The distinction between 'metaphysical conviction' and 'formal-mathematical reasoning' is philosophically unstable, as Weyl explicitly grounded beauty in the internal logic of infinitesimal geometry.
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A distinction or argument that philosophers would struggle to defend logically—it might seem shaky or unclear on close examination.
Weyl(as a historical reference in physics)
Hermann Weyl (1885-1955) was a German mathematician and physicist who identified a mathematical problem about how to connect measurements made in different reference frames in a consistent way.
internal logic(as used in philosophy)
The consistent reasoning and rules that something is based on; when those rules contradict themselves, something violates that logic.