By Hannah Goff
BBC News education reporter
The seven-year-olds sit cross-legged on the carpet scratching their chins philosophically.
Children are working on questions first asked by the ancient Greeks
These bright, young pupils have been asked to consider "whether it is possible to step in the same river twice?".
They take a moment, focus on the middle distance, assemble their foreheads in the shape of a frown, and as the brain cogs start turning, their hands shoot up one by one.
Philosophy teacher at Eliot Bank Primary School in Forest Hill, south-east London, Peter Worley, passes one girl a ball. This means she's allowed to speak.
"Well - I think you can step in twice because if you step in once with one leg you can step in a second time with the other leg," she says.
Another counters that this would not qualify as stepping in twice because although two legs have been used - only one body has gone into the river.
The ball goes to another who says: "You could step in the river one day and then go home. Then the next day you could come back to the same river - as long as you know the way - and do it again."
Then, in a flash of inspiration, one of the boys who has been waggling his hand impatiently, now ventures hesitantly: "If you step in the river on Saturday and then you went to step in the river on the next day - where you stepped on Saturday would be gone because the river keeps on moving."
"Aha," says Mr Worley: "That's really interesting. It's really got me thinking."
Another girl, who hasn't said much so far, says that she has heard that all the seas and all the rivers in the world are all joined up: "It's really just one big ocean in a way."
The children have been trying to crack a puzzle that ancient Greek philosopher Heraclitus devised centuries ago.
"There's something wonderfully naive about the ancient Greeks because they were right at the beginning of it all," says Mr Worley.
"There's something that the children can identify with - it is at the same level as themselves, but it is also sophisticated in its own way," he adds.
Posing philosophical questions like these encourages the children to think in a different way to the one they are used to, he argues.
Children begin to work their way around these philosophical puzzles
"In philosophy instead of working out how to do a sum, we think about what maths actually is.
"As Einstein says, once a mind has been stretched over a new idea - it cannot be stretched back.
"It's opening up channels in the brain - teaching them to think for themselves by giving them the tools to do that.
"And they're learning skills in how to discuss and argue with people - but constructively."
And there is a maturity and a diplomacy in the way that these seven-year-olds tackle the puzzle, digging out the words to help them precis and understand what one another are saying.
They don't always get there - sometimes they lose their train of thought on the way and collapse in giggles - but they are enjoying trying.
Head teacher Kathy Palmer says: "It also teaches them that confusion can be a good thing - that it's OK to make a mistake.
"What we try to do is to give them a tool-kit so they know what to do when that happens."
A recent study suggested that children's IQs are boosted by learning philosophy at an early age.
Behaviour also tends to improve when children get a chance to gain some emotional intelligence through philosophy.
But at Eliot Bank the study of the subject has also led to gifted and talented children being identified.
Mrs Palmer says: "There are pupils who have not been up to speed on their writing, for example, but who have been shown to be able to put forward a very, very solid argument.
The head teacher says the project has identified gifted pupils
"Often speaking is thinking and for some children the writing part stops them thinking.
"With this they can just flow with thought. Self-esteem is everything and if they feel good about one aspect of their lives - we can take that through to the other parts."
Mr Worley says: "Philosophy is one of the most notorious degrees for being useless if you look at it vocationally, but it does come with transferable skills.
"It teaches you how to think things through, solve problems and deal with moral dilemmas."
Mrs Palmer adds: "Our children are going into such a changing world. We can't predict what they're going to need in terms of knowledge, but one thing we can give them is confidence and a sense of how to learn.
"Philosophy gives them those skills."