Isaac, five, is doing a spot of online shopping. He has some leftover holiday money to put towards a new game for the Wii, and I am trying to help him work out whether, with a couple of weeks of pocket money thrown in, it will be enough. "What did Grandad Philip always say?"

His elder sister, Athena, starts enumerating criteria on a thumb and two fingers: "Do I want it? Do I need it? Can I afford it?"

I'm not sure that all my father's purchases satisfied these three conditions. But his rule for parting with cash has become part of the children's own decision processes. He died 12 years ago, too soon to get to know any of his grandchildren. As time has gone on, I have wondered more and more about how the children are to know him, how I should talk about him and the rights and wrongs of negotiating the memory of someone who is no longer here.

Our memory of him is not a particularly visual one. We don't spend a lot of time, as a family, going through photographs and Dad died before digital pictures and video became ubiquitous. Talking to the children about Grandad Philip's funny pronouncements means he becomes more real for them than a photographic image. It allows the children to own a bit of him, to incorporate him into their way of looking at the world. The stories of his outraged behaviour in restaurants and hotels, his subtle ploys for getting a drink when he needed one, become real for the children, too. I want to say that they remember this affectionate, vulnerable, opinionated man, even though their stays on the planet did not overlap.

It's a harmless idea, surely. Grief and regret for what has gone, and pride and joy at what has arrived to take its place, have made me try to fix that broken link between the generations. I can't be the only parent who has tried to implant a child with a memory of a lost grandparent or, more tragically, of a dead parent or sibling. But something makes me uneasy. I am actively manipulating their take on the past, tampering with what I should leave alone. Among all the murky choices parents have to make, this one is rarely examined. Even if it were possible to seed a memory in this way, what kind of memory should it be? An honest, warts-and-all depiction, in which the dead are anything but perfect? Other reveries of lost family members can be too good to be true: those grandmothers of hazy memory too often did nothing but clutch children to their downy chins and bake exquisite cakes. In attachment research, romanticising past relationships in this way is taken as a sign that important failings in those relationships are being swept under the carpet. When we are remembering the dead, honesty seems the healthiest policy.

I also need to ask what kind of entity I am asking the children to remember. They sometimes hear me saying things like, "Just because you can't see him with your eyes, it doesn't mean he doesn't love you." It's as though the detail of him being dead were no obstacle to their getting to know him. I'm asking them to have a relationship with someone who can't be seen or heard, who never takes his turn at childcare during school holidays or calls to find out how the cricket match went. At least Santa Claus brings them a present once a year. The difference is that there is some documentary evidence for Grandad Philip's existence. The children can see photographs of him, some old cine film of him as a younger man. They know that he lived and breathed in ways that those other imaginary companions of childhood do not. He left documented traces, like the dinosaurs. As a verifiable historical personage, he has credentials that the tooth fairy lacks.

How do children make sense of the fact that a once living person can stop existing in this way? The developmental psychologist Paul Bloom has argued that young children are "dualists", wired to treat mind and body as separate entities. They get to grips with the biological facts of death relatively early (dead flies and gerbils play their morbid part). A person, though, is a soul as well as a body, and when the body dies, questions arise about the immaterial part. In fact, children who understand biological death perfectly well also believe in some continued psychological functioning after death. The specific form of children's beliefs about the afterlife are shaped by their culture, but a readiness to believe in life after death seems pretty much built-in.

When they are confronted with it in reality, death can do funny things to children's thought processes. At three, Athena found out that she was going to have a little brother or sister. When the pregnancy ended in a miscarriage, her thoughts turned to the fate of her lost grandfather. She had heard me talk about him, and seen me commemorate the anniversary of his death. She could begin to make sense of what had happened to this little not yet person by thinking about what had happened to that poorly old man.

Isaac has always been more interested in the metaphysical facts. He tells us that heaven is full of dragons, and when you're in heaven "you can't get died". If the developmental psychologists are right, he is fascinated by supernatural entities and spaces because he, like all children, is programmed to think of people in terms of souls as well as bodies. In our firmly non-religious household, he has invented God for himself, rather than having the idea thrust upon him. Telling the children that Grandad Philip is watching over them might not, then, be so alien to their own understanding.

"Autobiographical memory" is the term psychologists use to refer to our memory for the events that have happened to us. Rather than just being about factual knowledge of what occurred when, it gives us the capacity to relive those events from the inside, to inhabit the experienced moment, time and time again. I don't just know for a fact that my dad once appeared on Christmas morning wearing a leopard-print G-string, I remember it happening. I can close my eyes on this present reality and live the moment again. Strictly speaking, you should not be able to have this kind of first-person, there-in-the-moment memory for events you didn't actually live through. But it turns out that autobiographical memory is tricked in this way all the time.

That is because, when you form a memory, you don't simply record a mental DVD of events that gets played back at the moment of remembering. Autobiographical memory involves many different psychological and neural systems working together to construct a representation – a kind of personal narrative – of what happened. Fragments of sensory memory are dredged up from one part of the brain and fused with representations, from other neural areas, of more abstract knowledge about events. The entire mix is then reassembled according to the demands of the present. It is this process of active reconstruction that makes memory so fragile. For example, it turns out to be relatively simple to give someone a vivid memory of something that never happened to them. In one experimental study, adult participants were given photographs from their childhoods as cues to remembering the events depicted. One of the pictures was a digitally doctored fake: it showed the child taking a ride in a hot-air balloon (an event that could be verified as never having happened). Two weeks later, half of the participants "remembered" – sometimes in striking detail – their childhood balloon ride, and were surprised to learn that the photograph had not been genuine.

In childhood, when the constituent systems are still maturing, autobiographical memory is even more fragile. Memories from early childhood can be incredibly vivid, but they are also demonstrably unreliable. It seems to me quite possible that, in the editing suite of memory, the children will combine their knowledge of Dad's sayings with the visual images they have gathered of him, and end up with a lifelike "memory" of him speaking. Any such construction would presumably be no more or less "real" than my sketchy memories of Dad's own parents, or than the children's memories of Dad would have been had he lived until they were four or five. In fact, 12 years on, I wonder whether my own recollections are so trustworthy. Perhaps my memory lab has been beguiling me with constructed experiences that should be valued as a special kind of personal story, rather than as objective "truths" about how things were.

In the end, then, I am easy with what I am doing. I want the kids to have what I fear losing for myself: vivid memories of Dad as a living person. I want them to help me to remember him. I became a father before I'd even had a chance to finish mourning him, and those family roles are probably still powerfully entangled. Although the children have three (thankfully healthy) grandparents, it's important to me that they should have a fourth. I want to defend him against the forces of forgetting and I am calling on the children as allies.

These days, we have honed a ritual for commemorating him. On the anniversary of his death, we do what we did on the day he died: we light a candle, make a little shrine with framed photographs, and think about whatever image we have of him. Occasionally there are tears; more often questions. "When you get died," Isaac asks, "does your head get smaller and smaller and then go 'pop'?" One of the photos shows Dad standing on a bridge with his back to a nameless river. "I think of the water and the wind," Athena says, "and everything moving fast around him, and him just standing still."

Like everything's moving except him? "Yes. Like he's the only thing that never changes."