Most^[1] logical fallacies are obvious when arranged in their pattern, but when you encounter them in the wild they are usually transformed by rhetorics to mask that pattern. The "lack of rhetorical skills", then, may not be bad argumentation by itself - but it does help exposing it. If a pickpocket is caught in the act, it won't help them to claim that they were only caught because they were not dexterous enough and it's unfair to put someone in jail for a lack of skill. The fact remains that they tried to steal, and it would still be a crime if they were proficient enough to succeed. Similarly, just because one's rhetorical skills are not good enough to mask a bad argument does not make it a good argument.

A more important implication of my take on the nature of logical fallacies is that it is not enough to show that an argument fits the fallacy's pattern - the important part of countering it is showing how, when rearranged in that pattern, the argument loses its power to convince. If it still makes sense even in that form.

Note that in all of Scott's examples, he never just said "X is a noncentral member of Y" and left it at that. He always said "we usually hate Y because most of its members share the trait Z, but X is not Z and only happens to be in Y because of some other trait W, which we don't have such strong feeling about".

So, if we take your first example (the one about eating meat) and fully rearrange it by the noncentral fallacy not only with X and Y but also with Z and W, the counter-argument would look something like that:

It's true that animal farming (X) is technically cruelty (Y), but the central members of cruelty are things like torture and child abuse. What these things have in common is that they hurt humans (Z), and this is the reason why we should frown upon cruelty. Animal farming does not share that trait. Animal farming is only included in the cruelty category because it involves involuntary suffering (W) - a trait that we don't really care about.

Does this breakdown make the original argument lose its punch? Not really. Certainly not as much as breaking down the "MLK was a criminal" argument to the noncentral fallacy pattern makes that argument lose its punch. Here, at most, the breakdown exposes the underlying reasoning, and shifts the discussion from "whether or not meat is technically a cruelty" to "to what extent do animals deserve to be protected from involuntary suffering".

Which is a good thing. I believe the goal noticing logical fallacies is not to directly disprove claims, but to strip them from the rhetorical dressing and expose the actual argument underneath. That underlying argument can be bad, or it can be good - but it needs to be exposed before it can be properly discussed.

And a more natural clustering would reflect that.

What subspace are you doing your clustering in, though? Both the pro-capital-punishment and anti-capital-punishment side should be able to agree that capital punishment and "central" murder are similar in the "intentional killing of a human" aspects, but differ in the "motives and decision mechanism of the killer" aspects (where the "central" murderer is an individual, rather than a judicial institution). Each side has an incentive to try to bind the murder codeword in their shared language to a subspace that makes their own side's preferred policy look natural.

I feel like this really misses the point of the whole "non-central fallacy" idea. I would say, categories are heuristics and those heuristics have limits. When the category gets strained, the thing to do is to stop arguing using the category and start arguing the particular facts without relation to the category ("taboo your words").

You're saying that this sort of arguing-via-category is useful because it's actually aguing-via-similarity; but I see the point of Scott/Yvain's original article being that such arguing via similarity simply isn't useful in such cases, and has to be replaced with a direct assessment of the facts.

Like, one might say, similar in what way, and how do we know that this particular similarity is relevant in this case? But any answer to why the similarity is relevant, could be translated into an argument that doesn't rely on the similarity in the first place. Similarity can thus be a useful guide to finding arguments, but it shouldn't, in contentious cases, be considered compelling as an argument itself.

Yes, as you say, the argument is common because it is useful as a quick shorthand most of the time. But in contentious cases, in edge cases -- the cases that people are likely to be arguing about -- it breaks down. That is to say, it's an argument whose validity is largel to those cases where people aren't arguing to begin with!

Concerning the question of whom to call a murderer, there was a decision on that by the German Constitutional Court.

I think the badness of the fallacy (or 'fallacy') depends on the surrounding context.

If, in a one-way communication, someone presents 'X is an A' as if nothing more needs to be said, that's bad. Or if they're engaged in a conversation but they present it as some kind of unanswerable knockdown argument and refuse to discuss it, ditto. (Especially so if they're using it to smear the other side in the eyes of onlookers.)

But if it's a proper conversation and they are engaging in good faith, it's fine; the next step in the discussion can be to tease out which features of category membership are important in the present context, to what extent the entity in question has them, etc.

e.g.:

'MLK was a criminal'

'yeah, and normally that's a bad thing, but in this case he broke unjust laws in ways that were necessary to serve a very important end'

'I agree, but I still think we should be very reluctant to publicly celebrate criminality, lest we weaken the social foundations of respect for the law'

'fair enough, <but I disagree in general, because.../and I agree, but here's why this is an exceptional case...>'

At a glance, I don't think I've seen the following points made, so I'll do so:

