Fiat money is money that is money because the government said it is money and that it is valuable and, usually, is money that no one else is allowed to compete with. Bitcoin is certainly not fiat money.

This is just semantics but since we're talking about the semantics of something a real person actually said it would be useful to understand what that person means by the word.

Fiat money, such as paper dollars, is money without intrinsic value: It would be worthless if it were not used as money.

-Gregory Mankiw, "Principles of Economics". Bitcoin has no intrinsic value.

It's a complete non-sequitur, even if it is a standard non-sequitur. We'll get to it eventually.

No. Look. It might be wrong. I'm not equipped to fully evaluate the claim. But it isn't a non-sequitur because makes total sense that you might be able to encourage consumption and hiring by increasing the money supply and by increasing the rate of inflation.

It looks like a lack of curiosity when they casually hold beliefs they can't support with the evidence (Mankiw, if no one else, should oppose central banking because he has stated he has no reason for supporting it) and because economists simply don't talk or ask very much about why they think central banking is a good idea, even though it is so weird and different from the way economists normally do things.

Huh? Mankiw clearly has some notions about why it is a good idea even if he doesn't have a fully developed theory. He certainly doesn't appear to have more evidence against the belief than he has for it (which is, you know, the actual Bayesian requirement for disbelief).

The other thing is, Mankiw, and the field of economics in general is in the business of giving concrete and immediate advice to the public. That kind of activity tends to involve working within the status quo along plausible lines of reform. Most economists are focused on narrow areas of policy not trying to rethink the global economy from the ground up (though, of course there are those that do which is why the idea of free banking is in no way a new idea). Dismantling central social institutions, with the destablization that entails, is going to have to clear a higher bar of evidence before it gets seriously discussed.

even though it is so weird and different from the way economists normally do things.

You're just going to end up playing reference class tennis with this point. The extent to which it is "so weird and different" is clearly disputable.