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Language, Modal Logic and Semantics
Part III section III of The Philosophy of Rudolf Carnap
Notes on Carnap's replies to essays by other philosophers concerning his views on language, modal logic, and semantics.
11. Robert Feys on Modalities
12. John Myhill on Modal Logic and Semantics
13. Donald Davidson on Modalities and Semantlcs
14. Richard Martin on Semantics
15. W. V. Quine on Logical Truth
16. Herbert G. Bohnert on Definitions and Analyticity
17. Wilfrid Sellars on Abstract Entities in Semantlcs
18. E. W. Beth on Constructed Language Systems
19. P. F. Strawson on Linguistic Naturalism
20. Yehoshua Bar-Hillel on Linguistics and Metatheory...
9. My Conception of the Logic of Modalities
I. The logic of extensions

II. The logic of intensions; modalities

III. Two identity concepts

IV. Translation of a modal language into an extensional language

V. Translation of an extensional language into a modal language

VI. The logic of senses and synonymy

VII. Comparison of the logic of intensions and the logic of senses

10. My Conception of Semantics
I. The extensional metalanguage for semantics

Here Carnap describes not the language but rather what is to be done with the language. This consists of definitions of the following:

  • rules of formation (syntactic)
  • rules of relative designation (these give tbe designation of some phrase of the language relative to some model and value assignment)
  • rules of direct designation (which gives a model for the language)
  • definition of truth (a sentence is true if it designates truth in the model given by the rules of direct designation according to the rules of relative designation)
  • meaning postulates (these are axioms which express relations between the descriptive constants)
A model is said to be admissible if all the meaning postulates hold in it.

Analyticity (A-truth) is then defined as follows:

II. Models, model structures and interpretations

Carnap's terminology differs here from the terminology which I am accustomed to.

In my usage an interpretation is an assignment of values to the domains of quantification and the contants in some language (the details depend upon the kind of language under consideration), a model is an interpretation which satisfies the axioms of the theory.

In Carnap's usage a model is what I call an interpretation, a model structure is an isomorphism class of models. and an interpretation is some kind of definition of a model so that two distinct interpretations might describe the same model. Two interpretations are the same if they are logically equivalent.

III. Non-extensional metalanguages for semantics

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