• The general approach from math and the sciences is to make the definitions rigorous, from which the intended conclusions will necessarily follow.  For example, any object of mass 10kg near Earth's surface will experience a force of roughly 98.1 N toward's Earth's center due to Earth's gravity.  There is no "non-central example" of "an object of mass 10kg near Earth's surface"—well, perhaps I should specify what "near" is, for example as being within 1% of 6371 km of the km.  Then quantifying that allows me to quantify "roughly" as well, by plugging in GmM/r^2 for the minimum and maximum of the radius values.
• Observe how we refine both the conditions and the conclusions in the above.
• Arguments that have been refined in this way will be of the form "1. Object X meets the conditions of belonging to group Y.  2. It is a theorem that statement Z applies to all objects in group Y.  3. Therefore Z(X)."
• If you have the proof of the theorem at hand, then it should be easy to taboo the name of group Y and just plug X into the text of the proof and get an equally rigorous argument.  Sometimes that would be a better approach to the whole issue; though if group Y is common enough, it might be worth the work of establishing the definition.

To apply it to the "taxation is theft" argument: Well, basically, we want to make a rigorous definition of "theft" (or possibly a new term) that covers taxation, and see how much we can retain.

Taxation is nonconsensual taking of someone's rightful property (some might argue about "consent" in a democracy; let's assume that Bob is objecting to being taxed, and he did everything he could to vote against it, to support politicians who said they would reduce or even abolish taxes, etc., yet was unsuccessful).  We would therefore be able to make arguments like "under certain moral systems, taxation is immoral", and "because it doesn't require the consent of those being taxed, even if some instances of taxation were net good in some way, we'd expect to end up with a lot more instances than that unless there were strong barriers preventing it", and "taxation reduces people's incentive to trade their labor for property, because some of that property will go missing", and "taxation incentivizes people to spend energy arranging their possessions in ways that are less likely to get taken, which is a waste".

On the other hand, certain other characteristics that are common in theft are not the case: taxes are generally mostly known in advance, while theft is mostly unpredictable; and where theft might take a poor-ish person whose primary asset is a car and suddenly bankrupt them, taxes are unlikely to do that.

Taxation is centralized, systematized theft.  The systematization has its benefits and civilizing effects: economies of scale and reduced risk and variation in the collection process—similar to what you get when you industrialize other processes.  Also, we probably benefit from a "tragedy of the commons" among those who receive the taxes: most individuals don't have a strong incentive to raise taxes a lot.

For murder and capital punishment: Let's first note that the legal profession has made distinctions: "first-degree murder", "second-degree", etc. (it seems to vary by jurisdiction), not to mention manslaughter, and of course there are cases like self-defense where it may not even be a crime.  "Homicide" is what they call "killing" without implying anything about the legality.  First-degree murder, the worst, seems to mean "murder pre-meditated in cold blood", while the lesser degrees apply when there are extenuating circumstances and less pre-meditation.

Executing a prisoner is 100% pre-meditated in cold blood.  The argument for it to be legal is to cast it as self-defense and/or revenge.  Are revenge killings legal?  It seems like they sort of used to be, and then at some point States generally disallowed individuals from doing it, while arrogating that function to itself.  As for self-defense... one could argue that the criminal, having committed their crimes (like murder), has shown they are a threat, but really that's not a strong enough data point.  (What fraction of murderers do it again? ... A Google result says between 2% and 16% for different groups.  What if they killed their brother out of enmity that began in childhood, and they have no more brothers? Also, "got drunk and angry in a bar argument and killed a stranger" is a lot more likely to recur, yet would probably be second-degree, while the "brother" scenario might be first-degree.)

Capital punishment is centralized, systematized revenge-killing.  Once again, the systematization brings benefits and civilizing effects: economies of scale, reduced risk and variation.  I would not say that this changes the morality of it, only the tactical utility.  (I haven't actually said whether I think revenge-killing itself is moral.)

Anyway, on the subject of the original frame—"capital punishment is murder", given the definition "murder = killing without proper justification", is assuming the conclusion—that capital punishment should be illegal.  If you want a different definition, I would say use a different term.  If it were "capital punishment is killing", that would be an uncontroversial statement of fact; nor would the argument "killing is necessarily bad" persuade more than a few pacifists.

"Capital punishment is revenge-killing" would be the closest to an argument we can break into its pieces, "killing people for retaliation is bad (to the point where we should have a policy against it)" and "capital punishment is a policy of killing in retaliation", and attempt to justify both pieces.  Though some of the arguments people would like to make, like "revenge killings generally lead to generations-long family feuds", would not extend to the State's centralized revenge killings; in constructing or evaluating such arguments, the key technique of rigor is to notice statements that are actually "(we've seen in the past that) revenge killings (often) lead to family feuds" when they should be "(we can prove that) revenge killings (necessarily create conditions that likely) lead to family feuds", and in trying to prove that you should either notice that the definition of "revenge killing" doesn't specify that it's carried out by a family member—or, if it does, then notice that clause of the definition doesn't apply to capital punishment.

