This article considers three periods of the theory of predication in the Prague Linguistic Circle. The first belongs to the classical period, the second to the 1960s and the final and current one begins in the 1990s. The work of three particular authors, Mathesius, Danes, and Sgall, is discussed. Four questions arise: 1) Was Mathesius an inspirational source for the second 1929 Thesis? 2) What were the historical and epistemological roots of the rather strong link between philosophy of language and linguistics during the first period? 3) Why is indexicality not recognized by Danes as the semiotic device which associates predication with those aspects of the sentence which potentially place it in relation with a situation? 4)Why is the relationship between the Praguian idea of 'function' and the Fregean one, i.e. the logico-semantic concept which gives foundation to the philosophical truth-functional approach in semantics, and which explains the so-called 'predicative-argumental structure', not recognized as noteworthy? What, in fact, is a function? In conclusion, this article sketches the project of a Latin Dependency Treebank developed on the basis of the PDT, which bears witness to the far-reaching implications of the Circle's work and to an international, intercontinental prosecution of a tache abordee.