We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative Linear Logic (...) , we associate a vector space of“diadditive” uniform transformations. We then show that this space is generated by denotations of cut-free proofs of the sequent in the theory MLL + MIX. Thus we obtain a full completeness theorem in the sense of Abramsky and Jagadeesan, although our result differs from theirs in the use of dinatural transformations.As corollaries, we show that these dinatural transformations compose, and obtain a conservativity result: diadditive dinatural transformations which are uniform with respect to actions of the additive group of integers are also uniform with respect to the actions of arbitrary cocommutative Hopf algebras. Finally, we discuss several possible extensions of this work to noncommutative logic.It is well known that the intuitionistic version of Läuchli's semantics is a special case of the theory of logical relations, due to Plotkin and Statman. Thus, our work can also be viewed as a first step towards developing a theory of logical relations for linear logic and concurrency. (shrink)

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs in (...) CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

- How can anthropology improve our understanding of the interrelationship between nature and culture? - What can anthropology contribute to practical debates which depend on particular definitions of nature, such as that concerning sustainable development? Humankind has evolved over several million years by living in and utilizing 'nature' and by assimilating it into 'culture'. Indeed, the technological and cultural advancement of the species has been widely acknowledged to rest upon human domination and control of nature. Yet, by the 1960s, the (...) idea of culture in confrontation with nature was being challenged by science, philosophy and the environmental movement. Anthropology is increasingly concerned with such issues as they become more urgent for humankind as a whole. This important book reviews the current state of the concepts of 'nature' we use, both as scientific devices and ideological constructs, and is organised around three themes: - nature as a cultural construction; - the cultural management of the environment; and - relations between plants, animals and humans. (shrink)

It has come to be expected that collections issued by the Royal Institute of Philosophy will contain work that has quality or is otherwise interesting. This volume runs true to form and presents plenty of both. It gives the proceedings of the conference arranged by the Institute at Exeter in 1973, consisting of five symposia together with Chairman's remarks of about eight pages or so for each symposium, and in three cases postscripts by the first speaker. The contributors and topics (...) are: R. F. Dearden and Elizabeth Telfer on ‘Autonomy as an Educational Ideal’ with R. M. Hare as Chairman; R. K. Elliott and Glenn Langford on ‘Education and the Development of the Understanding’ with Paul Hirst as Chairman; David Cooper and Timothy O'Hagan on ‘Quality and Equality in Education’ with R. F. Atkinson as Chairman; Mary Warnock and Richard Norman on ‘The Neutral Teacher’ with Alan Montefiore as Chairman; Stuart Brown and A. Phillips Griffiths on ‘Academic Freedom’ with R. S. Peters as Chairman. (shrink)

L'auteur commence par signaler quelques problèmes concernant la reconstruction historique et l'appréciation toujours changeante du Siècle des Lumières. Ensuite il fait à l'occasion quelques remarques sur Rousseau et Voltaire en tant que caractères ou personnes. Le but essentiel de cette intervention est de démontrer à l'aide de quelques thèmes (Dieu et la religion institutionalisée ; l'univers et la place qu'y trouve l'Homme ; le problème du mal) que leurs idées en ces domaines concordent pour le moins globalement bien plus que (...) ne le laissent supposer leurs rapports polémico-personnels. Il est expliqué combien il est erroné de représenter le Siècle des Lumières comme une époque où régnait un optimisme sans nuances et de foi aveugle dans le progrès de l'Homme et d'oublier qu'une anthropologie mitigée constitue le fondement des idées tant de Rousseau que de Voltaire. Afin d'éloigner l'idée selon laquelle les deux philosophes constitueraient en quelque sorte une unité intellectuelle double, quelques points essentiels (politique, culture) sur lesquels les opinions des deux protagonistes s'opposent, sont eux aussi mis en lumière. (shrink)

Reading the Republic without reference to the less familiar Laws can lead to a distorted view of Plato's political theory. In the Republic the philosopher describes his ideal city; in his last and longest work he deals with the more detailed considerations involved in setting up a second-best 'practical utopia.' The relative neglect of the Laws has stemmed largely from the obscurity of its style and the apparent chaos of its organization so that, although good translations now exist, students of (...) philosophy and political science still find the text inaccessible. This first full-length philosophical introduction to the Laws will therefore prove invaluable. The opening chapters describe the general character of the dialogue and set it in the context of Plato's political philosophy as a whole. Each of the remaining chapters deals with a single topic, ranging over material scattered through the text and so drawing together the threads of the argument in a stimulating and readily comprehensible way. Those topics include education, punishment, responsibility, religion, virtue and pleasure as well as political matters and law itself. Throughout, the author encourages the reader to think critically about Plato's ideas and to see their relevance to present-day philosophical debate. No knowledge of Greek is required and only a limited background in philosophy. Although aimed primarily at students, the book will also be of interest to more advanced readers since it provides for the first time a philosophical, as opposed to linguistic or historical, commentary on the Laws in English. (shrink)

Overdenkingen in proza en poëzie over filosofische vraagstukken door de in ongenade gevallen Romeinse ex-consul (480-524).

It hardly needs to be said that the parallel between mental and physical health plays an important part in Plato's moral philosophy. One of the central claims of the Republicis that justice is to the soul what health is to the body .1 Similar points are made in other dialogues.2 This analogy between health and sickness on the one hand and virtue and vice on the other is closely connected to the so–called Socratic paradoxes. Throughout his life Plato seems to (...) have clung in some sense to the ideas that justice is our greatest good, that the unjust man is correspondingly miserable and that no one is therefore willingly unjust. It follows from these ideas that the unjust man, like the sick man, is in a wretched state which is not of his own choosing. (shrink)

Jung was intrigued from early in his career with coincidences, especially those surprising juxtapositions that scientific rationality could not adequately explain. He discussed these ideas with Albert Einstein before World War I, but first used the term "synchronicity" in a 1930 lecture, in reference to the unusual psychological insights generated from consulting the I Ching. A long correspondence and friendship with the Nobel Prize-winning physicist Wolfgang Pauli stimulated a final, mature statement of Jung's thinking on synchronicity, originally published in 1952 (...) and reproduced here. Together with a wealth of historical and contemporary material, this essay describes an astrological experiment Jung conducted to test his theory. Synchronicity reveals the full extent of Jung's research into a wide range of psychic phenomena. This paperback edition of Jung's classic work includes a new foreword by Sonu Shamdasani, Philemon Professor of Jung History at University College London. (shrink)