We carry out a systematic study of decidability for theories of real vector spaces, inner product spaces, and Hilbert spaces and of normed spaces, Banach spaces and metric spaces, all formalized using a 2-sorted first-order language. The theories for list turn out to be decidable while the theories for list are not even arithmetical: the theory of 2-dimensional Banach spaces, for example, has the same many-one degree as the set of truths of second-order arithmetic.We find that the purely universal and (...) purely existential fragments of the theory of normed spaces are decidable, as is the ∀∃ fragment of the theory of metric spaces. These results are sharp of their type: reductions of Hilbertʼs 10th problem show that the ∃∀ fragments for metric and normed spaces and the ∀∃ fragment for normed spaces are all undecidable. (shrink)

The philosophical papers comprising this volume range from process metaphysics and theology, through the phenomenological study of intentionality, to the foundations of geometry and of the system of real numbers. New light, it is thought, is shed on all these topics, some of them being of the highest interest and under intensive investigation in contemporary philosophical discussion. Metaphysi cians, process theologians, semanticists, theorists of knowledge, phenomenologists, and philosophers of mathematics will thus find in this book, it is hoped, helpful materials (...) and methods. The categoreal scheme of Whitehead's Process and Reality is discussed rather fully from a logical point of view in the first paper [I] in the light of the author's previous work on the logico-metaphysical theory of events. The clarification that results is thought to provide a new depth and precision to the problem of interpreting one of the most difficult books in the recent history of metaphysics and cosmol ogy. A detailed examination of some aspects of Hartshorne's recent Creative Synthesis and Philosophic Method is given in II. This book is perhaps the most significant work on process philosophy since Process and Reality itself, and its logical underpinnings thus merit a full critical discussion. (shrink)

We argue that thoughts are structures of concepts, and that concepts should be individuated by their origins, rather than in terms of their semantic or epistemic properties. Many features of cognition turn on the vehicles of content, thoughts, rather than on the nature of the contents they express. Originalism makes concepts available to explain, with no threat of circularity, puzzling cases concerning thought. In this paper, we mention Hesperus/Phosphorus puzzles, the Evans-Perry example of the ship seen through different windows, and (...) Mates cases, and we believe that there are many additional applications. (shrink)

Are fictional characters such as Sherlock Holmes real? What can fiction tell us about the nature of truth and reality? In this excellent introduction to the problem of fictionalism R. M. Sainsbury covers the following key topics: what is fiction? realism about fictional objects, including the arguments that fictional objects are real but non-existent; real but non-factual; real but non-concrete the relationship between fictional characters and non-actual worlds fictional entities as abstract artefacts fiction and intentionality and the problem of irrealism (...) fictionalism about possible worlds moral fictionalism. R. M. Sainsbury makes extensive use of examples from fiction, such as Sherlock Holmes, Anna Karenina and Madame Bovary and examines the work of philosophers who have made significant contributions to the topic, including Meinong, David Lewis, and Bas Van Fraassen. Additional features include chapter summaries, annotated further reading and a glossary of technical terms, making _Fiction and Fictionalism_ ideal for those coming to the issue for the first time. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

Scholars of Plato are divided between those who emphasize the literature of the dialogues and those who emphasize the argument of the dialogues, and between those who see a development in the thought of the dialogues and those who do not. In this important book Russell Dancy focuses on the arguments and defends a developmental picture. He explains the Theory of Forms of the Phaedo and Symposium as an outgrowth of the quest for definitions canvassed in the Socratic dialogues, by (...) constructing a Theory of Definition for the Socratic dialogues based on the refutations of definitions in those dialogues, and showing how that theory is mirrored in the Theory of Forms. His discussion, notable for both its clarity and its meticulous scholarship, ranges in detail over a number of Plato's early and middle dialogues, and will be of interest to readers in Plato studies and in ancient philosophy more generally. (shrink)

