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)

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)

Passing the Gāhā in review we may note that in composition (i.e., frequent patchwork) and vocabulary it could very well be a part of the Āyāranga, as Schubring suggested — an idea as ingenious as it is probably difficult to prove. Also, if Gāhā originally was the title of Āyār 2, 16, it is strange for a dozen tri $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s}$$ $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{t}$$ ubh stanzas to be thus called, for if the end leaves were exchanged, the text would hardly be separated from (...) the title (colophon).I therefore raised the question if Gāhā might mean ‘song praising men.’ N 141ab could support this, though the text is in prose. If, however, the stanzas of Āyār 2, 16 were the 16th lecture of Sūy 1, the itle of Gāhā is only justifiable in view of its being given to all Sūy 1 lectures, as said in Utt 31, 13, but in that case the number 16 must be added, as in fact is done in N 141cd (gāhā-solasa-nāma $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{m}$$ ajjhaya $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{n}$$ a $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{m}$$ ).This would be a canonical explanation, i.e., with the help of Samav 16 and Utt 31, 13.A post-canonical (Nijjutti) explanation would be to assume Gāhā to be short for Gāhā-solasaga, which would normally mean ‘(the lecture) of the 16 gāthās’, a title as strange for prose as it is for 12 tri $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s}$$ $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{t}$$ ubhs.Therefore, is gāhā not equivalent to Sa. gāthā or is Sūy l, 16 as we have it a substitute for a text lost and different from Āyār 2, 16? Or was the title of the prose Sūy 1, 16 lost and somehow substituted by the colophon of the Śrutaskandha? Is there a connection between this problem and the lacuna in the Sūyaga $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{d}$$ a-Nijjutti after stanza 22? At least this question I would tend to answer in the affirmative. (shrink)

Experientialist accounts of wellbeing are those accounts of wellbeing that subscribe to the experience requirement. Typically, these accounts are hedonistic. In this article I present the claim that hedonism is not the most plausible experientialist account of wellbeing. The value of experience should not be understood as being limited to pleasure, and as such, the most plausible experientialist account of wellbeing is pluralistic, not hedonistic. In support of this claim, I argue first that pleasure should not be understood as a (...) broad term to describe valuable experiences generally. I then analyze responses to the main argument against a monistic view on the value of experience: the philosophy of swine objection. I argue that such responses deviate from the central hedonistic view that only pleasure and pain matter for wellbeing. I then argue that the argument can be avoided on a pluralistic account, and formulate a plausible candidate for an account of pluralistic experientialism, in which, besides pleasure, non-hedonic aspects of experience like novelty, compassion, and aesthetic value also contribute to wellbeing. (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)

A marxist view on the priority of the function of the stimulation of creativity as compared to the other functions of art 59 2.3.1. ...

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)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...) establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

The concept of meaningful work is used to evaluate the quality of work. Typical cases of meaningless work that have been used to clarify this concept are assembly line work, and work involving other types of mindless tasks, but also David Graeber's ‘bullshit jobs’. I argue that there are at least two fundamental reasons to care about meaningful work: reasons from the wellbeing of the worker and reasons pertaining to meaningfulness of the worker's life. I first argue that a concept (...) of meaningful work needs to reflect these two values, but that these two values may come apart. Because of this, accounts that provide a single answer to the question to what extent a particular work context is meaningful work for a particular worker are unable to reflect these two values. I then survey three promising accounts of meaningful work: perfectionism, which captures the self-interested aspect of meaningful work well but fails to capture the meaningfulness aspect appropriately; consequentialism, which captures the meaningfulness aspect well but fails to capture the self-interested aspect; and Wolf's Fitting Fulfilment View of meaningful projects, which can be read as addressing both concerns but leads to implausible judgments about meaningful work. I then argue that we should conceive of the concerns that fall under the notion of meaningful work as two separate concepts and values. The best work incorporates both these dimensions but falling short on either dimension is problematic for different reasons. (shrink)

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)

The concept of meaningful work is used to evaluate the quality of work. Typical cases of meaningless work that have been used to clarify this concept are assembly line work, and work involving other types of mindless tasks, but also David Graeber's ‘bullshit jobs’. I argue that there are at least two fundamental reasons to care about meaningful work: reasons from the wellbeing of the worker and reasons pertaining to meaningfulness of the worker's life. I first argue that a concept (...) of meaningful work needs to reflect these two values, but that these two values may come apart. Because of this, accounts that provide a single answer to the question to what extent a particular work context is meaningful work for a particular worker are unable to reflect these two values. I then survey three promising accounts of meaningful work: perfectionism, which captures the self-interested aspect of meaningful work well but fails to capture the meaningfulness aspect appropriately; consequentialism, which captures the meaningfulness aspect well but fails to capture the self-interested aspect; and Wolf's Fitting Fulfilment View of meaningful projects, which can be read as addressing both concerns but leads to implausible judgments about meaningful work. I then argue that we should conceive of the concerns that fall under the notion of meaningful work as two separate concepts and values. The best work incorporates both these dimensions but falling short on either dimension is problematic for different reasons. (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.

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.

People maintain systems of beliefs that provide them with a sense of belongingness, control, identity, and meaning, more generally. Recent research shows that when these beliefs are threatened a syndrome of negatively valenced arousal is evoked that motivates people to seek comfort in their ideologies or other personally valued beliefs. In this paper we will provide an overview of this process and discuss areas for future research. Beginning with the neural foundations of meaning violations, we review findings that show the (...) anterior cingulate cortex (ACC) is responsible for detecting inconsistencies, and importantly, that this is experienced as aversive. Next, we evaluate the evidential support for a psychophysiological arousal response as measured by cardiography and skin conductance. We discuss how current theorizing proposes that subsequent behavioral approach ameliorates the negative arousal and serves as an effective, well-adapted coping response, but we also aim to further integrate this process in the existing threat-compensation literature. Finally, we speculate on whether approach motivation is likely to result when one feels capable of handling the threat, thereby incorporating the biopsychosocial model that distinguishes between challenge and threat into the motivational threat-response literature. We believe the current literature on threat and meaning has much to offer and we aim to provide new incentives for further development. (shrink)

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)

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)

According to Vallicella's‘Relations, Monism, and the Vindication of Bradley's Regress’ , if relations are to relate their relata, some special operator must do the relating. No other options will do. In this paper we reject Vallicella's conclusion by considering an important option that becomes visible only if we hold onto a precise distinction between the following three feature‐pairs of relations: internality/externality, universality/particularity, relata‐specificity/relata‐unspecificity. The conclusion we reach is that if external relations are to relate their relata, they must be relata‐specific (...) . As it eschews unmereological complexes, this outcome is of relevance to defenders of the extensionality of composition. (shrink)

Evolutionary psychologists tend to view the mind as a large collection of evolved, functionally specialized mechanisms, or modules. Cosmides and Tooby (1994) have presented four arguments in favor of this model of the mind: the engineering argument, the error argument, the poverty of the stimulus argument, and combinatorial explosion. Fodor (2000) has discussed each of these four arguments and rejected them all. In the present paper, we present and discuss the arguments for and against the massive modularity hypothesis. We conclude (...) that Cosmides and Tooby's arguments have considerable force and are too easily dismissed by Fodor. (shrink)