The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas by the principal figures in the history of the subject - Frege, Russell, Ramsey and Carnap - and in doing so illuminate current concerns about the nature of mathematical and theoretical knowledge. Issues addressed include the nature of arithmetical knowledge in the light of Frege's theorem; the status of realism about the theoretical entities of physics; and the proper interpretation of empirical theories that postulate abstract structural constraints.

These essays apply the core conceptual innovation underlying Frege's theory of number to the general analysis of theoretical knowledge.

This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics--neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition--which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.

A renowned philosopherÕs final work, illuminating how the logical empiricist tradition has failed to appreciate the role of actual experiments in forming its philosophy of science. The logical empiricist treatment of physics dominated twentieth-century philosophy of science. But the logical empiricist tradition, for all it accomplished, does not do justice to the way in which empirical evidence functions in modern physics. In his final work, the late philosopher of science William Demopoulos contends that philosophers have failed to provide an adequate epistemology of science because they have failed to appreciate the tightly woven character of theory and evidence. As a consequence, theory comes apart from evidence. This trouble is nowhere more evident than in theorizing about particle and quantum physics. Arguing that we must consider actual experiments as they have unfolded across history, Demopoulos provides a new epistemology of theories and evidence, albeit one that stands on the shoulders of giants. On Theories finds clarity in Isaac NewtonÕs suspicion of mere Òhypotheses.Ó NewtonÕs methodology lies in the background of Jean PerrinÕs experimental investigations of molecular reality and of the subatomic investigations of J. J. Thomson and Robert Millikan. Demopoulos extends this account to offer novel insights into the distinctive nature of quantum reality, where a logico-mathematical reconstruction of Bohrian complementarity meets John Stewart BellÕs empirical analysis of EinsteinÕs Òlocal realism.Ó On Theories ultimately provides a new interpretation of quantum probabilities as themselves objectively representing empirical reality.

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter

A diverse group of contributors reflect on the philosophical legacy of Fred Sommers and his efforts to revive and refashion traditional Aristotelian logic for a post-Fregean world.

Logic as Universal Science offers a detailed reconstruction of the underlying philosophy in The Principles of Mathematics showing how Russell sought to deliver a death blow to the dominant Kantian view that formal logic is a concise and dry science and unable to enlarge our understanding.