Can a psychic process never be proven purely through a chance experiment?

Question

No matter what test you use to try to prove a psychic, it would involve coming up with an outcome that seems too improbable to come true. This is what the James Randi prize is based on.

For example, if you had 1000 people all write down a number between 1 and 1000, or think of one, and the psychic guessed it correctly, almost no sane person on earth would still think it occurred by chance.

In fact, no matter how you design the experiment, almost anyone will think a psychic process is happening or that cheating must be going on. Either way, they would find it too unlikely to occur by chance. I want to focus on the latter part.

Suppose that there was an experiment designed that was quite literally impossible to cheat with. Every man and every woman on earth had tested this experiment. Let’s assume there is some sort of random number generator between 1 and 10^10 and the psychic simply guesses it five straight times.

Clearly, if the psychic guesses it right many times, almost every person on earth would think that chance did not cause that event.

But the logic of this would ultimately be:

1. X is too improbable under chance
2. X
3. X did not occur

Clearly, this is a fallacy. There is no such threshold, by definition. In fact, no matter how improbable an event is, it can happen.

One can more easily see this by imagining an experiment with multiple tries. For example, if the psychic guesses a number between 1 and 10^10 five straight times, one can imagine an experiment where the person tries guessing a number five straight times between 1 and 10^10 but simply has an infinite number of tries. Now on that particular series of tries he gets it eventually right, the probability of those particular trials would be the same as getting it right on just five tries, since each event is independent. This shows that any event, no matter how improbable, can happen, and in fact can be guaranteed to happen by simply repeating trials.

But if any event, no matter how improbable, can happen, is it then impossible to show that a psychic is operating purely through a chance experiment?

Note that I am not just saying that it seems impossible to definitely prove that a psychic is at work here using experiment. Of course, nothing can be definitely proven. But I am asking what reasoning one would use to show that a psychic is more likely at play here if he guessed a number between 1 and 10^10 vs. 1 and 3.

Because we don’t have any prior probabilities on psychics and can’t analyze a mechanism for it in this supposed experiment, I’m failing to see how even this more modest proof can be shown.

Answer 1

You can only prove certain classes of statement. If someone correctly guesses a number between 1 and 1,000,000,000 five times on the trot, that proves that the outcome was very unlikely to be a random effect. If you conjecture that the person was 'psychic', without explaining what you mean by that term, then in effect you are using the term 'the person is psychic' as shorthand for 'the person has done something that was very unlikely to have happened by chance', which is trivially true.

Answer 2

The problem with your reasoning is that it applies equally well to any result in experimental science. Can any general rule of nature be proved by virtue of a chance experiment? Obviously the answer is yes. The proof is that there are many complicated pieces of useful technology all around us.

Answer 3

In many instances a psychic can "stack the deck" in his/her favor. For example, asking some one to chose a number between 0 and 10 will nearly always yield an integer answer. Pi and e are perfectly acceptable answers since they are numbers but are rarely offered as answers so the odds of predicting a number increase dramatically. A true test for psychic behavior must eliminate all instances of this type of manipulation.