Carnap's Syntactical Method
Introduction
Rudolf Carnap, a leading figure in the Vienna Circle, visited London in 1934 and gave three lectures at the University of London. These lectures have since been published, most recently as a book entitled "Philosophy and Logical Syntax" [Carnap34]. This book provides a concise overview of the methods being advocated by the Vienna Circle at that time. I have made some notes from the book , which provide an even more compact, if personal, rendition of its content and I present here a distillation of the method, hyperlinked into slightly more detailed notes. Neither of these documents is intended to provide a critique, which I hope will eventually emerge in the course of relating more modern formal methods to some of their historical predecessors.
Probably the three most important influences on the syntactic phase of Carnap's analytic methodology were Russell, Hilbert and Gödel.
The method is decribed in formal detail in "The Logical Syntax of Language" [Carnap37], and less formally in "Philosophy and Logical Syntax" [Carnap35]
The Origins of The Syntactic Method
Probably the three most important influences on the syntactic phase of Carnap's analytic methodology were Russell, Hilbert and Gödel.
Russell
It was Russell's conception of philosophy as logic which seems to have been the most significant influence on Carnap in developing his syntactic methods.
Hilbert
It was probably the influence of Hilbert's formalism which accounts for this method being specifically and exclusively syntactic.
Goedel
The proximate inspiration, according to Carnap, for the syntactic method, was the papers in which Gödel presented his famous incompleteness results. This was not in fact because of the results themselves, which can been seen as proofs that a syntactic method could not suffice. Carnap was inspired by the technique of arithmetisation of syntax employed in the proofs. This demonstrated that it was possible to reason about languages without having to adopt a metalanaguage distinct from the object language. Admittedly the distinction related only to the syntax, but then Hilbert's influence lead Carnap to believe that semantic concepts could be reduced to syntax.
Notes on The Method
The method is decribed in formal detail in "The Logical Syntax of Language" [Carnap37], and less formally in "Philosophy and Logical Syntax" [Carnap35]
Philosophy and Logical Syntax
The starting position for this method is the rejection of metaphysics (quoting Hume's Enquiry Section XIII part 3 para 4), assigning all matters of fact to empirical science and confining philosophy to logical analysis. The principle of verification, that propositions with no verifiable consequences lack sense, is used against metaphysics, but this plays no major role in the syntactical method which follows, this being more concerned with establishing the status and logical structure of analytic and synthetic propositions.
In this lecture are defined those concepts in terms of which logical analysis is to be conducted. These concepts are exclusively of a syntactic nature. A language is defined by a set of formation rules, which define sentences, and transformation rules, which define direct consequence. Properly philosophical (i.e. analytic) statements in "the material mode" have a misleading appearance of not being about syntax, and should be translated into "the formal mode" to reveal their true nature.
Logical analysis first involves the translation of philosophical sentences expressed in the material mode into the formal mode. Failing this the sentence must either be synthetic or metaphysical (and hence not properly a part of philosophy). Translation accomplished, further syntactic analysis will tell us whether the sentence is analytic, contradictory or indeterminate. By this means philosophy is rendered scientific in the sense intended by Russell.
The Logical Syntax of Language

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