Uber, the pioneering taxi-hailing app and ride dispatch service, scored an impressive $18.2 billion valuation last week as it raised $1.2 billion in new venture capital.

Like any big new valuation it naturally raises the question: has the world gone mad? And perhaps it has. But there's a decent case on both sides of this.

The case against Uber

Christopher Mims at the Wall Street Journal thinks this is a crazy valuation, essentially on the grounds that Uber lacks a "moat" against competition. Right now, Uber competes against incumbent taxi operators and also against two other startups — Lyft and Sidecar — that have somewhat similar business models. Right now in the hottest markets the Uber/Lyft rivalry in particular is scoring short-term wins for drivers and long-term wins for customers. There just aren't going to be enormous profit margins here no matter how well Uber runs its business.

How big is the market?

If the case against Uber is wrong, it's almost certainly not because Mims is wrong about profit margins. But there's more to life than profit margins. Retail stores have been a notoriously low-margin business for decades. But Sam Walton built an extremely successful company based on undercutting those margins and then becoming enormous. Now Walmart is getting undercut by Amazon, a company with even more miniscule margins but even more potential for scale and ubiquity.

Mims writes that "even the most aggressive estimates of Uber's value — let's assume the company captures 50% of the world taxi market in 5 years — mean the company would still be worth less than $18.2 billion."

But what if the introduction of Uber and Uber-style apps greatly increases the size of the world taxi market?

Taxis everywhere

I went to Miami with some friends for a little vacation about a month ago. We rented a couple of vans. And since we had the vans, we drove them around town a fair amount. Had Uber existed in Miami at that time, we probably wouldn't have bothered with the vans and would have taken a bunch of Uber rides. Later this summer I'll be in Detroit for a couple of days for a wedding. I'm not planning to rent a car. The hotel's downtown so I can walk to some stuff, I'll be busy with wedding-related things for some of the time, and I can rely on Uber for the rest.

Right now, Uber is in a fight with Florida regulators and taxi incumbents. If Uber wins, it will poach market share from existing Miami-area cab companies. But it will do more than that. It will significantly increase the number of taxi rides that people in the Miami area take.

And that is the fundamental Uber value proposition. That by making it much easier to drive a cab to make money on the side (you just need a decent car and time on your hands) and much more convenient to hail a cab, you can greatly increase the size of the paid rides market.

The robot taxi utopia

The really bullish case for Uber is that at some point in the not-too-distant future, cars won't even need drivers.

Uber CEO @travisk on self-driving cars: "When there’s no other dude in the car, the cost of Uber becomes cheaper than owning a vehicle" — Doug MacMillan (@dmac1) May 28, 2014

In a world of driverless cars, essentially all rides become taxi rides. And having a lead on developing the best routing software, the best customer support, and the best brand looks like a decent moat. Dispatching fleets of cheap ubiquitous driverless taxis would absolutely be a low-margin business. But it would also be a gigantic business. Right now the taxi industry accounts for a tiny share of Americans' overall spending on transportation. But the transportation sector as a whole — buying and renting and maintaining and fueling vehicles — is about a trillion dollar business in the United States alone.

That's a big prize and Uber has the best position in the race to capture it.

All-purpose urban logistics

Right now, taxis (the delivery of human passengers to their destination) exist as an entirely separate regulatory category and business from the broader industry of delivering non-human cargo. But Uber's stabs into the courier and Christmas tree delivery industries are indicative of a larger aspiration to erase that distinction. Summoning vehicles and routing them to destinations works for people, but could also work for pizzas or groceries or anything else.

Hold your horses

None of this is to say that you should go rushing around trying to find a way to invest your money in Uber stock. The company could easily fail due to mismanagement, adverse politics, or innovative breakthroughs by rival companies. Mims' basic point that this is a hotly contested marketplace where Uber already faces competitors and will never enjoy fat monopoly profit margins is correct. There are dozens of ways in which Uber could fail to become the dominant global transportation provider of the 21st century.

But all most investments in startups are longshot plays. The key when betting on a longshot is to find one where the upside is high. And the upside for Uber really is very high.