This section discusses mostly some unsolved problems. . . .I hope that some mathematicians who are interested in a classification of sets of real numbers, in particular sets with Lebesgue measure zero, will read it and try to find solutions for the problems here outlined.

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.

Graham and Maitzen think my CORNEA principle is in trouble because it entails “intolerable violations of closure under known entailment.” I argue that the trouble arises from current befuddlement about closure itself, and that a distinction drawn by Rudolph Carnap, suitably extended, shows how closure, when properly understood, works in tandem with CORNEA. CORNEA does not obey Closure because it shouldn’t: it applies to “dynamic” epistemic operators, whereas closure principles hold only for “static” ones. What the authors see as (...) an intolerable vice of CORNEA is actually a virtue, helping us see what closure principles should—and shouldn’t—themselves be about. (shrink)

In Rudolph Camap (,) established himself as a professor in Vienna. The philosophical atmosphere awaiting him there was not new to him: the year before he ...

"Homage to Rudolph Carnap."--Hempel, C. G. Rudolf Carnap, logical empiricist.--Wedberg, A. How Carnap built the world in 1928.--Eberle, R. A construction of quality classes improved upon the Aufbau.--Carnap, R. Observation language and theoretical language.--Kaplan, D. Significance and analyticity: a comment of some recent proposals of Carnap.--Wójcicki, R. The factual content of empirical theories.--Williams, P. M. On the conservative extensions of semantical systems: a contribution to the problem of analyticity.--Winnie, J. A. Theoretical analyticity.--Wedberg, A. Decision and belief in science.--Bohnert, H. (...) G. Carnap's logicism.--Hintikka, J. Carnap's heritage in logical semantics.--Partee, B. H. The semantics of belief-sentences.--Kasher, A. Pragmatic representations and language-games.--Carnap, R. Notes on probability and induction.--Jeffrey, R. C. Carnap's inductive logic.--Hilpinen, R. Carnap's new system of inductive logic.--Kuipers, T. A. F. A generalization of Carnap's inductive logic. Essler, W. K. Hintikka versus Carnap.--Hintikka, J. Carnap and Essler versus inductive generalization.--Shimony, A. Carnap on entropy, introduction to "Two essays on entropy" by Rudolf Carnap. (shrink)

Most handbooks on statistics and the theory of probability leave the reader in a mysterious tangle of mathematical rules for computing apparently arbitrarily chosen numerical functions. At first sight, then, a treatise on the Logical Foundations of Probability raises hopes that it will be a guide to clarity in these matters. These hopes are strengthened if the reader remembers that the author, Professor Rudolph Carnap of the University of Chicago, is noted for his thesis that philosophy is the study (...) of the logic of science. On the other hand, a first glance into this book may discourage a reader who, though familiar with statistics, is not familiar with modern logic and its notation. For this reason particularly I shall try to give an account of this book that will enable the interested student to form some opinion of its usefulness to him. (shrink)

We present a novel semantic and conversational framework for a class of gradable-like constructions. These include metalinguistic comparatives, like "Ann is more a linguist than a philosopher", as well as metalinguistic equatives, degree modifications, and conditionals. To the extent previous literature discusses such metalinguistic gradability, the focus has been on comparatives. We extend our account of metalinguistic comparatives (Rudolph & Kocurek 2020) to cover a broader range of metalinguistic gradable constructions. On our semantic expressivist view, these all serve in (...) various ways to express speakers' relative commitments to different linguistic interpretations. (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)

The first chapters of Michalos’ book give an account of the controversy between Karl Popper and Rudolph Carnap following the former’s critique of Carnap in "Degree of Confirmation". Michalos very compactly summarizes the controversy and argues: 1) that Popper was mistaken when he tried to show that Carnap always identified the quantitative degree of confirmation with the acceptability of scientific theories; 2) that Popper is mistaken in accusing Carnap of confusing classificatory, comparative, and quantitative concepts; 3) that a conflict (...) between Popper and Carnap, apparently over the problem of unrestricted universals, was in fact over the everyday practical use of such universal sentences; 4) that Popper’s critique of Carnap’s theorem for the singular predictive inference is incorrect because Popper construes the theorem with respect to two different kinds of evidential statements. The final chapters of the book deal with some additional issues that have developed out of the central controversy. One chapter consists largely in a reply to Imre Lakatos in further defense of Carnap. A second presents a critique of the Hintikka-Hilpinen acceptance rule. The last chapter is a comparison of cost—benefit versus utility acceptance rules in which Michalos claims to show the superiority of the former. In general, the book is an attempt to defend an inductive logic against the criticisms offered by Popperian deductive methodologists. A great deal of this material already appeared in various forms. The book is useful insofar as it collects material in one place and provides references to the important contributions to the controversy. Unfortunately, the book is cramped, explicitly discussing only some of the narrow issues found in the journal literature, and some sections are so compact as to be incomprehensible without extensive knowledge of the source material. Michalos might have given himself wider scope so that he could develop the implications of these limited problems for the broader issues of the philosophy of science.—K. M. (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)

L'idée d'associer probabilité et induction n'est pas propre au xxe siècle, mais elle a reçu un développement systématique lorsque les philosophes néo-positivistes s'en sont emparés. Dès les années 1940, le philosophe Rudolf Carnap s'est proposé de relever le «défi humien» en fondant une théorie de la confirmation par la construction d'une logique probabiliste dite «inductive». Ce projet avait été esquissé à Cambridge dans les années 1920 par l'économiste John M. Keynes. Examiner le programme de Carnap dans sa totalité, le situer (...) dans son contexte historique, suivre son évolution et les influences qu'il a eues, tels sont les buts de cet article. The idea of associating probability and induction is not a theme suitable for the xxth century but it has received a systematic development when the neo-positivist philosophers seized it. Beginning with the 1940's, the philosopher Rudolph Carnap proposed to affront the «Humian challenge» by founding a theory of confirmation through the construction of a probabilistic logic called «inductive». This project had been outlined in Cambridge during the 1920's by the economist John M. Keynes. To examine Carnap's program in its totality, to situate it in its historical context, to follow its evolution and the influences it has had, these are the aims of this article. (shrink)

Das Ziel: Konstitutionssystem der Begriffe Das Ziel der vorliegenden Untersuchungen ist die Aufstellung eines erkenntnismäßig-logischen Systems der ...

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)

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.

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)

'My endeavour in these pages is to explain the main features of the method of philosophizing which we, the Vienna Circle, use, and by using try to develop further. It is the method of the logical analysis of science, or more precisely, of the syntactical analysis of scientific language.... The purpose of the book -- as of the lectures -- is to give a first impression of our method and of the direction of our questions and investigations to those who (...) are not yet acquainted with them.' -- From the Preface. (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 ...