Yes, this is the "Big Question"... does an economy work without perpetual debasement of the money supply? In the way I have phrased it, it almost answers itself, doesn't it? Stated differently to further point out the absurdity of the notion, will human beings stop trading with each other if the means of exchange they use isn't made increasingly worthless over time?
The answer, of course, is that yes, humans will trade with each other even if their money does not get debased. In fact, I would argue that in a world in which the currency is NOT debased, we might observe much healthier economic activity.
Charlie's points are representative of most of the world's opinion of monetary economics. We learn economics in school, and schools teach us (invariably) that inflation should be "low and constant", and that if we observe "deflation" the world will, in fact, end! We've been taught extensively that no matter what happens, the worst thing for an economy is deflation. The mere utterance of the word sends children crying for the hills.
Yet, what if the economics taught in school is wrong? What if deflation is, in fact, not the end of the world? Is this possible? Would people continue to buy and sell goods if they know the nominal price of those goods is likely to fall in the future? I argue that yes, absolutely people will buy things. There is certainly a question of extent here - if my grocery bill will be 1% of the price tomorrow (a 99% discount from today), then I might actually go without eating for the day, and enjoy more food tomorrow. BUT, I will not wait to eat forever. And it is in this phenomenon which the scary demon of deflation is slain.
For just as I won't wait forever to eat food (even if prices are falling), neither will I wait forever for other things. I need a car, and a house, and clothes, and a million goods that I enjoy. If prices are falling, I'll make a judgement - should I buy now, or later? The argument of the Scary Deflationists is that people will continually make the judgement "later" and will halt their purchases indefinitely, sending the economy into Paul Krugman's favorite terrifying term, a "deflationary spiral". Yikes! But upon just a bit of consideration, we know people will not halt their purchases forever. They will buy things, and consume things, and produce things. While the patterns of these behaviors may differ under and environment of inflation vs deflation, it cannot be true that trade simply stops under the latter.
In reality, what you would find is that people may spend and consume less than they would under inflation. This means they will necessarily save more. Inflation incentivizes people to save less, spend more. Deflation incentivizes people to save more, spend less. Why is it that economic text books (those found in public schools) argue in favor of the lower savings, and against the higher savings?
The reason tends to come from a misunderstanding of how economies work. Most people think that "consumption" is what drives an economy... basically that "eating things" is what makes economies strong. Those of the Austrian School of economics, on the other hand, argue that it is in fact "production" which drives an economy. That "making things" is what makes economies strong. And thus if you understand and agree with the production argument, you would find that an environment of high savings is much more suited to permit economic growth - for most development tends to come from capital that is saved and invested. Capital that is consumed cannot be invested. And thus a deflationary environment, where people are encouraged to save more and consume less, permits a fertile ground for investment and growth.
This big argument comes down to one's fundamental view of how economies work. The majority of the world advocates consumption, and a minority advocates production. I happen to be in the minority, and thus I look forward to a world where money is not debased in perpetuity - where instead of ongoing inflation we have a money supply that tends toward constancy. The constancy of money (even if it causes falling prices) will enable a vastly stronger economy than we have today, where savings is punished and destroyed.
Now, there are Nobel Prize winning economists on both sides of this debate. One side is right, and one is wrong... and again I refer back to my first remark. Will people trade with each other without their currency being debased? I think they will, and I think they'd come to prefer it.
We all live in a world where prices are always rising. It can be scary to imagine a world where they are falling. But perhaps, just perhaps, that is actually how an economy is supposed to work.