The post-Lee Kuan Yew world is proving every bit as challenging for Singapore as many people thought it would be.

Remember the old debate about whether the country can survive its founding prime minister?

I don't think anyone now doubts it can.

But there are questions about how well it will do, what will give, and how.

How much will Singapore change with the passing of the founding generation, and will those changes be for the better or worse?

Looking at what has taken place the last two years after Mr Lee's passing, you could be forgiven for fearing the worst.

The public squabbling among the Lee siblings tops many people's list of what can happen to the larger Singapore house when its strongman ruler is no more.

Mr Lee held the peace in the family even if the relationship among his children was already fraying at the edges.

They appeared a happy family under his watch, and then the sky fell when he was no longer.

Will the same happen to the country? What else might unravel in the years ahead?

If you are the worrying sort, plenty.

There is continuing concern over the economy, now into its fourth year of slow growth and with no turnaround in sight.

There is anxiety over whether Singapore can manage its foreign relations as well as it did in the past, especially with a stronger and more assertive China and a less dependable and inward-looking America.

Singapore's recent problems with China have added to the uncertainty.

Indeed just last week, a debate broke out between two of the country's former diplomats Bilahari Kausikan and Kishore Mahbubani over what lessons the current crisis in the Gulf states holds for small countries like Singapore.

Professor Mahbubani held that though Singapore under Mr Lee was able to play an outsized international role, "commenting openly and liberally on great powers including America and Russia, China and India", it should refrain from doing so now that he was no longer around.

"Small states must behave like small states," he argued, citing Qatar as an example of one which ignored this maxim to its peril.

His piece provoked a stinging response from Mr Kausikan, who wrote that Mr Lee and his comrades "never allowed themselves to be cowed or limited by our size or geography".

"Singapore did not survive and prosper by being anybody's tame poodle," he wrote.

It was the sort of debate that is likely to continue in post-LKY Singapore, not just in foreign relations, but also in politics, economics and social policy.

People who have worked under Mr Lee and understood his thinking and philosophy can come to very different conclusions on how they apply to today's new situation, as the two diplomats obviously did.

Policy and policy thinking aren't fungible and cannot be applied whatever the situation. Every problem is different, especially when circumstances have changed.

Mr Lee and his team understood this and excelled at overturning conventional thinking, charting their own course by working through the issues themselves.

I believe they would be the first to caution against blindly applying what they did, no matter how successful it might have been in the past.

The other problem is that policy is only half the story, execution is as critical.

If you can't execute a policy well because you lack the skills doing so, it can lead to disastrous consequences.

A case in point: Mr Lee's use of defamation suits to silence his political opponents.

Whether you agree with his approach - and there are many critics who did not - you have to admit he was skilful in doing so.

A lesser politician without the same killer instincts might not be able to pull it off as successfully, and will suffer the consequences.

Singapore and its leaders have to find new solutions to their problems, making use of their different skills and resources.

There are two areas though that they would do well to learn from the past and which are as relevant today.

One is understanding the unique position of Singapore and the realities facing a small independent country dependent on the outside world for its survival and success.

Out of this simple but realistic analysis, the founding leaders shaped Singapore's development in the early years.

But though the analysis is as valid today, leaders today have to find new approaches because the world and Singapore have since changed.

Example: Mr Kausikan cited many examples of how Singapore leaders stood up to major powers in the past when they attempted to intimidate them.

It doesn't mean current leaders should always try to do likewise.

But his analysis is correct: Small states like Singapore cannot allow their sovereignty and national interests to be dictated by others.

How to do so in today's changed geopolitical landscape?

That's what should be keeping our diplomats awake every night.

The second area where the past holds unchanging lessons for the present is in the values that shaped the country's approach to solving its problems: pragmatism, incorruptibility, meritocracy and multi-racialism.

They are as relevant today.

But one mustn't confuse adherence to these values and the methods used to uphold them.

Take the need to have men and women of the utmost integrity and competence in the political leadership.

It is as important to do so today as ever before.

But how do you find these people?

Is the old method of inducting them mainly from the public sector and the military the right one in today's changed circumstances?

Doing so has resulted in an ever narrowing band of people at the top, every one almost indistinguishable from the other.

There must be something wrong with the method and the approach when it has failed to find people outside this small circle in a country that has been so successful in many other fields.

Another prized quality from the past: The courage to think big and depart from the conventional.

Post-LKY Singapore needs a big dollop of this if it wants to continue being exceptional.

But what to do courageously and unconventionally?

That's what should be keeping the country awake at night.

• The writer is also a senior fellow at the S. Rajaratnam School of International Studies, Nanyang Technological University