The relation between indicative conditionals in natural language and material implication wasn't a major topic in the Lvov-Warsaw school. However, a major defense of the claim that the truth conditions of these two are the same has been developed by Ajdukiewicz (Studia Logica IV:117–134, 1956). The first major goal of this paper is to present, assess, and improve his strategy. It turns out that it is quite similar to the approach developed by Grice (Studies in the Way of Words, Harvard University Press, Cambridge, MA, 1991), so our second goal is to compare these two and to argue that the accuracy of Ajdukiewicz's explanation is less dependent on controversial properties of a systematic but convoluted general theory of cooperative communicative behavior. In Lvov-Warsaw school the relation between material implication and indicative conditionals was also discussed by Goł ąb (Matematyka 3(5):27–29, 1949) and Słupecki (Matematyka 4(6):32–35, 1949), so the third part of our paper is devoted to their discussion and relating it to Ajdukiewicz's views.