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 language and logic. In The Logical Syntax of Language, Carnap explains how his entire theory of language structure came to him like a vision when he was ill. He postulates that concepts of the theory of logic are purely syntactical and therefore can be formulated in logical syntax.
Rudolf Carnap, a German-born philosopher and naturalized U.S. citizen, was a leading exponent of logical positivism and was one of the major philosophers of the twentieth century. He made significant contributions to philosophy of science, philosophy of language, the theory of probability, inductive logic and modal logic. He rejected metaphysics as meaningless because metaphysical statements cannot be proved or disproved by experience. He asserted that many philosophical problems are indeed pseudo-problems, the outcome of a misuse of language.
The point of this book is to give an outline of the logical syntax of language, meaning a formal construction consisting of symbols and statements together with formal rules that govern their manipulation. In the first half of the book, Carnap presents two formal languages with varying degrees of richness, with the power to express arithmetic and first-order logic. And showing that these can be defined purely syntactically, without any reference to the "meaning" or "sense" of the symbols. The only "meaning" being their rules for manipulation. Carnap also discusses a similar method for the development of a general syntax and for a syntax of the language of science. So that all claims can be translated into claims about syntax, i.e. claims about terms and sentences. When such a move has been made, many philosophical problems are shown to not be problems at all, but simply different proposed languages. None more true than any other. An example of a problem that disappears when analyzing it from this point of view is the question of ”What is a number?”. There have been disputes between people claiming 1. that numbers are classes of classes of things, while others have claimed 2. that numbers are platonic simple objects. When translating these claims into claims about the syntax of the language, they are transformed into something like 1. ”In L1, number expressions are class expressions of the second level” and 2. ”In L1, number expressions are zero level expressions.” The problem is then shown not to be about ”the nature of numbers”, but simply about the choice of what language to use. The claim is also that there is no true or accurate language of science. Instead, there is only the choice of what language to adopt on pragmatic grounds, which is purely conventional.
For a book of mathematical logic, the book is written in easy to be read manner even when speaking about the most abstract topics such as the difference between formal logic and other philosophy concerning the syntaxical composition of sentences.