2022 Abstracts Stage 3

Exploring mathematics’ fundamental flaw: can analytical and moral philosophy be utilised to reform our understanding of Gödel’s Incompleteness Theorem as an example of self-reference paradoxes within mathematics?

Piercing a hole through the foundation of mathematics, Gödel’s Incompleteness Theorem resides outside the scope of consistency, provability, and solvability. A mathematical manifestation of self-referential paradoxes, the doctrine shattered the possibility of sustaining a complete system within mathematics, as Gödel utilised arithmetic itself to convey that there will always be axiomatic statements within mathematics that cannot be proved with certainty. However, in pursuit of clarity, can the philosophical attribution of morality and analytics be utilised to elevate an understanding of the paradoxical theorem? With both enterprises positing an abstract delineation of how truth and falsity are classified, the anomalous nature of the Incompleteness Theorem perhaps necessitates similar ascription. Whilst it is essential to note that the profundity of mathematical inquiry eradicates the possibility of the paradox being ‘solved’, the attribution of philosophy can perhaps offer avenues of illuminating novel aspects of the theorem. In doing so, the findings can be strung away from pessimism and towards mere curiosity. Mathematics may be defined by its incompleteness, but can philosophy offer an elevated insight that transcends an understanding beyond the mathematical enterprise?