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Full Idea
Facts about geometric laws receive satisfying explanations, by the intrinsic facts about physical space, i.e. those laid down without reference to numbers in Hilbert's axioms.
Gist of Idea
Hilbert explains geometry, by non-numerical facts about space
Source
Hartry Field (Science without Numbers [1980], 3)
Book Ref
Field,Hartry: 'Science without Number' [Blackwell 1980], p.27
A Reaction
Hilbert's axioms mention points, betweenness, segment-congruence and angle-congruence (Field 25-26). Field cites arithmetic and geometry (as well as Newtonian mechanics) as not being dependent on number.