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How many ways can you make a logical mistake?

A while back I got interested in the various taxonomies of fallacies, such as the Fallacy Files, each giving their own set of names. It set me thinking: how many fallacies are there? From that question it hit me: there are as many fallacies as their are of unique ways of being wrong or misleading in argument, and that is rather like asking “how many mathematical mistakes are there?” So I started reading Locke, Whately, Mill and other nineteenth century logicians to see how it developed, and never finished, But Siris has done some of this already, so I don’t need to do any hard work…

But the taxonomic question remains. How many fallacies are there and how to divide them up. Each “fallacist” does their own taxonomy, some dividing them into rhetorical and formal fallacies, some into practical and logical, and so on. The reason why there is no universal list of fallacies is interesting: it’s like asking how many ways there are to make a mathematical mistake, and of course there are as many as there are errors in different deductions. A mistake is something that is not something else (i.e., correct reasoning). Classifying things that are not something else leads to inconsistent or subjective classes of these not-things; hence fallacies are either a heterogeneous trashcan of a categorial, or they are just a report on what seems most interesting from the battlefields of debate. The fundamental logical error is to fail to preserve truth value from premises to conclusions; everything else is just dressing it up for teaching purposes.

One thing that did hit me is that many of the supposed fallacies are not, in their own right, fallacies at all, but only in the illicit use of them (which raises the question, what are the licit uses of them?). For example, Siris’ discussed example of Argumentum ad vericundiam, or appeal to authority. Is it the case that if I appeal to an authority I am committing a fallacy of reasoning or argument? Surely not, or all science is fallacious. I must appeal to a proper authority in a proper manner. For example, if I appeal to a physicist for the claim that there must be dark matter, a topic about which I know very little, and that physicist not only works on the topic, but is regarded as one of the best of the program of research, I have committed no errors of fact or reasoning. But if I appeal to that physicist to bolster the claim that natural selection doesn’t work, or that autism is caused by vaccines, then it is a fallacious argument, because that “authority” is not authoritative in that context.

Moreover, an authority can be wrong, so an absolute appeal to an authority will serve to block further investigation and perhaps progress. So appealing to that physicist in a manner that fundamentally undercuts the way in which that authority is an authority (by the use of debate and research in science) is fallacious. But merely appealing to authority is not a fallacy.

Likewise, ad hominem. As Whately himself noted, sometimes the person’s character is exactly relevant to the argument you are trying to rebut. If an advocate for “family values” wishes to restrict my behaviour for being, as that person sees it, immoral, and they have (as Newt Gingrich and other members of the “family values party” did) a mistress or a homosexual affair, or pay prostitutes, and the like, then that is precisely relevant to the probative force of their arguments. In the law, as Whately notes, the fact that a witness is a serial liar is relevant to the argument against their testimony being useful.

Ad hominem is only a fallacy when you illicitly appeal to a person’s character in argument, again raising the issue of when it is illicit to do that. In both these cases, you need a prior standard of what makes a fallacy fallacious, and in both cases it is because you attempt to change the truth preservation from premises to conclusion, either in the mind of the hearer, or in the formal structure of the argument itself. In other words, a fallacy makes false conclusions. Which is hardly news.

I have even read a (Christian) site that claims that modus tollens is a fallacy. For those who do not know, this is the form of quite legitimate reasoning that uses a single instance or more of a negative to prove that a universal claim for a positive is true false. It is the refutation of “all swans are white” by the discovery that there are black swans in Perth. This is not a fallacy, but the site author clearly meant that the universal claim has been shown to be false. The very notion of fallacy is overdrawn in the popular mind, I think, in part because of all these taxonomies and technical terms. There is only one fallacy, to fail to preserve truth value; all the rest of it is just the handy names we give to common ways of making it.


  1. …this is the form of quite legitimate reasoning that uses a single instance or more of a negative to prove that a universal claim for a positive is true.

    Do you mean “false”? Or is this some strange fallacy with an obscure Latin name I’ve just committed?

  2. Snowflake Snowflake

    That’s known as “Authorius correctus”. It’s very bad manners…

  3. Good job I never learned Latin.

  4. clinteas clinteas

    Am I wrong to point out that those informal fallacies you mention (ad hom,ad ver) do not in fact have to,as you call it,preserve truth value,and that this is something reserved for arguments in formal logic?

