We must begin with two convictions prevalent in Western thought and old as philosophy itself, one that concerns us as cognitive beings, another the nature of reality itself. To take the better-known first: in geometry, the scientifically oriented human mind has found its apogee of clarity, lucidity, and certainty. Through the tumults that gave birth to the modern era, the status of geometry remained strong: nature itself was seen, to an increasing degree, in its terms. There is perhaps no more striking indication of this than the memorable passage in Galileo’s The Assayer of 1623:

Only geometry is thus able to capture the very texture of nature: the universe is written with its characters. This spirit finds its way to the thought of Benedict de Spinoza (1632–77), who in his masterpiece, the Ethics, claims that however profound and intricate a question, it can be answered, but only after realizing a fundamental truth:

That the philosopher renowned for expressing his ideas in geometrical order has a high regard for mathematics is of course only what we should expect; but it should be appreciated that here geometry is not conceived of as a method or manner of exposition. Rather, it is the branch that has revealed the inner make-up of things. This idea manifests itself in various ways in Spinoza’s thought, and forms one of the recurring themes of this study.