We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single (...) predicate. (shrink)

The purpose of this paper is to make a simple observation regarding the Johnson -Carnap continuum of inductive methods. From the outset, a common criticism of this continuum was its failure to permit the confirmation of universal generalizations: that is, if an event has unfailingly occurred in the past, the failure of the continuum to give some weight to the possibility that the event will continue to occur without fail in the future. The Johnson -Carnap continuum (...) is the mathematical consequence of an axiom termed Johnson 's sufficientness postulate, the thesis of this paper is that, properly viewed, the failure of the Johnson -Carnap continuum to confirm universal generalizations is not a deep fact, but rather an immediate consequence of the sufficientness postulate; and that if this postulate is modified in the minimal manner necessary to eliminate such an entailment, then the result is a new continuum that differs from the old one in precisely one respect: it enjoys the desideratum of confirming universal generalizations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Carnap’s Construction of the World. The Aufbau and the Emergence of Logical Empiricism by Alan W. RichardsonRolf GeorgeAlan W. Richardson. Carnap’s Construction of the World. The Aufbau and the Emergence of Logical Empiricism. Cambridge: Cambridge University Press, 1998. Pp. x + 242. Cloth, $49.95.According to the author, the “received view” of Carnap’s Kantian treatise of 1928, Der Logische Aufbau der Welt, promulgated mostly by Quine (10), takes it (...) to be a continuation of Russell’s “external world program,” an attempt at “providing a systematic reduction of empirical discourse generally to discourse involving only sense data” (21). One of Richardson’s aims is to show that this is wrong: while Carnap holds that our knowledge begins in sensation, our “elementary experiences” are not conscious and thus do not obey Russell’s “principle of acquaintance.” While we have no conscious access to the first elements of cognition, logical constructions based on them lead to sense qualities, phenomenal items, and eventually to physical and even cultural objects.These constructions are also meant to solve the problem of objectivity. According to Carnap, individual streams of experience are not comparable at all, but “certain structural properties agree for all streams of experience” (Aufbau §66, 32), a point that Kant had also made: “In the relation between sensations lies something that is generally valid, even though each sensation has only private validity” (Reflection 653).Richardson describes Carnap’s constructions in a couple of well written and accessible chapters (31–91), one of them an overview, the other a discussion of the problem of objectivity. Then comes the “Kantian Problematic,” (92–116), centered on the synthetic a priori. He repeats Michael Friedman’s now familiar but mistaken point that, due to the limitations of Aristotelian logic, Kant could not have formulated simple statements about order structures: “between any two points there lies another” could not be formulated in any logic he knew, and he therefore had to call in pure intuition to handle mathematical constructions. But he could, and in fact did, make just such claims in the vernacular, which was the sole vehicle for the pellucid formulations of the classical theory of the continuum, from Bolzano to Weyerstrass.The next chapter brings us the heart of Richardson’s concerns, which is to establish neo-Kantian antecedents of the Aufbau. There are some biographical details of doubtful merit. The neo-Kantian Bauch is identified as Carnap’s “dissertation director,” and, in a perhaps unconscious slight to Carnap’s intelligence, as “the philosopher from whom Carnap learned what he knew about Kant” (116). Ten years before Carnap had indeed taken a seminar in the Critique of Pure Reason from Bauch, but perusal of the latter’s work does not encourage the thought that he had much to do with the thesis “Der Raum” (1922). In the event, a German ordinarius did not usually have a hand in the construction of a thesis, and often did not even read it. His job was to accept it on behalf of the university. We now know, for example, that Bauch’s teacher Rickert had an assistant evaluate Heidegger’s Habilitationsschrift never reading it himself. (It passed.)Richardson’s reflection on the neo-Kantian project relies mostly on Cassirer. This points to another problem with the Bauch connection. Bauch was a zealous anti-Semite, and did not think much of Cassirer and the Marburg school in general. He gave up the editorship of Kantstudien in 1916 because of the Jewish presence in the Kant Society, and [End Page 179] founded his own group and journal. Carnap nonetheless chose Kantstudien to publish his dissertation, perhaps to put more distance between himself and Bauch. Space does not permit me to cite Bauch’s vicious remarks about Einstein; he could not have guided Carnap through the discussion of physical space in “Der Raum.”I return to Richardson’s reconstruction. According to the neo-Kantian, objective knowledge is found in mathematical physics, not in uninformed experience. He acknowledges that theoretical physics relies on conventions, and that these conventions go beyond mere experience to provide the mathematical structure necessary for objectivity (131). The responses to the problem this poses... (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 ...

