#### EXCERPT

In the next three chapters we will review other examples of high mathematics in action, in the conviction that advanced mathematics—and, in this case, contemporary mathematics—provides philosophy with *new* problematics and instruments, as we shall see in part 3 of this work. But firstly, in order to present the mathematical landscape more commodiously, we will sort a few of its striking creative contributions into three complementary spectra: *eidal*, *quiddital* and *archeal* mathematics. Of course, these mathematical realms (and the neologisms that denote them) *do not exist in a well-defined way* as such, and must be understood only as expository subterfuges for easing the presentation and to help us get our bearings in a complex terrain…