The irony of calculus versus philosophy.
Within the context of mathematics, Leibniz is one of the most intuitive, creative, but most of all, structured thinkers in the history of the world. However, his philosophy is bizarre and abstract and requires a tremendous amount of charity. Now, this irony aspect of his work does make some sense—after all, the scientific mind that brought calculus into the world is being applied to questions as broad and infinite in scope as "Is there a God?" so his answers are bound to be surprising.
The irony of the infinite.
The logical conclusion that Leibniz draws about the structure of reality itself is that the universe seems to be composed of an infinite amount of something infinitely small. This idea seems very similar to Leibniz's mathematical theories about limits and infinite values in calculus. Basically, in order for the static material world to exist, Leibniz says depends on a complex paradox of an infinite nature. This is ironic, given that to human eyes, the universe seems so obvious and natural.
The irony of perception.
Another strange aspect of Leibniz's work is the way he treats perception in the Monadologie. For Leibniz, in order for collections of organic matter to be capable of the kind of perception that we find in the brain, some other factors need to be true about the universe. He treats this with the idea of the monads, which he says contain the capacity for proto-consciousness, or even real consciousness. This is a strange idea, but the idea behind it, that the universe seems to be watching itself somehow, is now supported by scientific evidence. The universe does have a capacity for behaving differently when being observed, which must mean that Leibniz was actually on to something with these strange paradoxes.
The irony of metaphysical reality.
Even though technically reality seems to exist by its own virtue or "realness," that isn't necessarily the case. Leibniz makes the argument that the physical reality of timespace might be dependent on a metaphysical world that underpins it somehow. This argument could be seen as some kind of prophetic understanding of string theory.
The irony of time.
Another basic philosophical question that Leibniz must address in a philosophy of his type is the question of time. Is it a spectrum? Can the future be known? These are among the questions that Leibniz must consider, and ironically, the same person who gave us the science for rates of change, or calculus, also believes that time might also be a paradox.
