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The following problems are dealt with in the present paper: the introduction of the meaning of empirical (observational) predicates, immediate interpretation, ostensive definitions, vagueness of empirical predicates and the possibilities to remove it. The main purpose of the present work is to build up such a conceptual apparatus which would make it possible to speak about immediate interpretation as about a sufficient condition for the fixation of the meaning of empirical predicates. Przelecki’s work (14) is being reviewed; on the basis of its results, it is necessary to accept that immediate interpretation of predicates is not a procedure whose nature can be apprehended by semantic means. An attempt is made to find the solution in the sphere of pure pragmatism and the assumption is accepted that the meaning of the primitive empirical predicate P of the language / is being fixed, for the person y, as follows: 1. The user x of the language J demonstrates arbitrarily a positive and negative pattern of the predicate P to the person y. The positive pattern of the predicate P of n arguments is represented by the set k of couples of the form {P; < al1 , al2,.. . , aln > }, where l =< j =< k, and the negative pattern is represented by the set m of the couples of the form {P’; < b1, bj2, .. . , bjn>}, where l =< j =< m, while alr, bjs, where l =< r, s =< n, are perceivable objects and P' is the negation of the predicate P. 2. Person у makes up for himself a criterion of the predicate P. This criterion may be represented by such a partial transformation φyp of the set of all ordered n-tuples of perceivable objects from the universe U (let us denote this set as Un) into the set {P, P’}, that for a ε Un a φyp = P then and only then, when у recognizes a as the designation P and а фур = P’ then and only then, when у does not recognize a for the designation P. The accepted assumption makes it possible to assert that immediate interpretation is sufficient for the introduction of the meaning of empirical predicates as well as for the explanation of the fact that empirical predicates are vague. Two concepts of a vague predicate are defined and by means of them problems are analyzed which are connected with the fixation of the meaning of empirical predicates, mainly the problem of intersubjectiveness of their meaning. Two concepts of the measure of nonintersubjectiveness of empirical predicates are defined and, in the conclusion, some procedures are dealt with briefly which make it possible to reduce this measure of nonintersubjectiveness and build exact conceptual apparatuses.