The unbuilt public sculpture has a respectable record. Vladimir Tatlin's gigantic
Monument to the Third International (1920), designed to be bigger than the Eiffel Tower, never got raised in revolutionary Moscow. Reg Butler's
Monument to the Unknown Political Prisoner (1953) won a major international competition but didn't get erected either. Neither work advanced beyond the model stage. But both have achieved a lasting place in the art history books. Which makes you wonder: do these things actually need to be made?

Of the six new proposals for the Trafalgar Square fourth plinth, five seem to me highly, and perhaps deliberately, implausible. Antony Gormley's scheme for a succession of volunteers to stand as living statues on the plinth-top, 24 hours a day, for an hour each, has administrative and security implications that will surely be prohibitive. I doubt whether you can make a glass bottle on the scale that Yinka Shonibare envisages.

Bounce direct sunlight off Anish Kapoor's big concave/convex mirrors, and you'll have a blinding health-and-safety nightmare. Jeremy Deller's grim political irony is much too negative for this essentially upbeat project. And Tracey Emin's posse of meerkats is well over the edge of daft tweeness though I guess that may count in its favour too.

These ideas seem to be not so much realistic plans as hypothetical possibilities. Wouldn't it be funny, amazing, weird, if the model became an artwork in its own right, an imaginative proposal as to how the world, or Trafalgar Square at least, might be. They're not blueprints to be executed. They're a form of fiction.

Taken in those terms, the display in the National Gallery is perfectly enjoyable. You might not need or want these things to be made, but as fancies to be briefly entertained they're entertaining enough. Still, if the game really is fantasy sculpture, why aren't the ideas even madder? And why isn't the competition open to the general public?

Visitors can also enjoy the wonderfully high-minded language on the labels, as each of the artists tries to explain why their idea is an especially good one (another form of fiction). Antony Gormley believes that "through elevation onto the plinth and removal from common ground the subjective living body becomes both representation and representative, encouraging consideration of diversity, vulnerability and the individual in contemporary society." For Yinka Shonibare, his enormous ship in a bottle is "a celebration of London's immense ethnic wealth, giving expression to and honouring the many cultures and ethnicities that are still breathing precious wind into the sails of the UK."

Tracey Emin sees the meerkat as a symbol of unity and safety, and has noticed that "whenever Britain is in crisis or, as a nation, is experiencing sadness and loss, the next programme on television is Meerkats United." Well, at least she doesn't sound like James Purnell.

While Anish Kapoor's says: "The plinth is thought of as an object which is dematerialised by the mirrors. They turn the world upside down and in so doing bring the sky down to the ground." Ooh, I bet they don't.

Only one of these designs seems worth realising that of Bob and Roberta Smith, aka the artist Patrick Brill. His monumental bit of fairground scaffolding comes with wind power, solar power and illuminated words that say "Make Art Not War" but in French. If built, it would be the largest piece ever to occupy the plinth, and mad enough to have been thought up by a member of the public.