Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply ``There is no royal road to mathematics.'' Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and (...) mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: 'Doets and van Eijck's ``The Haskell Road to Logic, Maths and Programming'' is an astonishingly extensive and accessible textbook on logic, maths, and Haskell.' Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau. (shrink)

First published in 1992. Routledge is an imprint of Taylor & Francis, an informa company.

Recently, metaphysical coherentism has been propounded as an alternative to metaphysical foundationalism and infinitism. The view replaces the picture of reality as a hierarchy of levels with that of a network of objects or facts standing in symmetric or, more generally, cyclic relations of metaphysical dependence. This paper defends the orthodox picture of a well-founded hierarchy against the claimed superiority of coherentism. First, it will be argued that alleged theoretical advantages of coherentism do not hold up to scrutiny. Secondly, examples (...) that are claimed to support coherentism are either misdescribed as involving metaphysical interdependence, or foundationalist treatments fare at least as good and often better than coherentist interpretations. Thirdly, a similar diagnosis applies to a recently proposed coherentist interpretation of quantum entanglement. The more general diagnosis is that claims of metaphysical dependence are convincing only if there is a detailed account of how one item metaphysically explains another. While foundationalists can resort to various specific explanatory relations, coherentism seems to be incapable of providing detailed explanations. (shrink)

MoralischePrinzip(ien)DoppelwirkungsprinzipBewertungenBewertung, moralischekönnenTun, Unterlassen, Zulassen sich auf Unterschiedliches beziehen, beispielsweise auf Personen, Gesetze oder ganze Gesellschaften. Im Zentrum der Moral stehen aber Handlungen und Handlungsweisen, denn durch Handlungen greifen Menschen in die Welt ein und müssen sich folglich auch dafür verantworten (s. Kap. 31). Während sich konsequentialistischeKonsequentialismus Ethiken darauf beschränken, Handlungen allein an ihren Folgen zu messen, legen nicht-konsequentialistische Ethiken andere oder zusätzliche Maßstäbe an.

A “multifactorial” model should accommodate a psychological perspective, aiming to relate the phenomenology of complex visual hallucinations not only to neurobiological findings but also an understanding of the patient's psychological problems and situation in life. Greater attention needs to be paid to the role of the “lack of insight” patients may have into their hallucinations and its relationship to cognitive impairment.

The least common subsumer of a set of concept descriptions is the most specific concept description that subsumes all of the concept descriptions in the given set. By computing the lcs, commonalities between concept descriptions can be made explicit. This is an important inference task useful in several applications, including, for instance, the bottom-up construction of description logic knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many (...) applications, however, require to combine these constructors. In this work, we present an algorithm for computing the lcs in the description logic ALEN which comprises both constructors—number and existential restrictions—as well as concept conjunction, primitive negation, and value restrictions. To prove correctness of our lcs algorithm, we develop a structural characterization of subsumption in ALEN. (shrink)

For ordinals α beginning a Σ1 gap in equation image, where equation image is closed under number quantification, we give an inner model-theoretic proof that every thin equation image equivalence relation is equation image in a real parameter from the hypothesis equation image.

Do we sometimes know what will happen in the future? There are two intuitively plausible answers. The prognostic thesis says that we frequently know what will happen, the agnostic thesis says that we never do. Examining the question in the light of different conditions of knowledge supports the prognostic thesis. Yet there is still room for the agnostic intuition, as an expression of oUf necessarily suboptimal epistemic situation with respect to the future, but also of our freedom, in principle, to (...) shape the world as we like to. (shrink)

ABSTRACTThis paper addresses the problem of opaque sweetening and argues that one should use stochastic dominance in comparing lotteries even when dealing with incomplete orderings that allow for non-comparable outcomes.

