All eyes will be on Berlin this afternoon, as Angela Merkel and François Hollande meet for the first time with the ostensible goal of thrashing out their differences over the solution to the eurozone's problems. The meeting is billed as a showdown between the fundamentally opposing world views of austerity and growth, the outcome of which might either save the single currency or hasten its demise. The reality, however, is both more prosaic and more alarming.

For all the rhetoric about his leading an anti-austerity backlash, Mr Hollande's divergences from Ms Merkel are largely a matter of emphasis. The German Chancellor favours structural measures, such as labour market reforms, to boost Europe's flagging growth; her newly elected French counterpart speaks warmly of EU-wide "project bonds" to finance stimulatory infrastructure investment. In fact, Europe needs both. And the most likely outcome of today's meeting is a diplomatic fudge.

Meanwhile, both leaders continue to dodge the reality of what they must do. For all the anti-austerity rhetoric, Mr Hollande has only tweaked his predecessor's deficit-reduction targets. But he has shied away from mentioning any of the reforms that will be necessary to meet them. Similarly, the German Chancellor remains implacably committed to austerity as the only solution, although her Finance Minister has, at least, hinted that Germany could tolerate the higher inflation needed to boost growth across the eurozone.

So pronounced a lack of leadership at the heart of Europe is troubling enough. Worse still, the future of the single currency is rapidly being decided elsewhere. At the general election on 6 May, Greek voters took the opportunity to register their disgust at the political class that, by its squandering and pandering, led Greece into a debt crisis that has slashed the economy by nearly a fifth and shows little sign of abating. The result was so splintered that it has proved impossible for any party to form a government and another election, in four weeks' time, is increasingly likely. What is not certain is whether the result will be any different. And with siren voices from the political extremes promising an end to biting austerity, it is not certain that Greek voters are aware of the magnitude of their choice.

The majority of Greeks still want to stay in the eurozone. Some politicians – notably the leader of the leftist Syriza party catapulted to second place in last week's vote – claim it is possible for Greece to both reject austerity (for which, read default on its debts) and yet remain within the single currency. It is not. For flusher euro countries to continue to bankroll neighbours who renege on their promises would only replace Greece's political instability with ructions elsewhere – in Germany, for example.

Then there are the full implications of a Greek exit to be considered. The best-case scenario is a return to the drachma, rapid depreciation, and a relatively swift increase in competitiveness – albeit accompanied by a massive, overnight devaluation of assets, a crash in living standards as the price of euro-denominated imports soars, and the likely collapse of the banking system. Less optimistically, there is also the very real danger of undisciplined money-printing and hyperinflation, with all that entails.

The prognosis outside Greece is little rosier. More sanguine commentators suggest that the boosted bailout fund and the ECB could, between them, protect the other vulnerable eurozone economies such as Portugal, Spain and even Italy. But that is far from certain – as yesterday's spiralling borrowing costs in Spain attest. And even if they can, the massive losses in Greece would still ricochet around the European – and world – financial systems, punching yet another hole in banks' balance sheets, paralysing lending, and choking off already-faltering economic growth. The potential repercussions can hardly be overstated, rippling right out to Barack Obama's chances of re-election.

There is real suffering in Greece. And the assumption that it is better off remaining in the euro is no longer as secure as it was. The decision, rightly, rests with the Greek people. But it is not only their own future which is in their hands.