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

As a leading member of the Vienna Circle, Rudolph Carnap's aim was to bring about a "unified science" by applying a method of logical analysis to the empirical data of all the sciences. This work, first published in English in 1934, endeavors to work out a way in which the observation statements required for verification are not private to the observer. The work shows the strong influence of Wittgenstein, Russell, and Frege.

Three indexes have been compiled: authors of main articles (including our special departments such as ‘Projects in progress’ and ‘Notes and discussions’); essay reviews; and book reviews. Co-author...

Stimulating, thought-provoking text by one of the 20th century’s most creative philosophers clearly and discerningly makes accessible such topics as probability, measurement and quantitative language, structure of space, causality and determinism, theoretical laws and concepts and much more. "...the best book available for the intelligent reader who wants to gain some insight into the nature of contemporary philosophy of science."—Choice.

The first volume of the Library of Living Philosophers (LLP) appeared in 1939, the brainchild of the late Professor Paul A. Schilpp. Schilpp saw that it would help to eliminate confusion and endless sterile disputes over interpretation if great philosophers could be confronted by their capable philosophical peers and asked to reply. As well as a number of critical essays with the chosen philosopher's replies to each essay, each volume would include an intellectual autobiography and an up-to-date bibliography The LLP (...) series has exceeded even Schilpp's expectations, enabling great philosophers to do more than clarify by extending and elaborating their thoughts. A volume in the Library of Living Philosophers is not merely a commentary on a philosopher's work; it is a critical part of that work. (shrink)

Autour du Manifeste de Vienne se trouvent reunis des textes fondateurs ecrits autour de 1929. Leurs auteurs: Carnap, Hahn, Neurath, Schlick l'ame du Cercle de Vienne, et Waismann plus proche de Wittgenstein, temoignent d'un courant philosophique constituant aujourd'hui la tradition analytique de source continentale a la fois empiriste et logique. Forme de maniere informelle a Vienne, au coeur de l'Europe, le Cercle reunissait des savants de differentes branches qui voulaient se donner une philosophie susceptible d' unifier leurs vues. Echo aux (...) reves d'unite de la science, cette philosophie en exprime aussi le renversement complet. Veritable Discours de la methode, mais d'esprit anti-cartesien, elle entend reconstruire la science de maniere a evincer la speculation metaphysique, le but etant qu'aucun enonce ne soit laisse a l'exterieur de cette grande architecture de symboles s'il etait pourvu de sens. La declaration de guerre contre la metaphysique est un geste de militance a une epoque riche en differents manifestes. Incomprehensible en dehors du contexte socio-politique viennois de ces annees, elle porte aussi un programme de reconstruction rationnelle qui, au dela du langage de la science, devait toucher tous les secteurs de la vie. Plus complexe qu'il n'y parait, ce programme contient, en reference a Wittgenstein, son prestigieux representant a cote d'Einstein et Russell, une mise en garde contre differentes formes d'irrationalismes, qui est d'actualite. (shrink)

"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy. As two introductory essays by Gottfried Gabriel and by Erich H. Reck and Steve Awodey explain, Carnap's notes allow us to better understand Frege's deep influence on Carnap and analytic philosophy, as well as the broader philosophical matrix from which both continental and analytic styles of thought emerged in the 20th century."--BOOK JACKET.

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

This is the Spanish translation, by Valeria Sol Valiño, of Rudolf Carnap’s classical text “Die logizistische Grundlegung der Mathematik”, which was originally presented at the Königsberg’s Symposium on Philosophy of Mathematics in 1930, and finally published in Erkenntnis in 1931.

