I would like to say entrepreneurship means different things. The plumber I call when my pipes are clogged is definitely an entrepreneur - he is self-employed and employs a help, he does not come alone. Yet there is not much idea behind it. It is just simply so that in these kinds of professions self-employment is more common than working for large corporations.
I have the impression that if you are approaching it from a Silicon Valley / Paul Grahamesque direction, what you call entrepreneurship is that subset of it that scales up easily, this seems to be the most important determining factor. Web based software, provided as a service and not as a purchasable shrinkwrap package, is the canonical example because it is relatively easy, free / cheap and barrier-free for theoretically even billions of people to start using something like Hipmunk or Beeminder. Their crucial feature is scaling up.
I think scaling up is why in such fields entrepreneurial ideas are dime a dozen, because of the ease of scaling means really high potential payoff and it means really intense competition - not only for customers but also e.g. for co-founders.
Compare opening a pizzeria in a small town. How much idea you need for that? Chances are there isn't a competitor at all and then you offer the basic types, if you have a competitor you just spend a few hours googling up some less usual but delicious sounding recipes.
The point is, if you fail at that pizzeria, you are doing something wrong. If you fail at that insanely competitive infinitely-scalable market, then it is not a failure and has no special reason, it is just like not winning the Olympics: someone was better, that is all.
I find it useful to use the term "startup" for Paul Grahamesque "startups" and "small-business" for pizzaria-esque "small-businesses."
Entrepreneurial ideas come and go. Some I don't give a second thought to. Others I commence market research for, examine the competitive landscape and explore the feasibility for development. This can be time consuming, and has yet to have produced any tangible, commercialized product.
I figure it's about time I devote the time I would spend to exploiting my existing repertoire of knowledge to develop an idea, to exploring parsimonious, efficient techniques for assessing viability.
In my search I found [Autopsy.io], a startup graveyard. Founders describe why their startups failed, concisely. It made me think about my past startup ideas and why they haven't flied.
I'm going to work that out, put it in a spreadsheet and regress to whatever problem keeps popping up - then, I'll work on improving my subject matter knowledge in that domain - for example, if its the feasibility of implementing with existing technology - I might learn more about the current technological landscape in general. Or, more about existing services for investors, if my product is a service for investors, like my last startup idea, which I have autopsied in detail here
I just thought I'd share my general strategy for anyone who'd want to copy this procedure for startup autopsy. Please use this space to suggest other appropriate diagnostic methods.