A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical (...) logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual. Key Features: Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms. Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study. (shrink)

The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that (...) the recursive extension of \sqema\ succeeds on the class of `recursive formulae'. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds. (shrink)

We provide syntactic necessary and sufficient conditions on the formulae reducible by the second-order quantifier elimination algorithm DLS. It is shown that DLS is compete for all modal Sahlqvist and Inductive formulae, and that all modal formulae in a single propositional variable on which DLS succeeds are canonical.

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions of (...) \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

We apply and extend the theory and methods of algorithmic correspondence theory for modal logics, developed over the past 20 years, to the language LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_R$$\end{document} of relevance logics with respect to their standard Routley–Meyer relational semantics. We develop the non-deterministic algorithmic procedure PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} for computing first-order equivalents of formulae of the language LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$$\mathcal {L}_R$$\end{document}, in terms of that semantics. PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} is an adaptation of the previously developed algorithmic procedures SQEMA and ALBA. We then identify a large syntactically defined class of inductive formulae in LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_R$$\end{document}, analogous to previously defined such classes in the classical, distributive and non-distributive modal logic settings, and show that PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} succeeds for every inductive formula and correctly computes a first-order definable condition which is equivalent to it with respect to frame validity. We also provide a detailed comparison with two earlier works, each extending the class of Sahlqvist formulae to relevance logics, and show that both are subsumed by simple subclasses of inductive formulae. (shrink)

Iris Murdoch's moral philosophy has long influenced contemporary ethics, yet it has not, in general, received the kind of sustained critical attention that it deserves. "Existentialists and Mystics" and "Metaphysics as a Guide to Morals" provide new access to most of Murdoch's philosophical writings and make possible a deeper appreciation of her contribution to current thought. After assessing the recent critical reception of Murdoch's thought, this review places her moral philosophy in the context of contemporary trends in ethics by tracing (...) her influence on the work of Charles Taylor, highlights the distinctive features of her moral philosophy, and suggests future directions for Murdochian ethics. (shrink)

Conducting empirical research on gender in medical ethics is a challenge from a theoretical as well as a practical point of view. It still has to be clarified how gender aspects can be integrated without sustaining gender stereotypes. The developmental psychologist Carol Gilligan was among the first to question ethics from a gendered point of view. The notion of care introduced by her challenged conventional developmental psychology as well as moral philosophy. Gilligan was criticised, however, because her concept of ‘two (...) different voices’ may reinforce gender stereotypes. Moreover, although Gilligan stressed relatedness, this is not reflected in her own empirical approach, which still focuses on individual moral reflection. Concepts from social psychology can help overcome both problems. Social categories like gender shape moral identity and moral decisions. If morality is understood as being lived through actions of persons in social relationships, gender becomes a helpful category of moral analysis. Our findings will provide a conceptual basis for the question how empirical research in medical ethics can successfully embrace a gendered perspective. (shrink)

Preparing words in speech production is normally a fast and accurate process. We generate them two or three per second in fluent conversation; and overtly naming a clear picture of an object can easily be initiated within 600 msec after picture onset. The underlying process, however, is exceedingly complex. The theory reviewed in this target article analyzes this process as staged and feedforward. After a first stage of conceptual preparation, word generation proceeds through lexical selection, morphological and phonological encoding, phonetic (...) encoding, and articulation itself. In addition, the speaker exerts some degree of output control, by monitoring of self-produced internal and overt speech. The core of the theory, ranging from lexical selection to the initiation of phonetic encoding, is captured in a computational model, called WEAVER++. Both the theory and the computational model have been developed in interaction with reaction time experiments, particularly in picture naming or related word production paradigms, with the aim of accounting for the real-time processing in normal word production. A comprehensive review of theory, model, and experiments is presented. The model can handle some of the main observations in the domain of speech errors (the major empirical domain for most other theories of lexical access), and the theory opens new ways of approaching the cerebral organization of speech production by way of high-temporal-resolution imaging. (shrink)

Robotic and artificially intelligent (AI) systems are becoming prevalent in our day-to-day lives. As human interaction is increasingly replaced by human–computer and human–robot interaction (HCI and HRI), we occasionally speak and act as though we are blaming or praising various technological devices. While such responses may arise naturally, they are still unusual. Indeed, for some authors, it is the programmers or users—and not the system itself—that we properly hold responsible in these cases. Furthermore, some argue that since directing blame or (...) praise at technology itself is unfitting, designing systems in ways that encourage such practices can only exacerbate the problem. On the other hand, there may be good moral reasons to continue engaging in our natural practices, even in cases involving AI systems or robots. In particular, daily interactions with technology may stand to impact the development of our moral practices in human-to-human interactions. In this paper, we put forward an empirically grounded argument in favor of some technologies being designed for social responsiveness. Although our usual practices will likely undergo adjustments in response to innovative technologies, some systems which we encounter can be designed to accommodate our natural moral responses. In short, fostering HCI and HRI that sustains and promotes our natural moral practices calls for a co-developmental process with some AI and robotic technologies. (shrink)

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora. These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science. In this paper we will do two things. First of all, we will propose a (...) general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

