In this survey the particularities of the first international conference “Philosophical Insights. Inspirations from Lviv-Warsaw School” organized by Lviv Philosophical Society named after Kasimir Twardowski are described and discussed. This event was not only pure scientific conference, but also some perspectives of Society’s activity in the scientific, educational and translation spheres were discussed by the members of Society. The members of Society who took part in this conference were agreed that Ukrainian society suffers from the lack of critical awareness, therefore, it needs absolutely a new handbook on critical thinking and how to teach it the young people not only in secondary schools but also in universities, how to popularize it among students. The papers delivered in the conference had a wide range of content: from Chwistek’s constructive ontology to the comparative analysis of Twardowski’s concept of thinking and its tasks and Krishnamurti's concept of choiceless awareness. Such comparative analysis helps to develop intercultural philosophy, which is a prove that philosophical thinking doesn’t have any borders.