegel in seinem verhältnis zur weltanschaung der aufklärung. Gibt es einen "Primat der praktischen vernunft" in der logik?--2. Die logik der philosophie und die kategorienlehre. Die lehre vom urteil.--3. Platon. Zum system der logik. Zum system der wissenschaften.

Atserias, Galesi, and Pudlák have shown that the monotone sequent calculus MLK quasipolynomially simulates proofs of monotone sequents in the full sequent calculus LK . We generalize the simulation to the fragment MCLK of LK which can prove arbitrary sequents, but restricts cut-formulas to be monotone. We also show that MLK as a refutation system for CNFs quasipolynomially simulates LK.

Pragmatist Conception of Participatory Democracy1 The paper considers the issue of participatory democracy which has recently got high in the European integration agenda. In the history of ideas, however, it has been a controversial as well as neglected idea associated mostly with Rousseauian and Leftist models of democracy. The autor points to the key features of participatory democracy such as the idea of self-mastery. The philosophical idea of participation lies at the heart of the pragmatist conception of democracy as developed (...) by J. Dewey. Its functioning may be illustrated by the concept of "democratic normative community". This conception of participatory democracy as a broad social rather than a narow political phenomenon provides the framework that makes it both a vital ideal and a creative task for current global as well as local efforts to bring about the sociopolitical change. (shrink)

This is a reproduction of a book published before 1923. This book may have occasional imperfections such 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 works worldwide. We appreciate your understanding of the imperfections (...) in the preservation process, and hope you enjoy this valuable book. (shrink)

In his Mathesis rationis Leibniz discounted out of hand four categorical propositions that would have considerably broadened the resultant syllogistic logic. He did this despite the facts both that he had devised a suitable manner for expressing the latent quantification over terms, and that he had reasoned adequately to determine which of the syllogisms in the resulting broadened logic were valid. Leibniz's reasons for discounting these non-standard propositions are shown to be inadequate, and the resultant syllogistic logic is outlined.

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)

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.

This paper argues for a comprehensive conception of empathy as comprising epistemic, affective, and motivational elements and introduces the ancient Stoic theory of attachment (Greek,oikeiōsis) as a model for describing the embodied, emotional response to others that we take to be distinctive of empathy. Our argument entails that in order to provide a suitable conceptual framework for the interdisciplinary study of empathy one must extend the scope of recent “simulationalist” and “enactivist” accounts of empathy in two important respects. First, against (...) the enactivist assumption that human mindreading capacities primarily rely on an immediate, quasi-perceptual understanding of other’s intentional states, we draw on Alfred Schutz’ analysis of social understanding to argue that reflective types of understanding play a distinct, but equally fundamental role in empathic engagements. Second, we insist that empathy also involves an affective response toward the other and their situation (as the empathizer perceives this). We suggest analyzing this response in terms of the Stoic concepts of attachment, concern, and a fundamental type of prosocial motivation, that can best be described as an “extended partiality.” By way of conclusion, we integrate the above concepts into a comprehensive conceptual framework for the study of empathy and briefly relate them to current debates about empathic perception and prosocial motivation. The result, we argue, is an account that stays neutral with regard to the exact nature of the processes involved in producing empathy and can therefore accommodate discussion across theoretical divides—e.g., those between enactivist, simulationalist, and so-called theory-theorist approaches. (shrink)

Grzegorczyk's modal logic corresponds to the class of upwards well-founded partially ordered Kripke frames, however all known proofs of this fact utilize some form of the Axiom of Choice; G. Boolos asked in [1], whether it is provable in plain ZF. We answer his question negatively: Grz corresponds to a class of frames, which does not provably coincide with upwards well-founded posets in ZF alone.

Materialism about the mind is the view that the mind and its properties are physical. Many believe that there is a serious problem for materialism about the mind stemming from the phenomenon of conscious experience. It is alleged by some that conscious experiences possess features that cannot be possessed by any physical thing. And, even many materialists agree that conscious experiences possess features that make it difficult to see how conscious experiences could be physical things. Consciousness and the Insignificance of (...) Materialism examines this supposed clash between consciousness and physicality. The conclusion reached is that the clash is an illusion. It is an illusion fostered by certain false assumptions, made by materialists and anti-materialists alike, about the nature of physicality. However, it is argued that this is a hollow victory for materialism about the mind. Once the nature of physicality is appropriately characterized, materialism about the mind is revealed as true, but uninterestingly true. In other words, materialism about the mind is an insignificant view concerning the nature of the mind and mentality. (shrink)

Über die Grenzen des Naturerkennens ist ein unveränderter, hochwertiger Nachdruck der Originalausgabe aus dem Jahr 1872. Hansebooks ist Herausgeber von Literatur zu unterschiedlichen Themengebieten wie Forschung und Wissenschaft, Reisen und Expeditionen, Kochen und Ernährung, Medizin und weiteren Genres.Der Schwerpunkt des Verlages liegt auf dem Erhalt historischer Literatur.Viele Werke historischer Schriftsteller und Wissenschaftler sind heute nur noch als Antiquitäten erhältlich. Hansebooks verlegt diese Bücher neu und trägt damit zum Erhalt selten gewordener Literatur und historischem Wissen auch für die Zukunft bei.

This paper experimentally investigates the altruistic behavior of physicians and whether this behavior is affected by payment system and uncertainty in health outcome. Subjects in the experiment take on the role of physicians and decide on the provision of medical care for different types of patients, who are identical in all respects other than the degree to which a given level of medical treatment affects their health. We investigate physician altruism from the perspective of ethical principles, by categorizing physicians according (...) to how well their treatment decisions align with different principles for priority setting. The experiment shows that many physicians are altruistic toward their patients but also that the degree of altruism varies across patients with different medical needs. We find a strong effect of payment system that is overall unaffected by the introduction of risk and ambiguity in patients health outcomes. There is, however, substantial heterogeneity across individuals, in particular under the capitation payment system where physicians responses to the introduction of uncertainty in patient health are modulated by their own generic risk and ambiguity preferences. (shrink)

The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard (Ann Pure Appl Log 33:1–21, 1987). There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the proof-theoretic strengths (...) of the consistent theories? The first question was answered completely by Friedman and Sheard; all subsets of the Optional Axioms were classified as either consistent or inconsistent giving rise to nine maximal consistent theories of truth.They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard. We will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to well-known theories ranging from PA to the theory of ${\Sigma^1_1}$ dependent choice. (shrink)