A formula ϕ in the one non-logical symbol ϵ with one free variable x is Russell if the sentence Vχ) is logically valid. This note describes a pattern common to the classical examples of Russell formulas, adds a couple of new ones, and constructs many formulas that are near-Russell.

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)

We axiomatize all quantifier properties which can be expressed by a universal condition on the class of algebras of sets.

We axiomatize all quantifier properties which can be expressed by a universal condition on the class of algebras of sets.

This note exploits back-and-forth characteristics to construct, using a single method, short proofs for ten classics of first-order and modal logic: interpolation theorems, preservation theorems, and Lindström's theorem.

This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.

This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give (...) the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science. (shrink)

This book gives a state-of-the-art survey of current research in logic and philosophy of science, as viewed by invited speakers selected by the most prestigious international organization in the field. In particular, it gives a coherent picture of foundational research into the various sciences, both natural and social. In addition, it has special interest items such as symposia on interfaces between logic and methodology, semantics and semiotics, as well as updates on the current state of the field in Eastern Europe (...) and the Far East. (shrink)

This interview with Jeremy Waldron covers three topics. Firstly, we dealt with the methodology debate, that is, the discussion about how to proceed in analyzing the nature of law. Does the question ‘What is law?’ require a descriptive analysis of the concept of law or, rather, a normative exercise in political philosophy? Secondly, we spoke about the role of law in response to historic injustice, especially in relation to the restitution of property rights. On this topic Waldron vindicates the ‘supersession-thesis’, (...) the idea that, due to changed circumstances and the passage of time, historic injustices become superseded. The third section of the interview is devoted to Waldron’s perspective on the citation of foreign law by national judges. (shrink)

A substantial amount of recent work in natural language generation has focused on the generation of ‘‘one‐shot’’ referring expressions whose only aim is to identify a target referent. Dale and Reiter's Incremental Algorithm (IA) is often thought to be the best algorithm for maximizing the similarity to referring expressions produced by people. We test this hypothesis by eliciting referring expressions from human subjects and computing the similarity between the expressions elicited and the ones generated by algorithms. It turns out that (...) the success of the IA depends substantially on the ‘‘preference order’’ (PO) employed by the IA, particularly in complex domains. While some POs cause the IA to produce referring expressions that are very similar to expressions produced by human subjects, others cause the IA to perform worse than its main competitors; moreover, it turns out to be difficult to predict the success of a PO on the basis of existing psycholinguistic findings or frequencies in corpora. We also examine the computational complexity of the algorithms in question and argue that there are no compelling reasons for preferring the IA over some of its main competitors on these grounds. We conclude that future research on the generation of referring expressions should explore alternatives to the IA, focusing on algorithms, inspired by the Greedy Algorithm, which do not work with a fixed PO. (shrink)

Dans cet article, composé en hommage aux travaux de Peter Sharratt, l’auteur examine l’attitude de Pierre de La Ramée (Ramus) et d’Omer Talon à l’égard de l’Éthique à Nicomaque. En tant qu’humanistes, ces derniers s’occupent intensément des arts du discours. Tout en reconnaissant la nécessité d’un fondement éthique dans tout discours, ils se montrent violemment hostiles au traité aristotélicien. Le traité posthume de théologie composé par Ramus propose le Décalogue comme source exclusive de la morale chrétienne. Ramus et Talon refusent (...) de la sorte de s’engager dans la voie ouverte quelques décennies plus tôt par Ph. Melanchthon, qui avait intégré de manière originale la morale antique, notamment celle d’Aristote, dans la théologie protestante. Toutefois, vers la fin du xvie siècle, le philosophe hollandais Rodolphe Snellius, père adoptif du théologien Arminius, composera un traité de morale dans lequel il tente de concilier la morale aristotélicienne avec la méthode développée par Ramus et son équipe. (shrink)

This paper asks why information should ever be expressed vaguely, re-assessing some previously proposed answers to this question and suggesting some new ones. Particular attention is paid to the benefits that vague expressions can have in situations where agreement over the meaning of an expression cannot be taken for granted. A distinction between two different versions of the above-mentioned question is advocated. The first asks why human languages contain vague expressions, the second question asks when and why a speaker should (...) choose a vague expression when communicating with a hearer. While the former question is purely theoretical, the latter has practical implications for the computational generation of utterances in Natural Language Generation (NLG). (shrink)

Recent findings necessitate revision of the traditional view of G protein‐coupled receptor (GPCR) signaling and expand the diversity of mechanisms by which receptor signaling influences cell behavior in general. GPCRs elicit signals at the plasma membrane and are then rapidly removed from the cell surface by endocytosis. Internalization of GPCRs has long been thought to serve as a mechanism to terminate the production of second messengers such as cAMP. However, recent studies show that internalized GPCRs can continue to either stimulate (...) or inhibit cAMP production in a sustained manner. They do so by remaining associated with their cognate G protein subunit and adenylyl cyclase at endosomal compartments. Once internalized, the GPCRs produce cellular responses distinct from those elicited at the cell surface. (shrink)

Radical and autopoietic enactivists disagree concerning how to understand the concept of sense-making in enactivist discourse and the extent of its distribution within the organic domain. I situate this debate within a broader conflict of commitments to naturalism on the part of radical enactivists, and to phenomenology on the part of autopoietic enactivists. I argue that autopoietic enactivists are in part responsible for the obscurity of the notion of sense-making by attributing it univocally to sentient and non-sentient beings and following (...) Hans Jonas in maintaining a phenomenological dimension to life-mind continuity among all living beings, sentient or non-sentient. I propose following Merleau-Ponty instead, who offers a properly phenomenological notion of sense-making for which sentience is a necessary condition. Against radicalist efforts to replace sense-making with a deflationary, naturalist conception of intentionality, I discuss the role of the phenomenological notion of sense-making for understanding animal behavior and experience. (shrink)

This paper clarifies Merleau-Ponty’s distinction between speaking and spoken speech, and the relation between the two, in his Phenomenology of Perception. Against a common interpretation, I argue on exegetical and philosophical grounds that the distinction should not be understood as one between two kinds of speech, but rather between two internally related dimensions present in all speech. This suggests an interdependence between speaking and spoken aspects of speech, and some commentators have critiqued Merleau-Ponty for claiming a priority of speaking over (...) spoken speech. However, there is a sense in which Merleau-Ponty is right to emphasize the priority, namely, in terms of the ontological priority of the speaking subject with respect to language understood as a constituted cultural ideality. The latter only maintains its ontological status insofar as it is taken up by a language community. I favorably contrast Merleau-Ponty’s views on this question to those of the late Heidegger and de Saussure, and suggest potential applications of this clarified position for contemporary discussions in philosophy of language. (shrink)