What is the self? And how does it relate to the body? In the second edition of Personal Identity, Harold Noonan presents the major historical theories of personal identity, particularly those of Locke, Leibniz, Butler, Reid and Hume. Noonan goes on to give a careful analysis of what the problem of personal identity is, and its place in the context of more general puzzles about identity. He then moves on to consider the main issues and arguments which are the (...) subject of current debate, including the work of Bernard Williams and Derek Parfit, and makes new and challenging interpretations of them. This new edition contains additional material assessing the biological approach which has become increasingly popular in recent years, and extends the treatment of indeterminate identity to take account of the epistemic view of vagueness. This book covers the problem of personal identity from its origin in Locke's work to the most recent debates in the philosophical literature, and will be invaluablereading for any student of the topic. (shrink)

In the first half of the first century BC the Academy of Athens broke up in disarray. From the wreckage of the semi-sceptical school there arose the new dogmatic philosophy of Antiochus, synthesized from Stoicism and Platonism, and the hardline Pyrrhonist scepticism of Aenesidemus. With his extensive knowledge of the ways in which Plato was read and invoked as an authority in late antiquity Dr Tarrant builds a most impressive reconstruction of Philo of Larissa's brand of Platonism and of its (...) arrival in Middle Platonism, particularly that of Plutarch, long after the Academy's institutional demise. Particularly valuable is his exploitation for this purpose of a text barely discussed since its publication 80 years ago - a commentary on Plato's Theaetetus whose unidentified author Dr Tarrant has cogently argued to be a follower of Philo. Among many other achievements, Dr Tarrant throws much light on the relation of Aenesideman scepticism to the Academy. (shrink)

Porphyry’s position in the ancient hermeneutic tradition should be considered separately from his place in the Platonic tradition. He shows considerable respect for allegorizing interpreters with links to Pythagoreanism, particularly Numenius and Cronius, prominent sources in On the Cave of the Nymphs. The language of Homer’s Cave passage is demonstrably distinctive, resembling the Shield passage in the Iliad, and such as to suggest an ecphrasis to early imperial readers. Ecphrasis in turn suggested deeper significance for the story. While largely content (...) to follow Numenian trends in interpreting Homer’s cave symbolically and in relation to multiple belief-systems, Porphyry shows occasionally signs of wanting to adhere more closely to Homeric evidence, resorting to symbolic interpretation mainly when no more straightforward truth is on offer. (shrink)

Every discipline has its foundational terms, those words that practitioners use to name what they study, or how they study, or why that study is valid. These terms often go unscrutinized when a discipline is up and running, but in the formative stages of a discipline and in periods of contention or crisis they often become subject to intensive criticism and attempts at redefinition. Challenging foundational terms is no simple task. Because they are foundational, they are difficult to do without, (...) even by those who would reject them. They are often used or assumed by those who question them, and after intensive questioning is done they often simply recur, even in their most unquestioned, naive form. The “foundational” nature of foundational terms, one begins to see, is not just a matter of a basic organizing concept or a description of some natural process, but of a term that is invested with aspirations of different sorts. The term also offers authorization to interpret, enacts a wish, suggests a cultural utopia, or puts in place a political program. The density of functions found in foundational terms guarantees that even the most questioned term will return. (shrink)

Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied lambda-calculus. (...) This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises. (shrink)

Most of the work produced by these scholars together and in collaboration with their students represent applications of their basic theory to a wide assortment ...

In this paper the existence or nonexistence of isomorphic mappings between graph models for the untyped lambda calculus is studied. It is shown that Engeler's D A is completely determined, up to isomorphism, by the cardinality of its `atom-set' A. A similar characterization is given for a collection of graph models of the Pω-type; from this some propositions regarding automorphisms are obtained. Also we give an indication of the complexity of the first-order theory of graph models by showing that the (...) second-order theory of first-order definable elements of a graph model is first-order expressable in the model. (shrink)

I survey the syntactic technique of tiering which can be used to restrict the power of a recursion scheme. I show how various results can be obtained entirely proof theoretically without the use of a model of computation.

Armed with a fresh analysis of Shakespeare's inherited resources for articulating anxieties rooted in philosophical doubt, Skulsky shows that in four plays—Hamlet, Measure for Measure, King Lear, and Othello—the drama of doubt in search of an exit gives its own kind of urgency to the more familiar Shakespearean drama of action and motive. From Skulsky's study, the four plays emerge as insidiously telling exercises in challenging our working faith in the objectivity of moral choice and the possibility of knowing other (...) minds. In particular, Skulsky notes that Shakespeare takes calculated risks with our personal interest in his heroes by assigning them disturbing convictions as well as contemptible actions. In one of the plays, such convictions end by looking just as threatening as they do at the outset. In the others, Shakespeare offers a special kind of affirmation and compassion—an affirmation designed to stand against the worst of pessimism, and a compassion that makes room for the worst of the damned. (shrink)