We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia (...) theorem and the theory of modal companions to systems of multiple-conclusion rules or (finitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property. (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)

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)

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 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)

1. Introduction The influence of Richard Rorty has not faded since his demise more than a decade ago. Some of his works have been published posthumously (Rorty 2010; Rorty 2016), others have been republished in valuable collections (Voparil & Bernstein 2010; Rorty 2014) and some of his unpublished work has already appeared too (Małecki & Voparil 2020). Important international symposia have been held around the world (see e.g. Penelas & Voparil 2014) and the Richard Rorty Society (RSS) was fou...

Einleitung. Die logik des wertens in der geschichtsphilosophie des deutschen idealismus.--Die logischen voraussetzungen von Kants und Hegels rationalismus und die einordnung Fichtes in den entwicklungsgang der deutschen spekulation.--Fichtes rationalismus und die irrationalität des empirischen.--Fichtes geschichtsphilosophie.

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.

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)

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.

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 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 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.

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)

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)

This appraisal became conventional opinion, and has remained conventional opinion until this day. In practically any history of philosophy which bothers with Schelling at all one can find this threefold condemnation of his work: that it consists of a number of more or less disconnected systems; that none of these is properly worked out; and that from 1804 on, they get worse and worse. As a result of this opinion, few historians have been interested in Schelling. When in 1944 air (...) raids destroyed the Munich University Library, among the treasures destroyed were thousands of Schelling manuscript pages, mostly written in his later years. It seems that in nearly one hundred years nobody was sufficiently interested in these manuscripts to do anything with them. (shrink)

The paper focuses on the pragmatist image of humanity based on a re-reading of the philosophical “manifesto” of Wilfrid Sellars in which he became entangled in the dichotomy between “scientific” and “manifest” images. The key to solving this problem, according to the author, is the new pragmatist understanding of science as a cultural practice, which provide us with a new framework for transcending this dichotomy. By reconstructing Sellars in an anthropological rather than a scientistic way and by drawing on humanistic (...) philosophical intentions that are present both in pragmatism and in Sellars, it becomes possible to outline a concept of “science with a human face.” The purpose of all kinds of images, including scientific ones, is to serve the enrichment of human understanding and life. (shrink)