Mathematics as Objective Knowledge
摘要
Among the various perspectives offered by philosophical studies about the status of mathematics, Immanuel Kant’s ideas, in my opinion, are a valuable and essential fil rouge that can highlight in a satisfactory way how mathematics and cognition are tightly intertwined. In order to avoid outdated ontological views, Kant offers a philosophical anti-metaphysical framework for mathematics that serves as a fundamental defense of its function in higher-order cognitive activities and its ability to render the world rationally intelligible. Kant shows how the empirical world is transformed into a world of mathematical relations to the aim of having excellent knowledge results. I claim that it is Kantian philosophy of mathematics that has cleared the way for later research on the cognitive and epistemic benefits of mathematics. I will make use of this traditional viewpoint to offer a fresh perspective on some of the primary issues surrounding the matter: (1) the naturalization and historicization of mathematics, which demonstrates the close connection between the cognitive processes of discovery and application of mathematics and their historical development, (2) the emphasis on the cognitive benefits of mathematical modeling in research as a counterbalance to the current overzealous focus on big data management, as a competitive means of producing scientific results, (3) the absence of a mathematically sound cognitive schematic endeavor to produce scientific intelligibility, which frequently results in flimsy substitute “modeling” that is falsely claimed to be scientific.