> They are the exception that proves the rule.

“Proves” in that saying means “tests”, not “establishes the validity of”.

People keep trotting out this etymology, but it's always been entirely speculative and there's no attested premodern usage of anything resembling the phrase with that meaning. What there is attested usage of is a Cicero argument of the form "if there's an exception that makes it illegal, then the general rule must be that it's legal outside of the exception".

Its been a while but I seem to remember that its adoption as a maxim outside of law is itself fairly modern, and coincides with that usage, but, in any case, even if that were not the traditional meaning outside of law, the maxim is (outside of its use as a maxim of legal analysis) simply false and illogical in any other sense. Exceptions disprove rules, they don’t prove them.

The legal maxim only makes sense in its domain because it rests on the idea that law is written by people, and that calling out a specific case for one treatment reveals a pre-existing understanding that outside of that case, that treatment would not apply.

Please refrain from inserting your own misinformation into my words.

But what do you classify an intersex person as when you see them, assuming you don't know this detail? Our social lens is focused to a binary, even if there isn't a definitive binary.

This is rapidly getting into "justified true belief" territory.

Let's say you have concrete definitions of man and woman (and as many additional categories as you please). You see a person and believe they fall into one category. As it turns out, you are wrong, and they are actually in another category.

That you miscategorized someone has no bearing on the validity (or lack thereof) of your definitions.