Models for the Lambek calculus of syntactic categories surveyed here are based on frames that are in principle of the same type as Kripke frames for intuitionistic logic. These models are extracted from the literature on models for relevant logics, in particular the ternary relationed models introduced in the early seventies. The purpose of this brief survey is to locate some open completeness problems for variants of the Lambek calculus in the context of completeness results based on various types of (...) ternary relational models. (shrink)

This is a review, with historical and critical comments, of a paper by I. E. Orlov from 1928, which gives the oldest known axiomatization of the implication-negation fragment of the relevant logic R. Orlov's paper also foreshadows the modal translation of systems with an intuitionistic negation into S4-type extensions of systems with a classical, involutive, negation. Orlov introduces the modal postulates of S4 before Becker, Lewis and Gödel. Orlov's work, which seems to be nearly completely ignored, is related to the (...) contemporaneous work on the axiomatization of intuitionistic logic. (shrink)

A SECOND COMPLETELY REVISED EDITION OF THIS TEXTBOOK ON INTERDISCIPLINARY RESEARCH WAS PUBLISHED WITH AMSTERDAM UNIVERSITY PRESS IN 2022. Check out that version here and a PDF of its ToC and Introduction, as this first edition (AUP 2016) is no longer available. [This book (128 pp.) serves as an introduction and manual to guide students through the interdisciplinary research process. We are becoming increasingly aware that, as a result of technological developments and globalisation, problems are becoming so complex that they (...) can only be solved through cooperation between multiple disciplines. Healthcare, climate change, food security, energy, financial markets and quality of life are just a few examples of issues that require scientists and academics to work in a crossdisciplinary way. As a result of these developments, an interdisciplinary approach is becoming increasingly popular in higher education and must be considered an absolute necessity. Young academics are being called on to step beyond the boundaries of traditional disciplines in order to contribute to addressing fundamental problems and solving challenges facing society. There is a need for people who are not afraid to ask critical questions, who can work together well and can look beyond the boundaries of their own field. This means students need to learn more about how they can integrate and apply knowledge, methods and skills from different fields. Interdisciplinary research projects and practical training courses offer students more than one perspective on the same subject. Comparing and contrasting, connecting, adding and adapting concepts, theories and methodologies from different disciplines ultimately results in new insights and better answers to complex problems.]. (shrink)

Showing how the law and medical knowledge intersect, Steph Jowett examines the law governing consent to medical treatment for trans youth in Australia, England and Wales. Using clear examples and accessible language, Jowett offers a comparative perspective that will benefit future reform efforts.

Current books on evolutionary theory all seem to take for granted the fact that students find evolution easy to understand when actually, from a psychological perspective, it is a rather counterintuitive idea. Evolutionary theory, like all scientific theories, is a means to understanding the natural world. Understanding Evolution is intended for undergraduate students in the life sciences, biology teachers or anyone wanting a basic introduction to evolutionary theory. Covering core concepts and the structure of evolutionary explanations, it clarifies both what (...) evolution is about and why so many people find it difficult to grasp. The book provides an introduction to the major concepts and conceptual obstacles to understanding evolution, including the development of Darwin's theory, and a detailed presentation of the most important evolutionary concepts. Bridging the gap between the concepts and conceptual obstacles, Understanding Evolution presents evolutionary theory with a clarity and vision students will quickly appreciate. (shrink)

In Neither Physics Nor Chemistry, Kostas Gavroglu and Ana Simoes examine the evolution of quantum chemistry into an autonomous discipline, tracing its development from the publication of early papers in the 1920s to the dramatic changes ...

Textbook descriptions of the foundations of Genetics give the impression that besides Mendel’s no other research on heredity took place during the nineteenth century. However, the publication of the Origin of Species in 1859, and the criticism that it received, placed the study of heredity at the centre of biological thought. Consequently, Herbert Spencer, Charles Darwin himself, Francis Galton, William Keith Brooks, Carl von Nägeli, August Weismann, and Hugo de Vries attempted to develop theories of heredity under an evolutionary perspective, (...) and they were all influenced by each other in various ways. Nonetheless, only Nägeli became aware of Mendel’s experimental work; it has also been questioned whether Mendel even had the intention to develop a theory of heredity. In this article, a short presentation of these theories is made, based on the original writings. The major aim of this article is to suggest that Mendel was definitely not the only one studying heredity before 1900, if he even did this, as may be inferred by textbooks. Although his work had a major impact after 1900, it had no impact during the latter half of the nineteenth century when an active community of students of heredity emerged. Thus, textbooks should not only present the work of Mendel, but also provide a wider view of the actual history and a depiction of science as a social process. (shrink)

