Let's lay out my credentials up front: I have few. I'm not an economist, or good at monetary theory, international finance, or Greece. I married into a Greek family, and I've spent numerous vacations there in the last 15 years. I don't really speak the language. Therefore, you can ignore me, if that saves time.
So what just happened?
Let's talk about some reference materials, in particular this interview of Piketty, (published in German, so we're trusting this translation and the second-hand analysis to some degree) regarding Greece.
Piketty points out that many countries, notably Germany, have defaulted. This is true. He feels, therefore, that Germany has no moral grounds on which to compel Greece to pay. This is an argument of straw. I'll stipulate that surely someone has argued the moral grounds by which Greece ought to pay its debts, but those moral grounds matter very little, just as they matter very little with any other sovereign debtor, be it Canada or Qatar. The main incentive for any sovereign state to repay debt is because repayment is the easy route to cheap access to financing. This is true for Greece as well.
But none of the serious people at the table care about the moral dimension of the debt. Maybe some principals have tried to use an appeal to the moral imperative to repay debt, but the best way to understand the current negotiation is as one of leverage (notably, Greek Finance Minister Yiannis Varoufakis is an expert in the academic field of game theory).
The levers on each side are relatively simple: the Eurogroup (the Euro zone national finance ministers), European Commerce Bank (ECB), and IMF (the "Troika") can offer very cheap financing on the current debt. There's also an implicit promise, based on previous negotiations and the realities, that eventually, the debt will be sufficiently forgiven to make it manageable. The other thing the Troika offers is continued comfort for Greece within the bosom of the Euro: there are good arguments the Euro is not a good currency for Greece to use, but it remains relentlessly popular among the Greeks, and there are plausible reasons for this popularity. The Troika also offers ongoing liquidity to the Greek banking system, as the ECB is the Euro equivalent of the Bank of Canada or the U.S. Federal Reserve: the implementation of monetary policy, including the vital bank-lender functions.
The Greeks offer default: the threat to simply repudiate their debts, in whole or in part, is an open avenue for most sovereign states, and there is almost no recourse for most debtors, but the ramifications make states think hard before exercising this option.
There is a poison pill for Greece in the Greek default threat, however: the ECB is effectively part of its creditor group, and is NOT ultimately beholden solely to the interests of Greece. It must heed the entire Eurozone, and set policy for all Euro-using member states. Because of that, cutting off the lending window to Greek banks is a near-certain consequence of default; indeed, the suspension of payments has already led to this happening, thus the ongoing bank run and slow-motion bank holiday in Greece. Eliding further details, this means yes, if Greece defaults, it will almost certainly lose access to crucial ECB functions, and given the choice between a banking-system collapse and forming a new currency (which I'll simply call the "drachma", because that's what everyone else refers to this putative currency as, and because that's what it probably would be called), it will almost certainly choose the latter.
This is why default is seen as leading to "Grexit," aka the departure of Greece from the Eurozone.
The playbook for changing currencies like this is known from previous, similar incidents, and I'm not going to get into that history. It's not pretty, it's not simple, and it's risky. It may still work out for the best, though.
My point is there's no useful moral imperative, on either side, driving negotiating positions.
Degrees of Forgiveness
There's some element of debt forgiveness built into the current repayment plan. In the long term, it's likely implicit, but unspoken. In the short term, the lending terms over the last few years, wherein Greece got refinanced at, more or less, Germany's interest rates, amount to a massive forgiveness of their open-market debt obligations (at peak Crisis a few years ago, Greek debt traded at implied interest rates that exceeded what my credit card offered me: I was a better unsecured credit risk than Greece was. (This was, in retrospect, correct)). Piketty is arguing above that the offered terms should be even more forgiving: presumably in the form of explicit forgiveness of some amount of debt, or lower effective interest rates, or an even longer term. I need to point out this is an argument that the Troika (and their financier, mainly the people of Germany) are already virtuous donors to the cause of Greece, we're just arguing now about the size of the donation.
Should it be more? It's been sized right now to be cheaper than default, more or less. At the start of this year, Tyler Cowen wrote a prescient post on Greece's debt and its interest rate. Note that the keys here are that Spain and Italy are in better (not great) financial states than Greece, and are not on the road to default FOR NOW. But both are still paying market rates. More importantly, both are bigger economies than Greece: Spain is much bigger, and Italy is huge, both in GDP and debt. Bailing out Italy, should that ever be necessary, is probably beyond the means (political, if not fiscal) of the Eurozone.
I think Cowen rightly predicted politics as the potential cause of Greece's downfall in the last seven months, and I would say that SYRIZA, whatever understandable impulses drove their election, has been specifically and largely responsible for unintentionally (but predictably) talking and working Greece into economic and state-revenue downturns to go along with their preexisting fiscal problem.
The Greeks voted "No."
Does the question even matter? At heart, "Yes" would have been a vote to accept the Troika's terms, refinance, and reopen the banks, and carry on, more or less. "No" was a vote to renegotiate with the Troika, but it was obvious to most that the Troika was not (and is not) likely to change its terms much. I think Greece is bereft of additional leverage.
So while there are still possible exits, "No" is likely a vote to default, and to (for the reasons mentioned above) exit the Euro.
This is dangerous, but not crazy. The long-cited issue with the Euro has been that it does not float at a value convenient to its smaller, poorer nations, and that includes Greece. The currency transition and default may, in the long term, help Greece exit from its present fiscal mess.
But the short term for Grexit is likely to be ugly, possibly very ugly. I cease making predictions at this point.
Also, I might as well note in passing that while I think it had no great effect on the final result, "No" Day is a potent cultural touchstone for Greeks, a symbol of their resistance to foreign invaders, and that allusion was alive to everybody in Greece.
I have guesses as to the range of possibilities; I can demonstrate them by my revealed preference: I have another Greek vacation scheduled for the Fall, and no plans to change it.
Don't take that as me thinking anything good happened today.