Almost Any Standard Would Be Better Than None
Some kind of gold standard, perhaps only a promise of convertibility of paper money into gold on demand, would at least focus the Fed on a single mandate as it goes about the task of deciding how much money to create. For various reasons having to do with its scarcity, fungibility, durability, density and ductility gold is ideal for this purpose. But other commodities, or a basket of commodities, might do about as well. The idea is to have the convenience of paper money, but to have thank money fundamentally linked to some form of objective value -- or, more precisely, a value set by the marketplace rather than by the government.
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Two problems with things you say in this argument:
"For various reasons having to do with its scarcity, fungibility, durability, density and ductility"
The point of having a debate is for you to explain these reasons, rather than just vaguely allude to them. They're not inherently obvious. Gold is scarce (along with nearly everything on earth, in the technical sense), but anyone could mine or find more; there are exactly as many paper bills and coins in circulation as we print, so their scarcity is more well-defined. I don't see any reason why gold is more fungible than currency. I suppose it is durable, but lots of things are. I have no clue why density or ductility would be inherent to something's money-worthiness.
"fundamentally linked to some form of objective value -- or, more precisely, a value set by the marketplace rather than by the government"
Gold has the value it does because people happen to want gold and sell gold at certain rates. There's nothing objective about that. It's entirely subjective and could change at any time. The marketplace is not some supernatural entity that always discerns the objective values of things. Aside from this, isn't the value of the dollar determined by the marketplace? Or are you just ignoring currency markets because they complicate your point?
"....there are exactly as many paper bills and coins in circulation as we print, so their scarcity is more well-defined."
Far from it, the Federal Reserve can basically print money out of thin air in a way that prevents us from knowing what future inflation and interest rates may look like:
http://video.google.com/videoplay?docid=-466210540567002553&ei=cs0pSfijIoTyqAPR2-yyCA&q=federal +reserve&emb=1
It can take years before people know what their actions were in the monetary system:
http://en.wikipedia.org/wiki/Federal_Reserve #Secrecy
"I don't see any reason why gold is more fungible than currency. I suppose it is durable, but lots of things are. I have no clue why density or ductility would be inherent to something's money-worthiness."
It would ensure that the currency you have wasn't just meaningless paper printed out of thin air that is constantly losing value. If there is no gold standard then they can freely "buy" their own debt at the expense of middle class citizens since the resulting inflation hits them the hardest.
"Gold has the value it does because people happen to want gold and sell gold at certain rates. There's nothing objective about that. It's entirely subjective and could change at any time."
The price of Gold was actually pretty stable while we were on the gold standard:
http://www.wisegeek.com/what-is-the-historical-price-of-gold.htm
Pay close attention to this quote from the above link:
"The price of an ounce of gold was fixed at $20.67 for many decades until 1934 at which point the price was raised to $35.00."
As we can see the price of gold only APPEARED to change as the result of rapid inflation; after Nixon finally severed the dollar's tie to gold (as seen in the above documentary from Mises,) in the 1960's, the price skyrocketed and fluctuated like crazy as the result of heavy monetary expansion from the Federal Reserve.
"The marketplace is not some supernatural entity that always discerns the objective values of things."
I'm not sure what the context is of this claim but if you're saying the market cannot effectively assign reasonable values and costs of products, then I would have to disagree:
http://mises.org/books/value.pdf
http://www.mises.org/journals/scholar/stringham4.pdf
"Aside from this, isn't the value of the dollar determined by the marketplace? Or are you just ignoring currency markets because they complicate your point?"
Yes and no, the value is determined by the market but the market does not CONTROL it's value since they are not the ones who inflate and produce the money.
Here's an overview of a system that WOULD allow the market to control the value of the dollar based on immediate market needs: http://mises.org/story/3204