Edge cases don't invalidate the general usefulness of abstracting messy collections of correlated observations into a single category. But they do strongly suggest that whatever rule of thumb you're using to categorize is a statistical heuristic, and not an objective criteria, because it fails in some cases. Put another way, it is correct to say that humans have 10 fingers, even though some humans have 9 fingers. But it would be incorrect to say that 9 fingered people are inhuman, because having 10 fingers is a general observed phenomenon and not an actual criteria that you need to meet to be human.
Take biological sex. Humans are sexually differentiated across almost every facet of our biology. Any intersex individual doesn't invalidate that. You can say that males are XY and females are XX and be right in the vast majority of cases. But if you're the medical doctor of an XY patient with Swyer's syndrome, you need to be able to understand that they still have female estrogen levels from hormone therapy, have developed female breasts, and so need breast cancer screening even though their genotype is male. In rare cases they may even be pregnant. At the individual level the broad categorizations of "female" and "male" aren't always useful or accurate, and you need to dig into the actual individual facts the categories are abstracting away. There is no one measurable criteria that is going to be always correct on defining category membership on the individual level, because a category is a statistical grouping, not an objective property in and of itself.
I disagree. Exceptions (which I think is what you mean by edge cases) DO indicate that a rule is incomplete or not universal. For categorization, this means it's more of a heuristic or a stereotype/generalization than a rule. For law, this is sometimes acceptible (when applied to machinery and taxation, for instance) even if it causes some distortion in behavior.
It's much less acceptable when applied to people. There, you should be very careful in your thinking to separate heuristics and group predictions from individual expectations and beliefs. Rules about people should be more formally correct than is implied by this post.
Exceptions (which I think is what you mean by edge cases) DO indicate that a rule is incomplete or not universal.
Yes! But rules don't have to be complete or universal to be acceptable.
Rules about people should be more formally correct than is implied by this post.
I think I see what you're getting at. My instinct kinda runs the other way, though: if people don't fit neatly into categories (and you care about the edge cases), it might be better to throw out the rule entirely rather than formalize it and categorize those edge cases. Could you give an example of where formalizing would be helpful?
Certainly in actual legislation, formalizing the criteria so that there are no exceptions is wise. This is often equivalent to throwing out the rule and rethinking why you're considering it in the first place, so as to have a more legible description of who it applies to.
To take a non-hotbutton topic, this is the very simple version of a rule for whether something is "prepared food" in Washington State and thus is taxed differently from groceries: https://dor.wa.gov/education/industry-guides/restaurants-and-retailers-prepared-food/retail-sales-tax. There are pages of details and exceptions to the exceptions in the actual legislation and case law around it.
This is very different in adversarial versus non-adversarial environments. Many heuristics are fine in non-adversarial environments, whereas many heuristics fall apart in adversarial environments.
Also, good neuron thought experiment. I hadn't heard the 'removing neurons' variation.
(Epistemic status: obvious in retrospect)
A standard thought experiment: design an artificial neuron that works just like a biological one. Then, replace the neurons in someone's brain, one by one. If consciousness is tied to the atoms of the neurons, or their biochemistry, then the person must not be conscious afterwards; but when did they become unconscious? It's hard to imagine them crossing a hidden threshold and becoming a p-zombie. Therefore, an artificial brain must be just as conscious as a biological brain.[1]
No, wait, don't do that. Instead of replacing the neurons, just remove them. Clearly, one missing neuron won't render someone unconscious. Therefore, an empty skull is just as conscious as a full one.
This is, of course, a sorties paradox. Some things are conscious, some aren't, and some... kinda are. You don't have to throw out your binary categorization, though. The existence of edge cases doesn't invalidate the grouping.
Some things like this:
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Car engines are sometimes taxed by displacement, with cutoffs at round numbers. You pay less for a 1.99-liter engine than a 2-liter engine.[2] This leads to a lot of cars with 1.99-liter engines. I don't think this is a big deal; maybe if the tax were smooth, some engines would be a few hundred cc's bigger or smaller. But I used to find it creepy, as if the law itself were at odds with reality. Really, I just hadn't accepted that it's okay for a rule to have small inconsistencies.
Some things like this:
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Paraphrased conversation with my friend, after we failed to hang out because we live in different time zones:
"Can we all just use UTC? That way, I'd know what time it is anywhere."
"But time zones are useful to know when people are awake and available to hang out. 'What time is it in Boston?' is easier to Google than 'is it okay to text my friend in Boston at 6pm?'"
"But what you really want to know isn't 'what time is it in Boston', it's 'is my friend available to chat?' They might work the night shift."
"True, but most people don't work the night shift. 'Follow time zones' is a heuristic that fails on edge cases, but most cases aren't edge cases. And if I learn that one friend does work at night, I can make an exception for them."
Some things like this:
I've seen this thought experiment in a few places, including "Artificial Intelligence: A Modern Approach" by Russell and Norvig. Not sure who invented it.
Varies per country. For example, Japan has thresholds every 500cc.