The Position of Fallibility in the Ontological Perception of Mathematics by Resorting to Realism

Subject Areas : MAth Education

mahmood koohgasht ¹ , Ahmad shahvarani semnani ^{2 *} , Mahmoud Abai Kopaei ³

1 - تهران جنوب دانشکده حقوق و علوم سیاسی
2 - دانشگاه استارا
3 - Assistant Professor, Department of Islamic Philosophy and Theology, South Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2023-08-21 Accepted : 2024-10-26 Published : 2025-12-01

Keywords: Mathematics, Fallibility, Ontology, Realism, Abstraction,

Abstract :

Abstract Understanding the ontology of mathematics faces a serious challenge when it goes beyond Platonism and interprets it as something real and physical in addition to being abstract and mental. Answering this challenge becomes more difficult when we consider mathematical facts as a human thing, a human being that can make mistakes. Now, mathematics, which was supposed to be considered provable and certain due to the mental matter, is doubted. To solve these doubts, philosophers try to reduce the distance between mental and physical objects in mathematics, but the process of understanding them in their realism faces a more serious challenge to create the concept of fallibility. Fallibility does not present itself as a problem, but is a positive feature for mathematics, and its place is in the understanding of the ontology of mathematics by resorting to realism as a driving element in the development of mathematics and its beating heart. Key words: Mathematics, Fallibility, Ontology, Realism, Abstraction

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