The big problem with telepathy, and with parapsychology as a field in general, is that science is all of a piece. Thus, physics is consistent with chemistry, biology and so on. So the question is not "what knowledge can we derive on the assumption that we know nothing?" - but "what knowledge can we derive given what we know already?"
Basic physics - extremely well-understood and well-tested physics - leaves it not looking good for parapsychology as a field in any way. Sean M. Carroll points out ("Telekinesis and Quantum Field Theory." Discover Blogs: Cosmic Variance 2008-02-18.) that both human brains and the spoons they try to bend are made, like all matter, of quarks and leptons; everything else they do is emergent properties of the behaviour of quarks and leptons. And the quarks and leptons interact through the four forces: strong, weak, electromagnetic and gravitational. Thus either it's one of the four known forces or it's a new force, and any new force with range over 1 millimetre must be at most a billionth the strength of gravity, or it will have been captured in experiments already done. (Sean M. Carroll. "Life and the forces of nature." Preposterous Universe, 2004-05-03.) So either it's electromagnetism, gravity or something weaker than gravity.
This leaves no force that could possibly account for telekinesis, for example. Telepathy would require a new force much weaker than gravity and a detector in the brain evolved to use it for signaling. Precognition, the receipt of information transmitted back in time, would violate quantum field theory.
What this means is that the ideas parapsychology purports to investigate have pretty much no chance of being right even before we test them directly.