Tom Lehrer, the American satirical lyricist, sang of the Spanish republican struggle against Franco: “He may have won all the battles, but we had all the good songs”.

Jeremy Corbyn seems to have all the good songs and is winning too. I say “seems” as the polls are always wrong, and yet, with the exception of Yvette Cooper, we go on believing every single one of them. And that belief has dramatic political effects. Whatever the truth, Corbyn is turning the contest to become the next leader of the Labour party upside down.

The election was already in terrible disarray, even before the polling caused such a stir. There was uproar in the party and confusion between the candidates over George Osborne’s benefit cuts, refracted equally confusedly through Harriet Harman, the acting leader.

None of the three mainstream candidates for the job – Cooper, Andy Burnham and Liz Kendall – is really proposing anything, only reacting. And as regards their own leadership status, all took a falsely modest position when asked who they might have in their shadow cabinet in the event of a win, each refusing to answer the question. Then Cooper and Kendall said they would not serve under Corbyn if they lost, and Burnham said he might.

Corbyn’s rivals have made it clear that they can already picture him at the dispatch box. All they are doing is enhancing his leadership status and diminishing their own even further. And he is already naming his cabinet – Ed Miliband will have the energy portfolio!

So what began as a spectacularly ill-judged scramble for Ed’s fallen crown (and reliable rumour has it they were manoeuvring even before it slid from his head) has now become a mission to stop the “Syriza-Podemos candidate”. No Pasaran.

The standoff is playing out across a series of television debates (that everyone is now watching). These started off with the three front runners patronising the radical warhorse from the 1960s but now he is riding a rhetorical coach and horses through their platitudes.

PA/Lynne Cameron

How did this happen? Let us get one thing clear; it has absolutely nothing to do with being left wing or right wing. Corbyn is making such a strong media showing because of his style and language. And the others are coming across as mediocre because of theirs.

They have the rhetorically disadvantaged position (which they themselves chose) of talking about nothing in particular. Did we overspend in the last Labour government? Yes we did (Burnham). No we didn’t (Cooper). This was when much of Labour’s post-May 2015 recruits were seven or eight years old.

What is Corbyn talking about? Everything. More importantly, he embodies a wide and deep tradition in the UK left that we can all recognise and engage with. And, more importantly still, he does it with elegance, conviction, modesty and intellectual coherence.

The mainstream candidates are all extremely clever, but what do they embody? What image of them do we retain after a performance? What have they told us about themselves as a political persona and potential leader?

We know that Kendall urges realism, but we don’t really know what that means apart from not what Ed was doing. You can’t “see” realism.

As regards Cooper, the media snapped up remarks from one of her supporters about being a working mother and (almost) turned it into a spat between the two woman candidates. This sexist trivia gets media mileage because none of the mainstream candidates embodies a vision of a Labour Britain.

Burnham is apparently true Labour because he has a Northern accent – his flat As are getting flatter by the week. At weekends he goes back to where he was brought up and still meets up with the people he used to play football with.

This is dire stuff. Corbyn wants to talk about all the things that make people want to vote Labour or not, or join Labour or not, or consider joining Labour, and so on.

He is giving us all a lesson in politics: you have to represent something, you have to embody a political view or tradition, and you have to perform it to rhetorical effect. And you have to be – or at least seem to be – authentic and sincere while you do it.

All four of the candidates are all of these things. Corbyn is just doing it much better than the others. The poll may indeed be wrong, but he is doing everything right. I suspect Corbyn’s bedtime reading is not Marx’s Grundrisse but Aristotle’s Rhetoric.