ABSTRACT
Zeno's paradoxes were intended to bolster the static monistic metaphysic by demonstrating that alternative conceptions that posit a plurality of moving and changing objects collapse into absurdity. Aristotle objected that Zeno had overlooked the fact that both space and time are infinitely divisible. The main view concerning the microstructure of the continuum is that space and time are discrete, that is, composed of finite atomic units, or quanta. Georg Cantor used the one-to-one correspondence method of determining when two sets have the same size to establish a remarkable result. When demarcating finite from infinite collections or sets Cantor took Galileo's paradox as his starting-point. Commentators tend to agree that the Dichotomy is the more fundamental, and it is not difficult to see. Adolf Grünbaum goes on to point out that contemporary mathematics is equipped with a more general way of measuring the sizes of sets containing non-denumerably many members: the "measure theory", initially developed by Henri Lebesgue and others.
