"We Think That We Think Clearly, But That's Only Because We Don't Think Clearly": Mathematics, Mind, and the Human World

TL;DR

This paper explores the philosophical debate on the nature of knowledge, emphasizing the human-centered aspect of mathematics and science, and suggesting there may be deeper, yet undiscovered, forms of understanding.

Contribution

It analyzes philosophical dialogues and arguments to highlight the human influence on mathematical and scientific knowledge, proposing the existence of a deeper form of knowledge beyond current scientific understanding.

Findings

Mathematical truth is viewed as a human construct.

Scientific theories are shaped by specific mathematical and experimental tools.

There may be a deeper, undiscovered form of knowledge.

Abstract

This paper is concerned with a dialogue between Rabindranath Tagore and Albert Einstein, where Tagore argued that our knowledge is essentially human, while Einstein maintained that some kinds of knowledge are more objective. Arguments by Davis and Hersh concerning the nature of mathematics support the idea of mathematical truth being a human construct. It may further be argued that the scientific theories we arrive at are very much a result of the particular mathematical and experimental tools that we use. There may however be a deeper kind of knowledge that science has yet to understand.