This paper assesses the role of the Refutation of Idealism within the Critique of Pure Reason, as well as its relation to the treatment of idealism in the First Edition and to transcendental idealism more generally. It is argued that the Refutation is consistent with the Fourth Paralogism and that it can be considered as an extension of the Transcendental Deduction. While the Deduction, considered on its own, constitutes a 'regressive argument', the Refutation allows us to turn the Transcendental Analytic (...) into a 'progressive argument' that proceeds by the synthetic method. (shrink)

The present paper investigates the power of proper forcings to change the shape of the universe, in a certain well-defined respect. It turns out that the ranking among large cardinals can be used as a measure for that power. However, in order to establish the final result I had to isolate a new large cardinal concept, which I dubbed “remarkability.” Let us approach the exact formulation of the problem—and of its solution—at a slow pace.Breathtaking developments in the mid 1980s found (...) one of its culminations in the theorem, due to Martin, Steel, and Woodin, that the existence of infinitely many Woodin cardinals with a measurable cardinal above them all implies that AD, the axiom of determinacy, holds in the least inner model containing all the reals, L. One of the nice things about AD is that the theory ZF + AD + V = L appears as a choiceless “completion” of ZF in that any interesting question seems to find an at least attractive answer in that theory. Beyond that, AD is very canonical as may be illustrated as follows.Let us say that L is absolute for set-sized forcings if for all posets P ∈ V, for all formulae ϕ, and for all ∈ ℝ do we have thatwhere is a name for the set of reals in the extension. (shrink)

Let L[E] be an iterable tame extender model. We analyze to which extent L[E] knows fragments of its own iteration strategy. Specifically, we prove that inside L[E], for every cardinal K which is not a limit of Woodin cardinals there is some cutpoint t K > a>ω1 are cardinals, then ◊$_{K.\lambda }^* $ holds true, and if in addition λ is regular, then ◊$_{K.\lambda }^* $ holds true.

ABSTRACTOne prestudy based on a corpus analysis and four experiments in which participants had to invent novel names for persons or objects investigated how the valence of a face or an object affects the phonological characteristics of the respective novel name. Based on the articulatory feedback hypothesis, we predicted that /i:/ is included more frequently in fictional names for faces or objects with a positive valence than for those with a negative valence. For /o:/, the pattern should reverse. An analysis (...) of the Berlin Affective Word List – Reloaded yielded a higher number of occurrences of /o:/ in German words with negative valence than in words with positive valence; with /i:/ the situation is less clear. In Experiments 1 and 2, participants named persons showing a positive or a negative facial expression. Names for smiling persons included more /i:/s and fewer /o:/s than names for persons with a negative facial expression. In Experiments 3 and 4, participant... (shrink)

Inhalt Einfuhrung - Staat im Wandel. Rudiger Voigt zum 65. Geburtstag I. Konzeptualisierung und Systematisierung von Staatswandel Ralf Walkenhaus: Entwicklungslinien moderner Staatlichkeit.

If we call something ‘natural’ that occurs by itself without human intervention, and if cultural philosophy is interested precisely in what depends on human poiesis (production), praxis (action) and synthesis (conceptualization), then cultural philosophy refers ex negativo to the other of human intervention in the world. In this specific sense cultural philosophy can be understood as a negative philosophy of nature and is important for any kind of positive philosophy of nature insofar as it provokes natural facts to show themselves (...) in human poiesis, praxis and synthesis. (shrink)

Any attempt to elucidate the nature and mechanism of passivity phenomena, i.e., experiences that one’s conscious actions or thoughts have not been ‘willed’ by oneself, requires an integrative philosophical–neurobiological approach. The model proposed here adopts some fundamental positions that have long been advocated by philosophers and theoretical psychologists and have now found support from functional neuroanatomy. First, we experience our actions not from the standpoint of the executive but through the perception of its effects. Second, the ‘self’ is not an (...) agent of behaviour. Third, behaviour is energised and integrated by basic drives . Fourth, the view that the experience of an acting self is related to drive reduction associated with voluntary actions is perhaps less well developed. The model thus proposes that passivity phenomena are actions that are induced by the perception of salient events but that are not integrated with or conducive to the overall motivational state of the organism. It has been suggested that, following the perception of salient events, competition arises between automatic response tendencies seeking expression. The prefrontal cortex appears to play an important role not only in determining which events are to be perceived but also which of the corresponding response dispositions is to be selected and actualised in overt behaviour. Thus, action selection is the outcome of competition between response tendencies in the context of prefrontal biasing signals that represent drives and strivings for goals. Action selection may be uncoupled from drives and strivings as a result of a lowering of the threshold for action selection—as is suggested to be the case in schizophrenic passivity phenomena—or due to disconnection from prefrontal regions—as may be the case in the alien limb syndrome. (shrink)