It is common in online spaces dedicated to critical thinking, philosophy, logic, and related topics to find people trying to label instances of reasoning they find erroneous. Is it an ad hominem? A non-sequitur? Perhaps an appeal to authority or a red herring?

It is also almost as common, to see different people label the same fallacy differently. Someone disregards your argument based on a single spelling error? One might say that this is a non-sequitur, since the implied conclusion that one's argument is unsound does not follow from the premise that an expression of their argument contained a spelling error. One might also say that this is a special case of fallacies of relevance, as the conclusion bears little to no logical relevance to the premise.

So, which one is "correct"? Arguably, neither. Not all kinds of erroneous reasoning are named to highly descriptive precision, such that the name itself carries all the details about its nature. Similarly, not all kinds of named fallacies are mutually exclusive or precise to the same degree of detail and abstraction.

To say that a certain instance of erroneous reasoning is a non-sequitur only conveys that its conclusion does not follow. Not much else unless given further context. To say that it is a fallacy of relevance, on the other hand, would be to convey that its conclusion does not follow due to it not bearing logical relevance to its premises. One of these is more concrete and specific than another.

One could also apply more bespoke descriptions than predefined labels to it. One could say that to conflate erroneous spelling with erroneous reasoning is a case of conflating the expression of something, in this case an argument, with the thing itself. If erroneous spelling or grammar meant that an argument is unsound, then surely correcting the spelling or grammar should never make the argument sound again?

My essential point of course, is not about labeling the fallacious evaluation of soundness based on the presence of certain grammatical structures or spelling errors. It is about how it can be tempting to view "logical fallacies" as this list of jointly exhaustive and mutually exclusive scheme at every degree of abstraction.

A non-sequitur is an argument where the conclusion does not follow from the premises. At the same time, a valid argument in logic is one wherein the conclusion does necessarily follow from the premises. It would appear as though "non-sequitur" is apparently just another term for an invalid argument.

This would mean that any formal fallacy with a particular label could also be labeled a non-sequitur, as pointless as that might seem. Thus, it would often be futile to argue whether a particular formal fallacy is a non-sequitur or not, as any formal fallacy is one. If we already assumed that it is a formal fallacy, we have also assumed that it is a non-sequitur.

The term "logical fallacy" can be defined in multiple ways. In this post, I mostly used it in the sense of any line of erroneous reasoning, irrespective of commonality. Some sources define logical fallacies specifically as erroneous patterns in reasoning and argumentation with some degree of commonality, enough that they warrant their own terms.

In any case, it is clear that the "fallacies" that we refer to through established terms, and only established terms without any bespoke clarification, can be prone to imprecision. Like other terms, these terms can communicate little, or a lot, all depending on how they are used with respect to other terms and each other. Logical fallacies are not lists of jointly exhaustive and mutually exclusive terms fit for every possible degree of abstraction, but merely tools that can help us abstract over the details of repeated errors to ease language.