When the Prime Minister admitted to the TUC this week that there would be public spending cuts, he used a word which should strike fear into everyone connected with the arts.

He said there would be cancellations of projects that were not necessary. Commentators were quick to highlight the C word. Gordon Brown had at last mentioned cuts. But it was the N word that sent a shiver up my spine. Once more the leading representatives of Britain's culture are going to have to give demonstrable evidence that the arts are necessary.

It's not easy. At a conference sponsored by The Independent years ago at the Edinburgh Festival, the then Tory arts minister prefaced any number of answers to questions with the words "Because the arts are important, we are going to...". Eventually someone asked: "You keep saying that the arts are important. Why are they?" The poor minister was stumped. A look of terror spread across his face as he tried to recall the correct platitudes.

Since then, culture's spokesmen have smartened up their act. The two Johns, Carey and Tusa, have written books on the subject. Knights of the arts, such as Sir Nicholas Serota and Sir Richard Eyre, have attended seminars at Downing Street to put the case for culture. True, the case has subtly changed in recent years. For a time it was vogueish to press the economic case for the arts – also the title of a book. There were all those jobs and the money that culture brought to various cities and regions. But as quickly as that argument came in, it went out; the book was remaindered, and the advocates of the arts concentrated on more universal and metaphysical themes. The arts nurture the soul and the spirit, help us understand ourselves and society, help us grow. One could also add that they're enjoyable. And we're allowed a bit of enjoyment and entertainment, aren't we?

But does that make them "necessary?" Of course I would argue that it does. But it's not going to be an easy argument with Treasury mandarins, and it's going to be even less easy to argue that certain planned multimillion-pound public spending projects in the arts – expansion of the British Museum, an extension for Tate Modern, a new national film centre – are "necessary." Take the Tate Modern extension, for example. It will be designed by innovative architects Herzog & de Meuron; it will be a splendid addition to London's landscape; it will house great new modern art exhibitions and allow more of the Tate's permanent collection to be displayed. "But," said mandarin might reply, "Tate Modern is already acclaimed around the world. Is the extension strictly, how can I put it, necessary?"

I wish that Gordon Brown had used a different word: enriching, fulfilling, life-enhancing. There's something cold and utilitarian about "necessary" that makes me very uneasy.

Advocates of the arts need to start mustering all their arguments, old and new, for necessity. If I'm to make a prediction, it is that they might be able to win the argument sufficiently to stop radical cuts to arts spending which would close down theatre companies and the like. But whether they will convince the Government that new building projects for the arts are "necessary" is another matter. I have my doubts.

Punk, the musical

The world premiere of American Idiot, the debut musical by rock band Green Day, took place in California on Wednesday. It was rather sweet that theatre staff tried to behave in what they assumed was rock concert fashion. The house manager at the Berkeley Repertory Theatre ran on in a T-shirt and yelled: "Are you ready to rock?" The theatre's artistic director, Tony Taccone, wearing a skinny tie with red sequins threw an opening-night party in the theatre, with combat boots hung in trees and a "No Stage Diving" sign.

But the band, it seems, just want to be part of conventional musical theatre. Green Day's frontman, Billie Joe Armstrong, said that he sang tunes from musicals like Gypsy and Bye Bye Birdie as a boy, but "shied away from anybody knowing" once he discovered punk music. If the musical comes over here, theatre managements should avoid trying too hard to be hip.

Death by catchphrase

Popular culture doesn't always get the credit it deserves. After the tantrum thrown by Serena Williams at the US Open tennis, a number of newspapers said that the most famous outburst in tennis history was John McEnroe's one liner "You cannot be serious" to an umpire in Wimbledon in 1981. True. It is.

But I suspect it would not have achieved immortality if it had not also featured in a sketch on the hugely popular TV comedy sketch show of the time, Not the Nine O'Clock News. The sketch featured breakfast in the McEnroe household, and after John's mother told him not to slurp his food, McEnroe, played by Griff Rhys Jones, yelled at her: "You cannot be serious!"

I attended a lunch recently where McEnroe was the guest speaker. He asked if there were any questions. Someone shouted out: "Can you be SERIOUS?" A weary McEnroe observed that usually there is the formality of four or five tennis questions before that one is reached. I think he can blame Griff Rhys Jones and co.