My question pertains to how intuitionist perspectives on the philosophy of mathematics might apply to Greek geometry and number theory. It seems that the standard examples given to justify the intuitionist point of view are ultimately rooted in ambiguities arising from 1) the arithmetization of the continuum or 2) assumptions about actual as opposed to potential infinities. However, given that the Greek tradition 1) establishes a fundamental separation between the study of number and continuous magnitudes (length, area, volume, etc.) and 2) rejects the notion of actual infinity, I am curious about whether there are any instances at all of results from Greek geometry and/or number theory that an intuitionist might find unsatisfactory in some way.
To be slightly more specific, perhaps I can request an example (if one exists) of a proposition derived from, say, Hilbert's axioms for Euclidean geometry that is provable in classical but not intutionistic logic.
