Quick Neutral Geometry Question Is the parallel postulate a statement in Neutral geometry that cannot be proven or disproved? I believe it is since neutral geometrys purpose is to not use the parallel postulate.
 A: The whole point of neutral geometry (aka absolute geometry) is to be neutral with respect to the parallel postulate. So, neither the parallel postulate nor its negation (nor any of a myriad of equivalent formulations) may be used in deriving proofs in neutral geometry. 
The fact the the parallel postulate can't be proved or disproved in neutral geometry follows by the existence of models (e.g., euclidean, hyperbolic, projective) in which the parallel axiom may hold or not (and if it does not, it can fail in different ways). If the parallel axiom was provable in neutral geometry, no non-Euclidean models of geometry would exist. If the negation of the parallel axiom was provable in neutral geometry, then the standard Euclidean geometry models would not exist. 
A: Precisely. Neutral Geometry, also known as Absolute Geometry, does not assume the parallel postulate. 
Roughly speaking, it uses Euclid's Axioms, apart from the parallel postulate. But careful treatments add axioms implicitly assumed by Euclid. 
