A [mathematical] ceiling is a [philosophic] term used to describe “the unseen, [unacknowledged, peer-enforced] barrier that keeps [many modern scientists] from rising to the upper rungs of [knowledge and truth], regardless of their qualifications or achievements.” (Adapted by this blogger from http://en.wikipedia.org/wiki/Glass_ceiling )
IF Plato (/ Socrates) is right:
▪ that “The Divided Line”1 as found in Plato’s Republic (Book VI: 509d-513e) describes two ruling powers and four levels of reality;
▪ that the ruling powers are set over two worlds: the visible and the intellectual [/ invisible];
▪ that each level of reality [from Images (A) to Sensible Things (B) to Mathematical Objects (C) to Form (D)] depends on the next higher level to make sense of itself;
▪ that each section has “different degrees of truth and that the copy is to the original as the sphere of opinion to the sphere of knowledge” (Plato);
▪ that each lower level collapses into image as we move to the next higher level, (i.e., “everything is but an image of a higher reality”);
▪ that we have potential to progress through levels of increasing intelligibility and “into a world that is above hypotheses” (Plato);
▪ that mathematics (C) exerts a powerful downward force—a type of “intellectual gravity”2 pulling back toward sensible things (B) (i.e., things of the senses), and thus, into a downward turning away from Form (D)—being the “world that is above hypotheses”;
THEN, has modern science fallen victim to the weight of this intellectual gravity, such that it will never be able to discover the truth, the whole truth, and nothing but the truth, unless it turns around?
2. See The Great Courses/The Teaching Company, Plato’s Republic, Prof. David Roochnik, Lecture 13.