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 ...

Academic misconduct is widespread in all cultures, and factors that influence it have been investigated for many years. An act of reporting peers’ misconduct not only identifies and prevents misconduct, but also encourages a student to think and act morally and raises awareness about academic integrity. The aim of this study was to determine factors that prevent students from reporting academic misconduct. A questionnaire to assess views on reporting the academic misconduct of a colleague was developed and sent to all (...) students enrolled at the University of Rijeka, Croatia. Results indicate that a tendency to protect fellow student and to comply with other opinions is the most influential factor that prevents students from reporting peers’ misbehavior. Furthermore, scientific discipline, gender, and age are all significant factors in students’ intention to report peer misconduct. Understanding the factors that influence students’ willingness to report academic misconduct enables faculties, administrators and students to strengthen the ethical culture in the academic community. (shrink)

We show that $$ VTC ^0$$, the basic theory of bounded arithmetic corresponding to the complexity class $$\mathrm {TC}^0$$, proves the $$ IMUL $$ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the $$\mathrm {TC}^0$$ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, $$ VTC ^0$$ can also prove the integer division axiom, and (by our previous results) the $$ RSUV $$ -translation of induction and minimization for sharply (...) bounded formulas. Similar consequences hold for the related theories $$\Delta ^b_1\text{- } CR $$ and $$C^0_2$$. As a side result, we also prove that there is a well-behaved $$\Delta _0$$ definition of modular powering in $$I\Delta _0+ WPHP (\Delta _0)$$. (shrink)

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)

We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.

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)

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)

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

We show that \, the basic theory of bounded arithmetic corresponding to the complexity class \, proves the \ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the \ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, \ can also prove the integer division axiom, and the \-translation of induction and minimization for sharply bounded formulas. Similar consequences hold for the related theories \ and \. As a side (...) result, we also prove that there is a well-behaved \ definition of modular powering in \\). (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)

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)

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 show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.

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)

Das Buch erkundet Wege und Umwege des Gedachtnisses in Philosophie und erzahlender Literatur. Es fragt nach der existentiellen Bedeutung der Erinnerung: Wieso verlangt der Mensch nach Erinnerung? Wonach strebt die Suche nach der verlorenen Zeit? Lebenserinnerung verfolgt ein zweifaches Ziel: die zerrinnende Zeit anzuhalten und sich in seinem Leben gegenwartig zu werden. Sie wehrt sich gegen das Vergehen und Vergessen, in ihr sucht der Mensch sich zu finden und sich uber sein Leben zu verstandigen. Erinnerung vollzieht sich in mannigfachen Formen. (...) Das Vergangene kann in spontanen Bildern wiederkehren oder verschlossen sein und sich nur der beharrlichen Arbeit des Gedachtnisses offnen; Erinnerungen konnen in Leidenserfahrungen und in Glucksversprechen wurzeln. Sich erinnern entspricht einem ursprunglichen Bedurfnis der Menschen und geht ein in den Vollzug eines gelingenden Lebens. (shrink)

This is a reproduction of a book published before 1923. This book may have occasional imperfectionssuch 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 worksworldwide. We appreciate your understanding of the imperfections in the (...) preservation process, and hope you enjoy this valuable book.++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Naturwissenschaftliche Plaudereien 3 Emil Arnold Budde. (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)

We prove that the sharply bounded arithmetic T02 in a language containing the function symbol ⌊x /2y⌋ is equivalent to PV1.

"Jewish Philosophy and the Academy reflects in broad terms on the current state of Jewish philosophy in the university. This generation of university teachers lives at a unique historic junction. It is the last to be taught by the giants of European Wissenschaft des Judentums and the first to experience the remarkable expansion of Judaic scholarship in Israel and abroad." "Emil Fackenheim suggests that if we are indebted to Athens for the philosophical method, we are also indebted to Jerusalem (...) for the ethical content of philosophy, which is both an intellectual and a moral challenge. This dual challenge shapes the diverse papers in this volume."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

Excerpt from Goethe als Geschichtsphilosoph und die Geschichtsphilosophische Bewegung Seiner Zeit Eine Pflanze ist in ihrer Erscheinung nur recht zu begreifen, wenn man die Umgebung, wenn man den Boden kennt, dem sie entsprossen ist. Und je langer sie an einem Standorte beharrte, desto mehr kommt dieser Boden, diese Umgebung charakteristisch in ihr zum Ausdruck. Ja, wird sie verpflanzt und in andere Umgebung gebracht, nur langsam und schwer wird sie sich andern. So lange wie sie vermag, bleibt sie ihrem alten Charakter (...) getreu, und immer wieder zeigen sich von der einstigen Umgebung uberkommene Zuge. 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)

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)

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 an arithmetical theory and its variant , corresponding to “slightly nonuniform” . Our theories sit between and , and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propositional translations of -formulas provable in admit L-uniform polynomial-size Frege proofs.

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)

A detailed exploration of Jewish thought and how it compares with the ideas of modern philosophy.

If, in content and in method, philosophy and religion conflict, can there be a Jewish philosophy? What makes a Jewish thinker a philosopher? Emil L. Fackenheim confronts these questions in a profound and insightful series of essays on the great Jewish thinkers from Maimonides through Hermann Cohen, Martin Buber, Franz Rosenzweig, and Leo Strauss. Fackenheim also contemplates the task of Jewish philosophy after the Holocaust. While providing access to key Jewish thinkers of the past, this volume highlights the exciting (...) achievements of one of today's most creative and most important Jewish philosophers. (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.

We show that the universally axiomatized, induction-free theory equation image is a sequential theory in the sense of Pudlák's 5, in contrast to the closely related Robinson's arithmetic.

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.

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)

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)

This book is a defense of the methods of analytic philosophy against a recent empirical challenge to the soundness of those methods. The challenge is raised by practitioners of “experimental philosophy” and concerns the extent to which analytic philosophy relies on intuition—in particular, the extent to which analytic philosophers treat intuitions as evidence in arguing for philosophical conclusions. Experimental philosophers say that analytic philosophers place a great deal of evidential weight on people’s intuitions about hypothetical cases and thought experiments. This (...) book argues that this view of traditional philosophical method is a myth, part of “metaphilosophical folklore.” Analytic philosophy makes regular use of hypothetical examples and thought experiments, but philosophers argue for their claims about what is true or not true in these examples and thought experiments. It is these arguments, not intuitions, that are treated as evidence for the claims. The book discusses xphi and some recent xphi studies; critiques a variety of other metaphilosophical claims; examines such famous arguments as Gettier’s refutation of the JTB theory and Kripke’s Gödel Case argument against descriptivism about proper names, and shows that they rely on reasoning rather than intuition; and finds existing critiques of xphi, the “Multiple Concepts” and “Expertise” replies, to be severely lacking. (shrink)

The paper discusses the relation of philosophical pragmatism to empiricism as the backdrop to understanding human being. The crux of the problem is the relation between language and experience. The author argues that pragmatist empiricism is based on the concept that human practices are transactions, which includes both non-linguistic as well as linguistic practices. Within pragmatist anthropological philosophy, experience is a complex of transactions between humans and reality. Humans are both natural/physical and cultural/linguistic beings, whose living experience involves transactions with (...) both the natural and the sociocultural environment. The dualism between language and experience is false and should be abandoned. (shrink)