Gleason's theorem has a constructive proof (Q1582232)

The paper deals with the problem of finding a constructive proof of Gleason's theorem (stating that if \(f\) is a nonnegative function on the unit sphere with the property that \(f({\mathbf x})+ f({\mathbf y})+ f({\mathbf z})\) is a fixed constant for each triple \({\mathbf x}\), \({\mathbf y}\), \({\mathbf z}\) of mutually orthogonal unit vectors, then \(f\) is a quadratic form). Some solutions of this problem and the following discussions that appeared in the Journal of Philosophical Logic are examined.