TL;DR
This paper explores historical and philosophical perspectives on the metaphysics of mathematics, focusing on the existence of mathematical entities and the concept of infinity, highlighting common themes across different philosophies.
Contribution
It provides a comparative analysis of prominent metaphysical philosophies in mathematics, emphasizing biographical influences and shared underlying ideas.
Findings
Identifies key philosophical positions on mathematical existence.
Highlights common themes despite differing conclusions.
Connects biographical backgrounds to philosophical developments.
Abstract
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main topics will be the independent existence of mathematics and controversies over the nature of the mathematical infinite. After describing these ideas, I will demonstrate some of the similarities that are common to these philosophies, showing that despite reaching different conclusions many are guided by the same driving idea.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Mathematical and Theoretical Analysis · Quantum Mechanics and Applications