"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)

In this paper, we discuss how to conceptual engineer ‘entropy’ and ‘information’ as they are used in information theory or statistical mechanics. Initially, we evaluate the extent to which the all-pervasive entangled use of entropy and information notions can be somehow defective in these domains, such as being meaningless or generating confusion. Then, we assess the main ameliorative strategies to improve this defective conceptual practice. The first strategy is to substitute the terms ‘entropy’ and ‘information’ by non-loaded (...) terms, as it was first argued by Bar-Hillel (1955). A second strategy is to prescribe how these terms should be correctly used to be meaningful, as it was pioneered by Carnap (1952 [1977]) in Two Essays on Entropy. However, the actual implementation of these two ameliorative strategies has been historically unsuccessful due to the low credentials that philosophers as conceptual prescribers have among scientists. Finally, to try to solve these obstacles, we propose a third strategy based on leveraging evidence from the contribution of ‘Philosophy in Science’ (à la Pradeau et al. 2024) to integrate conceptual prescriptions and analyses of entropy and information as part of the scientific practices in which these notions are used. (shrink)

In this paper I aim to demonstrate that Rudolf Carnap's analysis of the application of information theory within physics, an intellectual-historical precedent of current philosophical criticisms toward this tendency, is justified. First, Carnap and Bar-Hillel (1952) underlined the unjustified ‘semantification’ of Shannon entropy Furthermore, Carnap criticized the ‘physicalization’ of Shannon entropy, but that criticism was not accepted by the physics community of the 1950s (Köhler 2001). Finally, in the posthumously published "Two Essays on Entropy" (...) Carnap (1977) developed a critical assessment of entropy concepts that showed some deep conceptual and interpretative deficiencies in Jaynes (1957a) and Brillouin’s (1956) informational approaches to thermophysics. (shrink)

The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of (...) the sublanguage increases; selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations. (shrink)

Among the various meanings in which the word ‘probability’ is used in everyday language, in the discussion of scientists, and in the theories of probability, there are especially two which must be clearly distinguished. We shall use for them the terms ‘probability1’ and ‘probability2'. Probability1 is a logical concept, a certain logical relation between two sentences ; it is the same as the concept of degree of confirmation. I shall write briefly “c” for “degree of confirmation,” and “c” for “the (...) degree of confirmation of the hypothesis h on the evidence e“; the evidence is usually a report on the results of our observations. On the other hand, probability2 is an empirical concept; it is the relative frequency in the long run of one property with respect to another. The controversy between the so-called logical conception of probability, as represented e.g. by Keynes, and Jeffreys, and others, and the frequency conception, maintained e.g. by v. Mises and Reichenbach, seems to me futile. These two theories deal with two different probability concepts which are both of great importance for science. Therefore, the theories are not incompatible, but rather supplement each other. (shrink)

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)

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)

Carnap’s ‘Empiricism, Semantics, and Ontology’ (Carnap (1950a), ESO hereafter) is certainly a classic of twentieth century analytic philosophy. For decades now, most undergraduates are expected to read it at some point in their studies. Lately, it is being seen as the inspiration for a host of positions in the field of metaontology. Despite the widespread agreement on the importance of the paper, there is a lack of agreement on what Carnap attempts to do in the paper. My (...) main aim in this chapter is to defend an interpretation of ESO by displaying its relation to Carnap’s earlier works. My secondary goal will be to draw a lesson from this discussion for Carnap’s later work on unobservable entities in science. (shrink)

A new direction in philosophy Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional (...) philosophy with a new set of doctrines more firmly grounded in logic and science. Criticism and decline Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology. A resurgence of interest During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence. Hard-to-find core writings now available This collection makes available a selection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers. (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. (shrink)

In the paper translated here, Carnap and Bachmann shows that the apparently metalinguistic ?extremal' axioms that are added to some axiom systems to the effect that the foregoing axioms are to apply as broadly, or as narrowly, as possible may be formulated directly as proper axioms. They analyze such axioms into four fundamental types, with the help of a concept of ?complete? isomorphism.

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.

"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)

We review some notions for general quantum entropies. The entropy of the compound systems is discussed and a numerical computation of the quantum dynamical systems is carried for the noisy optical channel.

We review some techniques and notions for quantum information theory. It is shown that the dynamical entropies is discussed and some numerical computations of these entropies are carried for several states.

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)

W. Mays; II—Carnap on Logic and Language, Proceedings of the Aristotelian Society, Volume 62, Issue 1, 1 June 1962, Pages 21–38, https://doi.org/10.1093/aristot.

Unified science is a recurring theme in Carnap's work from the time of the Aufbau until the end of the 1930's. The theme is not constant, but knows several variations. I shall extract three quite precise formulations of the thesis of unified science from Carnap's work during this period: from the Aufbau, from Carnap's so-called syntactic period, and from "Testability and Meaning" and related papers. My main objective is to explain these formulations and to discuss their relation, (...) both to each other and to other aspects of Carnap's work. (shrink)

This paper provides a historically sensitive discussion of Carnaps theory will be assessed with respect to two interpretive issues. The first concerns his mathematical sources, that is, the mathematical axioms on which his extremal axioms were based. The second concerns Carnapcompleteness of the modelss different attempts to explicate the extremal properties of a theory and puts his results in context with related metamathematical research at the time.

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic and (...) hence with the notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (shrink)