GRICE E CARAPELLE: META-LINGUAGGIO

 Let “A(p)** mean “I assert p between 5.29 and 5.31’*. Then q is “there is a  proposition p such that A(p) and p is fake”. The contradiction emerges from the  supposition that q is the proposition p in question. But if there is a hierarchy of  meanings of the word “false** corresponding to a hierarchy of propositions, we  shall have to substitute for q something more definite, i.e. “there is a proposition  p of order «, such that k{p) and p has falsehood of order n*\ Here n may be any  integer: but whatever integer it is, q will be of order « + i? and will not be capable  of truth or falsehood of order n. Since I make no assertion of order n, q is false,   62      THE OBJECT-LANGUAGE   The hierarchy must extend upwards indefinitely, but not  downwards, since, if it did, language could never get started.  There must, therefore, be a language of lowest type. I shall  define one such language, not the only possible one.* I shall call  this sometimes the “object-language”, sometimes the “primary  language”. My purpose, in the present chapter, is to define and  describe this basic lai^age. The languages which follow in the  hierarchy I shall call secondary, tertiary, and so on; it is to be  understood that each language contains all its predecessors.   The primary language, we shall find, can be defined both  logically and psychologically; but before attempting formal  definitions it will be well to make a preliminary informal explora-  tion.   It is clear, from Tarski’s argument, that the words “true”  and “false” cannot occur in the primary language; for these  words, as applied to sentences in the language, belong to the  (« -t- language. This does not mean that sentences in the  primary language are neither true nor false, but that, if “/>” is a  sentence in this language, the two sentences “p is true” and  “p is false” belong to the secondary language. This is, indeed,  obvious apart from Tarski’s argument. For, if there is a primary  language, its words must not be such as presuppose the existence  of a language. Now “true” and “false” are words applicable to  sentences, and thus presuppose the existence of language. (I  do not mean to deny that a memory consisting of images, not  words, may be “true” or “false”; but this is in a somewhat  different sense, which need not concern us at present.) In the  primary language, therefore, though we can make assertions, we  cannot say that our own assertions or those of others are either  true or false.   When I say that we make assertions in the primary language,  I must guard against a misunderstanding, for the word “assertion”   and, since q is not a possible value of p, the argument that q is also true collapses.  The man who says ‘T am telling a lie of order n” is telling a He, but of order  n 4 - I. Other ways of evading the paradox have been suggested, e.g. by Ramsey,  “Foundations of Mathematics”, p. 48.   * My liierarchy of languages is not identical with Carnap's or Tarski's. Proceeding psychologically, I construct a  language (not the language) fulfilling the logical conditions for  the langu^e of lowest type; I call this the “object-language” or  the “primary language”. In this language, every word “denotes”  or “means” a sensible object or set of such objects, and, when  used alone, asserts the sensible presence of the object, or of one of   *9     AN INQUIRY INTO MEANING AND TRUTH   the set of objects, which it denotes or means. In defining this  language, it is necessary to define “denoting” or “meaning” as  applied to object-words, i.e., to the words of this language.