    Modus tollens :
    If P, Then Q.
    Therefore, ~P.

    First post at the new place,Yay ! SB is still broken LOL.

  5. Snowflake Snowflake

    Well I am saying that a good argument is one that preserves truth value, and communicates it clearly to the hearer. A fallacy is an argument, or something presented as one, that fails to do both. Of course, highly technical formal logic fails to communicate to those uneducated in formal logic, but it isn’t a fallacious argument unless you attempt to, as we might quaintly say, baffle with bullshit, and I have seen people use technical logic to achieve just that (which makes it a rhetorical fallacy in my book).

  6. clinteas clinteas

    I guess what I wanted to say is,if I say Cheney’s position on Gitmo is wrong because he is an asshole and so commit an ad hom,the ad hom works without there having to be any preservation of truth from premise to conclusion.
    Im interested in this btw and plan on reading more on it,how exactly the committing of an informal fallacy weakens or invalidates,or influences,a statement/argument.

  7. Allen Hazen Allen Hazen

    Gerry Massey (Gerald J Massey), back in the 1970s, published a couple of articles– one with the title “Are there any good arguments that bad arguments are bad?”, attacking the idea of a fallacy: I think his point of view was compatible with yours.

  8. Snowflake Snowflake

    I never doubted that I was not novel; I am pleased to see that at least one other person has thought something I think and therefore am not immediately and stupidly wrong ๐Ÿ™‚

  9. llewelly llewelly

    If you had infinite computing power and research resources, all of these items would be fallacies.
    The reason no-one can question every authority is that people have finite resources. This forces trust in some authorities.
    Similarly for the other items.

  10. So, is there a name for the meta-fallacy that an argument bearing a superficial resemblance to a given fallacy is in fact an example of that fallacy?

    Incidentally, it was in a Christian book that I first came across the term “begging the question” used correctly. The author assumed the reader would understand it, but it confused me at the time.

  11. A claim that I’ve been hearing quite a bit (especially from Christians) is “Just because a claim is fallacious, doesn’t mean that it’s wrong.” While this is true in a trivial sense, I find it deeply troublng. Besides the claimant’s obvious appeal to “capital T truth”, our only real way to verify a logical claim is with solid arguments.

    If a math student, asked to prove the Pythagorean Theorem, wrote “Unicorns are invisible, therefore a^2 + b^2 = c^2”, said student would rightfully be given a big fat F. If an argument made in support of a claim is fallacious, then one must discard the argument and doubt the claim.


  12. jeff jeff

    “There is only one fallacy, to fail to preserve truth value;”

    That is a good statement, but fallacies are relative to the truth system being assumed (unless you assume that there is “absolute truth”). For example, there is little room for authority in mathematics, a bit more so in the sciences, and much more so in most religions. In fact in most religions, authority is vital, not a fallacy. But the truth system itself is subjective. Of course, most of us consider science as the most pragmatic truth system.

  13. Susan Silberstein Susan Silberstein

    Clinteas, Cheney’s position on everything is wrong.

  14. Wes Wes

    When I teach intro to logic, I usually divide fallacies between formal and informal, and then divide the informal fallacies into five categories: Relevance, Weak Induction, Presumption, Grammatical analogy, and Ambiguity.

    I doubt those categories are exhaustive, but I’ve found that at least most of the big fallacies can be loosely sorted that way.

  15. From a more practical and pedagogical standpoint (as opposed to a purely theoretical standpoint), the best fallacy taxonomy I’ve run across is in a short supplemental textbook called Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments by T. Edward Damer. The book isn’t without its flaws, but what I like about Damer’s approach is that he starts with a set of basic standards/rules for making GOOD arguments and categorizes fallacies by which rule they (primarily) violate. The idea is that a bad argument is any argument that fails to adhere to the standards of good arguments – and a fallacy is just a bad argument that is made commonly enough to identify, name, and define. Using this approach has enhanced my intro-level logic and critical thinking classes.

    • Snowflake Snowflake

      Thanks for that. I will chase it up.

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