"I'm not here as a person, I'm here as a Secretary of State." That was Karen Bradley's response when asked for her personal opinion on the Irish border question at the European Scrutiny Commission this morning.

Surreal though it was, her defence explains her muddled and contradictory testimony: only someone obliged to take the government's red lines as immutable could have offered it.

Take, for example, the Northern Ireland Secretary's promise of “no change” on the border itself: no new physical infrastructure or cameras. The obvious upshot of this is that “maximum facilitation” (max fac), the border technology-dependent customs model Bradley has been assigned to examine, as part of the cabinet’s protracted negotiations on the topic, cannot work.

The government can’t have it both ways, but is determined not to choose. How might it avoid doing so? Bradley herself admitted that the new customs partnership, her preferred option, has its own defects. Opposition from Brexiteers within and inside out of cabinet means it is unlikely to fly. The only conceivable way the government might fulfil its pledges on the border in the medium-term is by staying in a customs union for several years beyond exit day.

This delay and Bradley’s suggestion that some new infrastructure could be built away from the border in future - think lorry parks - likely reflects a feeling among some in government that this is the only way to stop Brexit foundering immediately on the border (consensus on this, however, will prove as elusive as it was on the new customs partnership and max fac).

Deferring the problem isn’t the same as solving it, though. Therein lies another problem with Bradley's testimony: her refusal to discuss what free trade deals with other countries might mean for the island of Ireland.

Asked about what would happen in the event of Britain agreeing a free trade agreement with the US that allowed imports of chlorinated chicken – banned in the EU, and thus the Republic – Bradley said she was "working towards" new customs arrangements and would not "speculate" on "matters for further down the line".

That response would be fair enough were these questions really matters for further down the line. Inconvenient though it is for the government, these are matters for now.

As long as ministers maintain that there will UK-wide free trade deals but be no hard land border, no sea border, and no chance of special status for Northern Ireland or UK-wide membership of a customs union, it's incumbent upon them to explain how these contradictions will be squared. If Bradley, the Secretary of State, can't see that doing so is impossible, surely Bradley the person can.