This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

This major publication is a history of the semantic tradition in philosophy from the early nineteenth century through its incarnation in the work of the Vienna Circle, the group of logical positivists that emerged in the years 1925–1935 in Vienna who were characterised by a strong commitment to empiricism, a high regard for science, and a conviction that modern logic is the primary tool of analytic philosophy. In the first part of the book, Alberto Coffa traces the roots of logical (...) positivism in a semantic tradition that arose in opposition to Kant's theory that a priori knowledge is based on pure intuition and the constitutive powers of the mind. In Part II, Coffa chronicles the development of this tradition by members and associates of the Vienna Circle. Much of Coffa's analysis draws on the unpublished notes and correspondence of many philosophers. The book, however, is not merely a history of the semantic tradition from Kant 'to the Vienna Station'. Coffa also critically reassesses the role of semantic notions in understanding the ground of a priori knowledge and its relation to empirical knowledge and questions the turn the tradition has taken since Vienna. (shrink)

In this collection of essays one of the preeminent philosophers of science writing offers a reinterpretation of the enduring significance of logical positivism, the revolutionary philosophical movement centered around the Vienna Circle in the 1920s and 30s. Michael Friedman argues that the logical positivists were radicals not by presenting a new version of empiricism but rather by offering a new conception of a priori knowledge and its role in empirical knowledge. This collection will be mandatory reading for any philosopher or (...) historian of science interested in the history of logical positivism in particular or the evolution of modern philosophy in general. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to (...) society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.

The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...) inference specific to a given local topic. Poincaré, a Kantian, disagreed with this. Indeed, he believed that the use of non-logical reasoning was essential to genuinely mathematical reasoning (proof). In this essay, I try to isolate and clarify this idea and to describe the mathematical epistemology which underlies it. Central to this epistemology (which is basically Kantian in orientation, and closely similar to that advocated by Brouwer) is a principle of epistemic conservation which says that knowledge of a given type cannot be extended by means of an inference unless that inference itself constitutes knowledge belonging to the given type. (shrink)

The book examines how Darwinism has been used to explain novelty and change in culture through the Darwinian approach to creativity and the theory of memes. The first claims that creativity is based on a Darwinian process of blind variation and selection, while the latter claims that culture is based on and explained by units - memes - that are similar to genes. Both theories try to describe and explain mind and culture by applying Darwinism by way of analogies. Kronfeldner (...) shows that the analogies involved in these theories lead to claims that give either wrong or at least no new descriptions or explanations of the phenomena at issue. Whereas the two approaches are usually defended or criticized on the basis that they are dangerous for our vision of ourselves, this book takes a different perspective: it questions the acuteness of these approaches. Darwinian theory is not like a dangerous wolf, hunting for our self image. Far from it, in the case of the two analogical applications addressed in this book, Darwinian theory is shown to behave more like a disoriented sheep in wolf's clothing. - A revised and much shortened version of a dissertation (2007, Darwinism, Memes and Creativity: A Critique of Analogical Reasoning from Nature to Culture). (shrink)

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

Arthur I. Miller is a historian of science whose approach has been strongly influenced by current work in cognitive science, and in this book he shows how the two fields might be fruitfully linked to yield new insights into the creative process.

This paper is divided into two parts. Part I provides a resumé of the evolution of the notion of predicativity. Part II describes our own work on the subject.Part I§1. Conceptions of sets.Statements about sets lie at the heart of most modern attempts to systematize all (or, at least, all known) mathematics. Technical and philosophical discussions concerning such systematizations and the underlying conceptions have thus occupied a considerable portion of the literature on the foundations of mathematics.

There is no substantive agreement about the philosophical views of analytic philosophers. Nevertheless, for much of them logical analysis is widely recognized to be important. It is true that Poincare used no logical analysis but refused nevertheless the old metaphysics. Indeed, the analytic tradition of philosophy of science is perhaps better characterized by several overlapping similarities, which are the clincher for my main thesis: Analytic philosophy of science has one of its origins in the philosophical network in France around 1900 (...) and, especially, in Poincare. (shrink)

Simonton examines the idea of the genius through his own theory called chance-configuration theory.

