This fallacy name is commonly applied to two similar but distinctly different fallacies: Appeal to Authority, and Appeal to Irrelevant Authority. It's more-or-less the opposite of Ad Hominem.
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Appeal to Authority (or Argument from Authority)
Implying or stating that there is a causal relationship between who says it and whether it's true or not:
"Newton said that for every action there is an equal and opposite reaction, so there is."
It is true for most physical interactions that there is an equal and opposite reaction to an action, and it's true that Newton said so, but it's not true because Newton said so.
While it can be valid to call upon expert opinion to support a position, it is not valid when the status of the person as an expert is the only thing called upon. While the statement may be true, it is not true because the authority stated it.
A particularly insidious variant will attempt to pass off an argument based on Mister Authority's statements as actually having been made by Mister Authority himself; the implication is "So you think you're smarter than Mister Authority?"
In real life, this fallacy shows up most often in discussions or arguments about both hard science and soft sciences like sociology.
Word of God, when used in the context of what an author or creator intended in his work. By definition, Word of God is true. Unless you subscribe to Death of the Author, of course, in which case, Word Of God carries no more weight more than Word Of The Guy Who Runs The Newspaper Kiosk or Word Of Your Sixth Grade Teacher.
Calling upon an expert in a field, but basing the argument upon something besides their status or assumed infallibility. For example, trusting a doctor's judgement in a medical manner not because because he is a doctor, but because he has demonstrated his knowledge and has charts or other evidence backing up his claims.
On QI, when discussing the fact if you fire a bullet parallel to the ground and drop a bullet from the same height at the same time, they will hit the ground at the same time, Stephen Fry appeals to the audience, saying, "Are there any scientists here who will back me up on this?" Rich Hall then seems to point out this fallacy by following up with, "Or any assassins?"
Urban legends site Snopes has a section called The Repository Of Lost Legends, which consists of completely ridiculous stories marked as true and obviously true stories marked false. The "additional information" section for each page links to an essay about why you shouldn't believe a story just because it comes from a seemingly reliable source.
In Doom House, when giving advice to Reginald P. Linux, Officer Cop likes to always remind Reginald that he is a cop just to give his advice that little bit extra persuasiveness. But this is, of course, a crafty ruse to get Reginald to inadvertently trust a terrorist.
More accurately called Irrelevant Authority, Inappropriate Authority, or Questionable Authority, Irrelevant Authority is citing someone as an expert even though they are not really an expert on the question under discussion; their expertise is in an unrelated field; their "expertise" is not in a legitimate discipline at all (e.g. an "expert" psychic or ghost hunter); their expertise is what is under discussion; they have not been demonstrated to actually exist; or they made the statement in a state where their judgment was suspect (ie, they were drunk, high, senile, stressed, angered, etc). In some cases, they do possess a legitimate expertise and renown in some field, it's just that said field is unrelated to the one being discussed.
In Rain Man, the title character is an autistic savant, and his condition proves to be a major asset in blackjack. Tom Cruise's character, impressed at his ability, then trusts his judgment at roulette, only to find that the advanced math skills that allow him to count cards accurately do nothing to predict the outcome of a roulette spin.
In Left Behind, the entire world believes a Technobabble nuclear physics explanation of the Rapture because a botanist and the president of Romania (note: not a nuclear scientist) say it's so. Later on in the book, the pseudo-religious explanation of the Rapture is accepted because it's espoused by an airline pilot.
In one episode of Dinosaurs, in a trial for the heretical view that the earth is round, the "expert" who testifies that the world is flat's stated qualifications are that he is wearing a white lab coat and his proof that the world is flat is the existence of a flat-earth "globe". If a man in a white lab coat has a flat-earth globe, he can't possibly be wrong. And not just one flat-earth globe! The company that makes 'em has a whole warehouse full of the things! What more proof do you need?
