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, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of (...) formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated. (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, ...

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)

Writing the history of elementary particle physics has all the problems common to writing the history of any other subject “in the making”. There is, however, an additional characteristic, unique to this branch of physics. The development of particle physics, unlike the situation in other branches of physics, reveals a continuously changing picture of what its object of investigation is, of what, in other words, the things we call particles are and how elementary they should be considered. The history of (...) elementary particle physics is, in a way, the history of the continuous reinterpretation of both the ontological and methodological status of the notion of elementarity. Hence, examining the history of elementary particle physics is also an attempt to explicate this changing collective consciousness of the scientific community about the elementarity of particles. In studying, therefore, (practically any aspect of) the history of elementary particle physics, one has to be sensitive about a number of philosophical, and primarily methodological issues which have acquired an added significance due to the relatively recent and mainly theoretical developments. (shrink)

What was science for the Orthodox Greek theologian of the nineteenth century? How did it feature in his (theologians were all men at the time) own work? This article is an attempt to describe the science and religion interactions by placing Greek Orthodox theologians of the nineteenth century in the center of the historical narrative, rather than treat them as occasional deuteragonists in the scientists’ historiography. The picture that emerges is far more complicated than one of antagonism, indifference, conflict, or (...) coexistence. Greek theologians saw themselves as scientists and treated theology as a positive, rational science. They developed strategies to delineate their disciplinary borders and safeguard their identity as expert scholars by harnessing their university and academic credentials. For that reason, they had to invoke famous German and other Western theologians, while ensuring that they were seen as true defenders of Orthodox Christianity. The idea of science was an integral part of this achievement. (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)

In standard model theory, deductions are not the things one models. But in general proof theory, in particular in categorial proof theory, one finds models of deductions, and the purpose here is to motivate a simple example of such models. This will be a model of deductions performed within an abstract context, where we do not have any particular logical constant, but something underlying all logical constants. In this context, deductions are represented by arrows in categories involved in a general (...) adjoint situation. To motivate the notion of adjointness, one of the central notions of category theory, and of mathematics in general, it is first considered how some features of it occur in set-theoretical axioms and in the axioms of the lambda calculus. Next, it is explained how this notion arises in the context of deduction, where it characterizes logical constants. It is shown also how the categorial point of view suggests an analysis of propositional identity. The problem of propositional identity, i.e., the problem of identity of meaning for propositions, is no doubt a philosophical problem, but the spirit of the analysis proposed here will be rather mathematical. Finally, it is considered whether models of deductions can pretend to be a semantics. This question, which as so many questions having to do with meaning brings us to that wall that blocked linguists and philosophers during the whole of the twentieth century, is merely posed. At the very end, there is the example of a geometrical model of adjunction. Without pretending that it is a semantics, it is hoped that this model may prove illuminating and useful. (shrink)

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)

LetSbe the group of finitely supported permutations of a countably infinite set. Let$K[S]$be the group algebra ofSover a fieldKof characteristic 0. According to a theorem of Formanek and Lawrence,$K[S]$satisfies the ascending chain condition for two-sided ideals. We study the reverse mathematics of this theorem, proving its equivalence over$RC{A_0}$ to the statement that${\omega ^\omega }$is well ordered. Our equivalence proof proceeds via the statement that the Young diagrams form a well partial ordering.

This paper analyzes the ongoing university reform in Russia by underlining historical roots and peculiarities of its system of higher education. It is pointed out that the Soviet model of economy, political and ideological bias deeply impacted the university system and enforced its estrangement from foreign universities. A limited number of the best Soviet higher education institutions which provided a military-oriented education and fundamental research were re-casted along the so called “PhysTech” system after the end of the WWII. As a (...) result of this system, higher education and R&D in Russia is not presently competitive in the educational international market. Closing the gap between Russian universities and the “global university” approach and raising university competitiveness are the main objectives of the current reform in science and education. As universities are considered core actors of knowledge economy, a new set of federal and national research universities was created. However, reform faces numerous conceptual and institutional obstacles, risks and constraints are significant, and positive outcomes elusive. (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.

"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.

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 ...

It is not possible to dismiss the atomistic paradigm because the proposed elementary particles are too many (and, hence, it is claimed, they do not provide a simple account of nature) or because it is not possible to observe quarks in an isolated manner. The developments in particle physics have brought about radical changes to our notions of simplicity and observability, and in this paper we elaborate on these changes. It is as a result of these changes that the present (...) situation in elementary particle physics justify us to claim that we have indeed reached a level of explanation where the constituent particles (quarks, leptons, gluons, and intermediate bosons) used for the explanation of the various phenomena considered to be delineating a particular level in the descriptive framework of the physical phenomena and a specific stratum in the organization of nature, can be regarded as elementary. (shrink)

(1984). Some methodological and historical considerations in low temperature physics: The case of superconductivity 1911–57. Annals of Science: Vol. 41, No. 2, pp. 135-149.

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.

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)

This is an examination, a commentary, of links between some philosophical views ascribed to Gödel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from an infinitistic ideal perspective. It is inquired whether this centrality of deduction could also be kept in the intensional logic of concepts whose building Gödel seems to have taken as the main task of logic for the future.

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)

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)

In three volumes, a distinguished group of scholars from a variety of disciplines in the natural and social sciences, the humanities and the arts contribute essays in honor of Robert S. Cohen, on the occasion of his 70th birthday. The range of the essays, as well as their originality, and their critical and historical depth, pay tribute to the extraordinary scope of Professor Cohen's intellectual interests, as a scientist-philosopher and a humanist, and also to his engagement in the world of (...) social and political practice. Science, Mind and Art, Volume III of Essays in honor of Robert S. Cohen focuses on issues in contemporary epistemology, aesthetics, and philosophy of mind as well as on the relations of science and human values in ethical and religious thought. It also has important new work in contemporary metaphysics, as well as in the history of philosophy, and on questions of multiculturalism in science education. Contributors include Paul Feyerabend, Adolf Grünbaum, Joseph Margolis, Joëlle Proust, Erazim Kohak, Elie Wiesel, Miriam Bienenstock, and John Silber, among others. (shrink)

This paper presents a coherence theorem for star-autonomous categories exactly analogous to Kelly and Mac Lane’s coherence theorem for symmetric monoidal closed categories. The proof of this theorem is based on a categorial cut-elimination result, which is presented in some detail.

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)

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)

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)

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)

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 components of the practice of science. (shrink)

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose arrows (...) correspond to diagrams. Edges in these diagrams join occurrences of variables that must remain the same in every generalization of the proof. It is found that assumptions about equality of proofs for equality are parallel to standard assumptions about equality of arrows in categories. They reproduce standard categorial assumptions on a different level. It is also found that assumptions for a preordering relation involve an adjoint situation. (shrink)

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)

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)