This came up in another thread, so rather than derail it, I'll start a new thread. I'm going to argue that the existence of both is equally probable.
First, what is the probability of advanced alien life existing (by advanced I mean the same tech level as we are (or higher))? I would argue that, at best, it is simply unknown, for three reasons:
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Lets use the word likely instead of probable. As everyone knows, calculating probabilities from on sample is impossible. So I would like to use the word likely in the hypothesis testing sense. Likelihood basically is the threshold of probability that one would bet on.
The likelihood of an organism having a sense that violates known laws of physics is not likely in my opinion. Therefore, I would say that advanced extraterrestrial life (ETL) somewhere in the universe is more probable than ESP because ESP has to violate the currently known laws of physics. However, the existence of advanced life forms obviously doesn't violate known laws of physics. I would argue that the total absence of life anywhere else in our vast universe doesn't satisfy currently known laws of physics.
In order for your question to make sense, one has to have tighter definitions of advanced life form and extrasensory perception. Otherwise, there the question is ambiguous. That is, there are far too many correct answers given the amount of information we have. So lets us narrow our discussion a little.
I believe that the definition of extrasensory perception (ESP) is a sense that violates laws of physics currently known by scientists on earth right now. Any sense that satisfies known laws of physics are not ESP.
As an example, consider electroreception. Lots of fish have been experimentally shown to have the electroreception sense. Electroreception has many of the characteristics that are often claimed for ESP. Now some people would claim that human ESP involves some type of electromagnetic field. However, few would say that electroreception is ESP. The reason is that the electric currents sensed by electroreception satisfy well known laws of physics.
Some birds have navigational abilities partly based on their ability to sense magnetic fields. Again, this is not called ESP since the properties of magnetic fields are well characterized experimentally and theoretically.
Dogs can use their sense of smell to distinguish between some emotional states. Dogs are often said to smell fear, which I think there has sufficient proof. They can track other animals. Humans can do some of the same, of course, though with far less reliability. However, olfaction is not considered ESP. The transport of gases satisfies known laws of physics, so olfaction is not considered ESP.
I was reading 'King Solomons Ring' by animal psychologist H. A. Lorenz. Someone owned a mule that supposedly could do arithmetic. Lorenz managed to show that the mule was actually reading the owners face very well. The mule couldn't do the arithmetic unless the owner knew the answer and the mule could look at his face. The owner for some reason was upset, since in his mind being able to read faces is a lesser skill than the ability to do arithmetic. The interesting part is that neither of them even considered calling the mules ability ESP. Having a 'natural explanation', which means not involving the violation of physics laws, was enough to exclude the possibility that the mule had ESP.
So ESP is a sense that somehow violates all known laws of physics. Now Homeopath practitioners and aurora therapists will disagree with me. However, I think that a biological function that transcends the physics of inorganic substances is unlikely to an astronomical degree.
Advanced life can be broadly defined as an organism that has behaviors analogous to humans with regard to thinking and memory. Basically, I think advanced life can be defined as organisms that can pass a Turing test.
There are several examples of advanced life on this planet, earth. Humans are the ones that developed the Turing test, so they certainly will pass it. However, I argue that there are a number of species that can pass the test albeit with a lower grade. Dolphins, octopi, and so forth. So there are a number of organisms with significantly different morphologies that can be said to be advance life.
All advanced organisms on earth are all related through a common ancestor, of course. So the probability of two organisms on earth being advanced is not independent. However, independence doesn't matter so far as violating the laws of physics. None of these organisms have been shown to violate the laws of physics. Hence, I can say with a high level of certainty that there can be advanced extraterrestrial life without violation of the laws of physics.
I would even go so far as to suggest the opposite. If humans on earth were the only advanced organisms in the visible universe, then some laws of physics may be be violated.
The statistical law of indifference would be violated. The law of indifference means that the probability of an independent event occurring is equal to an analogous event occurring under similar conditions. There are many places in the universe where similar conditions could occur. Indifference is really the basis of the Drake equation.
However, this may be controversial. Is the statistical law of indifference even a law? This is worth a separate thread entirely. So I won't push the law of indifference in this thread. I suggest that some of the other posters are unconsciously assuming that the law of indifference is a physical law.
So it comes down to asking whether a violation of known laws of physics are likely. Even if you show me an experiment where supposedly ESP is demonstrated, I would have to know how the laws of physics were violated. Whereas if a space probe photographs a cephalopod-shaped organism in the oceans of Europa, the likelihood of it being an advanced ET will be rather high. So I would say that the ET hypothesis is easier validated then the ESP hypothesis.