Upon rereading this it seems to me that this from DeWitt dramatizes best what I agree with him is the issue here "the quest of definitions is useless":
In that I presume he is evoking something similar to the Quest for the Holy Grail, and illustrating that with the absurdities Plato comes up with in Timaeus.
Obviously definitions do have some uses, and some definitions are highly useful.
But that's the issue, unless the limitations of "reason" or "logic"- in this case the use of words, in other cases the use of math and geometry - are kept firmly in mind, your subject to the worst kind of error from failing to keep the canonical faculties supreme.