Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

ABSTRACT: Rudolf Carnap’s “Empiricism, Semantics and Ontology” (ESO) has received a good deal of sympathetic interest over the years from philosophers who are not particularly sympathetic to verificationism, or suspicious of metaphysics in general. Recent work has favorably cited ESO in connection with doubts about the genuine content of debates in the metaphysics of material objects. But, when we look at how Carnap introduces his central notion of a ‘framework’, and the questions he wants to use it to deflate, there (...) seem to be significant differences in his approach and aim from that of contemporary deflationists about the metaphysics of material objects. This paper first looks at some of these differences, and suggests a way of seeing them as arising more from differences in focus and interest than fundamental approach. However, a further question is whether philosophers who may entirely disagree with Carnap about abstract entities, or the substantiveness of the debate between Realists and Idealists – possibly all of his negative conclusions in ESO - can really be seen as heirs to his approach and argument therein. We look first at his discussion of the Realism/Idealism debate, to sort out different aspects of his analysis, and determine to what extent one can disagree with it while not thinking this undermines other analyses using the same general strategy. In the course of this, we are able to distinguish the basic Carnapian analysis of metaphysical disputes, from the question of whether, if the analysis is correct, this actually subverts the disputes. I suggest that, if we put verificationism aside, ESO really provides us with an approach and a type of skeptical challenge more than an argument, and it is open to contemporary philosophers to think that this skeptical challenge can (or can’t) be met, or can be supplemented by further argument, on a case by case basis. (shrink)

Rudolf Carnap is widely regarded as one of the most important philosophers of the twentieth century. Born in Germany and later a US citizen, he was a founder of the philosophical movement known as Logical Empiricism. He was strongly influenced by a number of different philosophical traditions, and also by the German Youth Movement, the First World War, and radical socialism. This book places his central ideas in a broad cultural, political and intellectual context, showing how he synthesised many different (...) currents of thought to achieve a philosophical perspective that remains strikingly relevant in the twenty-first century. Its rich account of a philosopher's response to his times will appeal to all who are interested in the development of philosophy in the twentieth century. (shrink)

During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap’s notes cover a wide range of topics, but surprisingly, the (...) most prominent question is: If the number of physical items in the universe is finite, what form should scientific discourse take? This question is closely connected to an abiding philosophical problem: What is the relationship between the logico-mathematical realm and the material realm? Carnap, Tarski, and Quine’s attempts to answer this question involve issues central to philosophy today.This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine’s break from Carnap), and relates them when possible to contemporary treatments of these issues. (shrink)

This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

Metaontology – the study of the nature of ontological issues – has flourished in recent years. The focus of this summary will be on some views and arguments that are central to today’s debate. One theme will be that of how seriously to take ontology: whether there is reason to take a skeptical or deflationary attitude toward ontological claims, as theorists like Rudolf Carnap, Hilary Putnam, and Eli Hirsch in different ways have urged. The other theme will be that of (...) the viability of the Fregean and Quinean approaches to ontology that have been and still are central to analytic philosophy. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

My focus here will be Rudolf Carnap’s views on ontology, as these are presented in the seminal “Empiricism, Semantics and Ontology” (1950). I will first describe how I think Carnap’s distinction between external and internal questions is best understood. Then I will turn to broader issues regarding Carnap’s views on ontology. With certain reservations, I will ascribe to Carnap an ontological pluralist position roughly similar to the positions of Eli Hirsch and the later Hilary Putnam. Then I turn to some (...) interrelated arguments against the pluralist view. The arguments are not demonstrative. Some possible escape routes for the pluralist are outlined. But I think the arguments constitute a formidable challenge. There should be serious doubt as to whether the pluralist view, as it emerges after discussion of these arguments, will be worth defending. Moreover, there is an alternative ontological view which equally well subserves the motivations underlying ontological pluralism. (shrink)

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.... The chief virtue of the book is its systematic character. From Frege to Quine most philosophical logicians have restricted themselves by piecemeal and local assaults on the problems involved. The book is marked by a genial tolerance. Carnap sees himself as proposing conventions rather than asserting truths. However he provides plenty of matter (...) for argument."-Anthony Quinton, Hibbert Journal. (shrink)

