Zeno and Eubulides

A brief introduction is provided here to oceanic logic, a logic of continuity which, it will be argued in later chapters, is the logic of mysticism (as was of Bergson) and has been described in detail in my other book Theories of the Logos. The two main tools used are Zeno’s paradoxes and Eubulides’ sorites. In a Zeno-like paradox I cannot reach point B from point A because before I get there I should get to the middle point between A and B, and to the middle point between A and that first middle point, and so on forever: I should get to infinitely many points, which I cannot do in a finite time. The paradox arises, I explain, because of the attempt at dividing space infinitely into points, which ends up not so much dividing as annihilating space, as space is not made of points and cannot be reconstituted from points. Contemporary attempts at “resolving” the paradox by astronomically multiplying the number of points fare no better: even if there are uncountably many of them, real numbers are irremediably distinct from one another and cannot possibly capture continuity. The “paradox,” turned to good use, is a reminder of this impossibility. Once Zeno’s paradoxes have brought us to this dead end, Eubulides’ sorites indicate a constructive way out. Qualities like “bald” or “heap” are also continuous, and cannot be reduced to a collection of individual elements like hairs or grains of sand; rather, everything is equally bald or non-bald, a heap or not a heap, depending on how one looks at it. As a matter of fact, all the qualities we encounter in everyday life (qualities like yellow or smooth) are continuous: we can use power to enforce Aristotelian definitions of them (to decide, say, what score it takes to be admitted to a given college), but sorites will always be there to insist that there is no essential difference between those who are and are not admitted.