ABSTRACT According to Genevieve Lloyd, conatus is manifested in body as a fixed ratio of motion and rest and in mind as increasing adequate understanding. The commentary provides textual analysis to resolve the apparent paradox that bodily stability corresponds to intellectual growth. The activity of adequate ideas and passivity of inadequate ideas are identified as analogues of motion and rest in Spinoza’s philosophy of mind and these are put to work in exploring what is required for increasing one’s adequate understanding: (...) that one can acquire adequate ideas only by extending one’s receptivity to being affected and by forming inadequate ideas. Thus a mind’s ratio between adequate and inadequate ideas is maintained even as it gains and exercises greater power. This appreciation of Spinoza’s epistemology supports Lloyd’s characterisation of his philosophy as “thinking from within the totality of being”. (shrink)

This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algebras with an additional unary operation). These results extend results of Goldblatt and Thomason about categories of relational frames for modal logic.

Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if after generalizing maximally (...) the rules involved in them they yield the same premises and conclusions up to a renaming of variables. These two proposals proved to be extensionally equivalent only for limited fragments of logic. The normalization proposal stands behind very successful applications of the typed lambda calculus and of category theory in the proof theory of intuitionistic logic. In classical logic, however, it did not fare well. The generality proposal was rather neglected in logic, though related matters were much studied in pure category theory in connection with coherence problems, and there are also links to low-dimensional topology and linear algebra. This proposal seems more promising than the other one for the general proof theory of classical logic. (shrink)

How happy it is to recall Imre Lakatos. Now, fifteen years after his death, his intelligence, wit, generosity are vivid. In the Preface to the book of Essays in Memory of Imre Lakatos, the editors wrote:... Lakatos was a man in search of rationality in all of its forms. He thought he had found it in the historical development of scientific knowledge, yet he also saw rationality endangered everywhere. To honor Lakatos is to honor his sharp and aggressive criticism as (...) well as his humane warmth and his quick wit. He was a person to love and to struggle with. The book before us carries old and new friends of that Lakatosian spirit further into the issues which he wanted to investigate. That the new friends include a dozen scientific, historical and philosophical scholars from Greece would have pleased Lakatos very much, and with an essay from China, he would have smiled all the more. But the key lies in the quality of these papers, and in the imaginative organization of the conference at Thessaloniki in summer 1986 which worked so well. (shrink)

Scientific knowledge is the most solid and robust kind of knowledge that humans have because of its inherent self-correcting character. Nevertheless, anti-evolutionists, climate denialists, and anti-vaxxers, among others, question some of the best-established scientific findings, making claims unsupported by empirical evidence. A common aspect of these claims is reference to the uncertainties of science concerning evolution, climate change, vaccination, and so on. This is inaccurate: whereas the broad picture is clear, there will always exist uncertainties about the details of the (...) respective phenomena. This book shows that uncertainty is an inherent feature of science that does not devalue it. In contrast, uncertainty advances science because it motivates further research. This is the first book on this topic that draws on philosophy of science to explain what uncertainty in science is and how it makes science advance. It contrasts evolution, climate change, and vaccination, where the uncertainties are exaggerated, and genetic testing and forensic science, where the uncertainties are usually overlooked. The goal is to discuss the scientific, psychological, and philosophical aspects of uncertainty in order to explain what it really is, what kinds of problems it actually poses, and why in the end it makes science advance. Contrary to public representations of scientific findings and conclusions that produce an intuitive but distorted view of science as certain, people need to understand and learn to live with uncertainty in science. This book is intended for anyone who wants to get a clear view of the nature of science. (shrink)

