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 One That Isn't There
Q: What's the most important leg of a three-legged stool? A: The one that isn't there. - traditional joke-riddle
A specific neurological lesion can sometimes damage or impair specific neurological functions without touching others. In the condition famously known as "Ondine's Curse", for example, automatic control of breathing is destroyed while conscious control remains, so that without modern medical intervention nerve-damaged patients can survive only as long as they can remain awake. Such conditions are nevertheless unusual exceptions to the more general principle that complex, recently-developed, and 'meta'-functions (those that monitor and control others) are first to be impaired and lost when the nervous system is stressed, damaged, or altered.
"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.
Pound of Feathers, Pound of Gold
Which weighs more: a pound of feathers, or a pound of gold?
Close consideration of this riddle - and the conditions under which people tend to get it wrong - is helpful in understanding the limits of human rationality. It is a specific example which leads us to general principles of rationality failure.
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.
In other words, we have to learn logic, we're not born with it.
No.
Electric charge doesn't spontaneously do arithmetic either.
No. It does nothing but mathematics.
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Alcohol is an just example. It's well-known that crude global brain impairment reduces self-monitoring first.