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)

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.

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)

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)

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)

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)

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 ...

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)

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)

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 article examines how new types of performance appraisal reconfigure everyday personal relationships at work. These systems deploy smartphone technologies to be used continuously by individuals to rate each other. Our aim is to show, in concrete terms, how these practices claim to configure a democratic space where individuals are liberated to express their views about each other’s work. On the contrary, we argue that by being placed in continuous confrontation with each other’s ratings, the genuine space for democratic contestation, (...) for the establishment of a genuine community, as well as for critique and dissent is—paradoxically—narrowed down. The first section of this article explores the context in which managerialism has become consolidated at the centre of neo-liberal politics in a dialogue with some of Mouffe’s and Rancière’s arguments. We use Rancière’s concept of “policing” to understand how managerial techniques subvert genuine democratic spaces, modes of participation and expression. Using performance appraisal systems as an example, the second part of the article provides a critical investigation which shows how managerialism intervenes at the very roots of possible democratic engagement and undermines dissent in subtle ways. (shrink)

U ovom radu razmatraju se pravi ciljevi tzv. medjunarodne zajednice na Balkanu, pod kojom se zapravo podrazumevaju Sjedinjene Americke Drzave Kao jedina preostala super sila, i Evropska unija, u kojoj kljucnu ulogu imaju Francuska, Velika Britanija i Nemacka. Pisac polazi od uverenja da stvarne, a narocito dugorocne namere ovih sila treba prevashodno izvoditi iz onoga sto one cine, pa tek onda uzimali u obzir i ono sto se javno ili tajno govorilo ili nagovestavalo. Analizom veceg broja primera na Balkanu i (...) u drugim delovima sveta pisac dolazi do neocekivanog ishoda. Dok su se velike zapadne sile na recima zalagale za multietnicnost i ocuvanje multietnickih drzava, na delu su postupale upravo suprotno: ne samo sto su podsticale bujanje nacionalizma i separatizma, nego su i pospesile i priznale raspad triju evropskih federacija na 22 manje-vise nacionalne drzave. I dok su se na recima prividno zalagale za tzv. demokratizaciju, u praksi su ne samo podrzavale autoritarne rezime nego su i same na tlu Balkana demokratiju poistovetile s okupacijom. (shrink)

The article deals with the legal, political, philosophical and religious dimensions of Socrates’ trial and execution. It considers the issue in five separate aspects: 1) the validity of charging Socrates with impiety and corrupting the youth of the Athens; 2) the legal basis of the philosopher’s indictment; 3) the then manner of conducting a legal trial in the Athens; 4) the extent to which Socrates’ conviction can ultimately be characterized as unjust and — finally — 5) the cultural ramifications of (...) the philosopher’s trial and execution. (shrink)

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)

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 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 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 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 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)

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)

Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the existence of a faithful functor from a free category with binary products and sums to the category of relations on finite ordinals. This result is obtained with the help of proof-theoretic normalizing techniques. When the terminal object is present, coherence may still be proved if of binary sums we keep just their bifunctorial properties. It (...) is found that with the simplest understanding of coherence this is the best one can hope for in bicartesian categories. The coherence for categories with binary products and sums provides an easy decision procedure for equality of arrows. It is also used to demonstrate that the categories in question are maximal, in the sense that in any such category that is not a preorder all the equations between arrows involving only binary products and sums are the same. This shows that the usual notion of equivalence of proofs in nondistributive conjunctive-disjunctive logic is optimally defined: further assumptions would make this notion collapse into triviality. (shrink)

Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the existence of a faithful functor from a free category with binary products and sums to the category of relations on finite ordinals. This result is obtained with the help of proof-theoretic normalizing techniques. When the terminal object is present, coherence may still be proved if of binary sums we keep just their bifunctorial properties. It (...) is found that with the simplest understanding of coherence this is the best one can hope for in bicartesian categories. The coherence for categories with binary products and sums provides an easy decision procedure for equality of arrows. It is also used to demonstrate that the categories in question are maximal, in the sense that in any such category that is not a preorder all the equations between arrows involving only binary products and sums are the same. This shows that the usual notion of equivalence of proofs in nondistributive conjunctive-disjunctive logic is optimally defined: further assumptions would make this notion collapse into triviality. (shrink)