Paradox

304 A BRIEF HISTORY OF THE PARADOX. . . No one knows, or even feels, that anything is a limitor a defect until he is at the same time above and beyond it.(1959, section 60)Hegel rejects the idea that reality is something which underliesappearance. He says that reality is manifest in appearance.Characteristics that we normally think apply only to ourrepresentations of reality actually apply to reality itself. Forinstance, we tend to think that vagueness is a property of ourdescriptions of clouds. But Hegel insists that the clouds arethemselves vague. The difference between the word “cloud”and a cloud in the sky is less drastic than “precise” philosopherscontend. The affinity between an object and its representationis ensured by Hegel’s retention of Kant’s theme thatreason constructs appearances. Reason dictates the structureof reality. Since reason is the ground for what is real, the realis what is rational.Kant believed there were only four antinomies becausehe thought there were only four ways to misapply transcendentalideas to phenomenal reality. Hegel rejects Kant’sassumption that the contradictions are products of transcendentalillusion. Hegel takes them to be accurate perceptionsof an inconsistent reality. It is possible to view the Penrosetriangle (fig. 1.2) and other impossible figures as consistentpatches of ink. But the correct way to see them is inconsistently.“Square circle,” “many-sided circle,” and “straightcurve” are self-contradictory. Yet geometers regard circles aspolygons composed of very short sides. In an era whenarithmetic was taken to be the science of quantity, mathematiciansstruggled to explain the usefulness of negative numbersand imaginary numbers such as 1. If multiplying anegative with negative number yields a positive number,