Similarly to an argument in logic, is it possible to deduce propositions by a computer from the Euclid's Elements just from postulates, common notions and definitions?
2026-03-26 19:11:53.1774552313
Is it possible to deduce by a computer all the propositions from the Euclid's Elements from its postulates, common notions and definitions?
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No. Euclid makes additional assumptions that aren't explicit. For example, he assumes two crossing lines have a common point (essentially the completeness axiom for real numbers).
Hilbert did work on building euclidean geometry on firm axiomatic basis, and if I recall correctly he needed around 20 axioms for it.