Frege begins Die Grundlagen der Arithmetik, the work that introduces the project which was to occupy him for most of his professional career, with the question, 'What is the number one?' It is a question to which even mathematicians, he says, have no satisfactory answer. And given this scandalous situation, he adds, there is small hope that we shall be able to say what number is. Frege intends to rectify the situation by providing definitions of the number one and the (...) concept of number. But what, exactly, is required of a definition? Surely it will not do to stipulate that the number one is Julius Caesar - that would change the subject. It seems reasonable to suppose that an acceptable definition must be a true statement containing a description that picks out the object to which the numeral '1' already refers. And, similarly, that an acceptable definition of the concept of number must contain a description that picks out precisely those objects that are numbers - those objects to which our numerals refer. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of '1' and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of ‘1’ and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. There is, as we shall see shortly, a great deal of evidence that Frege’s definitions are not intended to pick out objects to which our numerals already refer. But if this is so, how can these definitions teach us anything about our science of arithmetic? And what criteria must these definitions satisfy? To answer these questions, we need to understand what it is that Frege thinks we need to learn about the science of arithmetic. (shrink)

Rudolf Carnap's 1930s philosophy of logic, including his adherence to the principle of tolerance, is discussed. What theses did Carnap commit himself to, exactly? I argue that while Carnap did commit himself to a certain multitude thesis—there are different logics of different languages, and the choice between these languages is merely a matter of expediency—there is no evidence that he rejected a language-transcendent notion of fact, contrary to what Warren Goldfarb and Thomas Ricketts have prominently argued. (In fact, it is (...) obscure just what Goldfarb and Ricketts claim about Carnap). Toward the end I critically discuss Michael Friedman's suggestion that Carnap believed in a relative a priori. (shrink)

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. Stewart Shapiro explores various such views. He argues that the question of meaning shift is itself context-sensitive and interest-relative.

Carnap's ideal of explication has become a key concept in analytic philosophy and the basis of a method of analysis which may be considered as an alternative to various forms of naturalism, including Quine's conception of a naturalized epistemology. More recently, new light has been shed on this aspect of the classical Carnap-Quine debate by contemporary philosophers. Whereas Michael Friedman articulated a notion of relativized a priori which owes much to Carnap's internal/external distinction, André Carus attempted to restate Carnap's ideal (...) of explication in a way that bridges the gap between conceptual engineering and naturalism. On the other hand, Mark Wilson argued that concepts develop in unpredictable ways and cannot be planned in the way classical analytic philosophy has assumed from Frege and Russell onwards. This book consists of a series of defences as well as critiques of Carnap's programme, setting it in its historical context, discussing specific cases of explications, and enriching the on-going debate on conceptual engineering and naturalism in analytic philosophy.Carnap's ideal of explication has become a key concept in analytic philosophy and the basis of a method of analysis which may be considered as an alternative to various forms of naturalism, including Quine's conception of a naturalized epistemology. More recently, new light has been shed on this aspect of the classical Carnap-Quine debate by contemporary philosophers. Whereas Michael Friedman articulated a notion of relativized a priori which owes much to Carnap's internal/external distinction, André Carus attempted to restate Carnap's ideal of explication in a way that bridges the gap between conceptual engineering and naturalism. On the other hand, Mark Wilson argued that concepts develop in unpredictable ways and cannot be planned in the way classical analytic philosophy has assumed from Frege and Russell onwards. This book consists of a series of defences as well as critiques of Carnap's programme, setting it in its historical context, discussing specific cases of explications, and enriching the on-going debate on conceptual engineering and naturalism in analytic philosophy. (shrink)

Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...

To appear in David Chalmers, Ryan Wasserman and David Manley, eds., Metametaphysics (OUP, 2009).

Philosophers have ever declared that their problems lie at a different level from the problems of the empirical sciences. Perhaps one may agree with this assertion; the question is, however, where should one seek this level. The metaphysicians wish to seek their object behind the objects of empirical science; they wish to enquire after the essence, the ultimate cause of things. But the logical analysis of the pretended propositions of metaphysics has shown that they are not propositions at all, but (...) empty word arrays, which on account of notional and emotional connections arouse the false appearance of being propositions. This conception that the “propositions” of metaphysics, including those of ethics, have no theoretical content, is to be sure still disputed. We shall not, however, enter here on its demonstration, but, under its guidance, will limit ourselves to non-metaphysical and non-ethical philosophical problems. (shrink)

