Every system of signs that is defined in logical syntax may be called a formal language. It need not always be a language in the ordinary sense of the word. The rules of chess, e.g., can be expressed in the terminology of the syntax, but it would not occur to anybody to call chess a language.

A language in the ordinary sense has a meaning. That is to say that certain words in it are names of things or states or properties or relationships. In general it can be said that in any language having meaning all words subject to the rule of types are names. (Even sentences might be called names, i.e. names of facts, but we will not go so far.)

A syntax of a language L is a language with meaning, for the words of a definite type (in this paper of the type of individuals) contained in it are names of expressions of L.

If to a language we add its syntax, we get a language containing the syntax of one of its parts. If we formulate the syntax of a language L, in so far as its means allow, in the language L itself, we get a language containing a part of its syntax. We call such languages autosyntactic. It is well known that languages containing the whole of their own syntax do not exist.

Two errors have appeared in my dissertation. First, in the symbolic statement of Theorem (14.1), “r i ≁∧” should be “r i ≁∨.” Second, as J. C. C. McKinsey points out in his review, Theorem (10.8) is not correct. The error in the proof enters in the last application of Theorem (10.7), for which the hypothesis would be needed. The construction given at the bottom of page 35 is valid, however.

To state the correct theorem to replace Theorem (10.8), adopt the notation sylc (p) for any one of the mutually congruent polynomials resulting from the adjunction to p of all σ-terms informally included in p which are obtainable by eliminating c from pairs of terms of p.Then:

Theorem. .