Geometry and Chronometry in Philosophical Perspective was first published in 1968. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. In this volume Professor Grünbaum substantially extends and comments upon his essay "Geometry, Chronometry, and Empiricism," which was first published in Volume III of the Minnesota Studies in the Philosophy of Science. Commenting on the essay when it first appeared J. J. C. Smart wrote (...) in Mind (England): "In my opinion Adolf Grünbaum's paper ... supersedes nearly all that has been written on the logical status of physical geometry and chronometry." The full text of the essay is given here with the author's extension of it and his discussion of some of the critical comment it has evoked, particularly, a critique published by Hilary Putnam. Adolph Grünbaum is Andrew Mellon Professor of Philosophy at the University of Pittsburgh and the current president of the Philosophy of Science Association. (shrink)

A brief historical comment on scientific knowledge as Socratic ignorance -- Some critical comments on the text of this book, particularly on the theory of truth Exposition [1933] -- Problem of Induction (Experience and Hypothesis) -- Two Fundamental Problems of the Theory of Knowledge -- Formulation of the Problem -- The problem of induction and the problem of demarcation -- Deductivtsm and Inductivism -- Comments on how the solutions are reached and preliminary presentation of the solutions -- Rationalism and empiricism-deductivism (...) and inductivism -- The possibility of a deductivist psychology of knowledge -- The Problem of Induction -- The infinite regression (Hume's argument) --The inductivist positions -- The Normal-Statement Positions -- The normal-statement positions: naive inductivism, strict positivism and apriorism -- Critique of strict positivism - twofold transcendence of natural laws -- The transcendental method - presentation of apriorism -- Critique of apriorism -- Kant and Fries -- Supplement to the critique of apriorism. (Psychologism and transcendentalism in Kant and Fries.-On the question of the empirical basis.) -- Probability Positions -- The probability positions - subjective belief in probability -- Statements about the objective probability of events -- Probability as an objective degree of validity of universal empirical statements -- One way of more closely defining the concept of the probability of a hypothesis (primary and secondary probability of hypotheses). The concept of simplicity -- The concept of the corroboration of a hypothesis - positivist, pragmatist and probabilistic interpretations of the concept of corroboration -- The infinite regression of probability statements -- Pseudo-Statement Positions -- The pseudo-statement positions: new formulation of the problem -- Natural laws as "instructions for the formation of statements" -- "True - false" or "useful - useless"? Consistent pragmatism --Difficulties of consistent pragmatism -- Tool and schema as purely pragmatic constructs -- Natural laws as propositional functions -- Conventionalism -- The pseudo-statement positions will temporarily be put away: conventionalism -- The three interpretations of axiomatic systems. (The circle of problems surrounding conventionalism) -- Conventionalist implicit and explicit definitions Propositional function and propositional equation -- Conventionalist propositional equations as tautological general implications -- Can axiomatic-deductive systems also be understood as consequence classes of pure propositional functions (of pseudo-statements)? -- The coordinative definitions of empiricism: synthetic general implications -- Conventionalist and empiricist interpretations, illustrated by the example of applied geometry -- Strictly Universal Statements and Singular Statements -- Implication and general implication -- General implication and the distinction between strictly universal and singular statements -- Universal concept and individual concept-class and element -- Strictly universal statements-the problem of induction and the problem of universals -- Comments on the problem of universals -- Back to the Pseudo-Statement Positions -- Return to the discussion of the pseudo-statement positions -- Symmetry or asymmetry in the evaluation of natural laws? -- The negative evaluation of universal statements. Critique of the strictly symmetrical interpretation of pseudo-statements -- An infinite regression of pseudo-statements -- An apriorist pseudo-statement position -- Interpretation of the critique up to this point; comments on the unity of theory and practice -- A last chance for the pseudo-statement positions -- Pseudo-Statement Positions and the Concept of Meaning -- The concept of meaning and logical positivism -- The concept of meaning and the demarcation problem-the fundamental thesis of inductivism -- Critique of the inductivist dogma of meaning -- Fully decidable and partially decidable empirical statements-the antinomy of the knowability of the world. (Conclusion of the critique of the pseudo-statement positions.) -- The dialectical and the transcendental corroboration of the solution -- Is the problem of induction solved? (shrink)

