When the heroine of Cavendish’s "The Blazing World" is installed as empress, she receives a parade of different sorts of animal-men that includes spider-men mathematicians and lice-men “geometricians.” She dismisses the spider-men as a waste of her time and dissolves the society of lice-men, declaring that “there was neither Truth nor Justice in their Profession.” Why? Peterman provides an interpretation of Cavendish's metaphysics and epistemology with an eye to explaining how she thinks that the human mind represents the world. She goes on to show that Cavendish offers two kinds of critique of pure and applied mathematics. The first kind of critique shows that mathematics is inadequate to describing its purported objects. Pure mathematics describes non-beings, Cavendish thinks, and so represent nothing in nature. Applied mathematics cannot accurately represent nature for several reasons, including that nature’s figures and motions are infinitely diverse and cannot be categorized so that they can be enumerated, that art cannot imitate nature, and that since the whole is prior to the part in nature, parts cannot be defined independently of the whole, which is required for enumeration. But the second kind of criticism that Cavendish develops is even deeper and more unique. Instead of focusing on the ways that mathematics is inadequate to the object of scientific study, Cavendish’s materialism about the mind gives her ground to argue that mathematical thinking (and other formal methods in philosophy) deforms the subject of
representation, not just the object.