This guest lecture was given in September 2018 at the Fran Ramovš Institute of the Slovenian Language, Ljubljana (ZRC SAZU). The topic of this lecture is traditional for a research line in Slavic studies devoted to copular non-agreeing predicatives. I share the fascination of Lev Shcherba, Victor Vinogradov and their followers with this amazing class of forms but unlike them do not believe that it consitutes a separate part of speech in Russian or any other Slavic language. Moreover, I argue that an analysis of Slavic predicatives in terms of part of speech classification does not capture their semantics-to-grammar interface, contrary to Shcherba's initial claim (1928). Meanwhile, dative-predicative structures (DPS) constitute the core of the alleged part-of-speech dubbed 'category-of-state' by Shcherba, and the non-agreeing copular predicatives that license the DPS construction indeed express the categorial meaning of stage-level predicates (SLP). In this context, Nikolai Pospelov (1955) was quite right, when he claimed that the special feature of Russian (also Ukrainian, Belorussian, Serbian, Slovenian, Bulgarian and Macedonian predicatives is the total lack of agreeing morphology. Dative predicatives cannot select nominative subjects, and in languages like Modern Russian tbey do not select nominative objects either. The technical difficulty with this approach is that there exist morphologically ambivalent forms that represent pairs of the type 'morphologically defective adjectival head licensing the dative-nominative construction' vs 'non-agreeing predicative'. Comment 1. The analysis outlined here has been presented in detail in the following papers of mine: Zimmerling (1998, 2010, 2016, 2017, 2018ab, 2021, 2022). Similar ideas have been proposed by other scholars, first of all, Alla Gradinarova, Elena Ivanova, Sergej Say and Alexander Letuchiy. No one else, except of myself is responsible for the shortcomings. Comment 2. In 2018, I organized the panel of dative predicatives ( = 'thematic block') at the Slavic congress in Belgrad. The panel papers along with the papers of two other scholars were published in the special thematic issue of the journal "Russkij jazyk za rubezhom", see Gradinarova 2018, Ivanova 2018, Petrova 2018, Mitkovska 2018, Maric & Kerkez 2018, Uhlik 2018, Kulinich 2018, Bashmakova 2018 in the Reference. Comment 3. In this presentation, I do not use the semantic term 'Davidsonian state' (D-state) and the notion of spatiotemporality, but I stick to them in Zimmerling 2021, 2022, 2024. The interpretation is similar. Mind that the standard version of Davidson's theory excludes quantification of D-states, so one has to modify his theory to account for the quantification of intensional states: they are spatiotemporal in the sense that the referential subject-of-state (and dative subjects are typically referential in the Slavic languages and elsewhere) is always located somewhere.