The problem of infinity: A pendulous swing between empiricism and metaphysics

Abstract

This thesis is an attempt to evaluate the resolutions and further discussions about Zeno’s paradoxes of motion, which approach the matter from two different viewpoints: empirical and metaphysical. I examine the empirical arguments for the logical impossibility of completing an infinite series of task, and more generally, for the self-contradictoriness of the actual infinite, as well as the metaphysical arguments and analyses which attempt to provide infinity with an extensive comprehension by revising the language, or by understanding more about the language we presently use. I aim to show that the empirical arguments are not justified in claiming that the notion of infinity leads to a contradiction, and that we should strictly accept finitism. In addition, I examine the good and the rather poor examples of philosophical thought experiments about infinite processes, which helps to view infinity from new and substantial perspectives. Through such an examination, my objective is to argue that the arguments holding empirical and metaphysical concerns neither trivialize nor annihilates one another. In fact, they shed light on the notion of infinity by providing distinct understandings. In this regard, even the arguments by the empirical refusal of the actual infinite, when examined thoroughly so that their mistakes and shortcomings are revealed, are illuminating for further metaphysical inquiry.