The author endeavours to show that three chosen problems – the problem of individuals, of anaphora and of logic of imperatives – lend themselves to be being treated by transparent intensional logic (TIL), which can act as a successful explanatory grounding. In the first part of the article, the development of discussion about individuals is described and it is stated that despite the thorough treatment of this problematic and the advancing of convincing explication of many problems, some parts of the question may not have yet been fully engaged with. By contrast, the “story” of anaphora is basically finished and demonstrates a very successful application of TIL to the problematic which Tichý himself rather neglected. In the final part, focusing on logical prescriptions, the author argues for the view that the full exploitation of Tichý’s system with regard to the analysis and explication of imperatives remains to be undertaken. The development of research by Tichý’s followers here described on the three problems, the actual state of their treatment and other perspectives all indicate the fertile and yet to be tapped potential of the system which Tichý originated.