Question: Recently, I have been discussing the subject of parapsychology with a group of Objectivists. There seem to be four distinct perspectives on the subject: (1) Evidence strongly supports the existence of parapsychological phenomena (e.g., ESP, remote viewing, clairvoyance, the ability to influence random number generators). (2) The jury is still out as to whether parapsychological phenomena exist, and it is worth investigating further.
(3) While parapsychological phenomena could exist and the hypothesis is worthy of consideration, there is no evidence in favor of this hypothesis. It may or may not be worthy of further investigation, based on a cost-benefit analysis. (4) The hypothesis that parapsychological phenomena exist contradicts what we know about reality. Therefore, there could be no evidence that supports this hypothesis. What appears to be supporting evidence is the result of errors of interpretation. The subject is arbitrary and should be rejected outright.
Which perspective on parapsychological phenomena is justified from an Objectivist standpoint?
does not recognize "parapsychological phenomena." As far as I know, there is no reliable evidence for any of them. Some forms of the parapsychological (such as clairvoyance or foreseeing future events) appear to be obvious cases of mysticism. We wish we could know the future with the certainty and directness of perception, so some people feel they do. Other cases merely seem implausible and lack any strong evidence.
So I think an objective view of the parapsychological would vary between your perspectives (3) and (4) depending on the type in question and one's context of knowledge. For example, if one didn't know much about the brain and the nervous system, or if one didn't know much about physics, then one might reasonably take position (3) and consider it possible that humans naturally have E.S.P. But with a better understanding of the nervous system and brain, one would be very skeptical of parapsychological claims, not only because there would be no reliable evidence in their favor, but also because there would be no causal account for them that could integrate with what was already known.
holds that one should reject arbitrary claims out of hand. But given that knowledge is contextual and knowledge is worth having for its practical utility, I must emphasize that this is a practical epistemological position. One rejects the arbitrary because one has no reason to consider it; considering it is, for all we know, going to be a waste of time.
Now claims that are arbitrary in one context can be true in another. Suppose a tribesman in the New Guinea highlands 5000 years ago randomly declared: "Malaria is caused by an invisibly small parasitical organism." That would be arbitrary: He wouldn't have any evidence that clearly pointed to this rather than another hypothesis; he would never have seen any such organism, for example. But in fact, it is true that there is such a parasite. If the other tribesmen rejected any consideration of their fellow's medical claim (supposing that they did as Objectivism counsels in this case), they would have been practicing cognitive economy—and practicing strict objectivity.
So it may be that the pragmatical rejection of the parapsychological (3) is not all that different from the principled rejection of the parapsychological as arbitrary. Objectivism accepts all facts. And it demands, at a minimum, some factual reasons for even considering an idea. And that applies to parapsychological claims as much as to any others.