Recursive definitions are possible, but they must still be founded on a base level that does not reference itself. Each other level can then be defined in a way that is not self-referential.
"The definition of a mammal is simple: descent from the most recent common ancestor of all mammals."
Valid definitions cannot reference themselves.
".--but we admit to the category of mammals many animals that fail one or more of these criteria."
No, we don't. Dolphins have all of the required attributes to be considered mammals. If they didn't, we couldn't call them mammals any longer.
That is an absolutely charming interpretation, and one that makes a lot of sense. However, in my experience, it's not how the riddle is commonly used.
That would be a great way to show off your knowledge of jeweler's weights, though.
There's more to it, of course. Ask the question with substances that don't produce strong associations regarding "weight" (really, density), and people tend not to get it wrong no matter how much time pressure is involved.
The biological category of 'mammal' is quite well-defined, thank you.
And fuzzy definitions are fine until you're dealing with a case that lies in the penumbra, at which time it becomes a massive problem.
This looks sincere to me, and given that it's sincere, people really ought to be allowed more chance than this to recover from their mistakes.
I say that depends entirely on the nature of the mistake. Gross negligence should not be forgiven, although the proper response is not necessarily retributive.
Alcohol is an just example. It's well-known that crude global brain impairment reduces self-monitoring first.