Meaning and Necessity
Rudolf Carnap, 1947

Chapter I. The Method of Extension and Intension
The expressions of a semantical system S are (declarative) sentences, individual expressions and predicators. A sentence is L-true if its truth depends only on the semantical rules, not on any extralinguistics facts. Two expressions are equivalent if they are both true or both not true. These expressions are said to have the same extension. If two expressions are L-equivalent, they are said to have the same intension.

The extension of a predicator is the class of individuals to which it applies. Its intension is the property which it expresses. The extension of a sentence is its truth or falsity. Its intension is the proposition it expresses. The extension of an individual expression is the individual to which it refers. Its intension is a concept of a new kind expressed by it.

A sentence may contain an embedded expression. The sentence is extensional with respect to an embedded expression if its extension depends on the extensionality of the expression. A sentence is intensional with respect to an embedded expression if it is not extensional and its intension depends on the intension of the embedded expression. A modal sentence (for example, 'It is necessary that ...') is intensional with respect to its embedded expression. A psychological sentence (for example, 'John believes that ...') is neither intensional nor extensional with respect to its embedded expression. This problem of belief-sentences will be solved with the help of intensional structure.

1. Preliminary Explanations

2. L-Concepts

3. Equivalence and L-Equivalence

4. Classes and Properties

5. Extensions and Intensions

6. Extensions and Intensions of Sentences

7. Individual Descriptions

8. Frege's Method for Descriptions

9. Extensions and Intensions of Individual Descriptions

10. Variables

11. Extensional and Intensional Contexts

12. The Principles of Interchangability

13. Sentences about Beliefs

14. Intesional Structure

15. Applications of the Concept of Intesional Structure

16. Lewis' Method of Meaning Analysis

Chapter II. L-Determinacy

17. L-Determinate Designators

18. The Problem of L-Determinacy of Individual Expressions

19. Definition of L-Determinacy of Individual Expressions

20. L-Determinacy of Predicators

21. Logical and Descriptive Signs

22. L-Determinate Intensions

23. Reduction of Extensions to Intensions

Chapter III. The Method of the Name-Relation

24. The Name-Relation

25. An Ambiguity in the Method of the Name-Relation

26. The Unnecessary Duplication of Names

27. Names of Classes

28. Frege's Distinction between Nominatum and Sense

29. Nominatum and Sense: Extension and Intension

30. The Disadvantages of Frege's Method

31. The Antimony of the Name-Relation

32. Solutions of the Antimony

Chapter IV. On Metalanguages for Semantics

33. The Problem of a Reduction of the Entities

34. The Neutral Metalanguage M'

35. M' is Not Poorer than M

36. Neutral Variables in M'

37. On the Formulation of Semantics in The Neutral Metalanguage M'

38. On the Possibility of an Extensional Metalanguage for Semantics

Chapter V. On the Logic of Modalities

39. Logical Modalities

40. Modalities and Variables

41. Semantical Rules for the Modal System S2

42. Modalities in the Word Language

43. Modalities and Variables in the Word Language

44. Quine on Modalities

45. Conclusions

Supplement

A. Empiricism, Semantics and Ontology

B. Meaning Postulates

C. On Belief-Sentences. Reply to Alonzo Church

D. Meaning and Synonymy in Natural Languages

E. On some Concepts of Pragmatics


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