Game, set, maths : formal investigations into logic with imperfect information

With his book "The Principles of Mathematics Revisited" (1996), Jaakko Hintikka intends to "wake [his] fellow philosophers of mathematics from their skeptical slumbers, and to point out to them a wealth of new constructive possibilities in the foundations of mathematics" (p. ix). The latter is claimed to be provided by Hintikka's Independence Friendly logic together with Game Theoretical Semantics as the new basis for the foundations of mathematics (thereby replacing the traditional first order logic). Although the presented ideas were criticized in several reviews, and might not lead to the revolution in mathematics the writer is "preparing the ground for", they do deserve a further investigation.