This comment is mostly an aside, so feel free to skip reading if you're not interested in a digression.

To quote the quote of Huemer:

Similarly, if taxation is theft, then it would probably be wrong to tax people, say, to pay for an art museum.

I enjoyed much of the argument that you quoted, but this struck me.

I think maybe the "would probably be" should have been written "it might be".  I can think of arguments around the benefits to society of everyone getting to enjoy art in an art museum that do not seem to apply to the individual who steals to buy a piece of art for their home.

I haven't thought them all the way through, but, again, I found the quoted sentence quite incongruous.

The reader can probably fill in the blanks: just as we wouldn’t accept the justification “but that guy was evil” as a good one in the case of ordinary murder, maybe we should also be skeptical when the state makes the same excuse for capital punishment.

I wouldn't accept "that guy was evil" in the case of ordinary murder, because "is unjustified" is baked into the definition of "murder", not because that would be a non-central example. I might accept it in the case of killing rather than murder.

Furthermore, I'd point to the fact that many arguments against capital punishment prove too much. Would you accept "that guy was evil" in the case of ordinary kidnapping? Does that mean that we should be skeptical when the state makes this argument for prison?

It's funny because, in your farming example, we could also accuse Person B of non-central fallacy: torture and child abuse are just particularly extreme, non-central forms of cruelty, but most cruelty is more subtle – like a manager belittling employees. In some way, you could say that the center lies in the eye of the beholder. Perhaps the best way to deal with that is to always evaluate things in comparison to their alternatives: everything might involve some cruelty to some degree, but maybe there are easy ways to make farming comparatively less cruel?

Alice: I'm hungry.
Bob: Want a sandwich?
Alice: Meh... not really.
Bob: How about a hot dog?
Alice: Oh, yeah, that sounds good.
Bob: Aha! So you do want a sandwich.
Alice: What?
Bob: Well, technically a hot dog *is* a sandwich, so when I asked you if you wanted a sandwich and you said no, you were mistaken.
Alice: ...
Bob: (complicated internet argument proving a hot dog is a sandwich).
Alice: Okay, fine, whatever. I'm hungry.  Just make me a "sandwich".
Bob: (hands Alice a ham and cheese sandwich)
Alice: ...okay, see, this is literally the exact thing I *didn't* want.
Bob: But you said you wanted a sandwich!

What's happening in this parable is that Alice is making an honest attempt to communicate her preferences to meet a need, and Bob is playing word games.  The content or strength of (complicated internet argument proving a hot dog is a sandwich) is completely irrelevant to that assessment: whether or not Bob is justified in conflating "hot dog" with "sandwich", it is indisputable that Alice has clearly communicated a preference and Bob has provided something which does not satisfy that preference.

The "taxation is theft" argument is the same.  People and societies throughout history have established legal regimes which codify taxation into law but ban theft, which clearly communicates a preference for taxation and a dispreference for theft.  There is nothing remotely confusing or ambiguous about this distinction, and so just as any person operating in good faith can instantly distinguish between a hot dog and a sandwich, any person operating in good faith can instantly distinguish between taxation and theft.  Regardless of the content of (argument that taxation is theft), any attempt to substitute one for the other is justifiably going to be met with confusion and annoyance by people who are trying to use words in their regular senses to communicate regular pragmatic concepts in order to meet their needs.

I submit that deliberately making it harder to communicate detracts from reasonable discourse and should be avoided, as a general rule.

In general, there is no requirement that any particular word must describe a coherent category with clear membership.  This seems like an inherently different concept for people to master and internalize, because examples keep popping up throughout history - from Diogenes mocking Plato's "featherless biped" to "is cereal soup", we seem to always want to abstract a category definition from a collection of known category members, and then try to expand the category by re-analyzing non-members using the new abstracted definition.  Sometimes this works and yields insight, but sometimes it produces strife and confusion.  The key is not to mistake the proposed category definition for an ontological fact about the world, but rather use it as an experimental mental model which might or might not yield insights.

In the case of the "taxation is theft" argument, if the insight is something like "don't fund an art museum with taxpayer funds because taking someone's money to buy art is unjustified" I'm not even sure that "taxation is theft" is doing any intellectual work at all other than bringing a loaded term into the conversation so that people focus on arguing about rhetoric rather than arguing about the opportunity costs of art museums and the consequences of a society with a higher or lower tax rate.  In other words, you definitely could have realized those are important questions to consider without first conflating taxation and theft.  I think that in this case, as with Bob's ham and cheese sandwich, the conflation is just making it harder to communicate about what we actually want as a society.

To the extent that the non-central fallacy represents an instance of trying to reanalyze group membership based on some insight about what group members have in common, it can be a useful tool for producing hypotheses.  But to the extent that it is used as a rhetorical device, it seems to make it harder to communicate effectively and harder to think clearly about the object question, and seems to produce outcomes in conversations that are very similar to the outcomes from bad faith arguments.