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What Fallacy(s) is this?

Appeal to authority is a logical fallacy, so only if you are discussing the logical soundness of an argument is it a trump card.

All it is saying is that the type of argument alone can not be used to provide proof of a conclusion.

Unfortunately it is often used to try and undermine perfectly reasonable and sound conclusions that do not rely on the logic of an argument but on empirical evidence.

It is that adage that “there is only proof in mathematics”.

The world is simply too complex to be reduced to only statements that we can prove to be true (never mind Gödel) by logic alone. We will always end up relying on the work of authorities, we just need to keep in mind what that means in regards to the soundness of a conclusion.

ETA: An example

Claim: “I owed £1000 to the tax authorities”
Skeptic: “How did you know that?”
Claimant:”My accountant told me”
Skeptic: “Aha! That’s an appeal to an authority, you don’t know that!”
Claimant: “The tax authorities agreed with her”
Skeptic: “No that just an appeal to another authority, you simply don’t know that!”
Claimant: “The court agreed with her and the tax authorities”
Skeptic: “You keep appealing to these authorities, don’t you know that’s a fallacy!”

This is correct. On a related note, not everything that is wrong is a fallacy. A fallacy is an error in logic. There are other ways to be wrong.

In the case above, the claimant is basically saying, "I do not understand the tax code myself, but those who seem to understand it say that I owe $1,000." That is not an absolute, concrete, proof that you do in fact owe $1,000, but it is a reasonable conclusion. The skeptic is not presenting any actual argument in this case, simply complaining about an appeal to authority.

If the skeptic above were to say, "The tax code says this, and your situation is that, and therefore you do not owe $1,000," and the claimant were to respond, "but my accountant says so. You are clearly wrong", that would be an appeal to authority fallacy. On the other hand, if the claimant were to say, "I don't understand your argument, or his, but he's an authority so I'm going with him", that wouldn't be any sort of fallacy. That's a different statement than, "He's an authority so he must be right."
 
Bottom line, IMHO? An argument is either in agreement with evidence, knowledge, etc or it isn't. It doesn't matter one bit who makes the argument. "You aren't an expert," is an invalid objection made by people who, themselves, aren't in a position to judge the validity of the argument. Solid information trumps credentials every time.

When the argument goes against some bit of information they gleaned from someone they see as an authority, they would rather make the simple " you're not an expert" objection than actually think about it and question the authority figure. This is especially true when the information comports with their own internal world view: "Astrology is valid and Dr. Oz just said that your sign can help you understand your health!" Most people who watch "celebrity doctors" on TV digest the information presented unquestioningly, "Dr. Oz is a respected doctor! He wouldn't give me bad information." This is very hard to overcome. All we can do is present valid information and hope it sinks in.
 
Appeal to Authority is a fallacy, as has been explained, when the structure of the argument or rebuttal does not require authority. And "authority" in this case means something more broad than knowledge of the subject. If, for example, a celebrity endorses a proposition based on an argument that attempts only logic, and is reasoned poorly, then attempting to support it on the "authority" (i.e., notoriety) of the celebrity is a fallacy. Even if a true authority (i.e., an expert in a field) makes a purely illogical argument, the presumed knowledge in the field does not overcome that. An appeal to authority is a fallacy only when authority -- in the form of a correct understanding of specialized facts -- is irrelevant to the argument.

The notion, "You're not an expert, therefore your conclusion must be wrong," is simply a non sequitur fallacy. If the rebuttal is that the proponent lacks sufficient understanding of the matter at hand to reason properly about it, then the truth value of the thing asserted simply cannot be determined on the basis of the argument. To claim it must be false is as wrong as to claim it must be true, under an insufficiency rebuttal. The proponent may be accidentally right.

If a foundation of specialized knowledge is truly required for a particular argument, then academic credentials are only one way in which such a foundation can be laid. I know several people who lack my professional credentials, but who can speak with considerable correct understanding of it because they have studied it informally for many years. Ultimately if one can demonstrate correct understanding, then that understanding has evidentiary value.

All that depends, of course, on the nature of the argument and the degree to which a knowledge of special facts and expert judgment is required to create its logical structure. If someone who clearly lacks appropriate knowledge and judgment is making an argument that substitutes lay intuition for those facts and judgments, and those qualities are necessary for the argument to be valid logically, the fallacy there would be one of the oldest -- ignoratio elenchi. That's an informal group of problems that translates loosely into, "You're ignoring what's wrong with your argument."
 
This is correct. On a related note, not everything that is wrong is a fallacy. A fallacy is an error in logic. There are other ways to be wrong.

In the case above, the claimant is basically saying, "I do not understand the tax code myself, but those who seem to understand it say that I owe $1,000." That is not an absolute, concrete, proof that you do in fact owe $1,000, but it is a reasonable conclusion. The skeptic is not presenting any actual argument in this case, simply complaining about an appeal to authority.

If the skeptic above were to say, "The tax code says this, and your situation is that, and therefore you do not owe $1,000," and the claimant were to respond, "but my accountant says so. You are clearly wrong", that would be an appeal to authority fallacy. On the other hand, if the claimant were to say, "I don't understand your argument, or his, but he's an authority so I'm going with him", that wouldn't be any sort of fallacy. That's a different statement than, "He's an authority so he must be right."

Some authorities can not be argued with: when a court says you owe taxes, you owe taxes. ;)
 
Some authorities can not be argued with: when a court says you owe taxes, you owe taxes. ;)

Which is one kind of authority. It's easy to stumble around on both sides of any argument involving authority by equivocating the various meanings.

