The Lvov-Warsaw School’s logistic anti-irrationalism, especially as it has been examined in the works of Kazimierz Ajdukiewicz, Izydora Dąmbska, and Jan Woleński, offered an intellectually distinct alternative to the logical positivism of the Vienna Circle. However, the Lvov-Warsaw School’s attempt to critique the Franco-German currents of mysticism and romanticism in the late 19th and early 20th centuries, especially in the works of Henri Bergson, open it up to the question of whether its members fully appreciated the consequences of accepting that rational cognition is abstract and schematic. We argue that the abstract nature of rational cognition provides reasons to countenance approximate truth; but doing so seems to put the goal of knowledge out of reach. The consequences of these arguments seem not to have been anticipated in the works of Ajdukiewicz, Dąmbska, or Woleński, and point to a new direction for research about the achievability of certain ambitious goals of the Lvov-Warsaw School’s logistic anti-irrationalism.