Scottish university principals are worried about the impact of independence, and with good reason.

They are permitted under EU law to charge tuition to students from the rest of the UK (rUK), while providing it free to Scottish students.

This is because EU law permits discrimination inside member states while prohibiting discrimination between member states (meaning students from France, Germany and other EU countries attending a Scottish university enjoy free tuition, just like Scots, while students from the rest of the UK must pay the full amount).

Fair? Arguably not, but that is the reality of the system. So what would happen if Scotland became independent and joined the EU as a new member state? Logic would dictate that Scottish universities would have to start giving free tuition to rUK students, as citizens of a separate EU member state.

That would result in a major loss of income to Scottish universities and could lead to them being inundated with applications from rUK.

The Scottish Government maintains that this would not happen, and that universities could continue to charge fees to rUK students, pointing to the fact that the EU allows for "objective justification", meaning that it might be persuaded to bend the rules in exceptional circumstances.

Unsurprisingly, Universities Scotland is not reassured by ministers' "it'll-be-all-right-on-the-night" approach and, in a submission to Holyrood's education committee, has asked for "robust, legally defensible certainty" from the Scottish Government, in advance of independence, over whether it can continue charging fees to rUK students.

Now the Royal Society of Edinburgh (RSE) has weighed in with its own submission, stating it has considered two legal opinions and has concluded it would be very difficult for the Scottish Government to justify continuing to charge tuition to rUK students in the event of independence.

Coming from such a respected and impartial body, this will increase pressure on the Scottish Government to explain how it can guarantee that the present arrangements would continue.

The Scottish Government does not publish its legal advice, so there is no way of judging its strength or weakness but, as the RSE has made clear, heavyweight legal opinions suggest this is a difficult case to win.

Why would the EU consider Scotland's case exceptional? Ministers would no doubt argue that Scottish universities would be at risk of being swamped with applications from rUK students if tuition were free for them, because of their proximity to Scotland and their shared language and culture. But the RSE is not persuaded the EU would be moved by that argument.

As with the question of currency union, the Scottish Government has offered no Plan B as to what would happen if the EU did not allow Scottish universities to keep charging rUK students tuition fees.

Universities understandably fear it could result in a protracted court battle with an unfavourable outcome and they have demanded to know how ministers intend to win. They deserve a response.