The worst reason for thinking Jeremy Corbyn would be a bad prime minister is that he is too old. If senior civil servants think his policy on Brexit makes no sense, or that abolishing tuition fees is a handout to the middle classes, or that his foreign policy would embolden dictators, these are important questions that should be discussed.

But suggesting anonymously that Corbyn is “too ill” to be prime minister, as a “senior civil servant” is quoted as saying in The Times is quite wrong. I did not agree with the BBC suggesting without evidence that Gordon Brown took antidepressants in 2009, and I do not agree with civil servants – or anyone else – claiming without evidence that Corbyn is “too frail” and “losing his memory”.

It is legitimate to point out that Corbyn is older than Michael Foot was at the 1983 election, and that he would be, at 72, the oldest prime minister on first taking office if he won the 2022 election. But he would still be five years younger, and less pickled in alcohol, than Churchill was when he began his second term in 1951 at the age of 77. Churchill certainly was, as Roy Jenkins put it, gloriously unfit for office; and officials covered up a stroke he suffered in 1953.

Age is a factor, if only for the actuarial reason that health problems are more likely among the ageing holders of high-pressure jobs. I thought it was relevant, for example, that Joe Biden, 76, seemed slow and confused in the Democratic candidates’ debate this week.

And it is true that, in the past, Corbyn’s people have not helped him by implying he is a weak old man who needs to be protected from his political enemies. Three years ago, a “senior Labour source” told the press they had refused to let Tom Watson, deputy Labour leader, talk privately to Corbyn because he might “jab his finger at him”. This source, “close to the embattled leader”, was quoted as saying: “We are not letting that happen. He’s a 70-year-old man. [He was 67 at the time.] We have a duty of care.”

I find what Corbyn says about Brexit in particular cloudy, confused and contradictory, but I think that reflects the political tensions in the Labour Party rather than any mental incapacity.

Indeed, the Times report sheds more light on the conflict over Brexit policy in Corbyn’s office than it does on the Labour leader’s state of health. It includes a striking vignette of a “small meeting” after the European elections, in which the Liberal Democrats outpolled Labour not just nationally but in Corbyn’s own patch, Islington, after his aides had spent the campaign focused on the threat to Labour nationally from the Brexit Party.

Corbyn suggested in this meeting that the party should throw its weight behind a second referendum. At which, according to the Times’ source, Karie Murphy, his chief of staff, “screamed” at him: “We’re not doing that, we’re not selling out our class.” I cannot vouch for the specifics – and a Labour spokesperson denies the next bit, that Corbyn “sat back terrified” – but this is certainly the way the leader’s inner circle think, and it is a reminder of just how peculiar their politics is.

Yet, although the way the Corbyn clique argue for their positions by reference to class analysis is familiar only to those of us who collected the literature of tiny Marxist sects at Labour conferences in the mid-1980s, I think the true story of the split in the leader’s office over Brexit is one of conventional politics.

Corbyn finds himself in the traditional position of a party leader, “trying to find a common position that people can row behind in the next few weeks”, as his spokesperson put it this week. He is trying to bridge the gap between the Lexit (left-wing Brexit) position of both Murphy and Len McCluskey, the leader of Unite, Labour’s biggest union affiliate, and the pragmatism of John McDonnell, the shadow chancellor.

Both sides argue their position would be better for Labour’s electoral prospects: McDonnell argues that the party must come out in favour of staying in the EU to win back votes lost to the Lib Dems, Greens and nationalists; the Lexiteers say that such a shift would lose more votes of working-class Leavers than it would gain from middle-class Islingtonites. I am sure both sides still think the EU is a capitalist conspiracy, but this is an argument about tactics, not principle.

Corbyn, I think, leans to the McDonnell view but wants to bring Murphy and McCluskey with him. If he sounds incoherent there is no need for tasteless speculation about his faculties – his attempt to keep his inner team together is a perfectly adequate explanation.

There is a big debate raging over Labour’s Brexit policy. How should the party justify going back on its promise to respect the result of the 2016 referendum? What format of new referendum should Labour advocate? Does the party expect the new prime minister to fail to take the country out of the EU? Would Labour support a caretaker Tory prime minister who was willing to ask the EU for an extension, as a last resort, to prevent a no-deal Brexit? These are more important questions than speculating without evidence about Corbyn’s health.