Carnap: Logical Syntax of Language

The aim of the article is to analyze the situation of contemporary logic with reference to the issue concerning connections between the pluralism of logical systems and relativism in logic. Accordingly, I seek answers to the following questions: Can the plurality of logic, more specifically, a large number and variety of systems constructed by logicians, be justified in a rational way? Does pluralism in logic imply the thesis of relativism? Is logical relativism in the contemporary philosophy of logic just a (...) superstition or is it a duly substantiated view? (shrink)

Pierre Wagner (ed.): Carnap’s logical syntax of language . Palgrave-MacMillan, 2009, 288pp, £57.00 HB Content Type Journal Article Pages 1-2 DOI 10.1007/s11016-011-9522-8 Authors Alan Richardson, Department of Philosophy, University of British Columbia, 1866 Main Mall—E370, Vancouver, BC V6T 1Z1 Canada Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

Providing a principled characterization of the distinction between logical and non-logical expressions is a longstanding issue in the philosophy of logic. In the Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by "syntactic" means which sentences are valid and which are (...) not. Despite a renewed interest in the philosophical benefits of analyticity, both inside and outside of Carnap scholarship, Carnap's definition of logical expressions seems to have drawn too little attention. I shall argue that it is worth a second look. More precisely, my aim will be to defend this idea against some technical problems faced by Carnap's way of implementing it and against Quinean attacks on syntax-based conventionalism. Section 1 presents Carnap's definition in the context of Logical Syntax of Language, that is, how exactly the definition works, and why Carnap needs it. In section 2, I review three challenges that have been raised in the literature, and I propose to revise the definition accordingly. I argue that its modified version is immune to the previous challenges, and, to some extent, immune to new challenges as well. In the last section, I suggest that the definition has a philosophical interest of its own, because standard Quinean objections are not as conclusive as one might think when attention is paid to the fact that Carnap requires complete syntactic specification of validities. (shrink)

This volumes aim is to provide an introduction to Carnaps book from a historical and philosophical perspective, each chapter focusing on one specific issue. The book will be of interest not only to Carnap scholars but to all those interested in the history of analytical philosophy.

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict (...) between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this? (shrink)

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)

This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper (...) will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap's attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference. (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)

RésuméL'objectif principal de cet article est de clarifier le sens et l'extension du concept d'analyticité tel qu'il s'applique aux systèmes formels de la logique. L'enjeu plus général de cette étude est une évaluation ékthodologique des approches philosophiques axées sur la reconstruction formelle et l'analyse logique des langues naturelles. Nous avons d'abord soutenu que la reconstruction formelle de l'analyticitéélaborée par Rudolf Carnap dans Meaning and Necessity met en place des conditions correspondant aux propriétés éktalogiques de complétude déductive et de néga‐complétude. A (...) la lumère des théorèmes de complétude et d'incomplhde de Kurt Gödel, nous avons ensuite cherchéà déterminer dans quelle mesure et dans quelles circonstances ces propriétés pouvaient être réalisées dans des systèmes formels de la logique. Nous avons conch de cette étude, premièrement que la reconstruction carnapéenne de I'analyticité se butait à des contraintes inhérentes aux formalismes et ne pouvait par conséquent pas constituer une explication du concept d'analyticité, et deuxieèmement, que fort peu de systèmes formels étaient analytiques au sens oú Carnap I'entend et que peu d'entre eux, par conséquent, étaient susceptibles de représenter les conditions de l'analyticité que presuppose une analyse logique du langage. (shrink)

This book is a major contribution to the history of analytic philosophy in general and of logical positivism in particular. It provides the first detailed and comprehensive study of Rudolf Carnap, one of the most influential figures in twentieth-century philosophy. The focus of the book is Carnap's first major work: Der logische Aufbau der Welt. It reveals tensions within the context of German epistemology and philosophy of science in the early twentieth century. Alan Richardson argues that Carnap's move to philosophy (...) of science in the 1930s was largely an attempt to dissolve the tension in his early epistemology. This book fills a significant gap in the literature on the history of twentieth-century philosophy. It will be of particular importance to historians of analytic philosophy, philosophers of science, and historians of science. (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 ...

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 ...