Throughout the twentieth century, German writers, philosophers, theologians, and historians turned to Gnosticism to make sense of the modern condition. While some saw this ancient Christian heresy as a way to rethink modernity, most German intellectuals questioned Gnosticism's return in a contemporary setting. In No Spiritual Investment in the World, Willem Styfhals explores the Gnostic worldview's enigmatic place in these discourses on modernity, presenting a comprehensive intellectual history of Gnosticism's role in postwar German thought. Establishing the German-Jewish philosopher Jacob (...) Taubes at the nexus of the debate, Styfhals traces how such figures as Hans Blumenberg, Hans Jonas, Eric Voegelin, Odo Marquard, and Gershom Scholem contended with Gnosticism and its tenets on evil and divine absence as metaphorical detours to address issues of cultural crisis, nihilism, and the legitimacy of the modern world. These concerns, he argues, centered on the difficulty of spiritual engagement in a world from which the divine has withdrawn. Reading Gnosticism against the backdrop of postwar German debates about secularization, political theology, and post-secularism, No Spiritual Investment in the World sheds new light on the historical contours of postwar German philosophy. (shrink)

Joseph Butler als zedekundige beschouwd en gewaardeerd by Willem Hendrik Weeda. This book is a reproduction of the original book published in 1899 and may have some imperfections such as marks or hand-written notes.

Twaalf inheemse en religieuze leiders uit verschillende werelddelen spreken zich in dit boek uit over de heiligheid van de natuur. Hun eeuwenoude wijsheden inspireren ons om anders te gaan denken over onze omgang met alles wat leeft. Aan het woord komen de Groenlandse sjamaan Angakkorsuaq, de Amerikaanse indianenleider Chief Lane Jr., masaileider Mwarabu, de boeddhistische geestelijke Shih, de dichtende islamgeleerde Ur Rehman Chishti, orthodox rabbijn Slifkin, Maya-priester Sac Coyoy, hindoe-prins Jhala, Aztekenleider Sanchez, leider van de Canadese Bear Clan Wawatie, bisschop (...) Smeets van Roermond en theoloog Valerio van Rochester Cathedral. 0Oeroude natuurwijsheden uit alle streken! (shrink)

This article considers Ruth Millikan's relationship to Robert Brandom and most especially their common influence, Wilfrid Sellars.

Dr. Willem Meijer [van W. G. van der Tak]--Lijst der in druk verschenen geschriften van dr. W. Meijer. [Door E. E. Eckstein]--Benedicti de Spinoza philosophiæ brevis commentatio.--Extracten uit de jaarverslagen van den secretaris der vereeniging Het Spinozahuis over het tijdvak 1897-1922.--Lijst der in de verslagen van de vereeniging Het Spinozahuis besproken boeken en tijdschriftartikels.

This paper concentrates on some aspects of the history of the analyticsynthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio exprincipiis. But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

This chapter contains sections titled: Quine, the Dogmas, and Sellars The Transcendental Argument for Sense Impressions Are Sense Impressions Casually Idle? A Sideways‐On View from Nowhere Sensation and the Phenomenology of Perception Concluding Remarks Notes References.

A summary of Sellars' argument that the Given is a myth--there is no such thing as a given in our knowledge.

Inleiding, gebaseerd op een collegedictaat en een syllabus voor studenten aan de Economische hogeschool te Rotterdam.

This chapter contains section titled: “One Must Die to Know the Truth” “Prayer to the Cloud of Unknowing” Bored, as in Really Bored The Boxing of D'Anna Biers Notes.

Levelt, reviewing the AGL field from a psycholinguistic perspective, identifies various gaps and makes a number of concrete suggestions for improving several currently used experimental designs. He raises the question whether artificial (and natural) grammar learning is about detecting ‘rules’, as is commonly assumed, or rather the detection of a set of ‘constraints’. He cautions the community to not ignore ‘semantics’, and recommends to consider less artificial tasks, that may be needed for learning more complex rules by human or nonhuman (...) animals. (shrink)

Zuidema et al. illustrate how empirical AGL studies can benefit from computational models and techniques. Computational models can help clarifying theories, and thus in delineating research questions, but also in facilitating experimental design, stimulus generation, and data analysis. The authors show, with a series of examples, how computational modeling can be integrated with empirical AGL approaches, and how model selection techniques can indicate the most likely model to explain experimental outcomes.

Through a close reading of the opening pages of Occidental Eschatology, this paper analyzes how Jacob Taubes relied on Martin Heidegger’s philosophy to understand the nature of eschatology. Taubes implemented Heidegger’s notions of truth, error, and history from his seminal essay “On the Essence of Truth,” (mis)interpreting the essay by ascribing an eschatological meaning to it. This surprisingly allowed him to find in Heidegger a model to come to terms with the Jewish experience of history. In order to fully understand (...) this untimely use of Heidegger’s work, the paper turns its attention to the correspondence of Jacob Taubes with his first wife, Susan Taubes. The conclusion asks to what extent Jacob Taubes’s uncritical use of Heidegger’s thinking plays into the latter’s notorious antisemitism. (shrink)