Here’s the question:
We’ve already tasted gall. Now let’s try nerve.
Nerve has opposing aspects to it. On the one hand, you have the nerve that it takes a lot of – if you have the nerve to do something, it means that you have actually mustered the nerve to do it, an amount of nerve most people wouldn’t have. Even if, as is often the case, it’s a complaint – The nerve of that guy! Where did he get the nerve to do that? – there is at the very least a sense of strength of will, and perhaps even a grudging admiration: “I could never have the nerve to do that!” And if there are two opposing parties each trying to stare the other down, it can come to a war of nerves.
But on the other hand, you have nervous; if you have an attack of nerves, that means (paradoxically!) that you lack the nerve to do something. The same vibration (you can hear it in the /v/, even) that can give verve to nerve can also be the vibration of shivering with anxiety.
And of course there’s also the nerves that someone gets on. If someone has a lot of nerve, it can really get on your nerves, that’s for sure. (The /r/ nucleus in this word, with its straining growl, can be a very good vehicle for expressing this.) And in fact they may do something that touches a nerve – perhaps even touches a raw nerve.
Ah, nerves are electric. There is always some energy, always some vibration, but it can be positive or negative, bold or timorous, admirable or annoying. And all of those flavours are present whenever you use this word, though of course a particular sense will be more forward.
This multiplicity of sense comes in even in the sentence in question. If you say I can’t believe he had the nerve to do it, you could be admiring his courage, or you could be speaking resentfully of his impudence. The intonation will give the clue as much as anything. Is it “Wow, that took a lot of nerve!” or is it “The nerve of that guy!”?
Nerve, by the way, as you might suspect from the form of it and from its related form nervous, comes from Latin: nervus, “sinew, tendon, nerve, penis, etc.” (isn’t that quite a set of things!). The Latin has a cognate in Greek: νεῦρον neuron, meaning (in Greek) the same things as nervus. But while nerve, borrowed into English well before Shakespeare, has become a very common and often figurative word in English, neuron, which was borrowed in just over a century ago, is still rather technical and literal. You couldn’t say I can’t believe he had the neuron to do it, and if you say I can’t believe he had the neurons to do it people will probably assume you thought he was stupid.
Now, speaking of a term that expresses admiration, grudging or even ungrudging, we will look next at chutzpah.