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

Recently, there have been attempts at offering new justifications of the Rawlsian idea of public reason. Blain Neufeld has suggested that the ideal of political autonomy justifies public reason, while R.J. Leland and Han van Wietmarschen have sought to justify the idea by appealing to the value of political community. In this paper, I show that both proposals are vulnerable to a common problem. In realistic circumstances, they will often turn into reasons to oppose, rather than support, public reason. However, (...) this counterintuitive result can be avoided if we conceive of autonomy and community differently. (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)

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)

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)

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)

According to John Rawls’s famous Liberal Principle of Legitimacy, the exercise of political power is legitimate only if it is justifiable to all citizens. The currently dominant interpretation of what is justifiable to persons in this sense is an internalist one. On this view, what is justifiable to persons depends on their beliefs and commitments. In this paper I challenge this reading of Rawls’s principle, and instead suggest that it is most plausibly interpreted in externalist terms. On this alternative view, (...) what is justifiable to persons is not in any way dependent on, or relativized to, their beliefs and commitments. Instead, what is justifiable to all in the relevant sense is what all could accept as free and equal. I defend this reinterpretation of the view by showing how it is supported by Rawls’s account of the freedom and equality of persons. In addition, a considerable advantage of this suggestion is that it allows for an inclusive account of to whom the exercise of political power must be made justifiable. (shrink)

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)

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 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)

It has been argued that Hume's denial of infinite divisibility entails the falsity of most of the familiar theorems of Euclidean geometry, including the Pythagorean theorem and the bisection theorem. I argue that Hume's thesis that there are indivisibles is not incompatible with the Pythagorean theorem and other central theorems of Euclidean geometry, but only with those theorems that deal with matters of minuteness. The key to understanding Hume's view of geometry is the distinction he draws between a precise and (...) an imprecise standard of equality in extension. Hume's project is different from the attempt made by Berkeley in some of his later writings to save Euclidean geometry. Unlike Berkeley, who interprets the theorems of Euclidean geometry as false albeit useful approximations of geometrical facts, Hume is able to save most of the central theorems as true. (shrink)

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...) existential theories in the process. (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)

We study variants of Buss’s theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on \ induction schemes, which were so far neglected in the literature. We present inclusions and conservation results between the systems and \ of a new form), results on numbers of instances of the axioms or rules, connections to reflection principles for quantified propositional calculi, and separations between the systems.

This thesis is an inquiry into the Liberal Principle of Legitimacy, formulated by John Rawls in his later writings. According to this principle, the exercise of political power is legitimate only if it is justifiable to all citizens. This view can be interpreted in different ways, and I argue that the presently most popular way of doing so faces serious problems. The aim is to identify and defend a more plausible version of the principle, which overcomes these problems, and yet (...) preserves the most essential and appealing features of the approach. Among the most central issues for how to interpret the principle are how to understand the notion of justifiability to a person, and who should be included in the group of persons referred to as "all citizens". On the currently received view, only justifiability to those who count as "reasonable" matter, and justifiability to these persons is understood in non-moral terms, as being determined by what is accessible to them, given the beliefs that they happen to hold. I argue that we have good reasons to reject both of these suggestions. We should instead spell out justifiability to a person in terms of what could be reasonably accepted in a moral sense, which allows us to retain the appealing idea that legitimacy is dependent on justifiability to all citizens over whom political power is exercised. I further suggest that we can use the original position – Rawls’s version of the social contract – to determine what is justifiable to all in this sense. I defend this suggestion against the expected objection that it will not be able to take reasonable pluralism – the assumption of deep disagreement between citizens – into account, by explaining why we should sharply distinguish this principle of political legitimacy from the theory of Political Liberalism. This distinction also contributes to my response to the objection, raised against this principle, that it is self-defeating. That my suggested interpretation allows us to convincingly respond to this line of criticism is yet another reason as to why it is preferable to the standard view. (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)

Mixed strategies have been used to show that Pascal’s Wager fails to offer sufficient pragmatic reasons for believing in God. Their proponents have argued that, in addition to outright belief in God, rational agents can follow alternatives strategies whose expected utility is infinite as well. One objection that has been raised against this way of blocking Pascal’s Wager is that applying a mixed strategy in Pascal’s case is tantamount to applying an iterated mixed strategy which, properly understood, collapses into the (...) pure strategy of becoming a theist. I argue that since the assumptions used to develop the iterated mixed strategies response are even more questionable than those the initial objection relies on, this type of response to the mixed strategy objection fails. (shrink)

In his book The Intellectual Virtues and the Life of the Mind: On the Place of the Virtues in Contemporary Epistemology, Jonathan Kvanvig argues that there is an interchangeability of personal and doxastic justification, which ‘blocks the quick route to virtue epistemology’. To prove that personal justification is reducible to doxastic justification, he utilizes λ-calculus expressions that aim to show the logical equivalence of the two notions of justification. In this paper, I argue that he has made an illegitimate move (...) in his translation of the ordinary talk of personal justification into λ-expressions because his translation involves both an elimination from and an addition to the ordinary language. Pace Kvanvig, there is no logical equivalence of personal to doxastic justification. So, his argument for the reducibility of personal to doxastic justification founders. More importantly, since he has failed to disprove that personal justification is irreducibly primitive, he hasn’t shown that the prospects for virtue epistemology are ‘hopeless’. (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.

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)

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.

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...

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.

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)

D’Aquino et al. (J Symb Log 75(1):1–11, 2010) have recently shown that every real-closed field with an integer part satisfying the arithmetic theory IΣ4 is recursively saturated, and that this theorem fails if IΣ4 is replaced by IΔ0. We prove that the theorem holds if IΣ4 is replaced by weak subtheories of Buss’ bounded arithmetic: PV or $${\Sigma^b_1-IND^{|x|_k}}$$. It also holds for IΔ0 (and even its subtheory IE 2) under a rather mild assumption on cofinality. On the other hand, it (...) fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality. (shrink)

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.

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 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 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)