"...but ultimately the question is whether or not there is some level of ground truth that can be accessed in the form of mathematical theories." Didn't Gödel'

"...but ultimately the question is whether or not there is some level of ground truth that can be accessed in the form of mathematical theories." Didn't Gödel's Incompleteness Theorem show we should anticipate some unprovable fundamental Truths, since we are within the system we seek to define?