The Collaborative International Dictionary of English v.0.48:

Eleatic \E`le*at"ic\, a. [L. eleaticus, from Elea (or Velia) in
   Italy.]
   Of or pertaining to a certain school of Greek philosophers
   who taught that the only certain science is that which owes
   nothing to the senses, and all to the reason. -- n. A
   philosopher of the Eleatic school.
   [1913 Webster]