Carnap's Philosophy Research Articles

Carnap's philosophy of mathematics

AbstractFor several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly should we characterise Carnap's actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these issues by looking at Carnap's response to the incompleteness theorems. Drawing on arguments put forward by Gödel and Beth, I show that some crucial aspects of Carnap's positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap's position requires are made.

Hitting a Moving Target: Gödel, Carnap, and Mathematics as Logical Syntax†

From 1953 to 1959 Godel worked on a response to Carnap's philosophy of mathematics. The drafts display Godel's familiarity with Carnap's position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Godel's two principal points, however, will here be defended. Godel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap's later views. Carnap's position, however, had changed significantly in the intervening years, and to a significant extent, this mature position realizes much of what Godel himself wanted out of a philosophy of mathematics.

How Tolerant Can You Be? Carnap on Rationality

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well‐defined form of language or linguistic framework we please. A linguistic framework defines framework‐internal standards of correct reasoning that guide us in our first‐order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not itself constrained by these (framework‐internal) standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance.

Carnap and Kuhn on linguistic frameworks and scientific revolutions

Several recent works in history and philosophy of science have re-evaluated the alleged opposition between the theses put forth by logical empiricists such as Carnap and the so-called "post-positivists", such as Kuhn. Although the latter came to be viewed as having seriously challenged the logical positivist views of science, recent authors (e.g., Friedman, Reisch, Earman, Irzik and Grünberg) maintain that some of the most notable theses of the Kuhnian view of science have striking similarities with some aspects of Carnap's philosophy. Against that reading, Oliveira and Psillos argue that within Carnap's philosophy there is no place for the Kuhnian theses of incommensurability, holism, and theory-ladenness of observations. This paper presents each of those readings and argues that Carnap and Kuhn have non-opposing views on holism, incommensurability, the theory-ladenness of observations, and scientific revolutions. We note at the very end - without dwelling on the point, however - that they come apart on other matters, such as their views on metaphysics and on the context of discovery/justification distinction.

Stroud's Camap

In “Empiricism, Semantics, and Ontology” Camap drew his famous distinction between ‘internal’ and ‘external’ questions of existence, pronouncing the former meaningful and the latter meaningless. In The Significance of Philosophical Scepticism, Barry Stroud understands Carnap to be applying the verification criterion of meaningfulness in order to refute Cartesian skepticism. I suggest that Stroud misrepresents both Carnap's aim and method. Camap was responding to critics who suggested that his willingness to quantify over abstract entities in his work in semantics violated his commitment to empiricism. He rejected that criticism as presupposing a super‐scientific standpoint from which constraints on the admissible domain of entities of science could be delivered. Carnap wanted to insulate science from the imposition of first‐philosophical metaphysical prejudice, not to defuse scepticism by appeal to verificationism.

Carnap's philosophy of mind

Carnap's philosophy of mind

On the Metatheoretical Nature of Carnap's Philosophy

Rudolf Carnap defended two quite different critiques of traditional philosophy: in addition to the much discussed verifiability criterion, he also proposed a critique based upon “formalizability.” Formalizability rests upon the principle of tolerance plus an acceptance of a linguistic methodology. Standard interpreters of Carnap (e.g., [7] and [8]) assume that the principle of tolerance (and, hence, formalizability) gains its argumentative support from verificationism. Carnap, in fact, kept the two critiques separate and independent. Indeed, verificationism is even, in spirit, inconsistent with tolerance. If the formalizability approach is emphasized, traditional metaphysics is reconstructed, not banished. Philosophical disputes remain rationally decidable, but metatheoretical in nature. Two results follow: Carnap's metaphilosophy cannot be rejected merely on the basis of rejections of verifiability. Second, Carnap's conclusion that all philosophy concerns language provides no reason for despair.

Carnap's new system of inductive logic

During his life Carnap published two extensive, systematic works on inductive logic: Logical Foundations of Probability [4] and The Continuum of Inductive Methods [5]. These works report Carnap's research in induc tion and probability in the 1940's and early 1950's. After the publication of the Continuum in 1952 Carnap continued his research in inductive logic, and in the course of this research both his theory of inductive probability and his philosophy of induction underwent development. Most of Carnap's publications since 1952 have dealt with the philosophy and methodology of induction rather than inductive logic proper.1 A part of his recent research in inductive logic will be published in an extensive work 'The Basic System of Inductive Logic', forthcoming in Studies in Inductive Logic and Probability, I?II (edited by Rudolf Carnap and Richard Jeffrey).2 This paper discusses the development of Carnap's system of inductive logic and his philosophy of induction during the past twenty years. Our exposition and discussion of Carnap's inductive logic is based mainly on 'The Basic System of Inductive Logic' [13B-C] and partly on an earlier (unpublished) version of the same work, 'An Axiom System of Inductive Logic' [13A]. The theory presented in the 'Basic System' will be termed 'Carnap's New System' or the 'Basic System', and that presented in Log ical Foundations of Probability and the Continuum will be called 'Carnap's Old System'. Sections II?III of this paper discuss Carnap's philosophy of induction, Sections IV-VII contain an exposition of the main features of the 'Basic System', and the concluding Sections VIII-IX discuss the philosophical implications of Carnap's New System.

Professor Carnap's Philosophy of Probability

Professor Carnap's Philosophy of Probability