In March, 2019, David Gudeman wrote a post on his blog entitled ‘You Are Using the World “Logic” Wrong‘.

It is well-established that many people^[1] don’t fully understand logic and misapply it. Math and logic have been a passion of mine since I was a child. I went to college, got a degree in Computer Science at R.I.T., and took a whole handful of courses that required mastery of logic, such as two courses in discrete math. So, while the article was interesting and I interact with the logic-deprived frequently, I only gave it a passing thought.

The next day Gudeman published ‘Appealing to Authority is not a Fallacy; it is a sign of Wisdom‘. This clickbait immediately caught my attention. Why is it clickbait? Because appealing to an authority is only wise if that authority is correct. If they are wrong (or you interpret them incorrectly), appealing to them is folly. The title is deceptive, but in the article itself, Gudeman correctly notes a few of the potential pitfalls of appealing to authority. He concludes:

It is well-accepted that the argument from authority is sometimes, but not always, fallacious. Wikipedia, internet articles, university courses, books on logic, and experts on logic all, more-or-less, recognize this.^[5] But why is this the case? An appeal to expertise is often not fallacious in an inductive argument, but it is always a fallacy in a deductive argument.^[2]

There are two kinds of arguments: deductive and inductive. A properly formed—that is, logically valid—deductive argument is guaranteed to be true if all of the premises are true. By contrast, in an inductive argument, the truth of the premises makes the conclusion likely to be true. It is probabilistic. An appeal to authority is intended to increase the probability that the conclusion of your argument is true. It is always fallacious in a deductive argument because it can’t ever make a premise true.

Ironically, Gudeman referenced this distinction in his first post:

In my refutation of his post (which you can read at the link), I cited Gudeman as an authority for why he shouldn’t be holding forth on logic. He was not amused:
It’s a pretty laughable comment, but I decided to proceed anyway by citing an expert logician to further disprove his claim.^[4] Following in the footsteps of the intellectual giants of old, he deleted my comment. Having learned to expect such things from people who don’t like their opinions challenged, I saved my comment so I could post a rebuttal here. It’s time to set the record straight.

In 1995, Edwin Coleman authored the definitive work on the subject, “There is no Fallacy of Arguing from Authority“. At only 19-pages, this paper is well worth reading. Now, on the surface, this paper appears to completely support Gudeman’s initial claim, but upon closer examination it does not, at least not fully. Coleman is only making the argument that an appeal to authority is not a fallacy in an inductive argument using a specific strict definition of fallacy.^[2]

A number of definitions of ‘fallacy’ exist. In the less strict semantic use of ‘fallacy’, logicians call it a “partial fallacy” or “informal fallacy.” The colloquial use of fallacy—in the informal sense—is common among both academic and layman. Despite its utility, Gudeman mocks anyone who uses the words ‘fallacy’ (or ‘logic’) informally.^[3]

Coleman’s use of the term is the stricter, more formal, one. Notice, however, that Coleman’s definition of fallacy applies only to the strength or weakness of arguments. It cannot apply to arguments where the conclusion is necessarily true if the premises are true. He makes this abundantly clear:

If arguing from authority is not conclusive—and it isn’t—then it necessarily cannot be used to prove deductive arguments. The premise of such a deductive argument gives no support to the conclusion, so the argument is deductively invalid. This is a logical fallacy even under the stricter semantic use of the word that Coleman uses. Therefore, the claim that the appeal to authority is not a fallacy is incorrect, exactly as I stated above.

Additionally, as a practical matter, appeals to authority are useless if there is contention. All parties to the argument must recognize the authority, or else the argument is ungrounded. This is sometimes what is meant by “informal fallacy.”^[7] Coleman aptly points out that such arguments are not logically invalid and thus not a fallacy in the strictest semantic sense. Yet, they are still often informal fallacies: they are ungrounded and do not prove the point.

Those, like Gudeman, who insist that language can only be used a certain way, miss the point. When people make arguments by citing an authority that they know will not convince anyone, they are not being wise. They are being foolish.

In this post, Gudeman argues the following:

Is this merely a matter of epistemology and not logic? No. Notice he said “The anti-creationist may disagree on whether God is a greater source of knowledge”. This assumes that God exists in order to use him as an authority to win an argument. That is massively begging the question. You can’t use God as an authority if you have not first proven that he exists. All Gudeman has done here is treat the existence of God as an axiom so that they can use him as an authority. As explained above, even if this isn’t a formal fallacy, it is for sure an informal one.^[6]

Those who make an appeal to a higher source of knowledge are wasting their time. It is anything but wise to use such arguments to try to convince people. You must first convince them to accept the authority. Only then can you make appeals to authority, of any type. Logic is one of the tools you will need to use if you want to convince people to accept the authority.

Remember Gudeman’s list of various potential pitfalls? These are not potential problems to be dismissed, they are fundamental problems. It is irrelevant that some appeals to authority are not fallacious. What matters is that some are and such fallacious arguments are used frequently. Spend time on Twitter or most any random blog and you’ll see someone trying to prove conclusively (i.e. deductively) such-and-such because so-and-so said so. This is a fallacy every single time and it’s easy to identify. Appealing to such authority is not wisdom, it is folly. Moreover, in his post, Gudeman asserts that appeals to organizational authority are fallacious, but appeals to expertise are not. But such use is always a fallacy, whether it is an appeal to expertise or organizational authority.

Notice that in all of the examples that Gudeman gave (Santa; sergeant), the person accepted the authority as authoritative, so it wasn’t a fallacy. It would have been otherwise. No examples were given where this is not the case. All we need to do is consider the case where we appeal to the authority of the logicians, professors, textbooks, websites, articles, and papers that do call it a fallacy. Oh wait, I did do that. Isn’t that ironic?

^[1] People, not blowhards. Not only are Gudeman’s posts and comments are full of unpleasant blustering and boasting, but his portrayal of logic-deprived individuals as ‘blowhards’ is—ironically—an ad hominem fallacy, not a matter of logic at all.

^[2] But why not make this distinction explicitly? Because no respectable logician makes a deductive argument from authority. It’s stupid. In a deductive arguments, your premises must be 100% true for the conclusion to be true. A deductively sound argument is one where everyone accepts the premises as true. You can do that without an appeal to authority. If your opponent does not accept the authority, then your argument is unsound anyway. But if you have proof from the authority that a premise is true, you don’t need the authority. Just cite the proof and ignore the authority. Citing an authority is just a lazy way to avoid citing a proof. If you don’t have a proof, then citing the authority doesn’t establish anything.

^[3] The thought police who insist on controlling language are the first to block, ban, and attack.

^[4] Oh, the glorious irony.

^[5] Some call this the “argument from irrelevant authority”, to separate the legitimate uses from the illegitimate ones. However, this terminology does not tell you which authorities are relevant and when it is relevant to use them, only that it must be done properly.

^[6] Begging-the-question, that is, circular reasoning, is an informal fallacy. It is informal because a circular argument is logically valid, but because it is circular it is also meaningless. Saying God is an authority because God is an authority—showing how an axiom’s self-attestation is circular—is utterly meaningless. It can’t be used in an argument even as an informal fallacy.

^[7] Somewhat confusingly, “informal fallacy” has two separate, but common, uses.

First, logicians contrast between formal and informal fallacies where an argument is fallacious in form or context (respectively).Whether a fallacy is formal or informal, both are equally fatal—fallacious—to the argument being made.

Second, an informal fallacy also refers to a fallacy whose application is less logically or mathematicaly rigid, strict, or structured as in a partial fallacy. These are usually considered lesser faults in an argument, sometimes but not always fatal.