The article contains the results of the analysis of concepts connected with semantic functions of names. The conception of Jacek Jadacki, exposed in his 'Spór o granice jezyka' (Controversy on the limits of language), is the point of departure of this analysis. The following theses are formulated and argued for: (1) There are two basic semantic functions of names: the referential and the descriptive one. The first function consists in indicating some objects; the second one consists in ascribing properties to some objects; (2) The concepts of indicating and ascribing are primitive ones; (3) The referential function of denotation and the descriptive function of connotation are mutually independent. The term 'connotation' can be defined without using the term 'denotation' and vice versa; (4) Names perform not only the function of designating, i.e. referring to particular objects, but also the function of denominating, i.e. referring to universal (resp. postulated) objects; (5) The connotation of a given name is genetically or conventionally connected with the pragmatic function of ascribing properties to respective objects; (6) In sciences, such connotations of names are sought after, which are, at the same time, essences of designates of these names.
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