A distinction often drawn is one between conservative versus revisionary conceptions of philosophical analysis with respect to commonsensical beliefs and intuitions. This paper offers a comparative investigation of two revisionary methods: Carnapian explication and ameliorative analysis as developed by S. Haslanger. It is argued that they have a number of common features, and in particular that they share a crucial political dimension: they both have the potential to serve as instrument for social reform. Indeed, they may produce improved versions of (...) key concepts of everyday life, for example those pertaining to social categories such as gender and race, which in turn may lead to social change. The systematic comparison of these two frameworks offered here, where similarities as well as differences are discussed, is likely to provide useful guidance to practitioners of both approaches, as it will highlight important aspects of each of them that tend to remain implicit and under-theorized in existing applications of these methodologies to specific questions. (shrink)

Carnap and Goodman developed methods of conceptual re-engineering known respectively as explication and reflective equilibrium. These methods aim at advancing theories by developing concepts that are simultaneously guided by pre-existing concepts and intended to replace these concepts. This paper shows that Carnap’s and Goodman’s methods are historically closely related, analyses their structural interconnections, and argues that there is great systematic potential in interpreting them as aspects of one method, which ultimately must be conceived as a component of theory development. The (...) main results are: an adequate method of conceptual re-engineering must focus not on individual concepts but on systems of concepts and theories; the linear structure of Carnapian explication must be replaced by a process of mutual adjustments as described by Goodman; Carnap’s condition of similarity can be analysed into two components, one securing a relation to the specific extensions of the pre-existing concepts, one regulating the transition to the new system of concepts; these two criteria of adequacy can be built into Goodman’s account of reflective equilibrium to ensure that the resulting concepts promote theoretical virtues while being sufficiently similar to the concepts we started out with. (shrink)

It is not the aim of the present essay to defend the principle of empiricism against apriorism or anti-empiricist metaphysics. Taking empirism for granted, we wish to discuss, the question what is meaningful. The word ‘meaning’ will here be taken in its empiricist sense; an expression of language has meaning in this sense if we know how to use it in speaking about empirical facts, either actual or possible ones. Now our problem is what expressions are meaningful in this sense. (...) We may restrict this question to sentences because expressions other than sentences are meaningful if and only if they can occur in a meaningful sentence. (shrink)

Rudolf Carnap and W. V. Quine, two of the twentieth century's most important philosophers, corresponded at length—and over a long period of time—on matters personal, professional, and philosophical. Their friendship encompassed issues and disagreements that go to the heart of contemporary philosophic discussions. Carnap was a founder and leader of the logical positivist school. The younger Quine began as his staunch admirer but diverged from him increasingly over questions in the analysis of meaning and the justification of belief. That they (...) remained close, relishing their differences through years of correspondence, shows their stature both as thinkers and as friends. The letters are presented here, in full, for the first time. The substantial introduction by Richard Creath offers a lively overview of Carnap's and Quine's careers and backgrounds, allowing the nonspecialist to see their writings in historical and intellectual perspective. Creath also provides a judicious analysis of the philosophical divide between them, showing how deep the issues cut into the discipline, and how to a large extent they remain unresolved. (shrink)

The first complete English translation of a groundbreaking work. An ambitious account of the relation of mathematics to logic. Includes a foreword by Crispin Wright, translators' Introduction, and an appendix on Frege's logic by Roy T. Cook. The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was (...) to be the pinnacle of Freges lifes work. It represents the final stage of his logicist project the idea that arithmetic and analysis are reducible to logic and contains his mature philosophy of mathematics and logic. The aim of Basic Laws of Arithmetic is to demonstrate the logical nature of mathematical theorems by providing gapless proofs in Frege's formal system using only basic laws of logic, logical inference, and explicit definitions. The work contains a philosophical foreword, an introduction to Frege's logic, a derivation of arithmetic from this logic, a critique of contemporary approaches to the real numbers, and the beginnings of a logicist treatment of real analysis. As is well-known, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that his basic law V, governing the identity of value-ranges, leads into inconsistency. Frege discusses a revision to basic law V written in response to Russells letter in an afterword to volume II. The continuing importance of Basic Laws of Arithmetic lies not only in its bearing on issues in the foundations of mathematics and logic but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. Philip Ebert and Marcus Rossberg present the first full English translation of both volumes of Freges major work preserving the original formalism and pagination. The edition contains a foreword by Crispin Wright and an extensive appendix providing an introduction to Frege's formal system by Roy T. Cook. Readership: Scholars and advanced students in philosophy of logic, philosophy of mathematics, and early analytic philosophy. (shrink)