Ensure learners truly understand all the essential TOK foundations and provide a practical learning scaffold to confidently progress them onto higher order thinking. Comprehensively supporting the TOK course book and mapped to the 2013 syllabus, this focused guide distils the big TOK ideas and builds student confidence right from the start.

Ensure learners truly understand all the essential TOK foundations and provide a practical learning scaffold to confidently progress them onto higher order thinking. Comprehensively supporting the TOK course book and mapped to the 2013 syllabus, this focused guide distils the big TOK ideas and builds student confidence right from the start.

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)

A number of issues related to the challenges menacing the future of history of science are discussed. It has become increasingly more difficult to engage scientists in the ways historians of science deal with their subjects, while at the same time the implicit historiography of science textbooks has created an ideology among scientists that makes such engagement even more strenuous. An additional complication is the deep belief of many scientists in anachronism. Another threatening prospect is the instrumentalist view held by (...) funding bodies whereby the social sciences and humanities have to explore ways in which they can respond successfully to societal needs. (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)

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)

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)

Theories of global justice have moved from issues relating to crimes against humanity and war crimes or, furthermore, ?negative duties? with respect to non-citizens, towards problems of distributive justice and global inequality. Thomas Nagel's Storrs Lectures from 2005, exemplifying Rawlsian internationalism, argue that liberal requirements concerning duties of distributive justice apply exclusively within a single nation-state, and do not extend to duties of this nature between rich and poor countries. Nagel even argues that the demand for global equality is not (...) a demand of justice at all. In the present article I will try to offer a normative basis for the criticism of such a view. Following Kant and more recently Philip Pettit, I locate this normative basis on political freedom conceived as non-domination. Such a conception opens up the possibility of a political cosmopolitanism, which is based not on an empirical interdependence among people at a global level, but on a normative interdependence. Subsequent cosmopolitan duties extend both to the elimination of domination everywhere in the world and to the equal enjoyment of non-dominated choice. Thus, it will be argued that modern republicanism is falsely identified with a particular, bounded community, but supports a political, not simply a moral, cosmopolitanism. This kind of cosmopolitanism conceives of sovereign states neither as useless constructions, nor as mere instruments for realizing the pre-institutional value of justice among human beings. Instead, their existence is what gives the value of justice its application. Cosmopolitanism is not after all about the abolishment of all boundaries, but about the essential capacity to draw and redraw them infinitely under conditions of global justice. (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 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)

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)

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)

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)

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.

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)

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference. This paper examines in the (...) setting of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof if and only if they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality. This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer. (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)

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, ...

How did it become possible to philosophize about history? Man has generally sought to locate himself in natural space rather than in historical time. The various oriental philosophies give no place to history. “Humanistic” Greece herself, in other respects so eager to explore human conduct in all its characteristic dimensions and in all its aspects, prudently recoiled from anything which might give value to time or cause history to appear as the specifically human mode of existence. No other culture, perhaps, (...) carried so far the concern for harmonizing human relationships, and yet the idea of progress was completely lacking in it. The organization of the terrestrial city always remained the central point of the reflection of Greek poets and philosophers, who were almost all teachers and law-givers—but they never thought to situate the true destiny of man in the historical world, much less to grant man a place in the universe which would make him forget the precariousness of his condition and his subordination to that which surpasses him. And, if we listen to Aristotle: “The life of moral virtue,” he says, “is happy only in a secondary degree. For the moral activities are purely human, ανθρωπικαι.” Naturally, “it is true that, being a man and living in the society of others, he chooses to engage in virtuous action, and so will need external goods to carry on his life as a human being, πρos τo ανθρωπɛνɛσθαι.” But we must take care not to assert “that man is superior to the other animals … since there are other things far more divine in their nature than man, for instance, to mention the most visible (ϕανɛρωτατα), the things of which the things of which the celestial system is composed.” Aristotle was referring to the stars—and, indeed, it was in the circular motions of the luminaries, much more than in the human domain, that the classic Greeks saw that which is manifested in being with the greatest splendor. If we limit ourselves to the specifically human—as do those whom Plotinus designates under the frankly disdainful term oι ανθρωπικωτɛρoι—we risk losing contact with the Good that revolves in the cosmos and is our sole guaranty against the senseless non-being which threatens us from every side. Under these conditions the question of knowing whether or not history has meaning, and whether or not it is provided with an appropriate logic which expresses the profound structure of our being, appears meaningless. (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)

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)

Die Frage der Erhaltung der Parität bei der Wechselwirkung von Elementarteilchen, der Vorschlag ihrer Verletzung, die experimentelle Bestätigung dieses Vorschlags und die daraus sich ergebenden Folgerungen, die zur Formulierung der mathematischen Struktur der schwachen Wechselwirkungen führten, sind die wichtigsten Entwicklungen in der Elementarteilchenphysik während der Periode von 1953 bis 1958. Vorliegender Aufsatz versucht die rationale Rekonstruktion dieser Periode und des Forschungsprogrammes, welches als eines der progressivsten Programme der modernen Physik angesehen wird. Hierzu benutzen wir eine modifizierte Fassung von Poppers tetradischem (...) Schema als auch die Bemerkungen von Lakatos über gewisse Aspekte der Methodologie von Forschungsprogrammen. Es wird unterstrichen, daß die Dynamik der positiven Heuristik derart war, daß die theoretische Forschung fortgeführt werden konnte, trotz experimenteller Resultate, die nur als Gegenbeweise gegen die vorgeschlagene Struktur der schwachen Wechselwirkungen angesehen werden konnten. (shrink)