The Philosophical Implications of Set Theory in Infinity

Abstract

What does the term “Infinity” mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scription of the three philosophical foundations of mathematics – formalism, intuitionism and logicism – in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic aforementioned definitions of infinity. Indeed for example, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals’ beauty fully (Nũnez, 2005). This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness (Maor, 1986). Actually, in essence this is what mathematics is: the science of researching the limitless.