"Musil's thinking maintains a remarkably straight trajectory(...) At the core of his thinking is an idea expressed most succinctly in a mathematical metaphor(...) There is an infinity of rational numbers, that is to say, numbers that can be written as the ratio of two whole numbers. There is also an infinity of irrational numbers, numbers that cannot be expressed as any such ratio. But their two orders of infinity are not comparable. The infinity of irrationals is "greater" than the infinity of rationals. In particular, between any two rationals, no matter how close, lies a cluster of irrationals. Stepping from one rational to the next, as we do every day, is (...) like crossing a bridge whose piers are joined by something that does not "really" exist.

To live and function in the world of the rational, we must deliberately banish from our awareness the irrational that lies dense under our feet and about us. We must accept a convention regarding what is to be treated as belonging to the real world. Such a convention will define everyday language (here Musil is close to his Austrian contemporary Wittgenstein). However, Musil proceeds, accepting the fact of a linguistic contract should not mean that we are committed to the repression of the irrational. (...) we can maintain a certain reserve toward the real world, a living sense of alternative possibilities. This reserve defines one as (...) "possibilitarian," someone prepared to exist in "a web of haze, imaginings, fantasy and the subjunctive mode," to live a "hovering life" without ideological commitment, to be a "man without qualities" whose natural mode will be the mode of irony ("With me," said Musil in an interview, "irony is not a gesture of condescension but a form of struggle").