Becker–Blaschke problem of space

• I reconstruct Becker–Blaschke problem of space.
• This gives new insights on the geometrical foundations of relativity theories.
• Becker and Weyl differently connect the infinitesimal and finite levels of space.
• Becker and Weyl disagree on the role of isotropy in relativity theories.

In a letter to Weyl, Becker proposed a new way to solve the problem of space in the relativistic context. This is the result of Becker׳s encounter with the two traditions of thinking about space: Husserlian transcendental phenomenology and Blaschke׳s equiaffine differential geometry. I reconstruct the mathematical content of the Becker–Blaschke solution to the problem of space and highlight the philosophical ideas that guide this construction. This permits me to underline some common properties of Riemannian and Minkowskian manifolds in terms of an unusual notion of isotropy. Finally, I will use this construction as a support to analyze several philosophical differences between Weyl׳s and Becker׳s proposals.