Introduction to Semantics

by Rudolf Carnap (1942)

I must admit this was too tough for me. I keep my critical doubtful view over the empirico-logical tradition, but I fail to ground it into any inner logical contradiction. I feel however that Carnap cannot either reach very conclusive results. Besides, he is driven by the same kind --in the opposite direction-- of prejudices as mine.

Preface p viii

Some metaphysicians have indeed raised futile issues concerning truth, or rather the Truth, and I certainly should not like to revive them.

18 L-Range, p 95

A semantical system will, in general contain not only true but also false sentences. If a false sentence is not L-false, hence not self-contradictory, it describes a situation which is possible though not real.

D Syntax, p 155

Pure syntax, i.e. the theory of syntactical systems or calculi.

A syntactical system or calculus K is a system of formal rules. It consists of a classification of signs, the rules of formation, and the rules of deduction[...] Sometimes, K contains also rules of refutation.

§ 31. C-Concepts (3), p 186

K and Li may be such that Li is both C-true and C-false in K; in this case we shall call Li C-ambivalent in K and K a C-inconsistent calculus.

Appendix, § 37: Terminological Remarks, p 234

Prefixes: 2. Choice of letters as prefixes

  • 'C-true' for 'true in a calculus'
  • 'L-true' for 'logically true'
  • 'F-true' for 'factually true'

p 235

'Proposition'. The term is used for two different concepts, namely for certain expressions and for their designata.

§ 38 Outline of Further Semantical Problems, p 243

e. Antinomies

The modern analysis of these antinomies and of their consequences for logic, especially by Russell, Ramsey, Gödel, and Tarski, has brought clarity concerning the nature of the antinomies, shown ways of avoiding them, and led to further important results,

§ 39 Remarks on "Logical Syntax of Language", p 246

Certain concepts, especially the L-concepts, are now regarded as semantical, not syntactical; hence, the earlier attempts at syntactical definitions for them are abandoned.

[Quoted by Popper]