Nonmathematicians really don't know how to write explanatory prose.
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This is an argument for not defining things, not for defining things in a way that makes your definition impossible to follow.
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It's perfectly fine to define things by saying "I don't quite know how to define this yet, but here are some examples of what I do and don't mean, and here's the rough idea I'm trying to capture", but the structure should make it clear that you're doing that.
End of conversation
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