On the Reality of Mathematics
Mathematics is an integral cornerstone of science and society at large, and its implications and derivations should be considered. That mathematics is frequently abstracted from reality is a notion not countered, but one must also think upon its physical basis as well. By segmenting mathematics into its different, abstract philosophies and real-world applications, this paper seeks to peer into the space that mathematics seems to fill; that is, to understand how and why it works. Under mathematical theory, Platonism, Nominalism, and Fictionalism are analyzed for their validity and their shortcomings, in addition to the evaluation of infinities and infinitesimals, to show that mathematics, in its purest form, has little to do with tangible things. Under the physics section, quantum mechanics and astrophysics are investigated, but for the opposite purpose: to show, using the examples of black holes and quantum entanglement, that mathematics is, at base, still the language of the “real” and formal sciences. All of these pieces are contrasted with their philosophical and theological principles to show their ramifications with regard to both atheistic and theistic worldviews. Finally, my personal, synthetic philosophy concerning numbers is delineated in contrast to the ideologies mentioned before.