False sublimity is any writing that has the outward appearance of sublimity whilst not succeeding in transporting the reader through real, genuine elevated language. For Longinus, any writing that truly achieves the state of sublimity can easily be discerned through its impact on the reader, which he likens to a state of flight. Truly sublime writing elevates the soul of the reader and will, in addition, be writing that will stand re-reading and will stand the test of time, never losing its ability to transport the reader.
False sublimity therefore is writing that tries to attain sublimity but fails to achieve its goal. Note what Longinus says about writing that can be described as being falsely sublime:
They are turbid in expression and confused in imagery rather than the product of intensity, and each one of them, if examined in the light of day, sinks little by little from the terrible into the contemptible.
Longinus therefore develops his description of literature that is "not sublime but high-flown," and thus helps to distinguish between writing that achieves sublimity and writing that does not through the author trying too hard or aiming for sublimity but falling short of the mark and merely ending up using bombastic language that fails to elevate the reader.