Deleuze’s reversal of Platonism shifted the traditional emphasis on thinking that which participates in a concept to that in which a claim to participation occurs. The first part of this article presents a reading of this reversal that highlights the implications of Deleuze’s ontology for his non-ontological account of participation, highlighting how this ontology builds on aspects of Plato’s philosophy recovered from beneath the later Platonic tradition of philosophy and supports Deleuze’s account of the rival claims of philosophy and opinion (...) to participate in thought. The second part outlines the difficulties presented by philosophy’s constitutive participation in friendship, love, and rivalry for it to be able to achieve its distinctive task of creating concepts that defeat opinion’s rival claims to address the problems that present themselves to thought. (shrink)

The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of ‘absolute space’. When applied to classical mechanics, under the guise of an extended symmetry group, this procedure is known to lead to an equation of motion with inertial-like forces that are sourced by the mass distribution of the system itself. In this paper we follow a similar procedure and reformulate the Schrödinger equation of non-relativistic quantum mechanics (...) in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system, leaving no room for the notion of absolute space. (shrink)

Les absents jouent un rôle considérable dans la création des signes qui servent, dans toute société, à désigner, nommer, et même instituer les places des présents et celles des absents tout en mettant du sens dans leurs relations. La sémiotique conçoit ainsi le processus d'humanisation à travers la création des signes alors que la psychanalyse a permis, à sa manière, de voir combien le monde des absents participe à la construction psychique du sujet. La fonction de l'absence perceptive chez le (...) bébé est également étudiée dans cet ouvrage dans sa contribution à la transformation des signes gestuels binaires en signes ternaires qui intègrent du sens. Ces transformations sémiotiques sont aussi éclairées par le regard des poètes et des philosophes présents dans cet ouvrage. (shrink)

The romance Imberios and Margarona does not belong to the Renaissance. It does not acknowledge many of the issues which become current in the age of Humanism: the value of individual consciousness, to name but one, will wait until the seventeenth century to be explored in Greek literature. And yet, the vintage of Imberios is hybrid: being late medieval and modelled after a popular European prototype, it slants ever so gently towards what will later be fully fledged humanistic sensibilities.

This paper presents an emerging aspect of intentionality through recent Artificial Intelligence (AI) developments in art and design. Our main thesis is that, if we focus just on the outcome of the artistic process, the intentionality of the artist does not have any relevance. Intention is measured as a result of actions regardless of whether they are human-based or not as long as there is an esthetical value intersubjectively acknowledged. In other words, what matters is the ‘intentio’ embedded in the (...) work of art (the output) rather than the ‘intendere’ (the process). By considering the former aspect, intentionality becomes free of human intervention, therefore 'unintentional'. This thesis is supported through a range of examples related to AI in general and AI art in particular. However, in the case of a self-driving vehicle, the macro-goal of the system is fixed by humans, even though the AI system itself will take care of decomposing the macro-goal into a set of micro-goals and take the corresponding decisions. In the case of art, the system does not need to have any exterior goal to the extent that art is pure freedom of expression, as many philosophers have acknowledged. In this sense, the decisions of any AI system generating art or design are independent of humans and must be judged only on the ground of the final outcome. A work of art will be judged ‘artistic’ to the extent that humans will recognize an artistic intent in the work itself. In particular, the introduction of random processes makes an AI-generated artwork fully independent of human creativity. (shrink)

Ambient Intelligence provides the potential for vast and varied applications, bringing with it both promise and peril. The development of Ambient Intelligence applications poses a number of ethical and legal concerns. Mobile devices are increasingly evolving into tools to orientate in and interact with the environment, thus introducing a user-centric approach to Ambient Intelligence. The MINAmI (Micro-Nano integrated platform for transverse Ambient Intelligence applications) FP6 research project aims at creating core technologies for mobile device based Ambient Intelligence services. In this (...) paper we assess five scenarios that demonstrate forthcoming MINAmI-based applications focusing on healthcare, assistive technology, homecare, and everyday life in general. A legal and ethical analysis of the scenarios is conducted, which reveals various conflicting interests. The paper concludes with some thoughts on drafting ethical guidelines for Ambient Intelligence applications. (shrink)

The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the structural (...) rules. Next, Hubert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.The first part of the paper, which follows, contains the first two sections, which deal with sequent-systems and Hubert-formulations. The second part, due to appear in the next issue of this journal, will contain the third section, which deals with groupoid models. (shrink)