In the early part of the paper, I attempt to explain a dispute between two parties who endorse the compositionality of language but disagree about its implications: Paul Horwich, and Jerry Fodor and Ernest Lepore. In the remainder of the paper, I challenge the thesis on which they are agreed, that compositionality can be taken for granted. I suggest that it is not clear what compositionality involves nor whether it obtains. I consider some kinds of apparent counterexamples, and compositionalist responses (...) to them in terms of covert indexicality and unspecific meanings. I argue that the last option is the best for most of the cases I consider. I conclude by stressing, as against Horwich and Fodor and Lepore, that the appropriate question concerns the extent to which compositionality obtains in a natural language, rather than whether it obtains or not, so that the answer is essentially messy, requiring detailed consideration of a wide range of examples. (shrink)

This book is divided into three parts: in Part I, R. M. Hare offers a justification for the use of philosophy of language in the treatment of moral questions, together with an overview of his moral philosophy of ‘universal prescriptivism’. The second part, and the core of the book, consists of five chapters originally presented as a lecture series under the title ‘A Taxonomy of Ethical Theories’. Hare identifies descriptivism and non‐descriptivism as the two main positions in modern moral philosophy. (...) The former he divides into Naturalism and Intuitionism, and the latter into Emotivism and Rationalism. Hare argues that all forms of descriptivism tend to lead to Relativism because the truth conditions of moral statements are culturally variant. Of the positions discussed, only Hare's own position, a form of Rationalism, which he calls Universal Prescriptivism, meets all of the requirements that an adequate ethical theory should meet. Part III consists of Hare's previously published essay ‘Could Kant have been a Utilitarian?’ (Utilitas 5, 1993). Here, Hare puts forward the controversial thesis that Kant's moral philosophy is, in its basic principles, compatible with utilitarianism. (shrink)

The paper argues that intensional phenomena can be explained without appealing to "exotic" entities: one that don't exist, are merely possible, or are essentially abstract.

I had a strange dream, or half-waking vision, not long ago. I found myself at the top of a mountain in the mist, feeling very pleased with myself, not just for having climbed the mountain, but for having achieved my life's ambition, to find a way of answering moral questions rationally. But as I was preening myself on this achievement, the mist began to clear, and I saw that I was surrounded on the mountain top by the graves of all (...) those other philosophers, great and small, who had had the same ambition, and thought they had achieved it. And I have come to see, reflecting on my dream, that, ever since, the hard-working philosophical worms have been nibbling away at their systems and showing that the achievement was an illusion. True, their skeletons, indigestible to worms, remained, and were surprisingly similar to one another. But I was led to think again about what one can, and what one cannot, achieve in this direction. (shrink)

Politics and religion certainly ride together throughout the Dune saga. Rationales were given to support twentieth century dictator ships, whose citizens were encouraged to see their leaders as infallible. In this way, politics in a totalitarian state resembled a religion, with a community of faithful followers and its own special theology to justify the dictator's authority. This chapter, draws parallels between the religious dimensions of politics in Frank Herbert's Dune novels and some philosophers’ views on tyranny and justice here on (...) Earth. Even in democratic countries, leaders still tend to think of themselves as in service to some higher, impersonal standard, like a set of principles, a tradition, a flag, or a constitution. Plato's readers have sometimes described the relation between the higher plane of reality of universals and the world of everyday experience in terms of the relation between heaven and earth in the Abrahamic religions. (shrink)

Arrian's enthusiasm for Ptolemy's account of Alexander has often been echoed in modern times. With much justification it is generally agreed that Arrian's account of Alexander, through its reliance on the works of Ptolemy and Aristobulus, is our best and, on the whole, most reliable account of Alexander. Recent work, however, has illuminated Ptolemy's weaknesses, and we can no longer regard Ptolemy as utterly reliable in every important respect. His version of the Alexander story is centred on Alexander, therefore Alexander (...) is depicted out of the close context of the Macedonian court. It is only through the information preserved in other writers—traditionally, but undiscriminatingly, considered unreliable—that, for instance, the picture of Alexander's struggle with his Macedonian nobles has begun to emerge. And in matters of this kind Ptolemy's version is so much the court ‘official’ version that it cannot be regarded as trustworthy. (shrink)

Ugo Spirito (1896–1979) was a philosopher who changed his mind, repeatedly and sometimes radically, about many of his major commitments. At different times he called himself a fascist and a communi...