The English word paradox has its roots in Greek – and watching the attempts to reconcile the new Greek government's wishes for less punishing debt repayment conditions with the remaining part of the European Union, you can see why.
Monday's talks between Yanis Varoufakis, Greece's newly minted finance minister, his euro zone counterparts and European Central Bank (ECB) President, Mario Draghi, have been met with optimism in the stock markets, despite little evidence of progress over their conflicting ideas about Greece's future.
"I expect difficult negotiations, nevertheless I am full of confidence," new Greek Prime Minister Alexis Tsipras told Germany's Stern magazine over the weekend. He pledged that Greece would be a "completely different country" in six months if he was granted concessions.
However, Germany's irascible Finance Minister Wolfgang Schaeuble said he was "very sceptical" about a solution being reached Monday, in an interview with German radio.
Former European Commission President Jose Manuel Barroso told CNBC that the new government in Greece had to respect the other 18 members of the euro zone in the negotiations.
"It's fair that new governments come with new proposals. I think the partners should look at them attentively," he told CNBC.
"But I think it would be a huge mistake and it would be very bad for the euro zone if now we give the idea that because there is a political change in one of our member countries all the rules are put in question."
"The best we can hope from today is an agreement to move forward on," Nick Malkoutzis, the Athens-based editor of economic and political analysis website Macropolis, told CNBC.
The most immediate question is whether Greece should agree to an extension of its current bailout conditions (the favored position of the EU) or be given a bridging loan until the end of May, to give it time to renegotiate the bailout.
"For the man in the street, he wouldn't be able to put a figure on the primary surplus, but he would like to see some kind of concessions from where we are," Malkoutzis said.
As a result, the possibility of a Grexit – Greece leaving the euro zone - is being given increasing credence by international political and economic figures.
"I can't see how you can sensibly avoid the Greeks defaulting and the Greeks having to leave the Eurozone," Ken Clarke, a former U.K. Chancellor of the Exchequer who is one of the most prominent pro-EU figures in the Conservative Party, told the BBC Sunday.
Successive Greek governments have promised to crack down on endemic corruption, cronyism and tax avoidance, with limited success. The new government, led by Syriza, a party which is new to government, is more removed from the country's elite than previous administrations -- however, it may struggle to hold on to its currently popularity if Greeks don't see some delivery on its promises.
"The government can draw strength from two things: the deposit outflows generally lessening (partly because there isn't really that much loose change left for people to take out), and the public support for what they are doing," Malkoutis said.
"The banking system is the Achilles heel in all this. It's totally reliant on the emergency liquidity it's receiving from the ECB, and should something go wrong there then things will be extremely difficult."
- By CNBC's Catherine Boyle