Science appeared in modern Greece in the first decades after its establishment as a sovereign state in 1828. The University of Athens, the Royal Observatory, the Botanical Garden, and the Natural History Museum were quickly established as spaces of scientific activity. Greek scientists were enthusiastic participants in the emerging Greek public sphere, often not only as science experts, but also as poets, intellectuals and political personae. In a space whose cultural, intellectual and historical boundaries were still being negotiated, the choice (...) of language was not a given but a pressing, sensitive national desideratum. This article examines how Greek scientists used languages to communicate with their peers and with their publics, how they handled terminology and nomenclature, and how the issues surrounding the Greek language in particular affected their practice as scientists. The article aims to show that, in nineteenth-century Greece, languages were not passive, neutral vehicles of communication, but rather integral (though tacit) components of the practice of science. (shrink)

The purpose of this work is to present Gentzen-style formulations of S5 and S4 based on sequents of higher levels. Sequents of level 1 are like ordinary sequents, sequents of level 1 have collections of sequents of level 1 on the left and right of the turnstile, etc. Rules for modal constants involve sequents of level 2, whereas rules for customary logical constants of first-order logic with identity involve only sequents of level 1. A restriction on Thinning on the right (...) of level 2, which when applied to Thinning on the right of level 1 produces intuitionistic out of classical logic (without changing anything else), produces S4 out of S5 (without changing anything else). This characterization of modal constants with sequents of level 2 is unique in the following sense. If constants which differ only graphically are given a formally identical characterization, they can be shown inter-replaceable (not only uniformly) with the original constants salva provability. Customary characterizations of modal constants with sequents of level 1, as well as characterizations in Hilbert-style axiomatizations, are not unique in this sense. This parallels the case with implication, which is not uniquely characterized in Hilbert-style axiomatizations, but can be uniquely characterized with sequents of level 1. These results bear upon theories of philosophical logic which attempt to characterize logical constants syntactically. They also provide an illustration of how alternative logics differ only in their structural rules, whereas their rules for logical constants are identical. (shrink)

This book presents analyses of philosophical topics of importance to biology education. It is intended foremost for biology educators and teachers, and aims to show how philosophy of science in general, and philosophy of biology in particular, ...

This article critiques conspicuous displays of morality within public discourse, recently framed as ‘moral grandstanding’, from the perspective of an intersubjective Critical Realist theory of ethics. Drawing on Honneth’s recognition theory as the basis of a ‘qualified explanatory critique’, I argue that these practices are not mere aberrations within moral discourse, but a necessary consequence of the neoliberal imperative to turn all aspects of the self into market assets. Neoliberal commodity fetishism also and especially involves the commodification of moral character (...) as a means of economic competition, as exemplified in recent discussions of ‘ethical capital’. This objectification categorically precludes intersubjectivity as the basis of ethical life, and produces a cognitive structure resembling narcissistic pathology, characterized by the pervasive objectification of self and other. Critical Realists should therefore reject moral grandstanding not only for its detrimental effects on public discourse, but because in subordinating morality to the market, it is fundamentally anti-ethical. (shrink)

This is a companion to a paper by the authors entitled “Gödel on deduction”, which examined the links between some philosophical views ascribed to Gödel and general proof theory. When writing that other paper, the authors were not acquainted with a system of natural deduction that Gödel presented with the help of Gentzen’s sequents, which amounts to Jaśkowski’s natural deduction system of 1934, and which may be found in Gödel’s unpublished notes for the elementary logic course he gave in 1939 (...) at the University of Notre Dame. Here one finds a presentation of this system of Gödel accompanied by a brief reexamination in the light of the notes of some points concerning his interest in sequents made in the preceding paper. This is preceded by a brief summary of Gödel’s Notre Dame course, and is followed by comments concerning Gödel’s natural deduction system. (shrink)

Proof theory and category theory were first drawn together by Lambek some 30 years ago but, until now, the most fundamental notions of category theory have not been explained systematically in terms of proof theory. Here it is shown that these notions, in particular the notion of adjunction, can be formulated in such as way as to be characterised by composition elimination. Among the benefits of these composition-free formulations are syntactical and simple model-theoretical, geometrical decision procedures for the commuting of (...) diagrams of arrows. Composition elimination, in the form of Gentzen's cut elimination, takes in categories, and techniques inspired by Gentzen are shown to work even better in a purely categorical context than in logic. An acquaintance with the basic ideas of general proof theory is relied on only for the sake of motivation, however, and the treatment of matters related to categories is also in general self contained. Besides familiar topics, presented in a novel, simple way, the monograph also contains new results. It can be used as an introductory text in categorical proof theory. (shrink)

