The Fictionalist Concept of Numbers: A Critique - Akpan, Etorobong Godwin; Ihunda, Victor Chizi (Researchparks Publishing, 2023)
The philosophy of mathematics is primarily concerned with the meaning of ordinary mathematical sentences and the question of whether abstract mathematical objects exist, with the objectives of strengthening the mathematical theory and aiding mathematics education. On the existence of mathematical objects, positions advanced have tended to crystallise in a number of oppositions. We find Platonists who believe in the existence of abstract mathematical entities, as opposed to fictionalists who deny the existence of such entities and attempt to strip mathematics of its abstract qualities. We also find realists who believe in the objective mind-independence of mathematical truth-values, who are opposed by various types of anti-realists or fictionalists. We investigate the ontological mathematical divide between mathematical fictionalists and mathematical realists using critical analysis as our method. This conflict includes the question of the existence of abstract mathematical objects and entities, as well as their epistemological justification, if they exist at all. We further upheld mathematical realism based on its ability to prove mathematical objectivity, apodictic, a priori knowledge and promote ease in mathematics education.