Irrelevant appeals are very popular among religious believers, occultists and paranormalists. The irrelevant appeal to authority may be the chief fallacy committed by true believers, but this fallacy rarely occurs in isolation from other fallacies.
The irrelevant appeal to authority may be defined as the attempt to garner support for a controversial belief by appealing to the fact that one shares the belief with an important person, such as Einstein or Jesus. The important person is held up as giving authority to the belief. At the very least, the appeal to authority attempts to establish that one's belief puts one in good company. This appeal is generally combined with suppressed evidence, namely the failure to mention any important persons who hold the contrary opinion, such as Epicurus, Hobbes, Spinoza, Diderot or Bertrand Russell. On the contrary, the irrelevant appeal to authority is often joined with an ad hominem attack. One attempts to garner support against the contrary of one's belief by noting that evil or contemptible people agree with your enemy's viewpoint. For example, one notes that Nietzsche, who went insane, was an atheist.
The irrelevant appeal to authority is often a type of genetic fallacy, attempting to judge a belief by its origin rather than on the arguments for and against the belief. If the belief originated with an authoritative person such as Jesus or Einstein, then the belief is held to be true against a contrary belief not originating from a prestigious or noble source. Both the irrelevant appeal to authority and the ad hominem attack are based on the erroneous notion that an idea is a good one if good people believe it, and a belief is not to be trusted if the person holding the belief can't be trusted. This fallacious notion is sometimes expressed as: you can't trust the message if you can't trust the messenger.
A critical thinker will realize that good people sometimes have false beliefs and bad people sometimes have true beliefs. It may be true that Nietzsche went insane and that Aquinas was obese but even crazy fat men sometimes make sound arguments. It is their arguments which must be evaluated not their sanity or weight. On the other hand, even sane skinny persons sometimes reason unsoundly to unreasonable beliefs. Again, it is their arguments which must be evaluated not their size or their sanity.
The irrelevant appeals mentioned so far are often joined with another: the irrelevant appeal to popularity. Here one cites not one, but several, authorities as holding a view in common. A critical thinker should recognize that a belief does not become more reasonable as more people believe it. Even if there is a significant correlation between reasonable people and reasonable beliefs, and unreasonable people and unreasonable beliefs, it would not follow that there is necessarily a causal connection between the two. To reason that there is a causal connection between two items only because there is a significant correlation between the two items is to commit another fallacy, the fallacy of false cause reasoning. If there is a correlation between reasonable beliefs and reasonable people it is highly probable, as well as desirable, that it is the reasons for a belief which cause them to accept the belief. It is not very probable, nor desirable, that the fact that reasonable people believe something causes it to be reasonable.
The truth or falsity, reasonableness or unreasonableness, of a belief must stand independently of those who accept or reject the belief. Likewise, truth or reasonableness do not depend on how many people share a belief or not. Furthermore, one should examine the character of an argument not the character of the person making the argument to determine the argument's worth. Many worthy people make unworthy arguments; and many despicable people make good arguments at times.
For those who do not see the obviousness of these claims, consider the fact that at every period in history there have been large numbers of respected, decent, intelligent, authoritative people who have believed what we now know were errors. Consider, too, that an infinite number of infallible popes will not make 2 + 2 equal to 5 simply by virtue of the fact that so many reliable sources believe it to be so. Nor would an infinite number of Ph.D.'s in psychology from prestigious universities all believing that political conservatism is a mental illness make it so.
Theistic opponents of atheists often complete their irrelevant arguments by making straw manattacks, i.e., attacks on views not really held by the atheist. The alleged views which are attacked are selected because they seem close to the views of one's opponent and they are easy to refute.
For example, I have claimed that the belief in God is a delusion. I have never claimed that being deluded means one is stupid, ignorant, uneducated, unintelligent or illiterate. Yet, one of my critics has written:
I guess Mr. Tolkien is intellectually faulty, after all, he taught at Cambridge, not Sacramento City College. I guess we can say that all the Oxford philosophers who were theists (and religious, oh no!), were/are also "deluded". Poor C.S. Lewis, who graduated first place honors in philosophy from Oxford, or Father Copleston who graduated first place honors from Oxford, or Father Brian Davies, O.P., et al. Oh, and let us not forget the stupid deluded Jacques Maritain and M. Gilson, what with their pitiful Sorbonne education... Oh, and the most "deluded" of all? Hmmm, let's see, Newton, Leibniz, Pascal, Descartes, ...
As I noted above, I have never claimed that being deluded and being unintelligent were either the same thing or even related. In fact, I have stated that, as far as I can tell, intelligence is completely independent of the tendency to be deluded. In any case, I have never claimed that theists are stupid or unintelligent. Some are, of course, but I would agree with my critic that everyone he names (except for Fr. Davies, whom I've never heard of) is quite brilliant. But by making me out to hold the position that I have implied that these brilliant men are stupid, my critic tries to make my position look ridiculous. But it is a straw man he has attacked, not my position.
Note my theistic opponent's appeal to authority and popularity, as well. Finally, notice how, for good measure, my critic implies that since I do not teach at a prestigious university such as Oxford, but at Sacramento City College, I am not to be trusted. Apparently, since the arguer teaches at a community college, the argument he makes is to be rejected. This is an ad hominem attack, typical of desperate theists who can't even spell pitiful. (It is desperately painful to resist the ad hominem temptation and deliciously pleasant to give in to it. Hence, I can easily forgive my enemy for trying to cast doubt upon my opinions because I teach at a community college.)