In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 (...) consist? We seek to answer this question by placing Carnap’s shorthand manuscript in the context of his previous efforts to accommodate scientific theories and metalinguistic claims within Wittgenstein’s Tractatus theory of meaning. The breakthrough of January 1931 consists, from this viewpoint, in the rejection of the Tractatus theory in favor of the meta-mathematical perspective of Hilbert, Gödel, and Tarski. This was not yet the standpoint of the published Logical Syntax, as we show, but led naturally to the “principle of tolerance” and thus to Carnap’s mature philosophy, in which the inconsistencies between this first view and the principle of tolerance, which survived into the published Syntax, were overcome. (shrink)

One thing we have found out about logical empiricism, now that people are examining it more closely again, is that it was more a framework for a number of related views than a single doctrine. The pluralism of different approaches among various adherents to the Vienna and Berlin groups has been much emphasized. Some have gone so far as to suggest that the kind of speculative philosophy now often called "continental" (including, say, phenomenology) can be seen as falling within the (...) framework of views shared by the Vienna Circle. Much is made of Felix Kaufmann's membership in the Vienna Circle, for instance, or of its "Austrian" roots in the phenomenology of Brentano. (shrink)

In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...) that it provides important insights intoCarnap''s development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnap''s logicism. Moreover, we show how theAxiomatics influenced Carnap''s student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnap''s project. (shrink)

The article presents a critical semantic analysis of the so-called analytical truths as they were discussed by R. Carnap and building on some new empirical data that are not fully satisfactorily explained by Carnap’s theory. A theoretical reconstruction of Carnap’s theory of analytical truths is proposed. It is demonstrated how his understanding of analytical truths, as statements that are true in all possible worlds and amenable to a quite obvious definition on a par with the concepts of sense (meaning) and (...) synonymy, applies exclusively to artificial languages of logic. Therefore, Carnap’s theory remains unreachable for the well-known criticism of W. Quine, who, in turn, pointed out the difficulties in defining these concepts for natural languages. A theoretical reconstruction of Carnap’s explication of the mentioned concepts in the theory of meaning for natural languages is carried out. The connection of Carnap’s approach with the perspective of contemporary formal semantics is established. Subsequently, problematic cases and the difficulties they pose for Carnap’s concept are examined. An explanation is proposed for analytical truths as containing in their logical form an (unpronounced) quantifier over possible worlds (situations). (shrink)

Thirty years after the publication of Thomas Kuhn’s The Structure of Scientific Revolutions, sharp disagreement persists concerning the implications of Kuhn’s "historicist" challenge to empiricism. I discuss the historicist movement over the past thirty years, and the extent to which the discourse between two branches of the historical school has been influenced by tacit assumptions shared with Rudolf Carnap’s empiricism. I begin with an examination of Carnap’s logicism --his logic of science-- and his 1960 correspondence with Kuhn. I focus on (...) problems in the analysis applied to the unit of metascientific study or appraisal, arguing for a reassessment of historicist treatment of the internal/external distinction and historiographic meta-methodology. The critique of objectivism and relativism that eventuates from this re-assessment is a double-edged blade, undercutting both objectivist and relativist treatments of cognitive evaluation and scientific change. I use it to cut across an otherwise diverse group of historicist-influenced writers, including Imre Lakatos, Larry Laudan, H. M. Collins, Stephen Stich. I. Introduction.. (shrink)

