1 We assume the usual meaning of the phrase ' is written with', namely, the meaning of 'contains as a part of its writing'. On the other hand, it would be correct to say that, in the following expression, 'California' stands between quotes.

2 Such sentences belong to semantics; cf. p. 15.

3 Variable-quotes were first analyzed by A. Tarski, under the name of 'Anführungs-funktion', in 'Der Wahrheitsbegriff', Studia Philosophica, Leopoli, 1935, p. 14. Tarski has pointed out that the use of such quotes requires certain precautions. It is possible to eliminate variable-quotes by the use of special signs for sentence name variables, say Gothic letters, (Carnap). This is necessary, however, only when the metalanguage is formalized. For the informal use of the metalanguage in this book we prefer the variable-quotes because they simplify the notation considerably.

4 The word 'proposition' is occasionally used as synonymous, not with 'sentence', but with our term 'situation'; it is thus used by R. Carnap, Introduction to Semantics, Cambridge, Harvard University Press, 1942, p. 18. This notation does not seem advisable because it departs too far from established usage. When some logicians thought it necessary to distinguish between 'proposition' and 'sentence' they did so because they believed that there was a third thing between the sentence, i.e., the linguistic expression, and the situation. Such a third thing is certainly unnecessary, and we shall therefore identify sentence and proposition. Only occasionally may it appear useful to regard 'sentence' as a somewhat narrower term; thus we may say that 'Peter drives the car' and 'the car is driven by Peter' are different sentences but represent the same proposition. The term 'proposition', then, is used with a wider equisignificance relation.

5 The suggestion to construct a hierarchy of languages corresponding to the theory of types was first made by B. Russell in his introduction to Wittgenstein's Tractatus Logico-Philosophicus, London, 1922. The elaboration of this theory of levels of language is chiefly due to R. Carnap and A. Tarski, whose work is concentrated on syntax and semantics. The study of pragmatics has been advanced by C. Morris.

6 Cf. p. 187 and the author's Experience and Prediction, University of Chicago Press, Chicago, 1938, § 34.