Quelle conception de la science proposer aujourd'hui? Les grandes doctrines du XXe siècle se sont heurtées successivement à des difficultés, que ce soit le positivisme du Cercle de Vienne ou le rationalisme critique de Popper. Même la perspective historique inspirée par Bachelard et par Kuhn a donné lieu à des versions disparates. Pourtant, toutes ces tentatives partent d'un même constat : l'échec de la vision classique de la science et la nécessité d'un nouveau discours. On peut en retracer l'histoire. Face (...) à la pluralité des hypothèses possibles au sujet de l'espace, du temps et de la matière, Poincaré pose l'existence de conventions, ou mieux de libres décisions, au cœur de la science. Ainsi, dès la fin du XIXe siècle, il coupe court aux projets traditionnels de fondation : ni le synthétique a priori de Kant, ni les faits généraux de Comte ne sauraient expliquer la nature de l'activité scientifique. C'est la naissance d'un mouvement d'idées, le conventionnalisme, quia eu un impact décisif sur la philosophie viennoise et, à travers elle, sur la philosophie mondiale. Voilà un fil conducteur pour évaluer un siècle de débats. Que signifie donc libre décision en matière scientifique? On affirme la dimension historique irréductible de notre savoir ; on reconnaît la créativité et la responsabilité inhérentes à la science en tant qu'aventure humaine. (shrink)

Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...) this manner, intuition serves the epistemological function of warranting generalizations and justifying practices. In particular, it justifies the application of group-theoretic notions in geometry but not the use of set-theoretic notions in arithmetic. (shrink)

in die operative Logik und Mathematik Zweite Auflage Springer-Verlag Berlin Heidelberg New York 1969 Paul Lorenzen o. Prof. der Philosophie an der Universitat Erlangen Geschaftsfilhrende Herausgeber: Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich Prof. Dr. B. L. van cler Waerclen Mathematisches Institut der Universitat ZUrich ISBN 978-3-642-86519-0 ISBN 978-3-642-86518-3 (eBook) DOl 10.1007/978-3-642-86518-3 Aile Rechte vorbehalten. Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden © by Springer-Verlag Berlin· Heidelberg 1955 und 1969 (...) Softcover reprint of the hardcover 2nd edition 1969 Library of Congress Catalog Card Number 73-76724 Titel-Nr. 5061 Vorwort zur zweiten Auflage. Fiir die Neuauflage ist der Text nur unwesentlich geandert worden. Es ist - neben der Korrektur einiger Ungenauigkeiten - vor allem die Terminologie und Symbolik an meine spateren Arbeiten angeglichen. Obwohl ich - verstandlicherweise - jetzt die Ansatze der spateren Arbeiten fiir "sachgemaBer" halte, z. B. eine Logik der Dialoge statt einer Logik der Kalkiile, die Verwendung indefiniter Quantoren statt einer expliziten Konstruktion von Sprachschichten, enthalt diese Neu­ auflage den Inhalt der 1. Auflage unverandert. Der Leser kann also einen Vergleich mit meinen spateren Arbeiten (vgl. Literaturverzeichnis) seIber durchfiihren. Mein Dank gilt wiederum dem Verlag fiir seine entgegenkommende Mitarbeit bei der Vorbereitung dieser Neuauflage. Erlangen, den 1. November I968. PAUL LORENZEN. Vorwort zur ersten Auflage. (shrink)

XIV The stability of a philosophical construction will depend not only upon the solidity of the blocks, of the pillars and architraves that make it up, but also upon the way in which all these parts are connected. Of course, it will not be possible to argue for every single part of a philosophical building: to do so would mean to embark in a virtually endless enterprise. Accordingly, some of the parts of a philosophical building will have to be taken (...) from the literature on the subject as 'ready made' or 'semi-finished' elements, while others will be argued for in the course of building. This is what happened in my work too. In some cases (for in stance, in the case of epistemic relativism), my concern was to illustrate theses which I believed to be sufficiently consolidated, rather than to ar gue for them. In other cases - where I was directly engaged in building the theory that I want to fonnulate - I did exactly the opposite. This is what I have tried to achieve, for example, for those proper architraves of my construction, viz. the connection between scepticism and metaphysi cal realism. and the thesis of the nonnative value of the fundamental epistemological notions (truth, objectivity, and rationality). (shrink)

The cultures here in question are those of mathematics and of physics that I shall interpret with the goal of exploring different modes of creativity. As case studies I will consider two scientists who were exemplars of these cultures, the mathematician Henri Poincaré (1854-1912) and the physicist Albert Einstein (1879-1955). The modes of creativity that I will compare and contrast are their notions of aesthetics and intuition. In order to accomplish this we begin by studying their introspections.

In a definition (∀ x )(( x є r )↔D[ x ]) of the set r, the definiens D[ x ] must not depend on the definiendum r . This implies that all quantifiers in D[ x ] are independent of r and of (∀ x ). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious Circle Principle (...) was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if ( b є a ) or ( b ⊆ a ). Likewise, the truth of an ordinary first-order sentence with the Gödel number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r. (shrink)