The irony of belief as changing
Belief is a matter of staking one's personal opinion on an idea or principle for behavior. The irony of staking one's self on something essentially changing and fleeting is ironic, but that's precisely how Foucault describes belief. In his theory of the episteme, he shows that a belief is like a gene in evolution, and that it can mutate in individuals until perhaps they find a new modal variety that works better, and then by sharing that belief, they change the paradigm of their culture.
The irony of time
Time plays an ironic role in this work, because no one truly fathoms time, but yet we all experience it daily, without choice. Each day of life, we wake up without our own consent or permission, and each day has its own challenges and tasks. This is deeply ironic, because it makes human life adaptive, and it sort of pits time as the enemy of life, because after all, time is dragging each animal on the earth toward inevitable death. Foucault sees time as a field of tests that alter human belief.
The irony of mankind
What is a man or woman? They are people, to be sure, but what exactly is implied by that term? Foucault observes a sacred, ironic belief among human cultures, the preservation of the idea that humans are unique among God's creation and the animals. The irony is that this view might be true in some religious, metaphysical way, but in pure fact, there is simply no reason to suspect that humans are not only animals. The permanent assumption is very revealing into the ironic nature of human experience.
The ironic nature of truth and belief
Notice that Foucault demonstrates shared cultural assumptions and beliefs to be a kind of mechanism. It is a kind of inheritance that helps one to make sense of a perplexing reality. But, does that mean it is true? In one way, it is truer than fact: It is a true depiction of the human emotional landscape, just like language is a depiction of the human mind. But in another sense, cultural constructs are ironically false, usually, because after all, they are assumptions.