David Lewis presented Convention as an alternative to the conventionalism characteristic of early-twentieth-century analytic philosophy. Rudolf Carnap is well known for suggesting the arbitrariness of any particular linguistic convention for engaging in scientific inquiry. Analytic truths are self-consistent, and are not checked against empirical facts to ascertain their veracity. In keeping with the logical positivists before him, Lewis concludes that linguistic communication is conventional. However, despite his firm allegiance to conventions underlying not just languages but also social customs, he pioneered (...) the view that convening need not require any active agreement to participate. Lewis proposed that conventions arise from “an exchange of manifestations of a propensity to conform to a regularity” (87–8). In reasserting the conventional quality of languages and other practices resting on mutual expectations, Lewis comfortably works within the analytic tradition. Yet he also deviates from his predecessors because his conventionalist approach is comprehensively grounded in instrumentalism. Lewis adopts an extension of David Hume's desire-belief psychology articulated in rational choice theory. He develops his philosophy of convention relying on the highly formal mid-twentieth-century expected utility and game theories. This attempt to account for language and social customs wholly in terms of instrumental rationality has the implication of reducing normativity to preference satisfaction. Lewis’ approach continues in the trend of undermining normative political philosophy because institutions and practices arise spontaneously, without the deliberate involvement of agents. Perhaps Lewis’ Convention is best seen as a resurgent form of analytic philosophy, characterized by “a style of argument, hostility to [ambitious] metaphysics, focus on language, and the dominance of logic and formalization” that solves the dilemma of “combining the analytic inheritance…with normative concerns” by reducing normativity to individuals’ preference fulfillment consistent with the axioms of rational choice. (shrink)

The authors explore Carnap’s (1931) famous critique of Heidegger’s metaphysics and argue that, from the perspective of contemporary formal semantics of natural language, Carnap’s criticism is not convincing. Moreover, they provide direct empirical objections to Carnap’s criticism. In particular, using empirical evidence from languages like Russian that have negative concord, they show that Heidegger cannot be accused of assigning illegitimate logical forms to his sentences about Nothing because terms like “Nothing” can be used non-quantificationally and the fact that it is (...) not clear how their reference is established cannot be the reason why the corresponding sentences are ungrammatical (as Carnap seemed to suggest). The authors also critically discuss the view that natural language is insensitive to meaninglessness or contradiction. With reference to the work of J. Gajewsky, they show that this view is not true either. As a result of this investigation, they arrive at a position that an appeal to ungrammaticality like the one proposed by Carnap does not provide legitimate evidence against metaphysics. This conclusion relates to some recent criticism of the so-called non-analytical philosophers that can be traced back to Carnap’s paper. (shrink)

This chapter suggests that the state of nature is a continuum notion that lies in a segment along a larger continuum of the scope of private judgment, as does the continuum notion of civil authority. Jean Hampton saw Thomas Hobbes's state of nature as a “presocietal” condition of “isolated asocial individuals,” “stripped of their social connections.” There is plentiful evidence against Hampton's interpretation of the state of nature as an “asocial” condition in Hobbes's insistence across all his (...) political writings that men care deeply about their relative social standing and reputations, and that this is a major source of conflict in a state of nature. A potentially more promising way of understanding the state of nature is as a lawless condition. Societies exhibiting a high degree of consensus among private judgments may be able to tolerate incomplete removal from the mere state of nature, without threat to their stability. (shrink)

On Friday, November 15, 1940, Kurt Gödel gave a talk on set theory at Brown University. The topic was his recent proof of the consistency of Cantor’s Continuum Hypothesis with the axiomatic system ZFC for set theory. His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness.

Recent scholarship resuscitates the history and philosophy of a ‘left wing’ in the Vienna Circle, offering a counterhistory to the conventional image of analytic philosophy as politically conformist. This paper disputes the historical claim that early logical empiricists developed a political philosophy of science. Though some individuals in the Vienna Circle, including Rudolf Carnap and Otto Neurath, believed strongly in the importance of science to social progress, they did not construct a political philosophy of science. Both Carnap and Neurath were (...) committed to forms of political neutralism that run strongly against a political reading of their logical empiricism. In addition, Carnap and Neurath sharply differ on precisely the subject of the place of politics in logical empiricism, throwing into question the construct of the ‘Left Vienna Circle’ as a coherent, sociohistorical, programmatic unit within the Vienna Circle.Keywords: Vienna Circle; Rudolf Carnap; Otto Neurath; Logical empiricism; History of philosophy of science; Political philosophy of science. (shrink)