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

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 ...

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)

In Beyond the Limits of Thought [2002], Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink (...) virtually all orthodox solutions', and that the Inclosure Schema cannot be the structure that underlies the Liar paradox. Moreover, Ramsey was right in thinking that logical and semantic paradoxes are paradoxes of different kinds. (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)

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV₁ + dWPHP(PV).

In this article, Emil Sætra examines how teachers and students construct and experience aims and goods in classroom discussions of controversial issues. This study is situated within the emerging tradition of empirical ethics, and the research strategy comprised two main steps. First, Sætra used interview data to analyze, via the experiences of teachers and students, the following two empirical questions: (1) What goods normatively constitute educative discussions of controversial issues? (2) How are these goods constructed in time and space? (...) Second, in the concluding discussion, Sætra makes explicit some normative implications of the empirical findings and discusses theses in relation to previous research. In brief, what emerges from the conjoined experiences of teachers and students is the notion that practice comprises multiple aims and drives. Moreover, because aims and drives are multiple, decisions regarding priorities will sometimes have to be made, and teachers may be subject to conflicting expectations. This means that practitioners must be able to make reflective judgments about what comprises acceptable ends, what projects should be undertaken to achieve those ends, and what actions ought to be performed as part of those projects. (shrink)

This paper analyses the activities of five organizations shaping the debate over the global governance of genome editing in order to assess current approaches to public engagement (PE). We compare the recommendations of each group with its own practices. All recommend broad engagement with the general public, but their practices vary from expert-driven models dominated by scientists, experts, and civil society groups to citizen deliberation-driven models that feature bidirectional consultation with local citizens, as well as hybrid models that combine elements (...) of both approaches. Only one group practices PE that seeks community perspectives to advance equity. In most cases, PE does little more than record already well-known views held by the most vocal groups, and thus is unlikely to produce more just or equitable processes or policy outcomes. Our exploration of the strengths, weaknesses, and possibilities of current forms of PE suggests a need to rethink both “public” and “engagement.”. (shrink)

It has been argued that there is a genuine conflict between the views of geometry defended by Hume in the Treatise and in the Enquiry: while the former work attributes to geometry a different status from that of arithmetic and algebra, the latter attempts to restore its status as an exact and certain science. A closer reading of Hume shows that, in fact, there is no conflict between the two works with respect to geometry. The key to understanding Hume's view (...) of geometry is the distinction he draws between two standards of equality in extension. (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)

Comprises the Charles F. Deems Lectures delivered at New York University in 1968. Discusses the significance of the Holocaust, emphasizing theological issues, and its uniqueness in history. An authentic response to it - religious or secular - is a commitment to the autonomy and security of the State of Israel. Refers to Jewish midrash to explore the meaning and significance of the Holocaust and relates Jewish thinking about the Holocaust to Jewish thinking about earlier catastrophes. Jewish particularism remains a scandal (...) to modern secularism. Pt. 3 (p. 67-104), "The Commanding Voice of Auschwitz", states that the death of God occurs in the inward realm of the spirit alone and nowhere else. The imperative for Jews is not to flee being Jewish: "Jews are forbidden to hand Hitler posthumous victories. They are commanded to survive as Jews". (shrink)

IN THE PREFACE to his Philosophy of Right Hegel writes: "Was vernünftig ist, das ist wirklich; und was wirklich ist, das ist vernünftig"--"What is rational is actual, and what is actual is rational." In paragraph 6 of the third edition of his Encyclopedia of Philosophical Sciences he repeats this statement verbatim, calling it "simple." Few interpreters, however, have ever found it so. Even friendly critics are baffled; hostile ones dismiss it as either scandalous or senseless. Two centuries after Hegel's birth (...) there is thus still room for a modest exposition of the meaning of this famous Hegelian statement, much more so for one of its "simplicity." Both tasks, however--and in particular the second, seemingly hopeless one--should be undertaken in full awareness of two conditions which the Encyclopedia passage considers evident but which can be taken as such no longer. One is possession of "religion." The other is the kind of philosophical "culture" which includes "knowledge" of "God.". (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.

Investigates the assumptions of such philosophers as Kant, Hegel, Marx, Heidegger and Sartre regarding Jewish existence.

Vorwort.--Schultz, F. Die philosophisch-weltanschauliche entwicklung der literarhistorischen methode.--Gumbel, H. Dichtung und volkstum.--Cysarz, H. Das periodenprinzip in der literaturwissenschaft.--Petersen, J. Die literarischen generationen.--Medicus, F. Das problem einer vergleichenden geschichte der künste.--Petsch, R. Die analyse des dichtwerkes.--Muschg, W. Das dichterporträt in der literaturgeschichte.--Jung, C. G. Psychologie und dichtung.--Ermatinger, E. Das gesetz in der literaturwissenschaft.--Nadler, J. Das problem der stilgeschichte.--Wundt, M. Literaturwissenschaft und weltanschauungslehre.--Strich, F. Weltliteratur und vergleichende literaturgeschichte.--Sarnetzki, D. H. Literaturwissenschaft und die dichtung und kritik des tages.

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)

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)

One of the major works of the great German theologian Emil Brunner, The Divine Imperative deals with what we ought to do. People are unconvinced that there is an inviolable moral obligation governing human life because they do not believe that the 'good'can be precisely and clearly known. Haven't some generations called bad what others have called good? Aren't moral standards relative? Doesn't religion lack uniform and practical moral guidance? Brunner discusses the moral confusion we face. He analyses the (...) nature of the Good, showing why the Christian faith as understood by the Protestant Reformers provides the only true approach and answer to the ethical problem. Philosophical ethics, whether ancient or modern, cannot correctly define the Good, becausethe Good is regarded either as too abstract and absolute or as too concrete and relative. Christianity, by contrast, sees the moral problem as one of responsibility between humans who are created so as to respond to God. He created men for responsive fellowship with Him, establishing orderly ways of acting in the world. Correct understanding of the nature of society, family, state, economic life, is needed to discern one's duty. Because Brunner's analysis is at once fundamental and comprehensive, this book remains a fresh and compelling treatment of the moral problem. It offers a provocative discussion and solution of a perennial human problem. (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.

This paper explores in detail an argument for epistemic expressivism, what we call the Argument from Motivation. While the Argument from Motivation has sometimes been anticipated, it has never been set out in detail. The argument has three premises, roughly, that certain judgments expressed in attributions of knowledge are intrinsically motivating in a distinct way (P1); that motivation for action requires desire-like states or conative attitudes (HTM); and that the semantic content of knowledge attributions cannot be specified without reference to (...) the intrinsically motivating judgments that such attributions express (P2). We argue that these premises entail a version of ecumenical expressivism. Since the argument from motivation has not been explicitly stated before, there is no current discussion of the argument. In this paper we therefore consider and reject various objections that one might propose to the argument, including some that stem from the idea that knowledge is factive, or that knowledge involves evidence that rules out relevant alternatives. Other objections to (P1) specifically might be derived from cases of apparent lack of epistemic motivation considered in in Kvanvig (The value of knowledge and the pursuit of understanding, 2003) and Brown (Nous 42(2):167–189, 2008), as well as from general forms of externalism about epistemic motivation. We consider these and find them wanting. Finally, the paper offers some critical remarks about the prospect of denying (P2). (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)