Why Mathematics Shapes Reality: A Philosophical Inquiry

Abstract

Most discussions in the philosophy of mathematics have been dominated by questions concerning the nature of mathematical entities, such as numbers and sets, while comparatively little attention has been given to the applicability of mathematics. Yet mathematics has played an indispensable role in the development of the natural sciences, suggesting that any complete philosophy of mathematics must account for its remarkable effectiveness in describing the physical world. Two major schools of thought, namely Platonism and Nominalism, have largely neglected this issue and seem unable to provide a satisfactory explanation for the tremendous success of mathematics in the physical sciences. However, this limitation does not apply  universally across all philosophical approaches. This limitation specifically reflects the weakness of Platonism and Nominalism in connecting mathematical entities to empirical reality. In this article, we investigate the philosophy of mathematics from the standpoint of alternative views, particularly Steiner’s Anthropocentric approach and Franklin’s Aristotelian Realism, which offer promising frameworks for understanding the deep connections between mathematics and empirical reality. This preference for alternative approaches is justified by their potential to explain the effectiveness of mathematics as a tool in science, emphasizing its applicability and alignment with scientific contexts. The result of this study indicates that Aristotelian Realism provides a more robust framework for explaining the empirical success of mathematics compared to other approaches. Aristotelian Realism stands out as a superior philosophy of mathematics, centering its applicability as the core of its philosophical understanding.