TAPP is a total applicative theory, conservative over intuitionistic arithmetic. In this paper, we first show that the same holds for TAPP+ the choice principle EAC; then we extend TAPP with choice sequences and study the principle EBIa0. The resulting theories are used to characterise the arithmetical fragment of EL +EBIa0. As a digression, we use TAPP to show that P. Martin-Löf's basic extensional theory ML0 is conservative over intuitionistic arithmetic.

After a discussion of the different treatments in the literature of vacuous descriptions, the notion of descriptor is slightly generalized to function descriptor Ⅎ $\overset \rightarrow \to{y}(x)$ , so as to form partial functions φ = Ⅎ $y(\overset \rightarrow \to{x}).A(\overset \rightarrow \to{x},y)$ which satisfy $\forall \overset \rightarrow \to{x}z(z=\phi \overset \rightarrow \to{x}\leftrightarrow \forall y(A(\overset \rightarrow \to{x},y)\leftrightarrow y=z))$ . We use (intuitionistic, classical or intermediate) logic with existence predicate, as introduced by D. S. Scott, to handle partial functions, and prove that adding (...) function descriptors to a theory based on such a logic is conservative. For theories with quantification over functions, the situation is different: there the addition of Ⅎ yields new theorems in the Ⅎ-free fragment, but an axiomatisation is easily given. The proofs are syntactical. (shrink)

The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in several areas of computer science. We give a short overview, and focus on the theory of software systems and modules. An algebra of theories TA is presented, with a nonstandard interpretation of the existential quantifier ∃. In TA, the interpolation property of the underlying logic corresponds with the quantifier combination property ∃Σ (...) ∃П S ≡ ∃(Σ ∪ П) S. It is shown how the Modularization Theorem, the Factorization Lemma and the Normal Form Theorem for module expressions can be proved in TA. (shrink)

This Companion provides a fresh and comprehensive account of this outstanding work, which remains among the most frequently read works of Greek philosophy, indeed of Classical antiquity in general. The sixteen essays, by authors who represent various academic disciplines, bring a spectrum of interpretive approaches to bear in order to aid the understanding of a wide-ranging audience, from first-time readers of the Republic who require guidance, to more experienced readers who wish to explore contemporary currents in the work’s interpretation. The (...) three initial chapters address aspects of the work as a whole. They are followed by essays that match closely the sequence in which topics are presented in the ten books of the Republic. Since the Republic returns frequently to the same topics by different routes, so do the authors of this volume, who provide the readers with divergent yet complementary perspectives by which to appreciate the Republic’s principal concerns. (shrink)

We show in this paper that all fragments of intuitionistic propostional logic based on a subset of the connectives $\wedge, \vee, \rightarrow, \neg$ satisfy interpolation. Fragments containing $\leftrightarrow$ or $\neg\neg$ are briefly considered.

Tracing a central theme of Plato's Republic , G. R. F. Ferrari reconsiders in this study the nature and purpose of the comparison between the structure of society and that of the individual soul. In four chapters, Ferrari examines the personalities and social status of the brothers Glaucon and Adeimantus, Plato's notion of justice, coherence in Plato's description of the decline of states, and the tyrant and the philosopher king—a pair who, in their different ways, break with the terms of (...) the city-soul analogy. In addition to acknowledging familiar themes in the interpretation of the Republic —the sincerity of its utopianism, the justice of the philosopher's return to the Cave—Ferrari provocatively engages secondary literature by Leo Strauss, Bernard Williams, and Jonathan Lear. With admirable clarity and insight, Ferrari conveys the relation between the city and the soul and the choice between tyranny and philosophy. City and Soul in Plato's Republic will be of value to students of classics, philosophy, and political theory alike. (shrink)

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.

Volume 2 covers one of the richest eras for the philosophical study of religion. Covering the period from the 6th century to the Renaissance, this volume shows how Christian, Islamic and Jewish thinkers explicated and defended their religious faith in light of the philosophical traditions they inherited from the ancient Greeks and Romans. The enterprise of 'faith seeking understanding', as it was dubbed by the medievals themselves, emerges as a vibrant encounter between - and a complex synthesis of - the (...) Platonic, Aristotelian and Hellenistic traditions of antiquity on the one hand, and the scholastic and monastic religious schools of the medieval West, on the other. (shrink)

We give a tensor formulation of synchronization transformations within special relativity in order to bridge the gap between some philosophical discussions (e.g., by Grünbaum and Winnie) and the analyses given by physicists (e.g., Møller). As an application, we discuss a physical interpretation of the duality between covariant and contravariant indices in the tensor formulation.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Steve Biko died in detention in South Africa in 1977. Critical ethical issues are raised both by the conduct of the doctors responsible for Biko's care and by the subsequent response of the medical profession as a whole. Because those issues are relevant to all healthcare professionals everywhere, the Biko affair provides a useful case study in medical ethics. We discuss the case in this article, describing how we use it in our teaching.

This full-length study of Plato's dialogue Phaedrus, now in paperback, is written in the belief that such concerted scrutiny of a single dialogue is an important part of the project of understanding Plato so far as possible 'from the inside' - of gaining a feel for the man's philosophy. The focus of this account is on how the resources both of persuasive myth and of formal argument, for all that Plato sets them in strong contrast, nevertheless complement and reinforce each (...) other in his philosophy. Not only is the dialogue in its formal structure a dovetail of myth and argument, but the philosophic life that it praises is also shaped by an acknowledgement of the limitations of argument and the importance of mythical understanding. By means of this correlation of form and content Plato invites his readers, through the very act of reading, to take a first step along the path of the philosophical life. (shrink)