Practicing medicine without a license is an activity that governmental authority wants to prevent, with good cause. In a liberal democracy, that authority ultimately resides with the people but is delegated to individuals for practicality. In a different sense, a licensed medical practitioner exercises a different kind of authority, one that's more natural an inalienable. It stems from a mastery of a body of knowledge and, hopefully, experience gained over time. You can revoke someone's license to practice medicine, but the knowledge and judgment don't go away as a result.
 
Appeal to Authority is a fallacy, as has been explained, when the structure of the argument or rebuttal does not require authority. And "authority" in this case means something more broad than knowledge of the subject. If, for example, a celebrity endorses a proposition based on an argument that attempts only logic, and is reasoned poorly, then attempting to support it on the "authority" (i.e., notoriety) of the celebrity is a fallacy. Even if a true authority (i.e., an expert in a field) makes a purely illogical argument, the presumed knowledge in the field does not overcome that. An appeal to authority is a fallacy only when authority -- in the form of a correct understanding of specialized facts -- is irrelevant to the argument.

The notion, "You're not an expert, therefore your conclusion must be wrong," is simply a non sequitur fallacy. If the rebuttal is that the proponent lacks sufficient understanding of the matter at hand to reason properly about it, then the truth value of the thing asserted simply cannot be determined on the basis of the argument. To claim it must be false is as wrong as to claim it must be true, under an insufficiency rebuttal. The proponent may be accidentally right.

If a foundation of specialized knowledge is truly required for a particular argument, then academic credentials are only one way in which such a foundation can be laid. I know several people who lack my professional credentials, but who can speak with considerable correct understanding of it because they have studied it informally for many years. Ultimately if one can demonstrate correct understanding, then that understanding has evidentiary value.

All that depends, of course, on the nature of the argument and the degree to which a knowledge of special facts and expert judgment is required to create its logical structure. If someone who clearly lacks appropriate knowledge and judgment is making an argument that substitutes lay intuition for those facts and judgments, and those qualities are necessary for the argument to be valid logically, the fallacy there would be one of the oldest -- ignoratio elenchi. That's an informal group of problems that translates loosely into, "You're ignoring what's wrong with your argument."

Is there such an argument where the logic is entirely dependent on special facts and expert judgement? I can't really think of a practical example.

In medicine, for example, a doctor has the expert judgement to read the special facts revealed on an x-ray. You could premise it like this:

1. In order to read an x-ray, one must be a doctor.
2. Bill is not a radiologist.
Therefore: Bill cannot read an x-ray.

But Bill might be a knowledgeable layperson who has an interest in radiology for whatever reason. Reading an x-ray (or any other diagnostic test) isn't some magical gift that is only bestowed upon people with an MD after their name. In the argument above, Premise 1 is a false premise. I think it would be false no matter what expert judgement and special facts you might posit.

Now, change the premise to: 1. In order to legally read an x-ray and render a valid diagnosis, one must be a doctor. That premise may be sound and make the argument logically valid but it's an extremely narrow argument. Therefore, dismissing Bill's very ability to read an x-ray is still wrong; his reading is simply not legal or valid for medical purposes.

IOW: It still comes down to whether or not the underlying argument is valid or not: "You aren't a doctor, I am a doctor," does not address that at all.
 
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Is there such an argument where the logic is entirely dependent on special facts and expert judgement?

No, I don't think so. Usually knowledge and judgment play their part in determining the truth value of the premises. And then, not all arguments are purely deductive. A lot of the arguments I deal with are inductive, requiring an inductive leap. Judgment and knowledge go toward determining how wide is the gap that must be bridged.

On another forum, the argument was made that the deflectors for the Apollo 11 lunar module's steering jets should not have been installed after the vehicle had already been rolled out to the pad, and should not have been added anyway because they posed a serious untested risk to the stability of the spacecraft. The larger argument was that since these documented activities ran counter to the proponent's belief of what constituted acceptable aerospace safety, the Apollo missions were not credible as history. In other words, it's an inductive argument that asks the reader to conclude that a fake mission was a more parsimonious conclusion.

Of course the proponent's assumptions were completely wrong. There's nothing wrong with continuing the assembly of a rocket after it has been erected for launch. In fact, some operations such as the installation of pyrotechnics must be done at the very last minute while the rocket is on the pad. And the linearized free-body dynamics that govern how a plume deflector will affect the stability of the lunar module is straightforward math, though not the kind you learn unless you have an interest in the subject.

Your example of Bill the amateur radiologist is informative. Knowing how to build and operate spacecraft isn't magical knowledge either. But it's knowledge that you either have or don't, to varying degrees. And there are fields where the layman's intuitive understanding will be insufficient if not outright wrong. The problem is not so much in the syllogistic form of the argument as in the determination of the truth value of the premises that feed into it. If the proponent applies incorrect knowledge or uninformed judgment, he comes up with premises that simply don't hold. So to concede to your criticism, expertise doesn't affect the logical structure of the argument so much as the claims of fact that populate it.

Now in my example above, there is also a logical flaw. The argument ignores the excluded middle. But it doesn't take a subject matter expert to recognize logical flaws. The essence of appeal to authority as a fallacy is that someone's subject-matter understanding, stature in the field, or cultural notoriety is wrongly expected to mask simple flaws in logic.
 
In this case, a popular woo doctor says asymptomatic carriers cannot spread the corona virus.

I pointed out paper after paper that showed the opposite but I have been told I am wrong because I "do not have a medical degree"


Do the authors of the papers have degrees? Since it seems directed at you personally and not at the sources provided. I'd have to call it an Ad-hominem since it is about a person, the presenter, and not what was presented, the papers. While if you were drawing conclusions from the papers, based on their data, other than what the authors present themselves. Then it would be a refutation of your authority to draw those other conclusions. However, If you are just citing the conclusions of the authors then they need to refute those authors' conclusions or credentials and not just yours.
 

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