This article is concerned with the ways in which women narrate a move from a ‘working-class’ position to a position marked (in however fragmentary and complex a way) as ‘middle class’. While such a move might be seen in terms of a straightforward escape from a disadvantaged social position, I argue here that what has to be analysed is the pain and the sense of estrangement associated with this class movement. Drawing on the class narratives of a group of seven (...) white British women, the article uses Bourdieu's concepts of symbolic capital and habitus to explore the cultural and symbolic configurations of class. These configurations may be inscribed into the self, so that the self, itself, is class marked. Since working-class selves are frequently marked in pathological terms, this raises particular difficulties for the idea of an ‘escape’ from such a position. Class in this sense is embedded in people's history and so cannot be so easily ‘escaped’. The usual conventions of life-narratives – in which the self remains the same entity from birth to death and later events are a culmination of earlier ones – are also disrupted in this case. But if a working-class position is marked as pathological, so too is taking on the markers of middle-class existence. To do so is not only to risk ‘getting it wrong’, but it is also to risk the scorn attached to ‘pretentiousness’. There is a particular jeopardy here for women, since it is women who have been especially associated with desires for artefacts associated with bourgeois existence. The article argues for a focus for classed desires and class envy, not in pathological terms, but in terms of a coherent response to political and social exclusions. (shrink)

The purpose of this paper is to connect the proof theory and the model theory of a family of prepositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related to BCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the (...) structural rules. Next, Hilbert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.Below is the sequel to the first part of the paper, which appeared in the previous issue of this journal (vol. 47 (1988), pp. 353–386). The first part contained sections on sequent-systems and Hilbert-formulations, and here is the third section on groupoid models. This second part is meant to be read in conjunction with the first part. (shrink)

The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's.First a family of propositional logical systems is considered, which is obtained by gradually adding structural rules to a variant of the nonassociative Lambek calculus. In this family one (...) finds systems that correspond to the associative Lambek calculus, linear logic, relevant logics, BCK logic and intuitionistic logic. Above these basic systems, sequent systems parallel to the basic systems are constructed, which formalize various notions of derived rules for the basic systems. The deduction theorem is provable for the basic systems if, and only if, they are at least as strong as systems corresponding to linear logic, or BCK logic, depending on the language, and their deductive metalogic is not stronger than they are. (shrink)

The book in front of you is the first international academic volume on the legal, philosophical and economic aspects of the rise of 3D printing. In recent years 3D printing has become a hot topic. Some claim that it will revolutionize production and mass consumption, enabling consumers to print anything from clothing, automobile parts and guns to various foods, medication and spare parts for their home appliances. This may significantly reduce our environmental footprint, but also offers potential for innovation and (...) creativity. At the same time 3D printing raises social, ethical, regulatory and legal questions. If individuals can print anything they want, how does this affect existing systems of intellectual property rights? What are the societal consequences of the various types of products one can print with a 3D printer, for example weapons? Should all aspects of 3D printing be regulated, and if so, how and to what ends? How will businesses (have to) change their way of working and their revenue model in light of the shift to printing-on-demand? How will the role of product designers change in a world where everyone has the potential to design their own products? These and other questions are addressed in high quality and in-depth contributions by academics and experts, bringing together a wide variety of academic discussions on 3D printing from different disciplines as well as presenting new views, broadening the discussion beyond the merely technical dimension of 3D printing. Bibi van den Berg is Associate Professor at eLaw, the Center for Law and Digital Technologies at Leiden University, The Netherlands. Simone van der Hof is Full Professor at eLaw in Leiden and Eleni Kosta is Associate Professor at TILT, the Tilburg Institute for Law, Technology and Society at Tilburg University, The Netherlands. (shrink)

"Originally published in French in 1961, this book is one of the standard works on the question of alienation in Marx. In his study of Marx and the role of technology in the modern world, Kostas Axelos interprets Marx from his own distinctive, thought-provoking, philosophical position. Made available now in the translation by Ronald Bruzina, the book provides a meaningful interpretation of Marx and an introduction to Axelos's own philosophical thought" -- Book jacket.