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Claiming that inertial space is fictitious is equivalent to claiming that inertia itself is fictitious. Conversely, if you grant that inertia is a fact of physics and that inertial guidance systems exist and do excellent work, then you must also grant the viability of the concept of inertial space.
In the article it is stated:
"The scientific understanding of space and time is that there does not exist such a thing as measuring an object's position with respect to inertial space, and no such thing exists as measuring an object's velocity with respect to inertial space."
The above statements are not statements about the existence of inertial space itself, the statements are about existence of position with respect to inertial space and existence of velocity with respect to inertial space.