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.