Of all the many dreadful things that Boris Johnson has done to British politics in his quest to reach the next step on the cursus honoum, perhaps the most damaging is his elevation of cakeism to the status of dominant Tory ideology. “My policy on cake is pro having it and pro eating it,” is a cute way of evading a difficult question, but it's no way to run a country. There are zero-sum games and difficult choices, and for one group to win another must sometimes lose. There is a reason Johnson is more adept at writing columns than he is at actually governing.

Cakeism was much in evidence on the Tory fringe this week, as MPs fretted about the precipitous decline in homeownership rates, and everyone and their dog seemed to agree that improving the party's chances of ever winning a healthy majority would mean turning private renters into first-time buyers. As Mid-Norfolk MP George Freeman asked, “Why would you ever be a capitalist if you’ve got no chance of ever getting any capital?”

The problem is that the party isn't only promising to widen home ownership. It's equally committed to protecting the property rights of buy-to-let landlords, to preventing our cities from growing either outwards or up and, let’s be honest, to keeping house prices up, too.

And there is no way, logically, that those various commitments can be reconciled: young people can't buy because prices are too high, and anyway, any increase in home ownership must require either new homes to be built or for landlords to sell up. Short of encouraging existing homeowners to die, which would at least be consistent with Tory fundraising policy, there is no other source of homes. So, without either a mass building programme or an attempt to claw back the housing owned by buy-to-let landlords, any offer to first time buyers must be worthless: the Tory commitment to having its cake prevents it from eating it too.

Worryingly, it’s far from clear the party gets this. When George Osborne introduced Help To Buy, he at least seems to have realised that public subsidies to some buyers would further inflate house prices for everyone else: that, indeed, was probably the point of the exercise. But when Tory MPs spent this week intoning seriously about how the solution to the home ownership crisis was a slightly better ISA, they actually seemed to mean it. Tory strategists must be shitting themselves.

We've all seen this before, of course: the commitment to mutually exclusive positions; the desperate search for a policy so clever and so complicated that it can rewrite logic itself. Ensuring that there is a hard border between the EU and the UK, but no hard borders between Ireland and Northern Ireland or between Northern Ireland and Great Britain, is a puzzle with no solution. If A equals B, and B equals C, then C must equal A, too, and no amount of yelling about the will of the people can make it otherwise. It bothers me a little that many Tories really don't seem to know this.

Most criticism of a policy comes from people who disagree with its goals, or who don't think it can actually achieve them. This is different: the biggest challenge to the Tories now comes not from their political opponents but from reality itself. There's no Laffer Curve-style theory that can account for an unexpected result: the party's desired result is mathematically impossible within its own pre-determined parameters. You cannot both have your cake and eat it.

As someone who wants to see Tories lose elections, their increasingly delusional nature is pretty fun to watch. As someone who has to live in the country they govern, I am very, very scared.