When the Mass Effect sex-scene fiasco was at its height, Fox News brought in an "expert" who knew nothing about the game, and wasn't even regarded as an expert in her own field (child psychology).
In The Simpsons episode "The Monkey Suit", creationists seeking to ban the teaching of evolution succeed by getting a scientist to testify in court that evolution is a myth — a scientist with a degree in "Truthology" from "Christian Tech".
That and in another episode, when Marge said "children need discipline, just ask any certified advice columnist."
A product called "Vitamins Of Linus Pauling, Two Times Nobel Prize winner" is marketed. His first Nobel was for Chemistry, on the nature of chemical bonds. That's great, but it has rather little to do with vitamins. His second Nobel is the Peace Prize, which has nothing at all to do with vitamins. His connection with vitamins is that he became rather ...obsessed... with mega-doses of vitamin C in his later years, but that part of his work caused much controversy and his results were unreproducible.
Pierre Salinger gained much press attention for his claims of conspiracy involving TWA Flight 800. Salinger was President Kennedy's press secretary, a senator, and a journalist - including a stint as an award-winning foreign correspondent - but wasn't particularly an expert on aviation or international terrorism.
The American sandwich chain Firehouse Subs brags in its tagline that it was "Founded by Firemen." Needless to say, firefighters are not known for their cooking skills.
Marketers of pseudoscience do this quite frequently by appealing to Dr. So-And-So, who is possibly Not That Kind of Doctor or else regarded as a crank by his or her colleagues. For example, Deepak Chopra may have a legitimate medical degree, but his focus has moved on to pure pseudoscience and most practitioners of science-based, evidence-based medicine consider him to have gone over to the dark side. Saying, "Deepak Chopra said X, therefore it's true," is an Appeal To Authority. Saying, "Deepak Chopra is a quack, therefore this claim is false," is another fallacy, the Ad Hominem. The claim stands or falls based on evidence.
Penn & Teller: Bullshit! did an episode on multilevel marketing. A proprietary drink was marketed with Dr. Chopra's name getting dropped in the pitch. It did not impress the customer, who did not know who Dr. Chopra was.
The ol' lab coat routine. Lab coats are appropriate if you are in a clinical setting or worried about contaminating your clothing. Donning one out of context is an attempt to look like a scientist or physician. Lab coats are safety gear. They're designed to resist chemicals or catch pathogens, then be removed to minimize the amount of contamination or harm suffered by the wearer. It is like wearing a fireman's jacket while pretending to be an expert on safety.
Or, as XKCD puts it, "Did you know you can just buy lab coats?"
Diploma mills allow you to do this. These uncredited, unsanctioned bodies allow you to get a degree in whatever field you wish based on your "life experience," without a peer-reviewed course of study. For a small fee, you can be awarded a doctorate in any field you wish and then appeal to your status as a doctor. Don't expect it to carry any weight in a real academic setting. Note that a for-profit school is not the same thing as a diploma mill, as a For-Profit school can still insist on proper academic rigor and only becomes a diploma mill if it drops its standards.
Parodied at Thunderwood College, a website by Brian Dunning of Skeptoid, which allows any visitor to instantly create a very valid-looking diploma in just about any field of nonsense. It's actually useful for making cheap theater or table top game props.
Also addressed seriously by Skeptoid in an episode called "All Scientists Are Not Created Equal", pointing how much the media and other advocates of a particular position love to bring on 'a scientist' to back up their position without much in the way of context: "You need to know who they are, what their interest is, and especially what the preponderance of opinion in the scientific community is. You need to know if the scientist being quoted actually has anything to do with this particular subject."
On that note, appeals to Stephen Hawking when discussing religion (both in a positive and negative sense) are very common, despite the fact that his main field of study is Science, and he actually has very little expertise/experience with Theology.
Conversely, the list of scientists whom the supporters of "intelligent design" have come up with to support their claim; virtually all of these have their degrees in different areas of science. Project Steve is an attempt to show how ridiculous this means of supporting a scientific claim is.