The Collaborative International Dictionary of English v.0.48:

Pneumatology \Pneu`ma*tol"o*gy\, n. [Pneumato- + -logy: cf. F.
   pneumatologie.]
   1. The doctrine of, or a treatise on, air and other elastic
      fluids. See Pneumatics, 1.
      [1913 Webster]

   2. (Philos. & Theol.) The science of spiritual being or
      phenomena of any description.
      [1913 Webster]