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Philosophy of Mathematics

The Euclidean Programme

A systematic critical study of the traditional account of mathematical knowledge and methodology inspired by Euclid’s Elements.

Screenshot 2024-08-09 at 7.26.59 PM

 

Modern mathematics is not based only on deduction from self-evident first principles.

Project Leader: A.C. Paseau (Oxford) and Wesley Wrigley (LSE)

 

Mapwork of the project:

Aim

To give a rational reconstruction and critical evaluation of the traditional account of mathematical knowledge inspired by Euclid’s Elements.

Relevance

All of us have mathematical knowledge, but it seems to have a lot of peculiar properties, such as being unshakeably certain and requiring no experiment to discover. How is this possible?

Findings
  • The Euclidean Programme conceives of mathematical knowledge as based on watertight deduction from self-evidently true axioms (first principles). We argue that this account is not fit for understanding modern mathematics.

Publications

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Collaborations: University of Oxford