"Bob has achieved a thing, I have not achieved that exact same thing, therefore I'm not as generally competent as Bob" is a fallacy. (Not just an "unhelpful thought" in a psychological sense, but literally untrue.)
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It totally denies the possibility of specialization. What if Bob is better at something than you because that's what he's spent his time on, while you were doing something different? What if you're better than Bob in *your* field?
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If you can claim both A>B and B<A then you don't have a partial order, and comparative terms like "better than" don't make any sense for things that aren't partial orders.
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Replying to @s_r_constantin
I think I know what you mean, but if so, there is a double flip. Or are you making some more important point about ordering that I'm not following?
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Replying to @is8ac
I'm not seeing my mistake. Verbal comparators ("better than", "larger than") refer to https://en.wikipedia.org/wiki/Partially_ordered_set …; those words only make sense where an ordering exists. In particular, antisymmetry is required.
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Replying to @s_r_constantin
"A>B and B<A" Does A>B mean the same thing as B<A?
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I haven't studied order theory beyond skimming the Wikipedia page just now, so I may well be misunderstanding something.
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