The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.
Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.
Metaphysics, Mathematics, and Meaning brings together Nathan Salmon's influential papers on topics in the metaphysics of existence, non-existence, and fiction; modality and its logic; strict identity, including personal identity; numbers and numerical quantifiers; the philosophical significance of Godel's Incompleteness theorems; and semantic content and designation. Including a previously unpublished essay and a helpful new introduction to orient the reader, the volume offers rich and varied sustenance for philosophers and logicians. "
The study aims at exposing Meinong's ideas that may be of interest to analytic philosophers. It contains all the basic information concerning Meinong's theory of objects with a special focus upon 'objectives', which are Meinong's propositions. Meinong's theory of meaning and his epistemological views are discussed in detail. An outline of his conception of truth, which is classified as firmly realistic, is followed by a review of the critical works touching upon Meinong's epistemological ideas. Finally, Meinong's theory of objects is presented as inspiring the development of Meinongian logics, with his Aussersein as the prototype of an all-inclusive semantic domain. The issues considered include reference of terms and sentences as well as the general features of a Meinongian-style semantics.
Gottlob Frege is one of the greatest logicians ever and also a philosopher of great significance. In this book Rosado Haddock offers a critical presentation of the main topics of Frege's philosophy, including, among others, his philosophy of arithmetic, his sense-referent distinction, his distinction between function and object, and his criticisms of formalism and psychologism. More than just an introduction to Frege's philosophy this book is also a highly critical and mature assessment of it as a whole in which the limitations, confusions and other weaknesses of Frege's thought are closely examined. The author is also a Husserlian scholar and this book contains valuable discussions of Husserl's neglected views and comparisons between the two great philosophers.
The Harvard Review of Philosophy has long been a forum for new thoughts in the field — this collection includes some of the most important essays from that publication. Exploring the unexpected ways that philosophy impacts our world, this book considers the discipline as an essential element in our understanding of science, economics, and logic. This fascinating read for both laypeople and those familiar with philosophical concepts delves deep into questions of human nature, intellectual thought, and the manner in which our world operates. Using several different approaches, including puzzles, essays, and songs, this book challenges our basic assumptions about how things work.
Edmund Husserl introduces the term «noema in Ideas I in order to explicate his theory of intentionality. Given the ambiguities in Husserl's own usage of the noema, it is no surprise that the term is the subject of conflicting interpretations by scholars. This book undertakes a critical assessment of two such interpretations: the gestalt psychological interpretation of Aron Gurwitsch and the linguistic philosophical interpretation of the Frege scholars, David Woodruff Smith and Ronald McIntyre. The author argues that the ambiguities in Ideas I can only be resolved by appeal to Husserl's other works, especially his newly published texts and research manuscripts.
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Logic, Symbolic and mathematical by Arthur N. Prior
The relationship between formal logic and general philosophy is discussed under headings such as A Re-examination of Our Tense-Logical Postulates, Modal Logic in the Style of Frege, and Intentional Logic and Indeterminism.